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Theoretical and experimental studies on erythrocyte partition in aqueous polymer two phase systems Sharp, Kim Andrew 1985

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THEORETICAL AND EXPERIMENTAL STUDIES ON ERYTHROCYTE PARTITION IN AQUEOUS POLYMER TWO PHASE SYSTEMS by KIM ANDREW SHARP B.Sc, U n i v e r s i t y of Leeds, England, 1978 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF CHEMISTRY  We accept t h i s t h e s i s as conforming to the-^eODired standaitfJ  THE UNIVERSITY OF BRITISH COLUMBIA June 1985 © Kim Andrew Sharp, 1985  In p r e s e n t i n g  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of  requirements f o r an advanced degree at the  the  University  o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make it  f r e e l y a v a i l a b l e f o r reference  and  study.  I further  agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying o f t h i s t h e s i s f o r s c h o l a r l y purposes may  be granted by the head o f  department o r by h i s o r her  representatives.  my  It i s  understood t h a t copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain  s h a l l not be allowed without my  permission.  Department of  Oh^.yv\\<^Ofl  The U n i v e r s i t y of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3  Date  DE-6  (3/81)  k  ^\)c«  \<\%5  written  -i i -  Abstract  Aaueous polymer two phase systems containing dextran T500, PEG 8000, and buffer are widely used to separate and analyse c e l l s and other b i o l o g i c a l material based on the way they p a r t i t i o n between the two phases and t h e i r i n t e r f a c e . The behaviour of human erythrocytes i n such two phase systems was studied i n order to c h a r a c t e r i z e some of the physico-chemical i n t e r a c t i o n s important i n determining c e l l p a r t i t i o n .  Two aspects were studied: the r o l e  of e l e c t r o s t a t i c and a f f i n i t y l i g a n d e f f e c t s i n determining the r e l a t i v e a f f i n i t y of the c e l l for the two phases, and the r e l a t i o n s h i p of t h i s r e l a t i v e a f f i n i t y t o the c e l l p a r t i t i o n . The p o t e n t i a l d i f f e r e n c e produced by the unequal a f f i n i t y of the buffer cations and anions for each phase was r e l a t e d to the s a l t p a r t i t i o n by a thermodynamic model, which agreed with experimental r e s u l t s obtained i n s i n g l e and mixed s a l t systems. A thermodynamic theory f o r the e f f e c t s of an a f f i n i t y l i g a n d on the c e l l surface free energy d i f f e r e n c e between the phases was derived, and found to agree Q u a n t i t a t i v e l y with experimental r e s u l t s using the a f f i n i t y ligand PEG-palmitate. The change i n c e l l surface free energy d i f f e r e n c e as a function of p o t e n t i a l and ligand concentration was determined by contact angle measurements.  This change was very s m a l l , based e i t h e r on previous  estimates of the surface charge density, or on the amount of PEG-palmitate bound to the c e l l surface as determined by adsorption experiments.  This was  a t t r i b u t e d to p a r t i a l e x c l u s i o n of the phases from the c e l l glycocalyx. C e l l p a r t i t i o n i n t o the upper PEG r i c h phase increased as t h i s phase was  made more p o s i t i v e with respect to the lower phase, or as the amount of an a f f i n i t y l i g a n d , PEG-palmitate, i n the system was increased. Contact angle measurements were used to determine the energy of erythrocyte attachment to the i n t e r f a c e between the two phases.  The  dependence of the c e l l p a r t i t i o n on t h i s parameter showed that thermal energies are f a r too small to p a r t i t i o n c e l l s i n these systems.  The c e l l  p a r t i t i o n was unaffected by the density d i f f e r e n c e between the phases. This and other r e s u l t s l e d to the hypothesis that droplet coalescence i s the primary process by which large p a r t i c l e s ( > 1 ^im d i a . ) such as c e l l s are d i s t r i b u t e d between the i n t e r f a c e and one of the phases.  - i v-  Contents  Page  T i t l e Page  i  Abstract  i i  Contents  iv  L i s t of Tables  ix  L i s t of Figures  x  Acknowledgements  xii  Dedication  xiii  Chapter One. Introduction A. General Background and Objectives  1  B. H i s t o r i c a l Outline  10  C. T h e o r e t i c a l Aspects of P a r t i t i o n  17  i)  P h y s i c a l Chemistry of Phase Separation  17  ii)  P r o p e r t i e s of the Phase System  25  i i i ) Theory of Molecular P a r t i t i o n i n g  38  iv)  43  Theory of P a r t i c l e P a r t i t i o n i n g  D. The Erythrocyte  65  i)  Morphology and Erythrogenesis  65  ii)  Biochemistry of the Erythrocyte Membrane  67  Chapter Two. M a t e r i a l s and Methods A. General Methods  71 71  -V-  Contents continued  Chapter Two.  Page  M a t e r i a l s and Methods  B. Preparation and C h a r a c t e r i z a t i o n of Phase Systems  72  i)  Polymer Properties  72  ii)  Preparation of Phase Systems  76  i i i ) The Phase Diagram  78  iv)  I n t e r f a c i a l Tension  79  v)  E l e c t r o s t a t i c P o t e n t i a l Difference  80  C. P a r t i t i o n of Solutes i n the Phase System  82  i)  General Methods  82  ii)  Partition Coefficients  83  i i i ) PEG-palmitate C r i t i c a l M i c e l l e Concentrations  85  D. Preparation of Erythrocytes  85  E. Erythrocyte P a r t i t i o n  87  F. Polymer Adsorption to Erythrocytes  88  i)  Adsorption of PEG  ii)  PEG 8000-palmitate  88 Adsorption  i i i ) Desorption of PEG and PEG-palmitate G. Contact Angle Measurements  91 93 94  i)  Apparatus  94  ii)  Preparation of P i p e t t e s  96  i i i ) Experimental Procedure  96  iv)  97  Image A n a l y s i s  H. Treatment of Results and Experimental U n c e r t a i n t i e s  99  -vi  Contents continued  -  Chapter Three. Theoretical Results A. P o t e n t i a l Difference  i n Single S a l t Systems  Page  101 101  B. P o t e n t i a l Difference i n Mixed S a l t Systems  103  C. P o l y e l e c t r o l y t e P a r t i t i o n  108  D. Ligand Binding and P a r t i c l e P a r t i t i o n  113  Chapter Four. E l e c t r o s t a t i c E f f e c t s and the C e l l Surface Free Energy Difference  121  A. Introduction  121  B. E f f e c t s of Buffer Composition on Phase System Properties  122  i)  E f f e c t of Phosphate on the B i n o d i a l  122  ii)  E f f e c t of Buffer on I n t e r f a c i a l Tension  124  i i i ) Discussion C. P o t e n t i a l and S a l t P a r t i t i o n  125 127  i)  S a l t Bridge E f f e c t s  127  ii)  Single S a l t Systems  129  i i i ) Phosphate Concentration E f f e c t s  134  iv)  Mixed S a l t Systems  135  v)  Discussion  138  D. E l e c t r o s t a t i c Interactions and the Erythrocyte  142  i)  P a r t i t i o n and S a l t Composition  142  ii)  C e l l Surface Free Energy Difference and P o t e n t i a l  145  i i i ) Discussion  149  Contents continued  - vi i -  Page  Chapter Five. PEG-palmitate and the C e l l Surface Free Energy D i f f e r e n c e  154  A. Introduction  154  B. E f f e c t of PEG-palmitate on.the Phase System  155  i)  Compositional and E l e c t r o s t a t i c E f f e c t s  155  ii)  E f f e c t of Ester on Tension  156  i i i ) Discussion C. Behaviour of PEG-palmitate i n the phase system  157 157  i)  PEG-Palmitate P a r t i t i o n  157  ii)  PEG-Palmitate C r i t i c a l M i c e l l e Concentrations  159  i i i ) Discussion D. PEG-palmitate/Erythrocyte i n t e r a c t i o n s  160 165  i)  Cell Partition  165  ii)  Binding Studies  167  i i i ) PEG-palmitate and the C e l l Surface Free  iv)  Energy D i f f e r e n c e  177  Discussion  179  Chapter S i x . Factors Determining C e l l P a r t i t i o n  190  A. Introduction  190  B. Determinants of C e l l P a r t i t i o n  190  i)  P a r t i t i o n and I n t e r f a c i a l Tension  190  ii)  Polymer Composition and Contact Angle  191  i i i ) C e l l P a r t i t i o n and the C e l l / I n t e r f a c e I n t e r a c t i o n  195  -viii-  Contents Continued  Chapter S i x . Factors Determining C e l l B. Determinants of C e l l iv)  Page  Partition  Partition  Discussion  C. Mechanisms of C e l l P a r t i t i o n i)  C e l l P a r t i t i o n , Phase Density and Volume Ratio  ii)  Discussion and Proposal of a Mechanism for C e l l P a r t i t i o n  Chapter Seven. General Discussion and Summary A. Overview  198 204 204  209  220 220  B. Statement of New Results and Suggestions f o r Future Research C. Summary  227 230  Glossary o f Symbols and Abbreviations  235  Appendices  239  A. The Minimum Force Necessary t o P u l l a S p h e r i c a l P a r t i c l e o f f a L i a u i d Interface B. Mechanisms of C e l l P a r t i t i o n  Bibliography  239 240  247  -ix-  L i s t of Tables  Page  2.1  Description of Dextran Lots  73  2.2  Selected P h y s i c a l Properties of the Phase Polymers  7A  4.1  E f f e c t of Phase Composition on I n t e r f a c i a l Tension  125  4.2  E f f e c t of S a l t Concentration and Electrode Bridge Type on P o t e n t i a l  128  4.3  S a l t P a r t i t i o n and P o t e n t i a l i n Single S a l t Systems. I  130  4.4  S a l t P a r t i t i o n and P o t e n t i a l i n Single S a l t Systems. I I  131  4.5  S a l t P a r t i t i o n and P o t e n t i a l i n Single S a l t Systems. I l l  132  4.6  E f f e c t of Phosphate Concentration on P o t e n t i a l  134  4.7  Erythrocyte P a r t i t i o n and Ionic Strength  143  4.8  Erythrocyte P a r t i t i o n and Contact Angle- E f f e c t of  5.1  P o t e n t i a l and Ionic Strength  147  E f f e c t of Ester on Phase Compositions  155  5.2 E f f e c t of Phase Composition on I n t e r f a c i a l Tension  156  5.3  PEG Ester C r i t i c a l M i c e l l e Concentrations  160  5.4  Summary of Ester Binding Data from Scatchard P l o t s  177  5.5  Erythrocyte P a r t i t i o n and Contact Angle- E f f e c t of Ester  6.1  178  Erythrocyte P a r t i t i o n and Contact Angle- E f f e c t of Tension  6.2  Dimensionless Numbers Characterising for Phase System Droplets  193 F l u i d Flow Regimes 211  -X-  L i s t of Figures  "  Page  1.1  General Phase Diagram For a Two Polymer/Solvent  System  18  1.2  I n t e r a c t i o n of a S p h e r i c a l P a r t i c l e with the Interface  47  1.3  Schematic Diagram of the Erythrocyte Membrane  70  2.1  Measurement of Contact Angles  95  2.2  Photograph of Cell/Drop Contact Angle  98  3.1  P o t e n t i a l and S a l t Composition  109  3.2  Theory of P a r t i c l e A f f i n i t y Ligand P a r t i t i o n  118  3.3  E f f e c t of A f f i n i t y Ligand on C e l l Surface Free Energies  120  4.1  E f f e c t of S a l t s on the Phase Diagram  123  4.2  Comparison of T h e o r e t i c a l and Experimental P o t e n t i a l s  133  4.3  E f f e c t of S a l t Composition on Erythrocyte P a r t i t i o n  144  4.4  E f f e c t of P o t e n t i a l on the C e l l Surface Free Energy Difference  148  5.1  Behaviour of Ester i n the Phase System  158  5.2  Erythrocyte P a r t i t i o n and Ester Concentration  166  5.3  Adsorption of PEG 8000 to Erythrocytes  168  5.4  Ester Binding to Erythrocytes- E f f e c t of the Phases and C e l l Concentration  169  5.5  Comparison of PEG 8000, Dextran T500 and Ester Binding  171  5.6  Desorption of PEG and Ester from Erythrocytes  173  5.7  Comparison of Ester Adsorption and Desorption  175  5.8  Scatchard P l o t s of Ester Binding Data  176  -xi-  * L i s t of Figures continued  5.9  Page  E f f e c t of Ester on C e l l Surface Free EnergiesComparison with Theory  180  6.1  Erythrocyte P a r t i t i o n and I n t e r f a c i a l Tension  192  6.2  Good G i r i f a l c o P l o t s f o r Erythrocytes  194  6.3  Dependence of Erythrocyte P a r t i t i o n C o e f f i c i e n t on the C e l l / I n t e r f a c e I n t e r a c t i o n Energy  6.4  Dependence of Percent Erythrocyte P a r t i t i o n on the Detachment Force  6.5  196  197  E f f e c t of Phase Volume Ratio and Density Difference on Erythrocyte P a r t i t i o n  206  6.6  Appearance of C e l l P a r t i t i o n i n Isopycnic Systems  207  6.7  C e l l P a r t i t i o n i n Isopycnic Systems-  7.1  Microscopic View  208  Schematic Outline of the Process of C e l l P a r t i t i o n  228  -xi i -  Acknowledgements  I t i s a great pleasure f o r me t o be able to formally thank a l l the many people who combined t o provide me with a context f o r t h i s t h e s i s : In the l a b , p a r t i c u l a r l y Jim Van A l s t i n e and Tim Webber, for introducing me t o phase systems; Raymond Norris-Jones, the other member of " p a r t i t i o n row";  Johann Janzen for many discussions on binding; Stephan Bamberger for  help with the tension measurements; John Cavanagh f o r introducing me to column chromatography; Rob Snoek, on whom I could r e l y for h i s broad knowledge of the erythrocyte; Evan Evans for showing me how to measure contact angles with h i s elegant apparatus; Barbara Kukan, for help with the contact angle measurements.  I would e s p e c i a l l y  l i k e to thank my supervisor,  Don Brooks, from whom I l e a r n t much about the method, p o s s i b i l i t i e s and excitement o f research, and who always treated me as a f r i e n d . This t h e s i s benefited g r e a t l y from h i s generous flow of support, suggestions and advice. Outside the l a b , I would l i k e to thank a l l my other f r i e n d s , who provided me with the kind o f support that made everything so much e a s i e r , and the balance that I b e l i e v e i s necessary t o good science, and who made Vancouver such a wonderful place f o r me. In p a r t i c u l a r , Cynthia, Sandra and Rob f o r t h e i r music; Timmie f o r i n t r o d u c i n g me to the New Age; Judy and Ree, good t r a v e l l i n g companions; Evelyn and Rob, f o r days on the beach. I am g r a t e f u l t o the Medical Research Council of Canada for f i n a n c i a l support.  F i n a l l y I'd l i k e t o thank everyone i n the o f f i c e for t h e i r help  with the typing of t h i s  manuscript.  -xiii-  This t h e s i s i s dedicated to those who gave me  life  -1-  Chapter One. Introduction  Those who f a l l i n love with p r a c t i c e without science are l i k e a s a i l o r who enters a ship without helm or compass, and who never can be c e r t a i n whither he i s going- Leonardo da V i n c i  A. General Background and Objectives  Two of the landmarks i n the development of biochemistry and c e l l biology were undoubtedly the discovery of chromatography and the development of the ultracentrifuge.  In 1902 the Russian biochemist M. Tswett f i r s t used  adsorption chromatography to separate l e a f pigments'*" (hence the term chromatography).  A crude c e n t r i f u g a t i o n process had been used to separate  tung o i l as long ago as the tenth century, although the c e n t r i f u g e as a s o p h i s t i c a t e d a n a l y t i c a l t o o l d i d not e x i s t u n t i l the development, from 1923 onwards, of the high speed a n a l y t i c a l and preparative c e n t r i f u g e s by Svedburg and coworkers'''. Continuous improvements of, and developments from, these two techniques, plus the a d d i t i o n of others such as e l e c t r o p h o r e s i s (which was f i r s t developed by T i s e l i u s i n the  ^O's"*"),  gave researchers i n c r e a s i n g l y sharp and d i s c r i m i n a t i n g biochemical s c a l p e l s with which to d i s s e c t complex organisms and excise components of i n t e r e s t . I t i s f a i r to say that the s t a t e of any area i n biochemistry today depends to a great degree on the s o p h i s t i c a t i o n of the separation techniques a v a i l a b l e .  Encyclopaedia B r i t a n n i c a , 1968  Edn.  -2-  I t i s a sine qua non that any separation method must d i s c r i m i n a t e between d i f f e r e n t elements or properties o f a mixture while a l t e r i n g the m a t e r i a l as l i t t l e as p o s s i b l e : the separation method must be compatible with the m a t e r i a l .  As a r u l e the l a r g e r and more complex the m a t e r i a l , the  more s t r i n g e n t these requirements become. Thus while there are many methods for separating p r o t e i n s , carbohydrates  and l i p i d s , there are fewer methods  that can deal with complexes of p r o t e i n s , membranes, and c e l l o r g a n e l l e s , and there i s a paucity o f methods for separating i n t a c t v i a b l e c e l l s ( f o r a review see e.g. Catsimpoolas,  1977).  This t h e s i s i s concerned with p a r t i t i o n i n aqueous polymer two-phase systems (APTS) as a method o f c e l l separation and a n a l y s i s i n biochemistry and biophysics. While many c l a s s e s o f two and multi-phase systems e x i s t , the only type used t o any degree f o r separating or analysing c e l l s i s that formed from two incompatible n e u t r a l polymers i n aqueous s o l u t i o n . I f a s o l u t i o n i s made of two polymers i n a common solvent, and the energy o f i n t e r a c t i o n between segments o f the d i f f e r e n t polymers i s unfavourable,  then  at some c o n d i t i o n of s u f f i c i e n t l y high polymer molecular weights and concentrations the mixture w i l l separate i n t o two phases. Each phase w i l l be enriched i n one of the polymers and depleted i n the other polymer. I f the common solvent i s water, then these two phase systems may be buffered, made i s o t o n i c and (providing the polymers have no d e l e t e r i o u s e f f e c t s ) otherwise made compatible with s e n s i t i v e b i o l o g i c a l m a t e r i a l . Such two phase systems, p a r t i c u l a r l y those containing dextran and poly(ethylene g l y c o l ) (PEG), can be used i n a manner that I w i l l o u t l i n e s h o r t l y , for many separation  -3-  problems. Although t h i s technique i s not widely known, over f i v e hundred papers and a r t i c l e s have been published i n t h i s area. I t has proven to be an extremely v e r s a t i l e separation technique, having been used f o r amino-acids, p r o t e i n s , n u c l e i c a c i d s , membrane fragments, organelles, microrganisms and c e l l s , amongst others.  As a separation technique, p a r t i t i o n i n APTS i s unique, although i t i s analogous to c e r t a i n other separation methods. The simplest a p p l i c a t i o n i s the s i n g l e step p a r t i t i o n : the material of i n t e r e s t ( f o r convenience r e f e r r e d to hereafter as the s o l u t e , although i t may also be an i n s o l u b l e p a r t i c l e or c e l l ) i s added to the phase system, which i s mixed and allowed to s e t t l e . The solute w i l l then be found to have d i s t r i b u t e d , or p a r t i t i o n e d , between the two phases and t h e i r mutual i n t e r f a c e . For soluble material e s p e c i a l l y , t h i s i s analogous to solvent e x t r a c t i o n , the solute p a r t i t i o n i n g on the basis of i t s r e l a t i v e ' s o l u b i l i t y ' i n each of the phases.  I f t h i s s i n g l e step procedure i s repeated, by separating the phases  and adding to them fresh volumes of the complementary phase, mixing, s e t t l i n g , separating and so on, a multistep procedure of increased r e s o l u t i o n can be developed, known as countercurrent d i s t r i b u t i o n (CCD). This may be considered as a d i s c r e t e analogue of chromatography, where e i t h e r of the phases can be considered as the s t a t i o n a r y phase. I t i s an i n t e r e s t i n g h i s t o r i c a l note that CCD i n f a c t preceded p a r t i t i o n 2  chromatography. P r i o r to 1941 Martin and Synge  had attemped to use  CCD  to separate sheep wool p r o t e i n s . Not obtaining s u f f i c i e n t r e s o l u t i o n , they Encyclopaedia B r i t a n n i c a , 1968 Edn.  -4-  h i t on the idea of immobilising one of the phases on a porous matrix such as paper, thus developing the f i r s t type o f p a r t i t i o n chromatography. Continuous l i q u i d - l i a u i d e x t r a c t i o n procedures such as the c o i l c e n t r i f u g e and continuous flow-through  planet  centrifuges have a l s o been adapted t o  APTS, making the s i m i l a r i t y with chromatography even c l o s e r . By contrast, when c e l l s or p a r t i c l e s are being p a r t i t i o n e d the method has c l o s e r p a r a l l e l s with the separation of mineral ores by foam f l o t a t i o n than with solvent e x t r a c t i o n or chromatography: a f t e r the phases are mixed, and while they are separating, the p a r t i c l e s are i n t e r a c t i n g with a dense emulsion o f droplets which are e i t h e r f l o a t i n g or sedimenting t o t h e i r respective bulk phases, i n a manner analogous to the process whereby small ore p a r t i c l e s are attaching t o and detaching from the surface of small r i s i n g a i r bubbles (Clarke and Wilson, 1983).  Two phase systems have many features which contribute t o t h e i r success i n b i o l o g i c a l separations, some of which w i l l be discussed at more length l a t e r i n t h i s i n t r o d u c t i o n . Both phases c o n s i s t p r i m a r i l y of water ( t y p i c a l l y greater than eighty percent by weight) thus they can be buffered or modified by the a d d i t i o n of any s a l t s , f a c t o r s e t c . required by p a r t i c u l a r s o l u t e s . In a d d i t i o n the polymers used are b i o l o g i c a l l y i n e r t (vide i n f r a ) , both f a c t o r s r e s u l t i n g i n a benign environment for s e n s i t i v e s o l u t e s . The i n t e r f a c i a l tension between the phases i s extremely low -4 (10  -10  2 dynes/cm), thus reducing the chance of denaturing  solutes  adsorbed at the i n t e r f a c e . A very important aspect o f p a r t i t i o n i s that i t separates by means of d i f f e r e n c e s i n surface p r o p e r t i e s - except under p a r t i c u l a r conditions the p a r t i t i o n does not depend on the s i z e , shape or  -5-  density of the s o l u t e . This feature i s an advantage when t r y i n g to separate, for example, a mixture of c e l l s that have d i f f e r e n t functions, and hence which might be expected a p r i o r i to d i f f e r i n surface p r o p e r t i e s , but not i n density or s i z e . P a r t i t i o n i s extremely s e n s i t i v e , depending, as w i l l be seen s h o r t l y , on roughly the exponential  of the relevant  solute properties.  Moreover, what these relevant properties are, i . e . the p a r t i c u l a r surface c h a r a c t e r i s t i c s that determine the p a r t i t i o n , can be selected to a large extent by changing the polymer species and concentrations, the i o n i c composition of the phases, or by the a d d i t i o n of c e r t a i n l i g a n d s . By adding such a f f i n i t y l i g a n d s , whose mode of a c t i o n w i l l be o u t l i n e d l a t e r i n t h i s i n t r o d u c t i o n , the p a r t i t i o n can be made to depend p r i m a r i l y on the nature of the ligand/solute i n t e r a c t i o n . This adds the p o s s i b i l i t y of much greater c o n t r o l and s p e c i f i c i t y to the technique. P a r t i t i o n can be used for solutes ranging i n s i z e from angstroms to microns. The upper s i z e l i m i t i s determined by the need for the phases to separate before the solute i t s e l f s e t t l e s out, e i t h e r to the i n t e r f a c e or the bottom of the container.  The  lower s i z e l i m i t i s p r i n c i p a l l y determined by the f a c t that most small solutes (MWt.<=300 g/mole) have p a r t i t i o n c o e f f i c i e n t s around 1 + 20%.  In  p r a c t i c e both these s i z e l i m i t s manifest themselves as l o s s of r e s o l u t i o n or separating power. Within these l i m i t s APTS has been used f o r solutes of an almost continuous s i z e d i s t r i b u t i o n between amino acids and c e l l s . For solutes and small («=1 jjm dia.) p a r t i c l e s , at l e a s t , separation i s generally performed under e q u i l i b r i u m c o n d i t i o n s , or at l e a s t i n a time independent manner, which can s i m p l i f y the a n a l y s i s of the separation process.  Being a  l i q u i d / l i q u i d process i t can be scaled up e a s i l y , and has a large sample capacity.  -6-  There are of course drawbacks with t h i s technique. Very l i t t l e i s known about the p h y s i c a l chemistry of the phase systems, o r , more importantly the separation process i t s e l f . L i t t l e i s known about which of the s o l u t e surface p r o p e r t i e s are important i n determining the p a r t i t i o n c o e f f i c i e n t i n a given system, p a r t i c u l a r l y for c e l l s and p a r t i c l e s . The d e t a i l s of how large p a r t i c l e s and c e l l s , which of course do not d i f f u s e l i k e s o l u b l e m a t e r i a l , are a c t u a l l y d i s t r i b u t e d between the two phases and the i n t e r f a c e are unclear. While t h i s separation method i s very s e n s i t i v e to the surface properties of the s o l u t e , the separations obtained are generally based on b i o l o g i c a l l y n o n - s p e c i f i c d i f f e r e n c e s . B i o l o g i c a l l y s p e c i f i c separations, often of extremely high r e s o l u t i o n , can be obtained by a f f i n i t y methods, as i n other separation techniques such as chromatography, by using a n t i b o d i e s , c o f a c t o r s , ligands e t c . However although these have been applied to p r o t e i n , n u c l e i c a c i d and membrane receptor p u r i f i c a t i o n s i n APTS, so f a r these powerful approaches have not been applied to the p a r t i t i o n of c e l l s .  A d e t a i l e d theory of a f f i n i t y p a r t i t i o n , p a r t i c u l a r l y for c e l l s , i s a l s o needed. Lack of such knowledge  and techniques hampers the r a t i o n a l  a p p l i c a t i o n of APTS to many d i f f i c u l t separation problems. This i s compounded by the f a c t that there are many v a r i a b l e s which may be a l t e r e d i n making up two phase systems, such as the type, molecular weight and concentrations of both polymers, i o n i c composition e t c . This provides great v e r s a t i l i t y . I t a l s o makes s e l e c t i o n of a s u i t a b l e system l a r g e l y an e m p i r i c a l procedure, however.  The great s e n s i t i v i t y of the systems i s a l s o  a double-edged sword, since reproducible r e s u l t s may be d i f f i c u l t to o b t a i n , p a r t i c u l a r l y with l a r g e r p a r t i c l e s , unless experimental c o n d i t i o n s , such as  -7-  temperature, phase s e t t l i n g time e t c . are c a r e f u l l y c o n t r o l l e d . This problem i s exacerbated by p o l y d i s p e r s i t y i n the polymers, and conseauent l o t to l o t variations.  The high v i s c o s i t i e s and low density d i f f e r e n c e s of the phases  can lead to long separation times, which are disadvantageous, p a r t i c u l a r l y for l a b i l e b i o l o g i c a l samples. Depending on the polymers used, the method may not be cost e f f e c t i v e , e s p e c i a l l y i f the polymers cannot be recycled a f t e r use. F i n a l l y i n p a r t i c u l a r cases the polymers may bind t o , or i n other ways cause unwanted a l t e r a t i o n s to the s o l u t e . There are probably two main reasons why t h i s techniaue i s not more widely used: the number of parameters that have to be considered i n choosing a s u i t a b l e system, and the s e n s i t i v i t y of the method.  Objectives  I t has been stressed that c e l l p a r t i t i o n i s a method f o r separating and studying c e l l s based on surface p r o p e r t i e s , and furthermore, that l i t t l e Quantitative information i s a v a i l a b l e regarding the surface properties that are important, or how such separations are achieved. motivated t h i s study.  These considerations  This t h e s i s i n v e s t i g a t e s the p o s s i b i l i t y of using  physico-chemical and thermodynamic methods to study c e l l p a r t i t i o n i n aaueous polymer two phase systems.  1).  I t considers two auestions:  What r o l e do phase system and c e l l surface p r o p e r t i e s have i n  determining the i n t e r a c t i o n of the c e l l surface with each of the phases? In other words, what determines the r e l a t i v e a f f i n i t y of the c e l l f o r each phase?  Two aspects of t h i s i n t e r a c t i o n are studied: e l e c t r o s t a t i c e f f e c t s  -8-  and a f f i n i t y ligand e f f e c t s . These were chosen both because of t h e i r importance i n obtaining s p e c i f i c c e l l separations,  and because of t h e i r  experimental a c c e s s i b i l i t y .  2 ) . How  does c e l l p a r t i t i o n depend on the r e l a t i v e a f f i n i t y of the c e l l  surface for each phase, and i s the p a r t i t i o n behaviour completely characterised  by t h i s i n t e r a c t i o n ?  To examine these questions i t was also necessary to study the i n t e r r e l a t i o n s h i p s of some of the system properties themselves. objectives the p a r t i t i o n of human erythrocytes of dextran T500 and PEG  To pursue these  i n two phase systems composed  8000 was studied. This p a r t i c u l a r polymer  combination was chosen because i t i s by f a r the most widely used, e s p e c i a l l y for c e l l p a r t i t i o n . Human erythrocytes  were used because of t h e i r  a v a i l a b i l i t y , uniformity, and the d e t a i l e d knowledge a v a i l a b l e on t h e i r surface structure (section D below).  Outline of Thesis  The remainder of t h i s i n t r o d u c t i o n c o n s i s t s of three parts: -A b r i e f h i s t o r y of the  subject.  -A d e t a i l e d summary of the theory relevant to c e l l p a r t i t i o n .  This  s e c t i o n also gives more d e t a i l e d explanations of terms such as surface p r o p e r t i e s , surface i n t e r a c t i o n s , e l e c t r o s t a t i c i n t e r a c t i o n s  and  a f f i n i t y l i g a n d i n the context of p a r t i t i o n . -A b r i e f d e s c r i p t i o n of the erythrocyte,  and the surface  properties  -9-  important  for p a r t i t i o n .  Chapter Two describes the materials and methods used i n the experimental sections.  Chapter Three contains a l l the o r i g i n a l t h e o r e t i c a l r e s u l t s , some  of which are tested experimentally i n l a t e r chapters.  Chapters Four, Five  and S i x contain the experimental r e s u l t s , with Four and Five dealing p r i m a r i l y with the f i r s t question posed i n the o b j e c t i v e , and Chapter Six t r e a t i n g the second'.  Each chapter has a b r i e f i n t r o d u c t i o n o u t l i n i n g  the approach t o the problem.  Chapter Seven i s a general discussion chapter  i n which I t i e together the previous work and attempt t o put i t i n perspective.  The appendices contain some m a t e r i a l r e l a t e d to the discussion  on c e l l p a r t i t i o n mechanisms. given a f t e r Chapter Seven.  A glossary of symbols and abbreviations i s  -10-  B. H i s t o r i c a l Outline  The h i s t o r y of p a r t i t i o n i n g i n APTS c l e a r l y i l l u s t r a t e s the v e r s a t i l i t y of the method, i t s s e n s i t i v i t y and i t s growing commercial a p p l i c a t i o n s . The phenomenon of phase separation i n a three component, polymer/polymer solvent system was f i r s t reported i n 1896  ( B e i j e r i n c k ) for g e l a t i n / s t a r c h s o l u t i o n s .  Flory (1941) and Huggins (1941) independently worked out a s u c c e s s f u l theory for the thermodynamics of concentrated s o l u t i o n s of f l e x i b l e polymers. This was extended by Scott (1949) to describe phase separation phenomena i n s o l u t i o n s containing two incompatible polymers, showing that the Flory-Huggins  theory could q u a l i t a t i v e l y describe many of the properties of  these two phase systems.  The f i r s t work demonstrating  the usefulness of  APTS f o r separating b i o l o g i c a l m a t e r i a l was performed by Albertsson during his d o c t o r a l t h e s i s , and the f i r s t paper on t h i s a p p l i c a t i o n was i n 1958  published  (Albertsson, 1958). Two years l a t e r Albertsson published the f i r s t  book on the subject, a monograph based on h i s t h e s i s (Albertsson, 1960). Albertsson and h i s co-workers subsequently  pioneered the a p p l i c a t i o n of APTS  to a wide range of b i o l o g i c a l m a t e r i a l s . With the p u b l i c a t i o n of the f i r s t book, and p a r t i c u l a r l y with the issue of a r e v i s e d e d i t i o n . i n (Albertsson, 1971) other workers became i n t e r e s t e d i n t h i s  The f i r s t p u b l i c a t i o n s concerned p r o t e i n separations. immunological  1971  technique.  The study of  reactions was another e a r l y a p p l i c a t i o n (Albertsson and  P h i l i p s o n , 1960), as was the extension to l a r g e r molecules and p a r t i c l e s (Albertsson, 1961). DNA  was p a r t i t i o n e d i n 1962,  ( F r i c k and L i f ) , and the  f i r s t c e l l organelles, c h l o r o p l a s t s , were studied i n 1963  (Albertsson and  -11-  B a l t e s c h e f f s k y ) . Viruses were f i r s t studied i n APTS i n 1963  (Bengtsson and  P h i l i p s o n ) . Many other types of s o l u t e s , p a r t i c l e s and c e l l s were subsequently  studied by p a r t i t i o n i n g , i n c l u d i n g liposomes (Dahlgren et a l . ,  1977, Eriksson et a l . , 1978).  In 1965 Albertsson described a new type of  t h i n l a y e r CCD apparatus s p e c i a l l y designed to minimize the long separation times due to the small density d i f f e r e n c e and high v i s c o s i t i e s of the phase systems. Although other types of apparatus f o r multistep p a r t i t i o n were described by Albertsson (Albertsson, 1971; Blomquist and Albertsson, 1972), there were no extensive a p p l i c a t i o n s of new apparatus u n t i l 1978, when Sutherland and I t o described the use of the t o r o i d a l ' c o i l c e n t r i f u g e for p a r t i t i o n i n g c e l l s and o r g a n e l l e s , and i n d u s t r i a l s c a l e l i q u i d / l i q u i d e x t r a c t i o n was applied to p r o t e i n separation by APTS (Hustedt et a l . , 1978). Another t e c h n i c a l development was the adaption of APTS to the chromatography of DNA  fragments by the immobilization of one of the phases on a  chromatography bead (Mueller et a l . , 1979)  Albertsson and B a i r d (1962) described the f i r s t a p p l i c a t i o n to c e l l s e a r l y on i n the development of APTS. With the separation of young and o l d red blood c e l l s i n 1964, Walter et a l . f i r s t showed the connection between a s p e c i f i c b i o l o g i c a l property of the c e l l surface and p a r t i t i o n , and demonstrated the great s e n s i t i v i t y of c e l l p a r t i t i o n .  Subsequently various  other mammalian c e l l types have been p a r t i t i o n e d , i n c l u d i n g lymphocytes and leukocytes (Walter et a l . , 1969), hepatocytes  (Walter et a l . , 1973a),  p l a t e l e t s (Grant and Zucker, 1978), leukemia c e l l s (Kessel, 1980), mouse melanoma c e l l s (Miner et a l . , 1981). Walter and Selby introduced an a f f i n i t y l i g a n d for c e l l separations, dextran-DEAE, i n 1967. Johansson (1970a) l a t e r  -12-  introduced another a f f i n i t y l i g a n d , PEG-TMA, f o r p r o t e i n p a r t i t i o n . A t h i r d type o f l i g a n d , PEG-fatty a c i d e s t e r s , also known c o l l e c t i v e l y as hydrophobic a f f i n i t y l i g a n d s , was introduced by Shanbhag and Johansson (1974) f o r p r o t e i n p a r t i t i o n . This type of l i g a n d was f i r s t applied to c e l l p a r t i t i o n by Eriksson et a l . , (1976), and has become the most widely used c e l l a f f i n i t y ligands.  APTS have also been applied i n a n a l y t i c a l s t u d i e s . For example Albertsson  (1965b) used p a r t i t i o n i n g to study changes i n DNA conformation.  He also used i t to estimate p r o t e i n i s o e l e c t r i c points of proteins by a technique known as c r o s s - p a r t i t i o n (Albertsson et a l . , 1970), a method which can also be used to measure organelle i s o e l e c t r i c points ( E r i c s o n , 1974; Horie et a l . , 1979; Akerlund e t a l . , 1979). Antibody/antigen i n t e r a c t i o n s (Albertsson and P h i l i p s o n , 1960), p r o t e i n / l i g a n d i n t e r a c t i o n s (Gray and Chamberlain, 1971), p r o t e i n / p r o t e i n i n t e r a c t i o n s (Backman et a l . , 1977) and c e l l / c e l l i n t e r a c t i o n s (Walter et a l . , 1978) have a l l been studied using APTS. Non-partition uses of APTS include the measurement of c e l l  surface  free energy differences (Gerson, 1980; Schurch et a l . , 1981), and measurements o f a l t e r a t i o n s i n a r t e r i a l t i s s u e surface free energies (Boyce et a l . , 1983). P a r t i t i o n i n g i n APTS has been used i n the c l i n i c a l s e t t i n g , to develop a new type of immune assay, the p a r t i t i o n a f f i n i t y l i g a n d assay (PALA) (Mattiason, 1980), and as a possible t e s t f o r m u l t i p l e s c l e r o s i s (Van A l s t i n e and Brooks, 1984).  There were few e a r l y commercial a p p l i c a t i o n s f o r APTS (eg. v i r u s i s o l a t i o n , Grindrod and C l i v e r , 1970). However i n 1978  the f i r s t of a  -13-  s e r i e s of papers was published by Kula and her colleagues on a b i o t e c h n o l o g i c a l a p p l i c a t i o n - the large s c a l e p u r i f i c a t i o n of enzymes. Other a p p l i c a t i o n s include a l c o h o l i c fermentation  (Kuhn, 1980), enzyme  immobilization (Hahn-Hagerdal et a l . , 1981)  and bio-energy interconversion  (Smeds et a l . , 1983). Many papers have now been published on large scale enzyme separation, and p i l o t plants using t h i s technology are being tested i n Germany and Scandinavia.  Biotechnology  promises to be one of the f a s t e s t  growing areas of research i n APTS (Mattiason, 1983).  Although there have been many a p p l i c a t i o n s of APTS, progress i n t h e o r e t i c a l aspects of p a r t i t i o n i n g has been l e s s r a p i d .  The work of  Albertsson and Nyns i n 1961 on the e f f e c t s of s a l t s on p r o t e i n p a r t i t i o n represented  the f i r s t step towards understanding what  physicochemical  f a c t o r s a f f e c t the p a r t i t i o n . Johansson (1970b, 1974a) measured many s a l t and protein p a r t i t i o n c o e f f i c i e n t s , r e l a t i n g the two using a p a r t i a l thermodynamic  treatment of Albertsson's  (1971). Shanbhag (1971) showed that  the two phase i n t e r f a c e provided l i t t l e r e s i s t a n c e to the d i f f u s i o n of proteins between the phases. Albertsson had predicted that c e r t a i n s a l t s could give r i s e to Donnan type p o t e n t i a l s between the phases, and t h i s confirmed by d i r e c t measurements i n 1973  was  (Reitherman et a l . , ) . Johansson  (1974b) a l s o measured these p o t e n t i a l s i n d i r e c t l y by p r o t e i n p a r t i t i o n . However i t was not u n t i l r e c e n t l y that a f u l l thermodynamic r e l a t i o n s h i p between the p o t e n t i a l and s a l t p a r t i t i o n c o e f f i c i e n t s was derived confirmed experimentally  and  (Brooks et a l . , 1984). A c o n t r i b u t i o n to the  understanding of e l e c t r o s t a t i c e f f e c t s i n p r o t e i n p a r t i t i o n was made by deLigny and Gelsema (1982) who put the r e l a t i o n s h i p between s a l t and p r o t e i n  -14-  p a r t i t i o n c o e f f i c i e n t s on a firmer t h e o r e t i c a l f o o t i n g . The e f f e c t s o f polymer type and concentration were a l s o i n v e s t i g a t e d . Albertsson measured phase compositions for several polymer types and molecular weights, and many of the r e s u l t i n g phase diagrams are given i n h i s book (Albertsson, 1971). Albertsson a l s o gives a treatment o f the t h e o r e t i c a l framework o f p a r t i t i o n i n g i n t h i s book. Ryden and Albertsson (1971) i n v e s t i g a t e d the r e l a t i o n s h i p between the polymer concentrations and the i n t e r f a c i a l tension between the phases. Bamberger et a l . , (1984a,b) further i n v e s t i g a t e d the r o l e o f polymer concentrations, i n t e r f a c i a l tension, and s a l t p a r t i t i o n . In p a r t i c u l a r they r e l a t e d the s a l t p a r t i t i o n c o e f f i c i e n t s to the d i f f e r e n c e i n polymer concentrations between the phases, and e s t a b l i s h e d the fourth power dependence of the tension on t h i s d i f f e r e n c e .  The determinants o f c e l l p a r t i t i o n was a l s o a subject o f some i n t e r e s t . Walter and Coyle (1968) used enzymatic m o d i f i c a t i o n o f erythrocyte  surfaces  to i n v e s t i g a t e t h i s aspect. Walter et a l . , (1968b) a l s o looked a t the other side of the problem by i n v e s t i g a t i n g the e f f e c t s o f various phase system properties such as t o n i c i t y and pH on erythrocyte p a r t i t i o n . In 1971 Brooks et a l . , demonstrated that erythrocyte p a r t i t i o n c o r r e l a t e d with e l e c t r o p h o r e t i c m o b i l i t y , one o f the e a r l i e s t l i n k s between p a r t i t i o n and a s p e c i f i c c e l l surface c h a r a c t e r i s t i c . The e f f e c t s o f aldehyde f i x a t i o n on erythrocyte p a r t i t i o n were a l s o studied (Walter et a l . , 1973b). Flanagan and coworkers (Flanagan and Barondes, 1975; Flanagan et a l . , 1976) applied a f f i n i t y p a r t i t i o n t o p u r i f i c a t i o n of membrane bound receptors, and developed a p a r t i a l theory o f a f f i n i t y p a r t i t i o n . Subsequent work, however, f a i l e d t o support t h i s theory i n a l l i t s d e t a i l s (Flanagan et a l . , 1976;  -15-  Johansson, 1976; Johansson and Shanbhag, 198A). The r o l e o f n o n - e l e c t r o s t a t i c e f f e c t s i n c e l l p a r t i t i o n was studied by Walter et a l . , (1976) who c o r r e l a t e d erythrocyte p a r t i t i o n with membrane l i p i d composition. Eriksson et a l . , (1976) a l s o found a s i m i l a r c o r r e l a t i o n using  hydrophobic  a f f i n i t y p a r t i t i o n . Studies on liposomes as model membranes also helped e l u c i d a t e the r o l e of b i l a y e r l i p i d i n p a r t i t i o n (Eriksson and Albertsson, 1978).  Zaslavsky and coworkers (1978b, 1979, 1980, 1981, 1982) published a s e r i e s of papers containing some c o n t r o v e r s i a l work on the r o l e of i o n i c composition, i o n i c strength and hydrophobicity i n c e l l p a r t i t i o n . This prompted a d i c u s s i o n on the the meaning and r o l e of hydrophobic p a r t i t i o n (Walter and Anderson, 1981).  effects i n  The d i f f i c u l t i e s associated with the  process by which large p a r t i c l e s such as c e l l s are d i s t r i b u t e d i n the phase system, i n the absence o f a d i f f u s i o n mechanism have long been recognized. Gerson (1980) and Gerson and A k i t (1980) have used contact angle measurements, and Raymond and Fisher (1980) have observed the r o l e of c e l l / d r o p l e t i n t e r a c t i o n s i n systems o f low polymer concentration, i n attempts t o understand t h i s problem b e t t e r .  There remains much t o be discovered about the d e t a i l s of c e l l partition.  In retrospect many of the t h e o r e t i c a l studies o u t l i n e d b r i e f l y  above were hampered by the d i f f i c u l t y of manipulating- one property o f the phase system or s o l u t e surface independently o f the others, and some studies often f a i l e d t o account f o r the fact that more than one f a c t o r was being v a r i e d simultaneously. Thus many questions s t i l l remain unanswered i n t h i s  -16-  area, and we are s t i l l some way from a complete understanding of the i n t e r r e l a t i o n between phase system p r o p e r t i e s , and the determinants o f s o l u t e and c e l l p a r t i t i o n .  Increased i n t e r e s t i n APTS r e s u l t e d i n the f i r s t conference on p a r t i t i o n i n g being held i n Los Angeles i n 1979. Work on the various a p p l i c a t i o n s of APTS continues at an increasing r a t e . A complete computerized bibliography of the l i t e r a t u r e was s t a r t e d a f t e r the t h i r d conference i n Vancouver i n 1983, and now l i s t s over f i v e hundred p u b l i c a t i o n s . A t h i r d comprehensive  book on p a r t i t i o n i n g i n APTS,  co-authored by many o f the l e a d i n g reasearchers i n the f i e l d i s i n press (Walter et a l . , 1985), with the aim o f being published i n time f o r the fourth i n t e r n a t i o n a l meeting on p a r t i t i o n i n g i n Lund, Sweden i n August, 1985. Indeed the comment of Arne T i s e l i u s , the great Swedish biochemist, i n the foreword t o the f i r s t e d i t i o n o f Albertsson's book, i n 1960, seems t o be as apt today as i t was then:  "The method, i n a l l i t s s i m p l i c i t y , seems to o f f e r a great many p o s s i b i l i t i e s , and i s by no means f u l l y explored i n a l l i t s modifications yet."  -17-  C. T h e o r e t i c a l Aspects of P a r t i t i o n  i ) P h y s i c a l Chemistry of Phase Separation  a) The Phase Diagram.  A d i s c u s s i o n of phase separation i s c l a r i f i e d by  reference to what i s known as a phase diagram. For the purposes of t h i s t h e s i s , the most u s e f u l type i s the compositional phase diagram, constructed at a constant temperature, pressure, pH, polymer molecular weights, and s a l t composition. ( F i g . 1.1). This phase diagram contains two pieces o f information. I t i n d i c a t e s which compositions form one phase, and which separate to form two phases. I t a l s o provides the composition of both phases from any given bulk composition. In t h i s type of phase diagram, each of the axes represents the concentration of one of the polymers. In a three component system there are only two degrees of freedom, thus the water concentration can be obtained by s u b t r a c t i o n . The composition of any phase can therefore be represented by some point on the phase diagram. The axes of the diagram are drawn at r i g h t angles f o r convenience. From a t h e o r e t i c a l point of view the most u s e f u l concentration u n i t s are mole or volume f r a c t i o n s , but for p r a c t i c a l reasons weight/weight percentages are usually used f o r polymer systems.  The b i n o d i a l l i n e ABC separates points representing compositions where the polymer concentrations are i n s u f f i c i e n t to form two phases, e.g. D, from those that do, eg. E. Any composition that l i e s above the b i n o d i a l w i l l  -18-  POLYMER A  Figure 1.1 General Phase Diagram f o r a Two Polymer/Solvent system  -19-  phase separate u n t i l i t j u s t forms two s t a b l e phases. Hence these phases are represented by two p o i n t s , F and G, that l i e on the b i n o d i a l . The b i n o d i a l can be d i v i d e d i n t o two p a r t s , one of which (BC) represents compositions of the phase enriched i n polymer A, the other (BA) representing compositions of the phase enriched i n B. By convention the the polymer enriched i n the lower, more dense phase i s represented on the a b s c i s s a .  The c r i t i c a l or  p l a i t p o i n t , B, i s where the compositions and amounts of the phases are equal, i e . one phase i s formed.  The bulk concentration, c' of any of the three components of a phase system E must be given by the mean of the concentrations i n each of the b  3  phases, c*\ c , weighted by the amounts of each phase, a \ a* , thus:  c  ' x  , t t  = (a c  b  bv ./ t  b  + a c )/(a +a ) x  Cl.l]  where the s u p e r s c r i p t s t and b r e f e r to the top and bottom phases r e s p e c t i v e l y (See glossary of symbols). Therefore the points EFG are c o l l i n e a r , and form what i s c a l l e d the t i e l i n e .  A l l other points on the 3  t i e l i n e a l s o s a t i s f y [1.1], with d i f f e r e n t values of a*", a* . The t i e l i n e i s therefore the locus of a l l those compositions that give r i s e to the same two phases i n d i f f e r e n t r e l a t i v e amounts. From [1.1] and the f i g u r e i t can be seen that the weight r a t i o of phases i s given by  t  a /a  b  [1.2]  = FE/GE  I f the d e n s i t i e s of the phases are p  and  p  then the volume r a t i o  r  y  i s given by  r  y  t  =  b  p FE/ p GE  [1.3]  which i s approximately FE/GE i f the d e n s i t i e s are s i m i l a r , or both are close to one.  A general feature of APTS i s that as the polymer concentrations are increased, i e as the water concentration i s decreased, the degree of phase separation increases, each polymer becoming more enriched i n one phase, and depleted i n the other, as evinced by the approach of the upper ends of the b i n o d i a l to the axes i n F i g . 1.1. The length of the t i e l i n e ( t ^ ) i s a measure of t h i s d i s s i m i l a r i t y between the phase compositions, or of the degree of phase separation, becoming zero at the p l a i t p o i n t , and i n c r e a s i n g with i n c r e a s i n g polymer concentrations. An expression f o r t-^ i s e a s i l y obtained by geometry, being the orthogonal mean of the polymer concentration differences:  h  =  ( c  c  a" a  )  +  (  V  c  b  )  I t turns out that the t i e l i n e i s an extremely u s e f u l c h a r a c t e r i s t i c of a phase system, which can be used to r e l a t e and p r e d i c t i t s various properties.  b) Theory of Phase Separation.  Several classes of phase separation  phenomena can occur. Many o f these have been described by F l o r y (1953). Two phases w i l l occur i n polymer/salt/water systems i f the polymer strongly  -21-  r e j e c t s one of the s a l t ions (Albertsson, 1971). This type of phase system has been used widely f o r b i o l o g i c a l separations, most notably for l a r g e s c a l e p r o t e i n p u r i f i c a t i o n (Hustedt et a l . , 1978). However the high s a l t concentrations generally make t h i s type of system unsuitable for c e l l separations. The most important type of phase system f o r our purposes i s that formed from two incompatible polymers i n aqueous s o l u t i o n . This type of phase separation can be s u c c e s s f u l l y  treated using the Flory-Huggins theory  for concentrated polymer s o l u t i o n s ( S c o t t , 1949, Tanford, 1961)), which i s o u t l i n e d below. This theory i s a l s o a p p l i c a b l e to the p a r t i t i o n of c e r t a i n solutes themselves i n the phase system, since the s o l u t e i s of course j u s t another component of the system.  The free energy of formation of a s o l u t i o n from i t s pure components, known as the free energy of mixing, i s given by:  AG  = AH  m  m  -T AS m  where AH  m  and  [1.5] m  AS  are the enthalpy and entropy of mixing  m  r e s p e c t i v e l y . The chemical p o t e n t i a l of the i ^  component,  u.^, i n t h i s  s o l u t i o n i s given by the p a r t i a l molar free energy of mixing for that component  H  A  -  [1.6]  ^° = dAGm 9n ;  where the d e r i v a t i v e of AG  i s taken with respect to the number of moles m  of component i , keeping the amount of the other components, the  temperature  -22-  and pressure constant and  n? i s the i s the chemical p o t e n t i a l i n some  reference s t a t e , i e . the standard s t a t e chemical p o t e n t i a l . Now  the  conditions that must be s a t i s f i e d simultaneously f o r the formation of two s t a b l e phases i n thermodynamic e q u i l i b r i u m from a mixture of components are:  i ) the o v e r a l l free energy of mixing must be minimized. -  i i ) the chemical p o t e n t i a l of each component must be the same i n each phase:  li*. =  for a l l i  [1.7]  Phase separation, i e . p a r t i a l de-mixing of the polymers, r e s u l t s i n a decrease i n entropy, t h e r e f o r e i f AG i s to be decreased,  AH must a l s o  decrease. This w i l l occur i f the enthalpy of i n t e r a c t i o n between u n l i k e polymer segments i s unfavourable, or p o s i t i v e , since t h i s i n t e r a c t i o n i s decreased on phase separation. On a mole b a s i s , the enthalpy of mixing w i l l increase with molecular weight, whereas the entropy of mixing per mole w i l l be constant (neglecting the entropy c o n t r i b u t i o n from the polymer conformation). Thus f o r high molecular weight polymers one would expect that even very small p o s i t i v e enthalpies per segment can become important. This i s demonstrated  by the f a c t that polymer i n c o m p a t a b i l i t y i s the r u l e rather  than the exception (Dobry and Boyer-Kawenoki, 1947). Such e f f e c t s are a l s o r e f e r r e d to as excluded volume e f f e c t s .  In the Flory-Huggins theory, the s o l u t i o n i s envisaged as c o n s i s t i n g of  -23-  a l a t t i c e - i e . molecules or polymer segments are confined to a regular array o f i d e n t i c a l p o s i t i o n s , or l a t t i c e s i t e s . Each s i t e i s bounded by z other s i t e s , where z i s known as the l a t t i c e coordination number. For a cubic l a t t i c e z=6, f o r a hexagonal c l o s e packed l a t t i c z=12. I t i s assumed that one solvent molecule, or one polymer segment occupies one l a t t i c e s i t e , i e . that they have the same e f f e c t i v e volume, and that no volume changes occur on mixing,  AV =0. The term segment as used here i s thus an operational m  d e f i n i t i o n , defined by the r a t i o of polymer to solvent molecular volumes, and does not n e c e s s a r i l y r e f e r to the repeating monomer u n i t . This theory gives the free energy of mixing of an m component s o l u t i o n as: m  m [1.8]  where n^ i s the number of moles of the i t h component, <tK i t s volume fraction,  i t s number of segments, and X ^ j i s the Flory Huggins  i n t e r a c t i o n parameter d e s c r i b i n g the enthalpy of i n t e r a c t i o n between segments of compnents i and j . Component one i s the solvent, hence P^= 1. The Flory-Huggins i n t e r a c t i o n parameter can be i n t e r p r e t e d as the maximum change i n i n t e r a c t i o n energy, i n u n i t s of kT, occuring when a segment of the i t h component i s t r a n s f e r r e d from a l a t t i c e s i t e surrounded by other segments of i to a s i t e surrounded by segments of component j . I f t h i s i n t e r a c t i o n i s unfavourable, X j j > 0  which can r e s u l t i n an unfavourable  enthalpy of mixing.  For monodisperse polymers the conditions f o r phase separation and the form o f the phase diagram can i n p r i n c i p l e be obtained a n a l y t i c a l l y from  -24-  [1.5]. [1.6], [1.8] by s o l v i n g the m+1 simultaneous equations implied by conditions i ) and i i ) . For the s p e c i a l case of two polymers with the same molecular weight and s o l u b i l i t y , P =Pj 2  a n c l  =  T  ^12 *13* ^  e  c r  itical  molecular weight and concentration conditions f o r phase separation to occur are  <t> = <t> = 1 / P X 2  3  2  [1.9]  2 3  I t may be noted that the only i n t e r a c t i o n parameter that appears i s the polymer/polymer i n t e r a c t i o n parameter. In other words, providing X - j i s 2  p o s i t i v e , however s m a l l , phase separation w i l l occur at high enough polymer concentration and/or molecular weight. Also t h i s does not depend on the nature of the solvent, providing both polymers are soluble enough t o achieve the  c r i t i c a l concentrations. This q u a l i t a t i v e behaviour i s generally true  even f o r d i s s i m i l a r polymers, since i n c o m p a t i b i l i t y i s the r u l e rather than the  exception (Dobry and Boyer-Kawenoki, 1947). For the s p e c i a l case the  phase diagram i s symmetrical, and can e a s i l y be predicted i f X  2 3  is  known. In p r a c t i c e p r e d i c t i n g phase diagrams i s extremely d i f f i c u l t f o r u n l i k e , polydisperse polymers, such as dextran T500 and PEG 8000. For t h i s polymer p a i r the phase diagrams are assymmetrical, due p a r t l y to the d i f f e r e n c e i n molecular weights, with the dextran p a r t i t i o n i n g more unequally between the phases, as might be expected from i t s greater s i z e . Another d i f f i c u l t y with the p r e d i c t i o n o f phase diagrams i s that those systems used f o r b i o l o g i c a l a p p l i c a t i o n s nearly always contain s a l t s or other small s o l u t e s , some of which i n t e r a c t with the polymers.  -25-  i i ) P r o p e r t i e s of the Phase System  a) B i o l o g i c a l e f f e c t s of the phase polymers. The three polymers used to form phase systems i n t h i s work were: dextran T500 (Dx), an a 1-6 l i n k e d polymer of glucose, (ca. 5% branching), obtained from a b a c t e r i a l c e l l w a l l (Leuconostoc mesenteroides), with an approximate weight average molecular weight of 500,000 g/mole; polyethylene g l y c o l 8000, a polyether formed from ethylene oxide, with a number average molecular weight of 7500-8500 g/mole; F i c o l l 400 ( F i ) , a s y n t h e t i c , h i g h l y branched co-polymer of sucrose and epichlorohydrin with a weight average molecular weight of about 400,000 g/mole. These polymers are considered nontoxic, even i n gram q u a n t i t i e s (Reynolds, 1982). Most studies on c e l l p a r t i t i o n have demonstrated no d e l e t e r i o u s e f f e c t s due to the phase polymers. For example lymphocytes are f u l l y v i a b l e a f t e r p a r t i t i o n , as determined by a v a r i e t y of biochemical assays, such as complement binding and r o s e t t e formation  (Walter et a l . ,  1979). In fact the polymers often have a p r o t e c t i v e e f f e c t . For example erythrocytes are protected to a great degree from hypotonic l y s i s by the phase polymers (Walter et a l . , 1968b), presumably by allowing p r e - l y t i c leakage of potassium or other ions (Ponder, 1971). The other uses of the phase polymers a l s o a t t e s t to t h e i r b i o l o g i c a l i n e r t n e s s . Dextran has s u c c e s s f u l l y been used.for many years as a plasma expander. F i c o l l gradients are used r o u t i n e l y f o r density c e n t r i f u g a t i o n of c e l l s . PEG i s used to fuse c e l l s i n hybridoma and monoclonal technology. These c e l l fusions only take place at high PEG concentrations (30-40%), so do not occur under the conditions o f p a r t i t i o n , and the fact that v i a b l e hybrid c e l l s are produced i l l u s t r a t e s the inertness of PEG. The only e f f e c t s that these polymers  -26-  generally have i s to aggregate or disaggregate c e l l s . While t h i s  may  i n t e r f e r e with p r a c t i c a l d e t a i l s of p a r t i t i o n , i t does not appear to harm the c e l l s . The aggregation i s n o n - s p e c i f i c , i s f u l l y r e v e r s i b l e when the c e l l s are washed with polymer free b u f f e r , and can be i n h i b i t e d by using lower i o n i c strength b u f f e r s and reducing the polymer molecular weights (Brooks, 1973).  b) I n t e r f a c i a l Tension. As w i l l be seen i n s e c t i o n i v below, the i n t e r f a c i a l tension i s very important i n p a r t i c l e p a r t i t i o n . The tension has been found to vary as the t i e l i n e l e n g t h , t ^ , r a i s e d to the power 3.5 to 4.2  , the  exact power depending on the phase polymers and s a l t composition (Bamberger et a l . , 1984b).  Previous measurement by Ryden and Albertsson (1971) and  Schurch et a l . , (1981) a l s o show the same dependence although these authors o r i g i n a l l y i n t e r p r e t e d the dependence as an exponential f u n c t i o n of the t i e l i n e length. However t h i s c l e a r l y cannot hold down to the p l a i t p o i n t , where both the tension and the t i e l i n e length are zero.  The tension can be  expressed as  V  t b  = at^  [1.10]  The values of a and b f o r various systems are given i n Walter et a l . (1985, Ch. 3 ) . No t h e o r e t i c a l explanation f o r t h i s dependence has been given, although i t resembles the behavior of pure l i q u i d s near the c r i t i c a l temperature, where the surface tension depends on the fourth power of the density d i f f e r e n c e between the l i q u i d and i t s vapor (MacLeod, 1923).  -27-  Sodium c h l o r i d e has l i t t l e e f f e c t on the tension.  However i n c r e a s i n g  concentrations of phosphate, up t o 0.22 M increase the tension d r a m a t i c a l l y , up t o 300% f o r systems close t o the c r i t i c a l p o i n t , and l e s s further from the c r i t i c a l point.  A large part o f t h i s dependence i s due to the e f f e c t o f  phosphate i n i n c r e a s i n g the t i e l i n e length, although there i s s t i l l an increase i f systems of the same t i e l i n e length are compared.  This may be  due t o the phosphate gradient across the i n t e r f a c e (Bamberger et a l . , 1984b). From these r e s u l t s some general remarks may be made about the e f f e c t of a d d i t i v e s on the i n t e r f a c i a l tension.  i)  A substance that p a r t i t i o n s unequally between the phases, e.g.,  sodium phosphate w i l l generally increase the tension.  This may r e s u l t from  two e f f e c t s - the gradient o f the substance i t s e l f across the i n t e r f a c e , and the increase i n the extent of phase separation, and hence t i e l i n e length, due t o the unequal i n t e r a c t i o n of the substance with each of the phase polymers. ii)  Conversely a substance that p a r t i t i o n s equally between the phases,  such as sodium c h l o r i d e , w i l l have l i t t l e e f f e c t on the tension. i i i ) A substance that adsorbs a t the i n t e r f a c e w i l l lower the tension, an e f f e c t deducible from Gibbs equation  ( f o r example see Adamson, 1976).  i v ) The e f f e c t o f an unequally d i s t r i b u t e d substance w i l l be greater the c l o s e r the system i s t o the c r i t i c a l p o i n t , and the l a r g e r the f r a c t i o n of t o t a l s o l u t e i t comprises.  c) I n t e r f a c i a l p o t e n t i a l . When the anion and c a t i o n of a s a l t have d i f f e r e n t r e l a t i v e a f f i n i t i e s f o r each phase, the requirement o f e l e c t r o n e u t r a l i t y i n  -28-  each phase r e s u l t s i n a Donnan-type e l e c t r o s t a t i c p o t e n t i a l d i f f e r e n c e (Galvani or inner p o t e n t i a l d i f f e r e n c e ) , between the phases. This p o t e n t i a l d i f f e r e n c e i s an important parameter to be considered i n choosing s u i t a b l e phases systems, and has a large e f f e c t on the p a r t i t i o n of charged solutes and p a r t i c l e s . Work on the r o l e of these p o t e n t i a l d i f f e r e n c e s has been mainly empirical i n the past, and there has been some confusion i n the l i t e r a t u r e as to what i s meant by the i n t e r f a c i a l p o t e n t i a l . Thus the same systems have been i n t e r p r e t e d as having a s i g n i f i c a n t e l e c t r o s t a t i c p o t e n t i a l d i f f e r e n c e , no e l e c t r o s t a t i c p o t e n t i a l d i f f e r e n c e or even an e l e c t r o s t a t i c p o t e n t i a l d i f f e r e n c e of opposite s i g n , by  investigators  p a r t i t i o n i n g d i f f e r e n t material or using d i f f e r e n t c r i t e r i a . For  instance,  Dx/Fi systems containing 110 mM phosphate have been considered to have both no appreciable p o t e n t i a l , or a p o t e n t i a l of about lmV 1979  (Zaslavsky et a l . ,  and Zaslavsky et_ a l . , 1982). Dextran/PEG systems containing KCl were  found by Johansson (1974b, 1978)  to have a s i g n i f i c a n t p o t e n t i a l , while  potassium sulphate systems had a n e g l i g i b l e p o t e n t i a l , whereas the opposite r e s u l t was obtained by Brooks et al.,(1984).  This confusion has  arisen  because i t was not recognized that any t e s t ion (often c h l o r i d e ) or charged molecule which i s used to measure the p o t e n t i a l i s a p h y s i c a l e n t i t y . Therefore the measured p o t e n t i a l contains an unknown c o n t r i b u t i o n from the d i f f e r e n c e i n standard s t a t e chemical p o t e n t i a l of that ion or molecule between the phases, i . e . Galvani or inner p o t e n t i a l s are not d i r e c t l y measurable (Kortiim, 1965,  Adamson, 1976). In a d d i t i o n i f one wants to  p r e d i c t the e l e c t r o s t a t i c p o t e n t i a l by measuring the ion p a r t i t i o n s , then the equations r e l a t i n g them contain the standard s t a t e chemical p o t e n t i a l differences of the p o t e n t i a l determining ions. Such standard state chemical  -29-  p o t e n t i a l s are not d i r e c t l y measurable. A way t o deal with these d i f f i c u l t i e s was developed by t h i s author and co-workers (Brooks et a l . , 1984)  and i s discussed i n d e t a i l i n the t h e o r e t i c a l s e c t i o n of t h i s t h e s i s .  Another point that has not been given adequate a t t e n t i o n i s that when a s a l t p a r t i t i o n s unequally  there i s a d i f f e r e n c e i n i o n i c strength between the  phases. Since the a c t i v i t y c o e f f i c i e n t of a charged macromolecule and the free energy of a charged surface both decrease with i o n i c strength  (Tanford,  1961; Verwey and Overbeek, 1948), i t i s e n t i r e l y p o s s i b l e that such i o n i c strength d i f f e r e n c e s , as w e l l as the e l e c t r o s t a t i c p o t e n t i a l d i f f e r e n c e , may be important i n the p a r t i t i o n of charged m a t e r i a l . Such i o n i c strength e f f e c t s are p r o p o r t i o n a l t o the square of the net charge and would favour p a r t i t i o n i n t o the phase with the highest s a l t concentration.  They could  thus e i t h e r augment or diminish the e f f e c t of the e l e c t r o s t a t i c p o t e n t i a l difference.  Albertsson (1971) derived the f i r s t expressions  for the e l e c t r o s t a t i c  p o t e n t i a l d i f f e r e n c e i n phase systems, s t a r t i n g with the fundamental conditions that the chemical p o t e n t i a l of each i o n i c species i s the same i n both phases, and that both phases are e l e c t r i c a l l y , n e u t r a l . Thus f o r a s a l t z+  z  A B ~ , where the s u p e r s c r i p t s t and b r e f e r to the upper and lower phases, and the subscripts + and - r e f e r to the c a t i o n and anion r e s p e c t i v e l y , he obtained:  (z  +  + z )Ail>= (kT/e)ln r / r + ( A u ° - Au°)/e —  —  +  —  * +  + (kT/e)ln K where the s u p e r s c r i p t s t and b r e f e r to the upper and lower phases.  [1.11]  -30-  e  = the e l e c t r o n charge  r  = f * 7 f , the r a t i o o f i o n a c t i v i t y c o e f f i c i e n t s  A  = i^-^* ,  b  3  the d i f f e r e n c e i n galvani p o t e n t i a l s  A |A° = \i ^- H ° , the d i f f e r e n c e i n standard s t a t e chemical 0  b  potentials. K  b  = c V c , the r a t i o o f concentrations, i s the p a r t i t i o n c o e f f i c i e n t of the s a l t (both ions have the same K due to the e l e c t r o n e u t r a l i t y reauirements o f each phase i e . K = K+= K_)  Thus there w i l l be a p o t e n t i a l i f the ions have d i f f e r e n t r e l a t i v e a f f i n i t i e s f o r each phase, as expressed by d i f f e r e n c e s i n the standard  state  chemical p o t e n t i a l terms. Equation [1.11] d i f f e r s s l i g h t l y from Albertsson's o r i g i n a l expression i n that he expressed the i o n a f f i n i t i e s , through the a c t i v i t y c o e f f i c i e n t s , i n terms of hypothetical i o n p a r t i t i o n s i n the absence of p o t e n t i a l (these d i f f e r e n c e s i n formalism are discussed more f u l l y i n s e c t i o n i i i below). His notation tended to obscure the f a c t that the main c o n t r i b u t i o n to the i o n a f f i n i t y comes from the polymers, and that t h i s can therefore change with the phase compositions.  Equation 1.11  demonstrates that the p o t e n t i a l generated i s smaller f o r higher valence ions, providing the other terms are constant. In p r a c t i c e however, l a r g e r m u l t i v a l e n t inorganic ions often p a r t i t i o n more unequally, g i v i n g r i s e to l a r g e r p o t e n t i a l s than monovalent ions (Johansson, 1974a, 1974b, Reitherman et a l . , 1973). P o l y e l e c t r o l y t e s such as proteins or dextran-DEAE would however be expected to generate very small p o t e n t i a l s . Since most inorganic ions generally have p a r t i t i o n c o e f f i c i e n t s i n the range 0.8-1.2 (Johansson, 1974a, Brooks et a l . , 1984), the p o t e n t i a l s are expected to be i n the m i l l i v o l t range. This was f i r s t confirmed by Reitherman et a l . , (1973).  -31-  However [1.11] could not be not tested q u a n t i t a t i v e l y f o r the reasons given above.  Two basic methods o f measuring the p o t e n t i a l have been used; i ) Determination v i a the p a r t i t i o n o f a s o l u t e o f known and v a r i a b l e charge, f o r example a p r o t e i n . i i ) D i r e c t measurement using r e v e r s i b l e , non-polarizable electrodes. Method i ) has been used p r i n c i p a l l y by Johansson (1974b, 1978), where the net charge o f a p r o t e i n , determined previously by t i t r a t i o n , was a l t e r e d by varying the pH. The e l e c t r o s t a t i c p o t e n t i a l d i f f e r e n c e was then determined from the slope o f a p l o t o f l o g (protein p a r t i t i o n ) measured i n a s e r i e s o f systems with d i f f e r e n t pH, against net p r o t e i n charge. However t h i s method requires several systems o f varying pH t o be made up i n order to measure the p o t e n t i a l o f one system. In a d d i t i o n the method assumes that the protein standard s t a t e chemical p o t e n t i a l s and a c t i v i t y c o e f f i c i e n t s are constant with changing pH, and that no i o n binding to the p r o t e i n occur. Some o f these assumptions are examined i n Chapter Three. Most measurements o f the e l e c t r o s t a t i c p o t e n t i a l d i f f e r e n c e have used s i l v e r / s i l v e r c h l o r i d e e l e c t r o d e s , (Reitherman et a l . , 1973, Zaslavsky et_ a l . , 1982, Brooks et a l . , 1984) although the calomel electrode has a l s o been used ( B a l l a r d et a l . , 1979), the electrodes i n each case being connected to the phase system by s a l t bridges, which are u s u a l l y f i l l e d with agar or other polymer g e l t o reduce leakage. Johansson (1974a) used electrodes connected by s a l t bridges containing 12% PEG saturated with KC1 to the top phases o f two d i f f e r e n t systems, which i n turn had t h e i r lower phases connected by a 20% Dx/0.5M NH  4N03 s a l t bridge. Using t h i s system Johansson measured and tabulated  -32-  o  r e l a t i v e values of A j i f o r various ions, and s u c c e s s f u l l y predicted the p o t e n t i a l s of some systems. An advantage of t h i s arrangement for measuring p o t e n t i a l s i s that i t y i e l d s the differences i n p o t e n t i a l s between the two systems d i r e c t l y , although t h i s method has not been e x p l o i t e d  further.  Reitherman et a l . (1973) showed that the measured p o t e n t i a l was independent of the s a l t concentration i n t h e i r agar f i l l e d bridges, i n d i c a t i n g that j u n c t i o n p o t e n t i a l s due to the s a l t were n e g l i g i b l e . However j u n c t i o n p o t e n t i a l e f f e c t s may a r i s e from the g e l i n the s a l t bridge (Brooks et a l . , 1984), another complication  o f p o t e n t i a l measurements that was not known i n  e a r l i e r studies. The most commonly used way to manipulate the p o t e n t i a l has been to a l t e r the r a t i o of phosphate to c h l o r i d e ions i n the phase system. The p o t e n t i a l i s apparently proportional to the t i e l i n e length i n Dextran T500, PEG 8000 or PEG 30000 systems containing KC1 (Johansson, 1978), f o r t i e l i n e lengths from 8 to 17%, although i t i s not known whether such a p r o p o r t i o n a l i t y i s generally true f o r other polymer/salt systems. The measured e l e c t r o s t a t i c p o t e n t i a l d i f f e r e n c e was found to be r e l a t i v e l y independent of s a l t concentration for sodium phosphate by B a l l a r d et a l . , (1979), although there appeared to be a s l i g h t maximum around 20-30 mM. However Zaslavsky et a l . , (1982) found a decrease i n e l e c t r o s t a t i c p o t e n t i a l d i f f e r e n c e as the concentration was increased,  which they a t t r i b u t e d to differences i n polymer  l o t s , but t h i s may a l s o have been due to t h e i r use of a g a r - f i l l e d s a l t bridges. The e l e c t r o s t a t i c p o t e n t i a l d i f f e r e n c e was found by Brooks et a l . , (1984) to be independent of KC1 and potassium sulphate concentration i n the range 0.001 to 0.4 M providing the t i e l i n e length was constant.  -33-  The v a r i a t i o n of p o t e n t i a l with i o n type i s complex, and d i r e c t measurements of the e l e c t r o s t a t i c p o t e n t i a l d i f f e r e n c e have been made on only a few of the many combinations used i n phase systems. Since the p a r t i t i o n c o e f f i c i e n t s of s e v e r a l s a l t s i n a 5/4 Dextran T500, PEG 8000 system have been measured (Johansson, 1970b, 1974b), and Brooks et a l . , (1984) have experimentally confirmed the thermodynamic r e l a t i o n s h i p between the s a l t p a r t i t i o n and p o t e n t i a l s f o r KC1 and potassium sulphate, some general trends may be i n f e r r e d :  Larger ions such as phosphate, c i t r a t e and sulphate p a r t i t i o n more unequally than mono-atomic ions such as c h l o r i d e and so w i l l give a l a r g e r p o t e n t i a l . For the a l k a l i h a l i d e s a l t s , the p o t e n t i a l would be expected to +  +  +  increase f o r the s e r i e s K , Na , L i , and f o r C l ~ , Br", I ~ , based on t h e i r p a r t i t i o n c o e f f i c i e n t s .  Mono-basic phosphate has a smaller  p a r t i t i o n i n t o the lower phase than the d i - b a s i c i o n (Johansson, 1970), and i n fact the p o t e n t i a l was shown to be l e s s negative f o r the mono-basic s a l t (Zaslavsky et a l . , 1982).  I t has been pointed out that the p o t e n t i a l e f f e c t s of two s a l t s are not a d d i t i v e (Zaslavsky et a l . , 1982), and so must be determined e i t h e r by d i r e c t measurements or from a t h e o r e t i c a l approach such as that developed i n Chapter Three of t h i s t h e s i s . No systematic studies of the e f f e c t on the e l e c t r o s t a t i c p o t e n t i a l d i f f e r e n c e of polymer type have been published, though polymers such as PEG that s i g n i f i c a n t l y exclude c e r t a i n ions such as sulphate and phosphate w i l l produce r e l a t i v e l y large e l e c t r o s t a t i c p o t e n t i a l  OA-  differences.  Zaslavsky et a l . , (1982) found l a r g e r p o t e n t i a l s i n Dx/PEG  systems than i n Dx/Fi systems for the same t i e l i n e lengths. Using the method of protein p a r t i t i o n , Johansson (1978) found that a l t e r i n g the molecular weight of PEG at constant t i e l i n e length d i d not a f f e c t the e l e c t r o s t a t i c p o t e n t i a l d i f f e r e n c e i n KC1 containing systems. The i n c l u s i o n of charged polymers such as DEAE-dextran (Walter et a l . , 1968a, Reitherman et al.,1973) and trimethylamino-PEG (Johansson, 1978) may a l s o be used to produce e l e c t r o s t a t i c p o t e n t i a l d i f f e r e n c e s , although the e f f e c t o f these seems to be smaller than one would expect based on t h e i r p a r t i t i o n (Reitherman et al.,1973, Johansson, 1978).  d) V i s c o s i t y i s an important property of polymer s o l u t i o n s , which increases r a p i d l y with the s i z e and amount of polymer present. The phase v i s c o s i t i e s can be very high, i n the range of one poise, which has important e f f e c t s on the p a r t i t i o n process. The v i s c o s i t y and therefore the s e t t l i n g time of the phases increases with polymer concentration and molecular weight. However higher molecular weight polymers phase separate at lower concentrations, thus r e q u i r i n g lower bulk concentrations to give a system with the same t i e l i n e length or tension. At the same time the density d i f f e r e n c e between the phases increases with t i e l i n e length. The time required f o r phase separation may therefore be minimized by j u d i c i o u s choice of these f a c t o r s . The phase v i s c o s i t i e s are a l s o important i n the flow processes believed to play a r o l e i n c e l l p a r t i t i o n i n g (Raymond and Fisher 1980; Chapter S i x , below), i n i n d u s t r i a l scale a p p l i c a t i o n s where large volumes of phases must be e f f i c i e n t l y handled and separated (Hustedt et a l . , 1978), and i n a continuous flow apparatus such as the t o r o i d a l c o i l (Sutherland and I t o ,  -35-  1980) , where e f f e c t i v e mass t r a n s f e r between the phases and e f f i c i e n t retention  o f the stationary  phase are e s s e n t i a l i n order to take advantage  of the very high t h e o r e t i c a l separation e f f i c i e n c i e s .  In Dx/PEG systems the lower phase v i s c o s i t y i s much greater than the upper phase v i s c o s i t y , since the former i s enriched i n the higher molecular weight dextran. In fact the PEG molecular weight has l i t t l e e f f e c t on the lower phase v i s c o s i t y (Johansson, 1978)  e) Hydrophobicity. I t might be expected, since the phases d i f f e r i n both t h e i r polymer and s a l t compositions, that there would be a difference hydrophobicity of the two phases.  i n the  That i s , non-polar molecules or  constituents would p a r t i t i o n p r e f e r e n t i a l l y i n t o one o f the phases, which could then be l a b e l l e d as the more hydrophobic o f the two. This, i n f a c t , i s observed, and Albertsson (1971) has discussed a "hydrophobic ladder" of polymers which are mutually immiscible.  Zaslavsky and colleagues have published a number of papers which deal with hydrophobicity i n two polymer phase systems.  Using homologous s e r i e s  of surfactants i n a v a r i e t y of phase systems, Zaslavsky et a l . , (1978a, 1981) found a l i n e a r r e l a t i o n s h i p between the l o g of the p a r t i t i o n c o e f f i c i e n t and the number o f methylene groups i n the surfactant t a i l . The slope of t h i s l i n e was then used to c a l c u l a t e the hydrophobicity d i f f e r e n c e , AG™, , which was between 16 and 30 cal/mole, twenty to f o r t y times lower than t y p i c a l values f o r aqueous/organic phase systems. The F i and PEG-rich phases were found to be more hydrophobic than the Dx-rich  -36-  phase. For Dx/PEG systems t h i s d i f f e r e n c e was greater f o r charge s e n s i t i v e systems (containing 110 mM phosphate), and f o r i n c r e a s i n g concentrations o f KC1.  In s p i t e of t h i s work, the question of whether the hydrophobicity d i f f e r e n c e i s being measured by t h i s technique, and the connection  between  t h i s parameter and the p a r t i t i o n o f more complex s o l u t e s , p a r t i c l e s and c e l l s i s not at a l l c l e a r . In the f i r s t place the phenomenon of phase separation i s governed p r i m a r i l y by the i n c o m p a t i b i l i t y between the two polymers, as discussed i n s e c t i o n i above, and does not p a r t i c u l a r l y depend e i t h e r on the nature o f the s o l v e n t , or the r e l a t i v e hydrophobicities of the polymers.  Thus i t i s not mandatory that there be a d i f f e r e n c e i n  hydrophobicity between the phases. Secondly the i n t e r a c t i o n s that govern the p a r t i t i o n o f a molecule are s i m i l a r to those that determine phase separation, as i s discussed below i n s e c t i o n i i i . Therefore the predominant i n t e r a c t i o n s would be expected to be between the s o l u t e and the two polymers rather than between the solvent and the s o l u t e . This i s made more evident by a consideration of the phase diagram and [1.14] of s e c t i o n i i i below, since the r e l a t i v e d i f f e r e n c e i n water concentrations between the phases w i l l generally be small compared with the polymer concentration d i f f e r e n c e s , and could even be zero. S i m i l a r considerations apply to the surface free energy d i f f e r e n c e s that determine p a r t i c l e and c e l l p a r t i t i o n . Thus i t i s not c l e a r a p r i o r i that the main determinant o f surfactant p a r t i t i o n w i l l be the hydrophobicity d i f f e r e n c e between the phases, and t h i s a p p l i e s even more strongly when such conclusions are being extended to other s o l u t e s , often with complex surfaces. Zaslavsky et a l . , (1981) themselves pointed out that  -37-  the assumption that each part of the surfactant molecule contributes independently  to the free energy of t r a n s f e r between phases i s u n l i k e l y to  hold for more complex solutes or p a r t i c l e s . The determination of the r e l a t i v e hydrophobicities of erythrocytes (Zaslavsky et a l . , 1979), and the formulation of a general r u l e of p a r t i t i o n p o s t u l a t i n g hydrophobic f a c t o r s as the main determinants of p a r t i t i o n (Zaslavsky et a l . , 1978b) has also been c r i t i c i z e d by Walter and Anderson (1981) on other grounds. They pointed out that e x t r a p o l a t i o n from solutes to p a r t i c l e s , which p a r t i t i o n between the i n t e r f a c e and one of the phases, i s r i s k y . In a d d i t i o n they noted that several phase system parameters such as the e l e c t r o s t a t i c p o t e n t i a l d i f f e r e n c e and the i n t e r f a c i a l tension were a l s o being v a r i e d along with the hydrophobicity d i f f e r e n c e . I t may  a l s o be noted that the measured  d i f f e r e n c e s i n erythrocyte hydrophobicity  (Zaslavsky et a l . , 1979) were of  -22 the order of 10 difference,  AGq  m o l e s / c e l l , which combined with a hydrophobicity H  , of 16-30  cal/mole r e s u l t s i n surface free energy  d i f f e r e n c e s many orders of magnitude smaller than 10 2  to 10  ergs/cm , the t y p i c a l i n t e r f a c i a l tensions i n these systems, and thus they could hardly r e s u l t i n measureable p a r t i t i o n d i f f e r e n c e s . Therefore t h e i r conclusion that charge i s a determinant of p a r t i t i o n only as a f a c t o r a f f e c t i n g the r e l a t i v e hydrophobicity of the c e l l surface (Zaslavsky et a l . , 1979)  i s not j u s t i f i e d .  The terms 'hydrophobic' and 'non-charge* have often been used synonymously by workers i n the p a r t i t i o n f i e l d , although t h i s i s not c o r r e c t chemically speaking, and i n f a c t I believe that t h i s has l e d to a number of erroneous conclusions i n the past.  -38-  i i i ) Theory o f Molecular P a r t i t i o n i n g  a) The p a r t i t i o n of n e u t r a l molecules. The p a r t i t i o n behaviour of any molecule, m, i s governed by the same thermodynamic p r i n c i p l e s as the phase separation phenomenon i t s e l f . At e q u i l i b r i u m , therefore, c o n d i t i o n i i ) of section i holds, namely that the chemical p o t e n t i a l o f the species i s the same i n both phases. Thus:  0t  \L  +  kTln f V = R  0 b  h  +  kTln A  [1.12]  or rearranging:  f c  In K = - I n f / f  b  - (n  0 t  b  - H° )/kT = - I n r  - An°/kT  f  [1.13]  Neglecting a c t i v i t y c o e f f i c e n t s for the moment, i t can be seen that the p a r t i t i o n i s determined by the d i f f e r e n c e i n standard s t a t e chemical p o t e n t i a l between the phases. Now the standard s t a t e chemical p o t e n t i a l i n [1.12] i s the term that contains a l l the i n t e r a c t i o n s of the solute with the 'solvent', i e . the phase, which i s composed of water and the polymers (plus a constant term that depends on the concentration u n i t s used). The a c t i v i t y c o e f f i c i e n t contains a l l the c o n t r i b u t i o n s from i n t e r a c t i o n s with the other 3  solute molecules. Thus by d e f i n i t i o n f** and f* tend t o one i n the low concentration l i m i t . Albertsson (1971) however has viewed the r e l a t i o n s h i p of p a r t i t i o n to the chemical p o t e n t i a l d i f f e r e n t l y . He assumed that the standard s t a t e chemical p o t e n t i a l o f the solute i n both phases was the same  -39-  (presumably taking the pure s o l u t e as h i s reference) thus the a c t i v i t y c o e f f i c i e n t as he defined i t was the sole determinant of p a r t i t i o n , and contained a l l the i n t e r a c t i o n s of solute and polymers. This i s i n c o r r e c t since the a c t i v i t y c o e f f i c i e n t s do not then tend to one at low solute concentration. This formalism a l s o makes i t more d i f f i c u l t to separate out the c o n t r i b u t i o n of s o l u t e / s o l u t e i n t e r a c t i o n s to the chemical p o t e n t i a l .  Now  the i n t e r a c t i o n of a s o l u t e such as a n e u t r a l f l e x i b l e polymer with  the phase system can be treated using the Flory-Huggins theory by considering the solute as a fourth component of the phase system, present at a low concentration. Brooks (Brooks et a l . , 1985)  thus obtained  expression f o r the solute p a r t i t i o n c o e f f i c i e n t ,  K.:  an  [1.14]  where A<t>^ = <t>^ - <t>^, second order terms i n $ and i t was assumed that be equated with  <J>oc<J>^, 4> , Q^. 2  were neglected,  The exponent of [1.14] can  Au.°/kT i n [1.13], g i v i n g some i n s i g h t i n t o what  molecular i n t e r a c t i o n s contribute to the l a t t e r term. Equation 1.14  also  demonstrates very c l e a r l y some of the properties of molecular p a r t i t i o n .  a) The p a r t i t i o n depends exponentially on the s o l u t e molecular weight, becoming more one sided as i t increases. This e f f e c t has been observed experimentally  (Albertsson,  1971)  -40-  b) The p a r t i t i o n depends exponentially on the d i f f e r e n c e i n the standard s t a t e chemical p o t e n t i a l .  c) The standard s t a t e chemical p o t e n t i a l d i f f e r e n c e depends on the d i f f e r e n c e i n concentrations of a l l three phase system components, and on the i n t e r a c t i o n of the s o l u t e with a l l three components.  d) As the i n t e r a c t i o n between the solute and one o f the phase components increases, i e . as X ^ becomes more positive,- p a r t i t i o n i n t o the phase enriched i n that component decreases  e) molecular p a r t i t i o n becomes more one sided as the d i f f e r e n c e i n polymer concentrations, and hence the t i e l i n e length increases.  f ) I f the molecular weight of one of the polymers i s decreased, the p a r t i t i o n i s increased i n t o the phase enriched i n that polymer. This has been widely observed i n both molecular and p a r t i c l e p a r t i t i o n (Albertsson, 1971)  b) P a r t i t i o n of Charged Molecules. The treatment o f s e c t i o n i i i a above can be extended t o charged molecules as w e l l , since the electrochemical p o t e n t i a l o f a molecule with net charge z  pi = |A° + kTln f c + z e m m m n  and hence  m  can be w r i t t e n as:  [1.15]  -41-  l n K = -In T  P  - Aif/kT - z e Avp/kT  [1.16]  by analogy with [1.13]. I t can immediately be seen that the p a r t i t i o n c o e f f i c i e n t depends exponentially on the charge and the p o t e n t i a l , i f a l l the other terms are constant. This i s the b a s i s of Johansson's method o f measuring p o t e n t i a l s - by a l t e r i n g the pH of the system, and therefore z  m  of a charged p r o t e i n , and assuming that the a c t i v i t y c o e f f i c i e n t s and standard s t a t e chemical p o t e n t i a l s were constant, one can determine the p o t e n t i a l o f the system.  I f the s a l t i s i n excess over the s o l u t e , then i t i s the main determinant o f the p o t e n t i a l . From the e l e c t r o n e u t r a l i t y condition the p a r t i t i o n c o e f f i c i e n t s o f the two s a l t ions w i l l be eaual, t o a good approximation, so that [1.11] o f s e c t i o n i i b can be used t o eliminate Avjj i n [1.16] t o give:  In K = -In r - A u!/kT - z ( A u . ° - A u ° + kTln r / r ) • m m m m - + - + r  m  r  r  [1.17]  (z +z_).kT +  which can be w r i t t e n as:  l n K  m  = l n K  m-  Z . ( A t i ; - A ^ + kT.ln r . / r ) m  +  (z +z_).kT +  [1.18]  -42-  where  has been i n t e r p r e t e d by Johansson (1974) and Albertsson as the  p r o t e i n p a r t i t i o n i n the absence o f a p o t e n t i a l . Note that u s u a l l y z pc»z ,z , so the p r o t e i n p a r t i t i o n would be expected (1  (through the  +  O  0  standard s t a t e chemical p o t e n t i a l d i f f e r e n c e s A U , , Ap. +  —  i n [1.17]) t o be very  s e n s i t i v e t o the s a l t type added t o the phase system. This has i n fact been w e l l documented (Sasakawa and Walter, 1972; Johansson, 1970a; Albertsson, 1961). I f the ( p o s i t i v e l y charged) p r o t e i n i s i n excess then the other main i o n i c species i s the p r o t e i n counterion. I f the counterion i s u n i v a l e n t , we have by analogy with [1.13]:  In K_ = -In r _ - A J A V R T + e A + A T  [1.19]  E l i m i n a t i n g AI|J from [1.19] and [1.13], and noting from the e l e c t r o n e u t r a l i t y conditions that K = K , we have: M  In  = l/(z +l)[ln(l/rf r )-A^/kT - z ^ V k T J m  m  [1.20]  +  0  Again the p r o t e i n p a r t i t i o n depends g r e a t l y on the s a l t type since A H _ i s m u l t i p l i e d by z which i s often l a r g e . Note that as z m  m  increases the  p r o t e i n p a r t i t i o n tends to one. I f a c t i v i t y c o e f f i c i e n t s are neglected, then these equations are e s s e n t i a l l y the same as those derived by Albertsson, allowing f o r the d i f f e r e n c e i n formalism. Unfortunately n e i t h e r [1.18] nor [1.20] can be t e s t e d , even i f a c t i v i t y c o e f f i c i e n t s could be neglected, o  since the A(JL terms are not measurable. Also most ions and p o l y e l e c t r o l y t e s are non-ideal solutes even a t concentrations l e s s than 1M (Tanford, 1961;  -43-  Robinson and Stokes, 1959), so r i s not n e c e s s a r i l y u n i t y . deLigny and Gelsema (1982) proposed a way around the f i r s t problem by comparing the p r o t e i n p a r t i t i o n s i n two systems containing d i f f e r e n t s a l t s , K and K » M  M  For the s a l t i n excess, and n e g l e c t i n g a c t i v i t y c o e f f i c i e n t s , they obtained the expression  in K'/K mm  = zln m  K"  s  2  / K K'  [1.21  s s,  where « , K are the s a l t p a r t i t i o n c o e f f i c i e n t s i n the two systems, and S  K  S  G  i s the p a r t i t i o n c o e f f i c i e n t o f a s a l t  containing a common c a t i o n with  the f i r s t system, and a common anion with the second system, or v i c e versa. When they reanalysed the data o f Johansson using t h i s eauation, they obtained  l i n e a r p l o t s o f the l o g o f the r a t i o o f the two p r o t e i n p a r t i o n  c o e f f i c i e n t s versus p r o t e i n charge, as expected, but the equation i n c o r r e c t l y predicted the p a r t i t i o n o f the uncharged p r o t e i n . This may be due to the assumptions i n h e r e n t l y made i n d e r i v i n g [1.21]. These assumptions are examined, and a f u l l equation derived i n Chapter Three of t h i s t h e s i s .  i v ) Theory o f P a r t i c l e  Partitioning  a) R e l a t i o n s h i p o f p a r t i t i o n t o the i n t e r f a c i a l tension and c e l l surface free energies.  A convenient s t a r t i n g point f o r the d i s c u s s i o n o f the  t h e o r e t i c a l aspects o f p a r t i c l e p a r t i t i o n i s the Boltzmann equation. expression r e l a t e s the number (n^,n ) or concentration (c-pO,) o f 2  p a r t i c l e s i n two 'compartments', designated 1 and 2, or the r e l a t i v e p r o b a b i l i t i e s o f a p a r t i c l e being i n e i t h e r compartment (see, e.g.,  This  -44-  Guggenheim, 1959), to the energy, A E , necessary to move the p a r t i c l e between the compartments, scaled by a ' c h a r a c t e r i s t i c energy*.  (The term  compartments i n t h i s case r e f e r s both to the two phases and the i n t e r f a c e between them, and the c h a r a c t e r i s t i c energy i s kT). Thus  K = n /n x  2  = Cj/Cg = exp (- AE/kT)  [1.22]  where k i s Boltzmann's constant, and T i s the absolute temperature.  The  assumption behind the use of kT i n [1.22] i s that the p a r t i c l e d i f f u s e s f r e e l y , i . e . , that i t i s being d i s t r i b u t e d by random thermal motion. However, the a p p l i c a b i l i t y of the concepts of thermodynamic  equilibrium,  chemical p o t e n t i a l and Brownian d i s t r i b u t i o n to large p a r t i c l e s such as c e l l s i s not evident.  Moreover, i t i s not c l e a r a p r i o r i whether the  concentrations or the number of p a r t i c l e s i n each compartment should be used, e s p e c i a l l y when the p a r t i c l e s are p a r t i t i o n i n g between the i n t e r f a c e and one of the phases, which i s u s u a l l y the case f o r c e l l s . Albertsson and B a i r d (1962) found that the number of small b a c t e r i a i n the top phase was independent of the phase volume r a t i o , which suggests that the number r a t i o of p a r t i c l e s should be used.  The adsorption of p a r t i c l e s at the i n t e r f a c e  i s one of the c h a r a c t e r i s t i c s that d i s t i n g u i s h e s p a r t i c l e p a r t i t i o n from solute p a r t i t i o n .  This d i s t i n c t i o n a r i s e s from the f a c t that p a r t i c l e s  generally seem to be  partially  wetted by both phases, i e . that the  p a r t i c l e surface/two phase i n t e r f a c e contact angle l i e s between 0° and 180° (vide i n f r a ) .  -45-  The exponential form of [1.22] r e f l e c t s the f a c t that p a r t i t i o n i s a s t o c h a s t i c process, i . e . , a p a r t i c l e has a c e r t a i n p r o b a b i l i t y of being i n a p a r t i c u l a r compartment.  This i s i l l u s t r a t e d by the f a c t that i f a  homogeneous population of p a r t i c l e s i s p a r t i t i o n e d , and the p a r t i c l e s i n one of the compartments are c o l l e c t e d and r e p a r t i t i o n e d , they w i l l have the same p a r t i t i o n as the o r i g i n a l population from which they were drawn.  That i s , a  random f r a c t i o n of the p a r t i c l e s that were o r i g i n a l l y i n , say, compartment 1, w i l l now be found i n compartment 2.  In s p i t e of the r e s e r v a t i o n s i n applying [1.22] to p a r t i c l e p a r t i t i o n , i t seems reasonable to expect that the energy of p a r t i c l e t r a n s f e r between the two phases and the i n t e r f a c e w i l l be important i n determining behavior.  partition  The appropriate r e l a t i o n s h i p s f o r an i d e a l i z e d s p h e r i c a l p a r t i c l e  o f radius ap, i n a phase system characterized by an i n t e r f a c i a l tension Y^  ergs/cm  are derived below.  This treatment d i f f e r s from that of  Albertsson (1971), i n that the concept of the contact angle between the two phase i n t e r f a c e and the p a r t i c l e surface i s used.  This approach i s  a l g e b r a i c a l l y simpler and a l s o c l e a r l y demonstrates the i n t e r r e l a t i o n between p a r t i t i o n , the wetting of the p a r t i c l e by the phases and surface free energies, as w e l l as i n d i c a t i n g the r o l e of contact angle measurements.  When the p a r t i c l e i s i n the top or the bottom phase the particle/phase i n t e r f a c e i s characterized by an i n t e r f a c i a l free energy Y * or respectively.  Y  B  Assume that the s p h e r i c a l p a r t i c l e , experiencing no net  f o r c e , i s at e q u i l i b r i u m at a phase i n t e r f a c e (Figure 1.2a). equation (Adamson, 1976) r e l a t e s the i n t e r f a c i a l t e n s i o n , Y  T B  Then Young's ,  the surface  -46-  f r e e e n e r g i e s , Y \ Y , and the contact angle, 9: B  Y  -  T  Y  B  = AY= " Y  t b  cos9  [1.23]  I f the p a r t i c l e has equal a f f i n i t y f o r e i t h e r phase, i . e . , each phase wets the p a r t i c l e surface e q u a l l y , then the surface free energy d i f f e r e n c e , A Y i s zero and the contact angle i s ninety degrees. Providing |AY| *= Y  T  B  a contact angle  0°<:8<=l80  o  i s formed and the  p a r t i c l e w i l l be at the i n t e r f a c e at e q u i l i b r i u m . This i s the c o n d i t i o n f o r I f |AY| > Y  p a r t i c l e adsorption. 180°,  then the contact angle i s e i t h e r 0 or  U  depending on the s i g n of A Y , and the p a r t i c l e w i l l be completely  wetted by one of the phases. the bottom phase. the top phase  At e q u i l i b r i u m i t w i l l be i n e i t h e r the top or  The work of moving the p a r t i c l e from the i n t e r f a c e i n t o  A E ^ i s the sum o f two components: i ) the t r a n s f e r of part  o f the p a r t i c l e surface o f area A  b  from the bottom phase t o the top phase,  with a net energy change o f A A Y ; i i ) the increase i n surface area of the B  i n t e r f a c e by A ^ , with a net energy change of A ^ y ^ .  AE .  =AYA  t  b +  Y  t b  A  b  the contact angle.  A  b  :  [1.24]  t b  Expressions f o r A^ and A  T n u s  b  are e a s i l y obtained by trigonometry from  i s given by the area of a s p h e r i c a l cap o f height  h, as:  2  2TTho = 2 T T a J ( l - c o s 0 ) p  [1.25]  -47-  Fiqure 1.2 I n t e r a c t i o n of a S p h e r i c a l P a r t i c l e With the Interface, a) _ P a r t i c l e at e q u i l i b r i u m , experiencing no net f o r c e , forming an e q u i l i b r i u m contact angle 9 with the i n t e r f a c e , b) P a r t i c l e experiences a net force f d i s p l a c i n g i t to the l e f t , r e s u l t i n g i n a curved i n t e r f a c e  -48-  \b  *  s  9^-  ven b v  *-  ne a r e a  o f the c i r c l e of cross s e c t i o n of the sphere as:  TTa sin9 2  [1.26]  S u b s t i t u t i n g [1.25] and [1.26] i n t o [1.24] gives  AE  = T r a ( 2 ( l - c o s 6 ) AY + 2  t i  Y  2  t b  sin 6 )  [1.27]  S u b s t i t u t i n g f o r AY using [1.23], and reducing g i v e s :  AE  2  t i  = ^ a Y d-cos 6 )  2  "  t b  [1.28]  The energy of t r a n s f e r to the bottom phase, A E , can be obtained D T  s i m i l a r l y , or can be obtained d i r e c t l y from [1.28] by noting from F i g . 1.2a that the r o l e of top and bottom phases i s interchanged i f the complementary angle 9 = 180 - 9 i s used.  E  = TTa Y d + c o s 9 ) 2  b i  Noting that cos (180 - 0 ) = - cos 9 , we obtain:  [1.29]  2  t b  The energy o f t r a n s f e r from the bottom phase to the top phase, AE^ , i s b  obtained simply by s u b t r a c t i n g [1.29] from [1.28] which gives  AE  = 4 TT a AY 2  t b  which i s j u s t AY times the t o t a l p a r t i c l e area.  [1.30]  Note that [1.30] does not  -49-  involve the tension.  Equations 1.28 and 1.29 were derived f o r a planar i n t e r f a c e , although i n p r a c t i c e p a r t i c l e s can i n t e r a c t with droplets of many s i z e s during p a r t i t i o n . In t h i s case the energy o f p a r t i c l e / i n t e r f a c e attachment, and the force necessary for detachment w i l l be somewhat reduced. Equation 1.28 can now be s u b s t i t u t e d i n t o [1.21] to obtain an expression  for the p a r t i c l e  p a r t i t i o n c o e f f i c i e n t between the i n t e r f a c e and the top phase. In logarithmic form t h i s expression i s  [1.31]  I f cos © i s replaced using [1.23] then the expression i s obtained.  of Albertsson  (1971)  I f [1.30] i s s u b s t i t u t e d i n t o [1.22] i n s t e a d , we obtain  [1.32]  t/J) where now K = n /n . I f kT i s replaced by an e m p i r i c a l parameter and a constant added, the expression of Gerson (1980) f o r p a r t i c l e p a r t i t i o n between two phases i s obtained.  The above equations apply t o s p h e r i c a l  p a r t i c l e s and, while many c e l l s and p a r t i c l e s are not s p h e r i c a l , the same type o f arguments w i l l hold, so that these equations are adequate f o r a discussion o f the parameters important i n p a r t i t i o n .  Theoretical expressions for p a r t i c l e p a r t i t i o n have a l s o been derived by a s l i g h t l y d i f f e r e n t approach by Gerson (1980).  His s t a r t i n g point i s the  -50-  e q u a l i t y o f the chemical p o t e n t i a l of a c e l l i n each phase.  However, the  use o f a chemical p o t e n t i a l f o r c e l l s i s p r o b l e m a t i c a l , as a c t i v i t y c o e f f i c i e n t s and standard s t a t e chemical p o t e n t i a l s are defined f o r s o l u t e s , but not f o r c e l l s .  His f i n a l r e s u l t s , however, have the same form as [1.31]  and [1.32].  The l i m i t a t i o n s of [1.31] may be seen by s u b s t i t u t i n g i n some t y p i c a l values.  Letting  we obtain A E ^  Y  2  T B  = 0.006 erg/cm , a = 3 [ p and 9 = 45° i n [1.28]  = 1.5 x 10"  ergs.  This i s four orders o f magnitude -14  l a r g e r than  kT, which at room temperature i s about 4 x 10  ergs,  implying from [1.22] that v i r t u a l l y no c e l l s should d i s t r i b u t e i n t o the top phase.  However, appreciable p a r t i t i o n i n g o f p a r t i c l e s o f t h i s s i z e , (e.g.,  c e l l s ) i n systems with tensions o f t h i s magnitude, does occur.  This point  w i l l be discussed f u r t h e r i n s e c t i o n b) below. The measurement of p a r t i c l e surface free energy d i f f e r e n c e s by means o f contact angles ( s e c t i o n d  below) enables the r e l a t i o n s h i p s between the  surface p r o p e r t i e s , phase system properties and the p a r t i t i o n , which were developed above, t o be t e s t e d .  As noted above, the r e l a t i o n s h i p of the  p a r t i t i o n c o e f f i c i e n t to cos 9 i s p r o b l e m a t i c a l , because to obtain a p a r t i t i o n the phase system must be mixed and allowed t o coalesce and separate.  The p a r t i c l e s w i l l not d i f f u s e t o t h e i r e q u i l i b r i u m p a r t i t i o n  however long the systems are l e f t , u n l i k e s o l u t e s .  Gerson (1980, and Gerson and A k i t , 1980) tested [1.22] t o the p a r t i t i o n of c e l l s , using [1.30],  the a p p l i c a b i l i t y o f  and found a l i n e a r  -51-  r e l a t i o n s h i p between l o g ( p a r t i t i o n c o e f f i c i e n t ) and cos 9 f o r a number of d i f f e r e n t c e l l types. Experiments were done both by a l t e r i n g the polymer concentrations and by varying the c e l l type or p r o p e r t i e s . However as a t e s t of the theory of p a r t i c l e p a r t i t i o n i n g , t h i s work i s open to some c  objections. P a r t i c l e s such as c e l l s nearly always p a r t i t i o n between the i n t e r f a c e and one of the phases, so [1.30] i s not a p p l i c a b l e . In the c e l l p a r t i t i o n measurements described i n t h i s study, the systems were allowed t o s e t t l e f o r four hours and then c e n t r i f u g e d . This may have allowed c e l l s to sediment i n t o the lower phase, leading to the conclusion that the c e l l s were p a r t i t i o n i n g between the two phases.  b) P a r t i t i o n of large c e l l s . The t h e o r e t i c a l treatment of section a) does not account f o r some other important c h a r a c t e r i s t i c s of the p a r t i t i o n o f large ( > 1 jjm d i a . ) c e l l s . When the phases are f i r s t mixed, the c e l l s are uniformly d i s t r i b u t e d i n the emulsion formed by the phases, hence the apparent p a r t i t i o n c o e f f i c i e n t i s one.  Microscopic observation shows that  due to the low i n t e r f a c i a l tension the drops produced on mixing the phases are of the same order of s i z e as the c e l l s (1-5 jjm d i a . ) . separate by a combination of coalescence and s e t t l i n g .  The phases then  In systems  containing erythrocytes, which are easy to observe due to t h e i r c o l o u r , the d i f f e r e n c e between a system where a l l the c e l l s p a r t i t i o n to the i n t e r f a c e , and one where the c e l l s p a r t i t i o n to the upper phase i s apparent as soon as the drops themselves become l a r g e enough to see (Chapter S i x ; Van A l s t i n e , 1984), which i n d i c a t e s that c e l l p a r t i t i o n i s determined e a r l y on i n phase separation, as suggested by Van A l s t i n e , and Albertsson (1971, p 134). the phases separate s u f f i c i e n t l y r a p i d l y compared to the rate of c e l l  If  -52-  sedimentation, the p a r t i t i o n reaches some plateau value, and then eventually declines to zero as the c e l l s s e t t l e . The p a r t i t i o n i s therefore time dependent, the measured p a r t i t i o n u s u a l l y being taken somewhere on the plateau.  The p a r t i t i o n a l s o depends on the height of the phases. Walter (1985) showed that the c e l l p a r t i t i o n was higher i n a tube that was l a i d on i t s side a f t e r mixing, compared to a tube that was l e f t upright, even i f the s e t t l i n g time i n the h o r i z o n t a l tube was longer.  Another d i f f i c u l t y was noted by Raymond and Fisher (1980). In systems close to the c r i t i c a l point with small p o t e n t i a l s ,  almost a l l c e l l s are  attached to the i n t e r f a c e , even i f i t i s i n the form of small drops, irrespective  o f t h e i r p a r t i t i o n c o e f f i c i e n t . This i s t h e i r thermodynamic  e q u i l i b r i u m p o s i t i o n , as predicted from [1.31]. However i n s p i t e o f t h i s d i f f e r e n t species' erythrocytes s t i l l have d i f f e r e n t p a r t i t i o n  coefficients.  Ignoring for the moment these e f f e c t s , [1.31] does make some u s e f u l q u a l i t a t i v e p r e d i c t i o n s about p a r t i c l e p a r t i t i o n .  The p a r t i t i o n ought t o  depend exponentially on the surface properties of the p a r t i c l e s , t h e i r area, the temperature and the i n t e r f a c i a l t e n s i o n , r e s u l t i n g i n great s e n s i t i v i t y of the p a r t i t i o n i n g process to both the properties of the phase system and to p a r t i c l e surface p r o p e r t i e s .  As the p a r t i c l e area i s increased, the  p a r t i t i o n should become more one sided, e i t h e r a l l p a r t i c l e s p a r t i t i o n i n g to the i n t e r f a c e i f  < Y  T B  , or otherwise to one o f the phases.  As the  i n t e r f a c i a l tension i s increased, the adsorption of p a r t i c l e s at the  -53-  i n t e r f a c e should increase, t h i s increase being l a r g e r for bigger p a r t i c l e s .  c) The p a r t i c l e surface free energy d i f f e r e n c e , Ay importance i n a t h e o r e t i c a l understanding  , i s probably of great  of p a r t i t i o n , since t h i s term  contains a l l the c o n t r i b u t i o n s of the p a r t i c l e surface properties and t h e i r i n t e r a c t i o n with the phase system.  The a b i l i t y of phase systems to separate  d i f f e r e n t p a r t i c l e s , or to detect a l t e r a t i o n s i n surface p r o p e r t i e s , depends e n t i r e l y on d i f f e r e n c e s i n t h i s term.  Hence, considering [1.22], any  information that i s obtained by p a r t i t i o n can i n p r i n c i p l e be obtained by d i r e c t measurements of the contact angle.  The exception to t h i s statement  i s possible p a r t i t i o n d i f f e r e n c e s occurring with i d e n t i c a l p a r t i c l e s of d i f f e r e n t areas, although t h i s point has not been examined experimentally. The d i f f e r e n c e i n p a r t i c l e surface free energy depends on the net e f f e c t of a l l the f a c t o r s c o n t r i b u t i n g to p a r t i c l e surface energy, i . e . , on the sum of the i n t e r a c t i o n s between the surface and the components of the phase system.  The i n t e r a c t i o n s are of several types, which are l i s t e d and  described b r i e f l y here, noting whether they can be favorable ( i . e . , t a t t r a c t i v e , decreasing Y  b or Y  )» or unfavorable.  Some of these are  considered i n f u r t h e r d e t a i l i n the appropriate sections below. i)  van der Waals i n t e r a c t i o n s , or d i s p e r s i o n forces -  These are  n o n s p e c i f i c , almost always a t t r a c t i v e and of very short range. ii)  Hydrogen bonding -  Again the i n t e r a c t i o n i s short range and  a t t r a c t i v e , but requires the presence of s p e c i f i c chemical groups on the  + p a r t i c l e surface, e.g., OH or NH^ iii)  Hydration -  g  r o u p s <  This i s an e n t h a l p i c a l l y favorable i n t e r a c t i o n , the  -54-  binding of water to polar surface groups. i v ) Hydrophobic i n t e r a c t i o n -  In a sense t h i s i s the converse of  hydration - the e n t r o p i c a l l y unfavorable s t r u c t u r i n g of water around non-polar v)  groups.  Electrostatic interactions -  favorable or unfavorable.  These are long range and can be  They depend on the r e l a t i v e p o t e n t i a l of the  phase and the charge density of the surface.  Since the free energy of a  charged surface i s a l s o decreased by i n c r e a s i n g i o n i c strength, the concentration and valence of the ions i n the phases i s important. vi)  Polymer and ion binding or r e p u l s i o n -  The i n t e r a c t i o n of e i t h e r  of the polymers or ions with the surface, which may be mediated by any of the s p e c i f i c i n t e r a c t i o n s l i s t e d here.  Binding or adsorption w i l l  decrease the surface free energy, r e p u l s i o n w i l l increase i t .  I t must be stressed that the net e f f e c t on A-y depends on the d i f f e r e n c e i n the r e s u l t a n t of these e f f e c t s i n each of the phases. of  Also the d i v i s i o n  A Y i n t h i s way i s to some extent a r b i t r a r y , since these e f f e c t s cannot  a l l be i s o l a t e d , e i t h e r i n p r i n c i p l e or experimentally, and t h e i r e f f e c t s are not n e c e s s a r i l y a d d i t i v e . For example, the removal of  charge-bearing  s i a l i c acids from erythrocytes has opposite e f f e c t s on the p a r t i t i o n i n charge s e n s i t i v e and non-charge s e n s i t i v e phase systems (Walter et a l . , 1976).  Probably the most experimentally a c c e s s i b l e c o n t r i b u t i o n to A Y i s the e l e c t r o s t a t i c dependence.  The p o t e n t i a l d i f f e r e n c e between the phases can  a f f e c t the p a r t i t i o n of a charged p a r t i c l e as i t can a charged molecule.  -55-  The p a r t i t i o n of erythrocytes can f o r example be increased by increasing the r a t i o of phosphate to c h l o r i d e ions.  This i s one of the most commonly used  ways to manipulate the p a r t i t i o n of c e l l s .  That the charge on the c e l l  surface i s responsible i s supported by the f a c t that removal of negatively charged s i a l i c a c i d , which forms the bulk of the the erythrocyte surface charge, reduces t h e i r p a r t i t i o n i n a high phosphate system (Walter et a l . , 1976).  Non-electrostatic c o n t r i b u t i o n s to Ay i d e n t i f y and measure independently. been discussed i n s e c t i o n i i . to  Ay  are much more d i f f i c u l t to  The r o l e of hydrophobicity has already  The other most c l e a r l y defined c o n t r i b u t i o n  comes from polymer adsorption.  For a two component system, Gibbs  derived the f o l l o w i n g expression f o r the surface free energy  (e.g.,  Adamson, 1976):  -dy  where  = T du. s  [1.33]  s  i s the surface excess of s o l u t e , i e . the amount bound per u n i t area  of surface, and du. bulk s o l u t i o n .  &  i s the  change  i n solute chemical p o t e n t i a l i n the  This equation s t a t e s that the free energy  of a surface i s decreased by adsorption.  A s i m i l a r r e s u l t holds f o r  multicomponent systems, although the expressions are more complex.  Since  the concentrations of the two polymers i n each phase are d i f f e r e n t , and the d i f f e r e n t polymers are l i k e l y to adsorb to the p a r t i c l e surface i n d i f f e r e n t amounts, the c o n t r i b u t i o n of polymer adsorption to the surface free energy w i l l be d i f f e r e n t i n each phase, r e s u l t i n g i n a c o n t r i b u t i o n to Ay.  This  -56-  e f f e c t w i l l depend both on the nature of the surface and the phase compositions, but q u a l i t a t i v e l y , the phase enriched i n the polymer that adsorbs most strongly w i l l 'wet* the p a r t i c l e surface more.  There are no  q u a n t i t a t i v e theories a v a i l a b l e that r e l a t e non-specific polymer adsorption to Ay, and very l i t t l e work has been done on measuring phase polymer binding to p a r t i c l e s . Both Dx and PEG bind to the erythrocyte (Brooks et a l . , 1980;  surface  vide i n f r a )  Walter e_t a l . (1976) studied the p a r t i t i o n of erythrocytes  from several  species i n non-charge s e n s i t i v e systems and found c o r r e l a t i o n s with the l i p i d compositions of the membranes.  These were i n t e r p r e t e d as differences  i n i n t e r a c t i o n of the phase polymers, p a r t i c u l a r l y PEG, surfaces.  with the membrane  Support f o r t h i s idea comes from work on l i p i d b i l a y e r phase  transitions.  Both PEG  ( T i l c o c k and F i s h e r , 1979)  sucrose (Crowe et a l . , 1984)  and simple sugars such as  can a l t e r the phase t r a n s i t i o n c h a r a c t e r i s t i c s ,  i n d i c a t i n g that i n t e r a c t i o n s between these solutes and l i p i d do occur.  d) Contact Angles.  Direct measurements of contact angles are u s e f u l for two  reasons: i ) t h e o r e t i c a l , as the equations i n s e c t i o n a) i n d i c a t e , i n determining how  the p a r t i t i o n of c e l l s or p a r t i c l e s depends on p a r t i c u l a r surface  p r o p e r t i e s , such as surface charge density, and on the phase system p r o p e r t i e s , such as the e l e c t r o s t a t i c p o t e n t i a l d i f f e r e n c e or i n t e r f a c i a l tension. i i ) A n a l y t i c a l , where the surface free energy d i f f e r e n c e between the phases i s of d i r e c t i n t e r e s t , for example as a measure of the d i f f e r e n c e s i n  -57-  c e l l or t i s s u e p r o p e r t i e s .  Gerson (1980, and Gerson and A k i t , 1980) developed the ' c e l l lawn' method f o r measuring contact angles on c e l l s . This can be extended t o surfaces as w e l l as c e l l s or p a r t i c l e s (Schurch et a l , 1980; Schurch and Mclver, 1981; Boyce, 1983). In t h i s technique the contact angle i s measured on a drop o f the dense phase i n the l i g h t e r phase r e s t i n g on a l a y e r of cells  formed on a hydrated c e l l u l o s e acetate membrane by gentle f i l t r a t i o n  of a c e l l suspension.  Two f a c t o r s must a l s o be considered i n the a n a l y t i c a l  use o f contact angle measurements: f i r s t l y , the surface properties are almost c e r t a i n l y a l t e r e d upon contact with the phases, p a r t i c u l a r l y since both dextran and PEG adsorb t o c e l l surfaces (Brooks, 1973, vide i n f r a ) . I n a d d i t i o n , when the concentration o f polymer i n the s o l u t i o n i s lowered, the desorption of these polymers i s slow.  Secondly, the c h a r a c t e r i s t i c surface  energy obtained depends on where the apparent surface i s , as "seen" by the phase system. B i o l o g i c a l surfaces often have considerable s t r u c t u r e and thickness. Mclver and Schurch (1982) have shown that the c h a r a c t e r i s t i c surface free energies obtained by contact angle measurements depended on how far from the l i p i d b i l a y e r the i n t e r f a c e with the phase system was. I n s p i t e of t h i s , two polymer phase systems are uniquely s u i t e d to study changes i n the properties of b i o l o g i c a l surfaces since t h e i r surface free energies are of the same order of magnitude as the system i n t e r f a c i a l tensions  (Schurch  et a l . , 1981). Useful r e s u l t s can be obtained, with the provisos that (a) the b i o l o g i c a l s i g n i f i c a n c e of the changes i n the absence o f the phase polymers, and (b) the assignment o f the e f f e c t s to changes i n s p e c i f i c surface properties such as hydrophobicity, require independent  -58-  corroboration.  They cannot be assumed a p r i o r i simply from changes i n the  contact angle.  The a n a l y t i c a l use of phase systems has been demonstrated by Gerson (1980), Gerson and A k i t (1980). They c o r r e l a t e d the c e l l surface free energies of lymphocytes with t h e i r a b i l i t y to phagocytose and with t h e i r adherence to hydrophobic t e s t surfaces, i n t e r p r e t i n g the r e s u l t s as r e f l e c t i n g changes i n hydrophobic and van der Waals i n t e r a c t i o n s . Also Boyce et a l . , (1983) determined the surface free energy d i f f e r e n c e s of r a b b i t aorta endothelium by means of contact angle measurements i n DxT2000/PEG 20000 systems.  C o n t r o l l e d damage to the endothelium to expose the  subendothelial l a y e r was used to simulate changes i n atherogenesis.  The  damaged surface was wetted more s t r o n g l y by the dextran-rich phase, which was i n t e r p r e t e d as a decrease i n the apparent hydrophobicity of the surface, although t h e i r r e s u l t s could a l s o be explained by increased dextran adsorption or decreased PEG adsorption to the denuded surface.  Young's equation, and thus the expression for p a r t i c l e p a r t i t i o n , [1.31], depend only on the d i f f e r e n c e i n surface free energy. The determination of s o l i d surface free energies i s an outstanding problem i n c l a s s i c a l surface chemistry. Therefore there have been s e v e r a l attempts, based on models and e m p i r i c a l r e l a t i o n s , to obtain expressions for e i t h e r Y* or  that can be combined with Young's equation, so that they can  be estimated separately.  The f i r s t approach involves the concept of c r i t i c a l i n t e r f a c i a l tension  -59-  (Zisman, 1964).  For s o l i d / l i q u i d / v a p o u r systems where only d i s p e r s i o n  forces determine the surface free energy, such as i n l i q u i d hydrocarbons, G i r i f a l c o and Good (1957) and Fowkes (1963) argued that the surface  free  energy was equal to the c r i t i c a l i n t e r f a c i a l tension, at which one of the phases completely wetted the surface, i e . the contact angle was e i t h e r 0 or 180°.  Thus e x t r a p o l a t i o n of cos 6 (as a l i n e a r function of  -  7  2  tension * ' )  to ^1 could be used to estimate these surface free energies. These arguments assume that l i t t l e vapour i s adsorbed on the s o l i d surface, i e . that the spreading pressure i s n e g l i g i b l e . However Adamson and Ling (1964) maintain that some of t h e i r other assumptions imply that there i s s i g n i f i c a n t vapour adsorption, which increases as the s o l i d / l i q u i d surface free energy decreases. The v a l i d i t y of c r i t i c a l spreading tensions has not been convincingly demonstrated f o r c e l l surfaces exposed to two polymer phase systems, where adsorption c e r t a i n l y occurs, although l i n e a r cos © v. -1/2 Y.  p l o t s have been found for several c e l l types under a v a r i e t y of  to  conditions, i n c l u d i n g lymphocytes (Gerson, 1980), erythrocytes macrophages (Schurch et a l . , 1981)  and  i n Dx T500/PEG 20000 systems, and  erythrocytes i n Dx T500/PEG 6000 systems (Schurch et a l . , 1981). However some r e s u l t s i n t h i s t h e s i s show that large d i f f e r e n c e s i n estimates of the c e l l surface free energy can occur with small changes i n buffer type, i n d i c a t i n g the r e l a t i v e nature of such  estimates.  The second approach involves estimating equation of s t a t e .  ory^  from an e m p i r i c a l  An expression, a p p l i c a b l e to two component systems, was  found by Neumann et a l . , (1974). This equation of state also requires that the spreading pressure be n e g l i g i b l e .  As w i l l be argued l a t e r (Chapter  -60-  F i v e ) , r e s u l t s obtained by a l t e r i n g the c e l l / t w o phase contact angle a t constant i n t e r f a c i a l tension by means o f PEG-palmitate imply that t h i s equation o f s t a t e cannot be applied t o two phase systems.  Mclver and  Schurch (1982), and Boyce (1984) a l s o came t o t h i s conclusion.  Gerson  (1983) has a l s o used an e m p i r i c a l l y derived expression, s i m i l a r to that o f Good and G i r i f a l c o (1957).  In i n t e r p r e t i n g these surface free energies, i t  must be remembered that-the r e s u l t s obtained r e f e r t o the surface i n the phase system a t which the c r i t i c a l tension occurs, or at which the  equation  of s t a t e was applied. The surface energy therefore may be d i f f e r e n t i n other systems due t o a l t e r a t i o n s , p o s s i b l y i r r e v e r s i b l e , on exposure to the phase system r e s u l t i n g f o r example from polymer adsorption. minimizing these d i f f i c u l t i e s i s t o estimate  One approach t o  y^ or y^ in'various phase  systems to obtain an e m p i r i c a l dependence on the polymer concentrations and extrapolate the r e s u l t s back t o zero polymer (Gerson, 1983).  e). A f f i n i t y p a r t i t i o n of c e l l s and p a r t i c l e s . The other area i n which binding o f phase components i s important i s a f f i n i t y p a r t i t i o n .  Affinity  ligands are u s u a l l y molecules that are l i n k e d t o one o f the phase polymers and thus p a r t i t i o n unequally, and which a l s o bind t o the p a r t i c l e surface. When the l i g a n d binds, the p a r t i c l e surface e f f e c t i v e l y becomes coated with one o f the polymers, i n c r e a s i n g i t s p a r t i t i o n i n t o the phase r i c h i n that polymer.  The most common l i g a n d used for c e l l s has been  PEG-8000-palmitate.  PEG-palmitate was shown to a l t e r the p a r t i t i o n o f  liposomes i n a manner dependent mainly on the l i p i d head group, and t o a l e s s e r extent on the degree o f unsaturation o f the a l k y l chain t a i l group (Eriksson and Albertsson, 1978, Van A l s t i n e , 1984).  The p a r t i t i o n o f  -61-  erythrocytes i n the presence of PEG-palmitate has a l s o been c o r r e l a t e d with the r e l a t i v e amounts of sphingomyelin and phosphatidyl choline i n the membrane (Eriksson et a l . , 1976).  Erythrocyte p a r t i t i o n i s a l s o very  s e n s i t i v e to the chain length and degree o f unsaturation of PEG-fatty a c i d esters (Van A l s t i n e , 1984), erythrocytes from i n d i v i d u a l s s u f f e r i n g from m u l t i p l e s c l e r o s i s being d i s t i n g u i s h a b l e from c o n t r o l s on the basis of p a r t i t i o n i n g induced by such ligands (Van A l s t i n e and Brooks, 1984).  To date the e f f e c t s o f such ligands have only been studied semi-quantitatively.  Eriksson (1976) found that PEG palmitate was more  e f f e c t i v e than the o l e a t e , l i n o l e a t e , l i n o l e n a t e , or deoxycholate forms, while Van A l s t i n e (1984) c o r r e l a t e d the e f f e c t i v e n e s s of PEG-fatty a c i d esters with the hydrophobicity o f the f a t t y a c i d t a i l .  The more hydrophobic  f a t t y acids were more e f f e c t i v e presumably because they bound more strongly to the erythrocytes,  r e s u l t i n g i n a l a r g e r change i n A y .  Other a f f i n i t y ligands used f o r c e l l p a r t i t i o n included (Walter et a l . , 1968a) and 1970a).  DEAE-dextran  trimethylamino-PEG (TMA-PEG) (Johansson,  These are both charged l i g a n d s , and so t h e i r e f f e c t s would be  complicated by the e f f e c t s o f the i o n composition and p o t e n t i a l of the phase system.  In order to study c e l l / l i g a n d i n t e r a c t i o n s Reitherman e t al_. (1973)  measured the p a r t i t i o n o f DEAE-dextran i n a charge s e n s i t i v e phase system, i t s binding t o erythrocytes and the erythrocyte p a r t i t i o n .  They found that  the p o s i t i v e l y charged DEAE-dextran p a r t i t i o n e d i n t o the PEG r i c h phase when there was no p o t e n t i a l , and i n t o the negatively charged lower phase when there was a detectable p o t e n t i a l d i f f e r e n c e .  A r a t i o of more than three  -62-  l i g a n d s / c e l l surface charge were required to move the c e l l s i n t o the lower phase.  Such complications i n d i c a t e that a q u a n t i t a t i v e explanation of  a f f i n i t y p a r t i t i o n r e q u i r e s complete a n a l y s i s and measurements o f a l l the c e l l / l i g a n d / s y s t e m i n t e r a c t i o n s , along the l i n e s suggested i n Chapter Three of t h i s t h e s i s .  Flanagan and Barondes (1975) were the f i r s t t o t r e a t a f f i n i t y  partition  t h e o r e t i c a l l y when they derived an equation f o r the e f f e c t o f an a f f i n i t y l i g a n d , v a l i d for molecular p a r t i t i o n i n g a t high l i g a n d concentrations, i n connection.with t h e i r use o f TMA-PEG as a b i o s p e c i f i c a f f i n i t y l i g a n d f o r p u r i f y i n g c h o l i n e r g i c receptor containing membrane fragments (Flanagan et a l . , 1976). A f u l l expression for molecular a f f i n i t y p a r t i t i o n , v a l i d f o r any l i g a n d concentration has been derived independently by Mustacic and Weber (1978), Cordes et a l . (1984) and Brooks (Brooks et a l . 1985). Consider a substrate S which has n i d e n t i c a l binding s i t e s for a l i g a n d 3  molecule L, with a s s o c i a t i o n constants k*, k* , i n the upper and lower phases. Then a t e q u i l i b r i u m :  Top phase:  S L + L-  "5L^  i  + 1  , t Lower phase:  SL^ + L  " SL^ ^ +  k  where  i =0..n-l  b  -63-  k  fc  = [SL  t  i + 1  t  ] /CSL.] [L]  t  [1.34]  and  k  b  b  b  = [SL. ] /[SL.] [L]  b  [1.35]  + 1  are the l i g a n d binding a s s o c i a t i o n constants. K p  The substrate  partition,  i s given by the r a t i o o f the t o t a l amounts o f S i n each phase:  s  K  s1 = D ^ i ^ = IS] £  CSL.]  b  11  t  t  p(K [L] ) b  i  b  [1.36] b  [S] E(-VK CL] )  where the weighting f a c t o r ^  i  i s due to the number o f d i s t i n g u i s h a b l e ways  of arranging i ligands molecules on n s i t e s . Performing the sums (e.g. Van Holde, 1971) gives  K  t  where K  t  n  b  b  = K (l + k [L] ) /(l + k [L] )  s l  n  [1.37]  s  g  i s the p a r t i t i o n c o e f f i c i e n t of the free l i g a n d . Since the  binding i s o f the Langmuirtype (see [3.54]), [1.37] can a l s o be w r i t t e n as  K  where  S L  = K  s  [(kVk^.CLV'MnVo]  and n  b  n  c l  -  3 8 ]  are the average number of ligands bound per molecule i n  the upper and lower phases r e s p e c t i v e l y . Equation 1.38 can a l s o be w r i t t e n ©i i i n terms o f standard state free energy changes, where AG = -kTln k , or AG°= -kTln K:  -64-  3  AG°, = AG° + n ( A ( ? - AG* + AG, + kTln n V n )  [1.39]  At high ligand concentrations, n = n , and [1.38] y i e l d s  [1.40]  which was f i r s t derived by Flanagan and Barondes (1975). Eauation 1.40 i n d i c a t e s that the p a r t i t i o n should be very s e n s i t i v e to the number of ligands bound. However, t e s t s of t h i s eauation have shown a much smaller dependence on the number of binding s i t e s than predicted (Shanbhag and Johansson, 1974; Flanagan et a l . , 1976; Johansson and Shanbhag, 1984). This may p a r t l y be due to the assumption, made by the above authors, that k*= b  k . The i m p l i c a t i o n s of t h i s assumption, and i t s relevance to c e l l a f f i n i t y p a r t i t i o n are discussed i n further d e t a i l i n Chapters Three and Five of t h i s t h e s i s .  -65-  D. The Red Blood C e l l  i ) Morphology and Erythrogenesis  The mature human erythrocyte i n the absence of c i r c u l a t o r y shear forces i s a biconcave d i s c shaped c e l l , approximately  8.5 jjm i n diameter, maximum  thickness 2.4 pm, and minimum thickness, i n the centre, o f 1.0 pn. The 2 surface area i s around 145 jjm , with a volume i n plasma or i s o t o n i c 3  s a l i n e , o f 90 jjm , and a density o f 1.09 g/ml (Wintrobe, 1974). The erythrocyte thus has about 55% of the volume of a sphere with the same surface, area. I t s main function i s t o transport oxygen from the lungs to the t i s s u e s , and transport carbon dioxide back to the lungs.  The s t r u c t u r e of  the erythrocyte has evolved to optimise t h i s f u n c t i o n . The c e l l contains no nucleus or other c e l l organelles, these being extruded during  maturation.  Instead the c e l l i s f i l l e d with a concentrated s o l u t i o n (ca. 30% by weight o f the t o t a l c e l l ) o f the oxygen and C 0 binding p r o t e i n , haemoglobin. The 2  lack o f i n t e r n a l cytoplasmic s t r u c t u r e , and the mechanical properties o f the plasma membrane (Evans and Hochmuth, 1978) allow for great c e l l u l a r d e f o r m a b i l i t y . This allows the erythrocytes t o f r e e l y and repeatedly  transit  the m i c r o c i r c u l a t i o n , where c a p i l l a r i e s can be l e s s than the c e l l diameter. This a l s o r e s u l t s i n a very low whole blood v i s c o s i t y , considering the erythrocytes occupy a 43-47% volume f r a c t i o n . How low t h i s i s can be seen from the f a c t that the same volume f r a c t i o n o f r i g i d p a r t i c l e s would "..have the flow properties not u n l i k e those of w e l l matured asphalt 1981)  (Gratzer,  -66-  Erythrocytes a r i s e from hemopoietic stem c e l l s i n the spleen and bone marrow. These stem c e l l s d i v i d e to produce e r y t h r o b l a s t s , which r a p i d l y synthesis haemoglobin. The nucleus i s extruded to form the r e t i c u l o c y t e , which then enters the c i r c u l a t i o n . A small amount of haemoglobin synthesis continues f o r about a day. Loss of ribosomes and mitochondria h a l t s haemoglobin synthesis and c h a r a c t e r i z e s the t r a n s i t i o n to the erythrocyte, which at some point assumes the biconcave shape. Erythocytes c i r c u l a t e f o r about 120 days, with a small decrease i n surface area (Van Gastel et a l . , 1965) and a small increase i n density (Murphy, 1973). Unknown changes i n the membrane surface t r i g g e r t h e i r removal from c i r c u l a t i o n by erythrophagocytosis i n the r e t i c u l o e n d o t h e l i a l system.  Human red blood c e l l s have s e v e r a l advantages as model c e l l s f o r p a r t i t i o n studies. They are e a s i l y i s o l a t e d i n large q u a n t i t i e s , washed and p u r i f i e d from other c e l l types by successive c e n t r i f u g a t i o n and re-suspension i n p h y s i o l o g i c a l s a l i n e . They are remarkably uniform i n shape and s i z e , although there i s a small area decrease with age (ca. 10%). They are  r e l a t i v e l y uniform i n surface p r o p e r t i e s . This has been best  demonstrated by the p a r t i t i o n procedure i t s e l f . Erythrocytes give one of the narrowest peak p r o f i l e s i n CCD of any mammalian c e l l type (Walter, 1977), an i n d i c a t i o n of the small degree of heterogeneity. Although Walter and Selby (1966) have shown that there are age dependent changes i n p a r t i t i o n , i n c l u d i n g an apparent decrease i n surface charge, t h i s a p p l i e s p r i m a r i l y to r a t , not human erythrocytes (Walter et a l . , 1980).  -67-  i i ) Biochemistry of the Erythrocyte Membrane  The most important property o f the erythrocyte f o r p a r t i t i o n i s the composition  and s t r u c t u r e o f the outer plasma membrane, the only part o f the  c e l l that i n t e r a c t s with the phase system. The plasma membrane c o n s i s t s of a o  l i p i d b i l a y e r 50-70 A t h i c k associated w i t h which are two c l a s s e s o f p r o t e i n s , i n t r i n s i c and e x t r i n s i c (Fig.1.3). L i p i d s comprise about 44% o f the membrane by weight, which can be f u r t h e r subdivided as follows (Van Deenan and Gier, 1974): cholesterol.: 25%, neutral l i p i d s : 5%, g l y c o l i p i d s : 6-11%, 11%, phosphatidylcholine: 17%, phosphatidylethanolamine:  sphingomyelin:  17%,  phosphatidylserine: 8%  These are not a l l symmetrically d i s t r i b u t e d i n the two l e a f l e t s of the b i l a y e r , the outer l a y e r being enriched i n phosphotidylcholine, a z w i t t e r i o n i c l i p i d , and sphingomyelin, phosphatidylethanolamine  while the inner l a y e r i s enriched i n  and phosphatidylserine, a negatively charged l i p i d  (Van Deenan, 1981).  The remaining p o r t i o n o f the membrane c o n s i s t s of 49% protein and 7% carbohydrate,  of which 1.2% i s s i a l i c a c i d . I n t r i n s i c proteins are c l o s e l y  associated with the membrane by hydrophobic i n t e r a c t i o n s , being i n s e r t e d i n the b i l a y e r , and can be extracted by detergents or chaotropic agents. Some i n t r i n s i c p r o t e i n s , such as glycophorin, completely span the b i l a y e r , thus being exposed simultaneously  t o the cytoplasm and plasma. On the cytoplasmic  -68-  side o f the membrane are the second c l a s s of p r o t e i n s , such as s p e c t r i n and a c t i n , known as e x t r i n s i c p r o t e i n s . These proteins are associated with the membrane p r i m a r i l y by e l e c t r o s t a t i c i n t e r a c t i o n s , and can be extracted under conditions of low i o n i c strength (Gratzer, 1981). They l i e j u s t beyond the b i l a y e r , attached at c e r t a i n points t o some o f the i n t r i n s i c proteins such as Band 3, and form a continuous network on the i n t e r i o r of the membrane. The membrane l i p i d s provide a b a r r i e r to polar molecules, and r e s i s t membrane area changes because of the hydrophobic i n t e r a c t i o n s between the l i p i d t a i l groups, which form a cohesive two dimensional  hydrocarbon-like  l i q u i d . S p e c i f i c l i p i d s may a l s o contribute t o c e r t a i n i n t r i n s i c p r o t e i n functions. The e x t r i n s i c p r o t e i n s , and the i n t r i n s i c proteins, t o which they are attached form the cytoskeleton, which provides the membrane with i t s shear e l a s t i c i t y , maintaining i t s biconcave shape. Other i n t r i n s i c proteins are involved i n membrane t r a n s p o r t , immunological r e a c t i o n s , aggregation and r e c o g n i t i o n phenomena.  The outer surface of the membrane i s thus formed of the outer b i l a y e r l e a f l e t , and the associated g l y c o l i p i d s and glycoproteins. The main g l y c o l i p i d s are g l y c o s p h i n g o l i p i d , globosides and GM^ ganglioside. The main glycoproteins are glycophorins A, B, and C, and the anion transport p r o t e i n Band 3. An important c h a r a c t e r i s t i c o f the outer membrane surface i s that i t has a net negative charge. This i s p r i m a r i l y due to the s i a l i c a c i d . Enzymatic cleavage and a n a l y s i s shows that there are about 3 . 5 x l 0  7  sialic  molecules per c e l l (Cook, 1976), r e s u l t i n g i n a net negative charge density 4  2  of about 1.06xl0 esu/cm . Unfortunately l i t t l e i s known about the r e l a t i v e amounts and type o f other charged groups. Less than 5% of the  -69-  s i a l i c a c i d i s located on the g l y c o l i p i d s (Kunda et a l . , 1978). Twenty to f o r t y percent of the t o t a l carbohydrate, and f o r t y percent of the s i a l i c 5  a c i d i s located on glycophorin (Furthmayr, 1978). There are about 5x10 molecules of glycophorin per c e l l , each bearing around 31 charges on 16 carbohydrate  chains. Band 3, the other major g l y c o p r o t e i n , contains seven  percent of the carbohydrate  on 10^ molecules per c e l l . The l o c a t i o n of the  remaining s i a l i c a c i d i s not known p r e c i s e l y . The primary s t r u c t u r e of glycophorin A i s known i n some d e t a i l (Tomita et a l . , 1978, Geyer and Makovitovsky, 1980), and although the conformation  on the c e l l surface i s  not known i n d e t a i l (Stibenz and Geyer, 1980), the s i a l i c a c i d appears to be d i s t r i b u t e d along the e n t i r e e x t r a c e l l u l a r p o r t i o n .  The o v e r a l l p i c t u r e of the c e l l surface that emerges from the current s t a t e of research i s that of a l i p i d b i l a y e r whose outer surface i s composed p r i n c i p a l l y of n e u t r a l or z w i t t e r i o n i c head groups. E x t e r i o r to t h i s i s a d i f f u s e l a y e r of p o l y e l e c t r o l y t e , composed mostly of g l y c o p r o t e i n , with some g l y c o l i p i d head groups. Most of t h i s d i f f u s e l a y e r (ca. 80%) i s carbohydrate d i s t r i b u t e d throughout which are negatively charged s i a l i c a c i d s . E l e c t r o p h o r e t i c s t u d i e s (Donath and Pastushenko, 1978; Levine et a l . ,  1983)  and cytochemical work (Skutelsky et a l . , 1977) show that t h i s d i f f u s e l a y e r i s between f i f t y and one hundred angstroms t h i c k , that the charge appears to be f a i r l y uniformly d i s t r i b u t e d throughout the l a y e r , and that ions and water (and probably small molecules) f r e e l y penetrate t h i s l a y e r . The volume f r a c t i o n of g l y c o p r o t e i n i n t h i s l a y e r has been estimated as around 6% (Levine et a l . , 1983).  The general features of the outer surface of the  membrane are i l l u s t r a t e d schematically i n F i g . 1.3.  70  Figure 1.3 Schematic Diagram of the Erythrocyte Membrane. Major i n t r i n s i c p r o t e i n s : Band three (B), glycophorin (G). Major e x t r i n s i c p r o t e i n s : s p e c t r i n ( S ) , a c t i n (Ac), Band 2.1 (ankyrin) (A). L i p i d s : phospholipid b i l a y e r (PL), g l y c o l i p i d s (GL). Carbohydrate i s shown i n s o l i d black. No attempt has been made to show the true conformations, shapes and d i s t r i b u t i o n of these components. However the r e l a t i v e amounts, average volumes and separations between band three, glycophorin, the g l y c o l i p i d s and the phospholipids are shown to s c a l e , based on current estimates of t h e i r molecular weights, % carbohydrate and amounts per c e l l .  -71-  Chapter Two. M a t e r i a l s and Methods  With accurate experiment and observation to work upon imagination becomes the a r c h i t e c t o f p h y s i c a l theory- John Tyndall A. General Methods  The f o l l o w i n g materials and methods were used f o r a l l the work described i n t h i s t h e s i s , unless stated otherwise.  Experiments were c a r r i e d out i n a c o n t r o l l e d temperature laboratory a t 22 +0.5° C. A l l chemicals were of reagent or a n a l y t i c a l grade, and were used without further p u r i f i c a t i o n . They were obtained from the standard chemical supply houses. Glass d i s t i l l e d water, c o n d u c t i v i t y l e s s than 0.1 pwho/cm was used throughout t o make up a l l s o l u t i o n s . A l l buffer s o l u t i o n s and phase systems had a pH of 7.16. In p a r t i c u l a r phosphate buffered s a l i n e , r e f e r r e d to hereafter as PBS, which contained 7.4 mM monosodium phosphate, 2.6 mM disodium phosphate and 130 mM sodium c h l o r i d e , pH 7.16, was the most commonly used b u f f e r .  The term phosphate i s subsequently used to r e f e r t o  t o t a l phosphate present, unless these two species o f phosphate ions are e x p l i c i t l y distinguished.  A l l b u f f e r s had a t o n i c i t y of 285-300 mOsm,  determined by freezing point depression (Osmette I I osmometer, P r e c i s i o n Systems Inc., Waltham, Mass.). Phase system t o n i c i t i e s were determined with a vapour pressure osmometer (Wescor 5100C, Logan, Utah), due t o the anomalous freezing c h a r a c t e r i s t i c s o f polymer solutions,-and l a y between 290 and 305 mOsm. Sodium azide (0.02%) was added to a l l b u f f e r s and phase systems to i n h i b i t b a c t e r i a l growth. This had no detectable e f f e c t on any o f  -72-  the phase system properties studied. Because of the d i f f i c u l t y of volumetric measurements with viscous polymer s o l u t i o n s , a l l polymer concentrations  are  expressed i n percent weight per weight (%w/w). A l l d i l u t i o n s of polymer s o l u t i o n s were a l s o done by weight. Concentrations  of s a l t s and solutes i n  the phase system are expressed as moles per kilogram of phase system, but for s i m p l i c i t y are r e f e r r e d to as nominal m o l a r i t i e s (M).  B. Preparation and C h a r a c t e r i z a t i o n of Phase Systems  i ) Polymer properties  Sentry grade poly(ethylene g l y c o l ) 8000 (abbreviated to PEG 8000, previously known as PEG 6000) was obtained from Union Carbide Corp., Piscataway, N.J. The number average molecular weight was 7500-8000 g/mole. PEG was stored at A  0  C since prolonged storage at room temperature can  r e s u l t i n yellowing due to the added a n t i - o x i d a n t s , and f i n a l l y oxidation of the terminal alcohols to c a r b o x y l i c a c i d .  Dextran T500 was obtained as a spray d r i e d powder from Pharmacia Fine Chemicals, Uppsala, Sweden. Due to l i m i t e d production capacity, four l o t s , d i f f e r i n g s l i g h t l y i n molecular weight d i s t r i b u t i o n were used (Table  2.1)  S l i g h t d i f f e r e n c e s i n molecular weight d i s t r i b u t i o n and preparation of dextran can cause s i g n i f i c a n t d i f f e r e n c e s i n phase system properties and solute p a r t i t i o n (Zaslavsky et a l . , 1980)  so phase system compositions and  -73-  c e l l p a r t i t i o n s were compared i n a s e l e c t e d phase system made up with the o l d and new dextran l o t s before switching t o the new l o t . F i c o l l 400, l o t # IK33503, was obtained from Pharmacia.  TABLE 2.1 DESCRIPTION OF DEXTRAN LOTS Lot Number  7693 7830 FD16027 HD26066 a  Molecular Weight/1000 M M (g/mole) w  485 487 461 494  M /M w  n  195.5 181.5 181.7 181.2  2.48 2.68 2.54 2.73  n  3  Intrinsic Viscosity (ml/g)  0.54 0.51 0.50 0.54  Taken from Pharmacia information l e a f l e t s .  Because o f the v a r i a b l e water content of dextran and F i c o l l powders, and the d i f f i c u l t y o f making up standard s o l u t i o n s of these viscous polymers by volume, the f o l l o w i n g method was used to make up stock s o l u t i o n s of (ca.) 20% dextran, and 40% F i c o l l . Twenty two grams o f dextran, or f o r t y four grams of F i c o l l was mixed t o a paste with f o r t y grams o f water. Water was added to give a t o t a l weight o f one hundred grams. The s o l u t i o n s were then b o i l e d and s t i r r e d u n t i l the polymers completely d i s s o l v e d . The exact f i n a l concentrations of the dextran and f i c o l l stock s o l u t i o n s were determined by polarimetry (Drs. Steeg and Reuter, Hamburg, FDR, with a 20 cm tube, p r e c i s i o n 0.05°) or r e f r a c t i v e index (vide i n f r a ) on samples accurately d i l u t e d by weight. PEG stock s o l u t i o n s (30 %w/w) could be made up by accurate weighing o f the s o l i d PEG, since d i s s o l u t i o n o f t h i s polymer was  -74-  r a p i d and complete, and i t contained l e s s than 0.6% water as determined by exhaustive drying over phosphorus pentoxide at 60° C.  The r e f r a c t i v e index of standard polymer s o l u t i o n s was measured on a Bausch and Lomb refractometer ( p r e c i s i o n _+ 0.0005), which was c a l i b r a t e d using sucrose standards (CRC Handbook of Chemistry and P h y s i c s , 59th 1979), and the r e f r a c t i v e index increment of a 1% s o l u t i o n determined  Edn., (Table  2.2).  TABLE 2.2 SELECTED PHYSICAL PROPERTIES OF THE PHASE POLYMERS Polymer  Specific Optical Rotation °/(% m)  PEG F i c o l l 400 Dextran T500  0.0 5.65 19.9 a  a  R e f r a c t i v e Index Increment x l O (%-!) 3  1.39+0.03 1.53+0.03 1.53+0.04  P a r t i a l Specific Volume (ml/g)  0.833+0.005 0.650+0.005° 0.611^  a  A l b e r t s s o n , 1971 bpharmacia F i c o l l Paque Information Booklet Granath, 1958. c  The d e n s i t i e s of standard polymer s o l u t i o n s were measured i n a 2 ml volume pycnometer using a f i v e place a n a l y t i c a l balance. The r e f r a c t i v e index and density increments were found to be l i n e a r and a d d i t i v e f o r concentrations up to at l e a s t 10%. The p a r t i a l s p e c i f i c volumes were then c a l c u l a t e d (Table 2.2). R e f r a c t i v e index thus provided an a l t e r n a t i v e method to polarimetry or freeze drying f o r measuring polymer concentrations. Since polarimetry and r e f r a c t i v e index give concentrations i n volume percent,  -75-  these had to be converted  to weight percents using the s o l u t i o n d e n s i t i e s  c a l c u l a t e d from the p a r t i a l s p e c i f i c volumes i n Table  2.2.  PEG 8000-palmitate ester ( r e f e r r e d to i n t h i s t h e s i s as PEG ester or ester) was obtained from Chem Services Inc., P h i l a d e l p h i a , Pa. The ester  was  p u r i f i e d and analysed by Jim Van A l s t i n e and M i l t o n H a r r i s , and f u l l d e t a i l s are given by Van A l s t i n e (1984). The ester was p u r i f i e d by ether p r e c i p i t a t i o n from acetone s o l u t i o n , followed by LH-20 exclusion chromatography using methanol/water (5:1 v/v), to remove u n - e s t e r i f i e d p a l m i t i c a c i d . The p u r i t y from free f a t t y acids was checked by high pressure l i q u i d chromatography (HPLC, see H a r r i s et a l . , 1983) to be better than 99.9%  and by TLC,  and found  on a weight b a s i s . The ester molecular weight  was  found to be 6650+3% by HPLC. The degree of e s t e r i f i c a t i o n was determined by the hydroxamic a c i d ester assay (Van A l s t i n e , 1984); 9.9% were e s t e r i f i e d , g i v i n g 17.9%  of the end groups  mono-ester and 1% d i - e s t e r .  Radiolabelled ester was synthesized,  p u r i f i e d and analysed by Jim  Van  14 A l s t i n e , Poul Sorenson and Milton H a r r i s , using  C-palmitic acid  MBq/mmole, Amersham Radiochemicals), and p u r i f i e d PEG. synthesized  The ester  (0.22 was  by r e a c t i o n of the PEG with o x a l y l c h l o r i d e activated p a l m i t i c  a c i d i n anhydrous toluene (Van A l s t i n e , 1984). The ester was recovered and p u r i f i e d by ether p r e c i p i t a t i o n , followed by LH-20 chromatography to remove unreacted  p a l m i t i c a c i d , and hydrophobic a f f i n i t y chromatography on o c t y l  sepharose CL-4B to remove unreacted  PEG.  P u r i t y was checked by TLC,  p l a t e being analysed by l i q u i d s c i n t i l l a t i o n counting, and was 99.9%  on a weight b a s i s , 98.2%  ester on a mole b a s i s .  the  found to be  -76-  i i ) Preparation o f Phase Systems  Stock s o l u t i o n s of 20% dextran, 30% PEG and 40% F i c o l l , 0.3M sodium phosphate b u f f e r , 0.6M sodium c h l o r i d e and 0.6M d - s o r b i t o l s o l u t i o n s were made up. These stock s o l u t i o n s were then weighed i n t o a beaker, using a top loading balance t o an accuracy o f O.Olg, and made up t o weight with d i s t i l l e d water, so as to give the required f i n a l concentrations. Stock s o l u t i o n s o f other s a l t s or components required i n high concentrations were s u b s t i t u t e d as appropriate i f other compositions were required. The phase system was then mixed w e l l f o r f i f t e e n minutes. The phases were allowed to s e t t l e overnight, or centrifuged l i g h t l y (10 min at 200g). The phases were then separated i n a separating funnel ( f o r large volumes) or by c a r e f u l p i p e t t i n g using a wide tipped 10 ml glass p i p e t t e . The i n t e r f a c i a l region and the lower p o r t i o n of the lower phase were discarded, thus removing any dust or p a r t i c l e s that c o l l e c t there. This eliminated the need to f i l t e r the systems. The phases were stored at 4° C, and allowed t o reach room temperature j u s t before use. Systems were generally used w i t h i n two weeks, and stocks w i t h i n two months, to avoid changes due t o b i o l o g i c a l or chemical degradation. Whole phase systems could a l s o be frozen at -70° C f o r several months i f required. For most experiments equal volumes o f each phase at room temperature were combined and mixed t o allow complete r e - e q u i l i b r a t i o n . At t h i s stage a d d i t i o n of other components that were only required i n very small amounts, such as PEG e s t e r , was c a r r i e d out. A stock s o l u t i o n of the component, twenty t o one hundred times the f i n a l concentration, was made up i n a b u f f e r with the same s a l t composition as the system, or i n the upper phase of the system i t s e l f . This concentrated  stock  -77-  was then added i n amounts up to 50 j j l / m l of systems, to give the desired f i n a l concentration. This method allowed a s e r i e s of systems with the same polymer and s a l t compositions but varying amounts of a l i g a n d to be r a p i d l y made up.  For b r e v i t y and c l a r i t y phase system compositions are  subsequently  r e f e r r e d to using the f o l l o w i n g nomenclature: (x,y,z) p,q,r+s, where x, y and z are the weight percentages of dextran, PEG and F i c o l l r e s p e c t i v e l y , p, q and r r e f e r to the concentrations of sodium phosphate b u f f e r , sodium c h l o r i d e and s o r b i t o l r e s p e c t i v e l y , i n m i l l i m o l e s per kilogram of system (approximately equal to m o l a r i t y , mM,  i f the phase d e n s i t i e s are close to  one), and s i s the concentration of PEG 8000 palmitate e s t e r , i n pmoles/kg of system. I f e i t h e r z or s i s zero that term i s omitted.  Buffer  compositions are a l s o r e f e r r e d to using the above convention. Thus PBS i s equivalent to a 10,130,0 b u f f e r .  A l l d i f f e r e n c e s i n q u a n t i t i e s between the  phases are given as top - bottom, where the top phase i s the PEG r i c h phase. S i m i l a r l y a l l r a t i o s are expressed as top/bottom. The convention used to express the concentration of ligands or other a d d i t i v e s i s to give the bulk, or average concentration i n a system with equal phase volumes. This i s not equal to the concentration i n e i t h e r of the phases, or the bulk concentration for any other volume r a t i o , unless the a d d i t i v e had a p a r t i t i o n c o e f f i c i e n t of one. I f the p a r t i t i o n c o e f f i c i e n t , K, i s known these can be interconverted using the r e l a t i o n s h i p s  c  = (r DcWr K+l) v +  v  [2.1]  -78-  c  L  = (r +l)Kc/(r K+l) v  where c \  [2.2]  v  3  c , c', are the top, bottom and bulk concentrations, and r  y  t/..b i s the phase volume r a t i o , v /v .  i i i ) . The Phase Diagram  The phase diagrams of dextran/PEG systems were determined from a combination of polarimetry and r e f r a c t i v e index, using the data i n Table 2.2.  The dextran volume concentration, c^, was given by polarimetry, f o r a  20 cm tube length by:  c  where  d  = 0/2.98  [2.3]  0 was the o p t i c a l r o t a t i o n i n degrees.  The PEG concentration, c  was given by  [2.4]  where r i ^ was the r e f r a c t i v e index c o n t r i b u t i o n of the phase b u f f e r , and r i was the measured r e f r a c t i v e index r e l a t i v e to water. I t was assumed that the b u f f e r p a r t i t i o n e d e q u a l l y between the phases. This i s a good approximation,  and leads to l i t t l e e r r o r except f o r the PEG r i c h phase of  systems very f a r from the c r i t i c a l p o i n t , since most inorganic s a l t s have p a r t i t i o n c o e f f i c i e n t s i n the range 0.8  to 1.2  (Johansson, 1974a; Bamberger  et a l . , 1984a). I f t h i s i s not the case, another independent method of  -79-  concentration determination must be used for every component that does not p a r t i t i o n equally between the phases. The polymer concentrations were converted t o weight concentrations as before, using the p a r t i a l s p e c i f i c volumes. The t i e l i n e length was then c a l c u l a t e d from the d i f f e r e n c e s i n polymer concentrations between the phases, t o w i t h i n 0.5% (absolute e r r o r ) .  i v ) . I n t e r f a c i a l Tension  The i n t e r f a c i a l tension was measured by the r o t a t i n g drop method (Vonnegut, 1942, Princen et a l . , 1967, Bamberger et a l . , 1984a). The apparatus consisted o f a modified minature l a t h e (model 334 B400, Jensen Tools and A l l o y s , Tempe, Az.), f i t t e d with a t r a v e l l i n g microscope, f i l a r micrometer eyepiece (American O p t i c a l Co., B u f f a l o , N.Y.), and a d i a l gauge micrometer. The r a t e o f r o t a t i o n was c o n t r o l l e d by a continuously v a r i a b l e DC motor (model DPM-4330E, Bodine E l e c t r i c co., Chicago, I I . ) ,  and measured  using a d i g i t a l frequency counter (model HP 5381A, Hewlett Packard,  Palo  A l t o , Ca.). A 7mm d i a . by 100mm c y l i n d r i c a l glass tube was f i t t e d with s t e e l plugs at each end, sealed with rubber 0-rings. One of the plugs was d r i l l e d with a 1mm hole t o allow the expulsion of a i r bubbles from, and the i n j e c t i o n o f phase system i n t o the c y l i n d e r . The glass tube was bevelled on the inner surfaces at both ends, and was held i n the l a t h e between two b a l l bearings of a s l i g h t l y l a r g e r diameter than the tube. This automatically centred the tube along the h o r i z o n t a l a x i s o f r o t a t i o n .  To make a  measurement the tube was f i l l e d with the most dense phase, a i r bubbles were removed, and the tube sealed with the second plug. A drop o f the l i g h t e r phase, volume 0.5-10 JJI, was i n j e c t e d i n t o the c y l i n d e r with a microsyringe  -80-  (Hamilton, Reno, Nv.). The tube was immediately mounted on the l a t h e , and rotated at 500-2500 rpm, depending on the tension and s i z e o f the drop. C e n t r i f u g a l forces cause the drop t o migrate t o the a x i s of r o t a t i o n , and t o elongate along the a x i s . This elongation i s balanced by the surface tension forces which tend t o make the drop s p h e r i c a l . The drop s i z e and the r o t a t i o n rate were adjusted so that the e q u i l i b r i u m drop shape had a length to width r a t i o o f two t o f i v e , systems with higher tensions r e q u i r i n g l a r g e r drops and/or higher r o t a t i o n speeds. A f t e r the drop had come t o e q u i l i b r i u m , the length was measured by means o f the t r a v e l l i n g microscope and micrometer gauge. The width was measured using a micrometer eyepiece. The apparent width was corrected f o r the lens e f f e c t o f the glass c y l i n d e r by d i v i d i n g by the r e f r a c t i v e index o f the lower phase. The drop volume and tension were c a l c u l a t e d from the length, width, r o t a t i o n r a t e and density d i f f e r e n c e between the phases using the tables of Princen et a l . (1967). P r e c i s i o n was generally b e t t e r than 4%. The advantage o f the r o t a t i n g drop method i s that -5 i t r e t a i n s i t s accuracy, even f o r u l t r a low tension systems (10  -1 -10  dynes/cm), and does not i n v o l v e contact of the i n t e r f a c e with a t h i r d phase or surface. Secondary flows due t o buoyancy and i n e r t i a l e f f e c t s can a r i s e (Manning and S c r i v e n , 1977), but can be avoided by using s u f f i c i e n t l y small drops and high r o t a t i o n rates (Bamberger et a l . , 1984a). v) E l e c t r o s t a t i c P o t e n t i a l Difference  The i n t e r f a c i a l p o t e n t i a l d i f f e r e n c e between the phases was measured using r e v e r s i b l e Ag/AgCl electrodes. Two s i l v e r electrodes, area about lcm  each, were cleaned with xylene, acetone and then d i s t i l l e d water,  -81-  followed by b r i e f immersions i n 5 M n i t r i c a c i d u n t i l the surfaces had a uniform white 'mosaic' appearance. They were then r i n s e d with water, connected to the anode of a D.C. s o l u t i o n of 0.01 2 1 mA/cm  voltage supply and immersed i n a p l a t i n g  N h y d r o c h l o r i c a c i d . They were plated at a current of about  f o r two hours, with constant s t i r r i n g of the p l a t i n g s o l u t i o n .  The electrodes were tapped o c c a s i o n a l l y to remove any bubbles, and rotated ninety degrees every h a l f hour to ensure a uniform plum colored coating. The electrodes were then immersed i n 1 M KC1 s a l t bridges which were connected to m i c r o c a p i l l a r i e s with 20-50 pm i . d . t i p s , a l s o f i l l e d with 1 M KC1.  The  narrow openings of the m i c r o c a p l l a r i e s reduced leakage of s a l t without the need for agar.  The electrodes were then 'conditioned* by shorting them  across a 100 mV A.C source f o r one hour. M i c r o c a p i l l a r i e s were drawn from 1.5mm  i . d . glass tubing on a v e r t i c a l p i p e t t e p u l l e r (David Knopf  Instruments,  Tujunga, Ca.), then broken and heat polished to the required  t i p diameter using an e l e c t r i c a l l y heated nichrome wire mounted i n a micromanipulator.  Electrodes that showed signs of uneven p l a t i n g , or that  deplated during use, were r e - p l a t e d as above, a f t e r f i r s t removing the o l d AgCl with concentrated ammonia. The e l e c t r o d e / s a l t bridge p a i r s t y p i c a l l y had a r e s i s t a n c e of 1 MS7.  Abnormally high resistances i n d i c a t e d that the  m i c r o c a p i l l a r i e s had become blocked and needed replacing.The electrodes were connected to a high impedence d i g i t a l voltmeter (Hewlett Packard model 1 0  3A65A, impedence 1 0 f t ) using soldered connections and grounded c o a x i a l cables, free of ground loops, to reduce noise. The t i p s of the m i c r o c a p i l l a r i e s were immersed i n 20 ml of e q u i l i b r a t e d , w e l l s e t t l e d phase system, and the whole apparatus except the voltmeter enclosed by a grounded metal cage to s h i e l d i t from s t r a y voltages. One of the electrodes was moved  -82-  between the phases, and the d i f f e r e n c e i n voltmeter readings was taken as the e l e c t r o s t a t i c p o t e n t i a l d i f f e r e n c e . Generally at l e a s t ten readings were averaged. A b i a s voltage of more than 5 mV when both electrodes were i n the same phase u s u a l l y i n d i c a t e d poorly plated or conditioned electrodes, blocked m i c r o c a p i l l a r i e s or a non-equilibrated phase system.  The p r e c i s i o n  of t h i s method was 0.05 mV.  In some experiments agar f i l l e d s a l t bridges were used: 1% electrophoresis grade agar powder (Bio-Rad Laboratories, Richmond, Ca) was dispersed i n 1 M KC1 s o l u t i o n and heated t o 60° u n t i l d i s s o l v e d . The lower h a l f of Pasteur p i p e t t e s were then f i l l e d with the agar s o l u t i o n . The agar was allowed t o s e t , and the ends trimmed f l u s h with the pipet t i p t o ensure complete drainage of phase system from the t i p s . The electrodes were i n s e r t e d i n the KC1 f i l l e d upper ends of the p i p e t t e s .  C. P a r t i t i o n of Solutes i n the Phase System  i ) General Methods  Solute p a r t i t i o n c o e f f i c i e n t s were determined by measuring the s o l u t e concentration i n each phase a f t e r mixing and c e n t r i f u g a t i o n (10 min a t 200g). The apparent concentration r a t i o was then m u l t i p l i e d by three c o r r e c t i o n f a c t o r s t o obtain the true p a r t i t i o n .  a) Sampling volume c o r r e c t i o n . Due to the d i f f e r e n c e s i n v i s c o s i t i e s o f  -83-  the upper and lower phases, the automatic p i p e t t o r s used to sample the phases d e l i v e r e d d i f f e r e n t volumes of each phase. The c o r r e c t i o n f a c t o r was obtained by weighing a s e r i e s of pipetted samples and averaging. For 1ml samples t h i s c o r r e c t i o n f a c t o r was 0.973.  b) Polymer volume c o r r e c t i o n . The polymers occupy d i f f e r e n t volumes o f s o l u t i o n i n each phase, i e the concentration of water i n each phase i s d i f f e r e n t , due to the d i f f e r e n c e i n polymer concentrations and p a r t i a l s p e c i f i c volumes. This f a c t o r was 0.972 f o r a (5,4) system.  c) Assay c o r r e c t i o n . PEG and dextran can a f f e c t the assay used to determine the solute concentrations, often by d i f f e r e n t amounts i n each phase, eg. by quenching i n l i q u i d s c i n t i l l a t i o n counting. This c o r r e c t i o n f a c t o r was determined f o r each assay method as appropriate, using standards made up i n each phase.  In some cases the amount of solute was measured before a d d i t i o n to the phase system, and the t o t a l percentage recovered from each phase determined.  A f t e r applying the appropriate c o r r e c t i o n s , the d i f f e r e n c e  between these two amounts represented the amount of solute adsorbed at the i n t e r f a c e , or adsorbed n o n - s p e c i f i c a l l y to the tube or a i r water i n t e r f a c e .  i i ) Partition Coefficients  Chloride i o n p a r t i t i o n s were measured with a Buchler-Cotlove automatic c h l o r i d e t i t r a t e r , using 0.1ml samples. No c o r r e c t i o n f o r the e f f e c t s of the  -84-  phases was necessary. P r e c i s i o n was +2  mM.  Sulphate ion p a r t i t i o n s were measured using c a r r i e r free (3xl0  5  ^S0^~  Ba/ml of phase system, New England Nuclear (NEN), Boston, Mass.):  0.5ml d u p l i c a t e samples of each phase were taken i n t o 10ml of Atomlight s c i n t i l l a t i o n c o c k t a i l and counted i n a P h i l l i p s PW4700 l i q u i d  scintillation  counter. The r a t i o of counting e f f i c i e n c i e s i n each phase of a (5,4) system was 0.946, determined by counting known amounts of isotope added to e i t h e r the top or bottom phase.  14 PEG 8000-palmitate  e s t e r p a r t i t i o n s were measured using  r a d i o l a b e l e d e s t e r , f i n a l a c t i v i t y 1.46  C  Bq/mmole, mixed with u n l a b e l l e d  ester to give the desired s p e c i f i c a c t i v i t y . In some cases the amount adsorbed at the i n t e r f a c e was a l s o measured. P a l m i t i c a c i d p a r t i t i o n was measured by d i s s o l v i n g a sample of t r i t i a t e d p a l m i t i c a c i d (1.57xl0*  5  Bq/mmole, NEN)  i n ethanol. Ten m i c r o l i t r e s of  ethanol was added to 5ml of phase system, to give a f i n a l p a l m i t i c a c i d concentration of 1 0 ~ ^ (cmc)  M, w e l l below the c r i t i c a l m i c e l l e concentration  (2.8 jum, Mukerjhee and Mysels, 1971). Ethanol was required as a  c a r r i e r to s o l u b i l i z e the hydrophobic p a l m i t i c a c i d , and at these low concentrations has l i t t l e e f f e c t on the system (Van A l s t i n e , 1984). Samples were counted as for the e s t e r , except that counting e f f i c i e n c i e s were determined using the s c i n t i l l a t i o n counter i n t e r n a l standard, which had previously been c a l i b r a t e d using a s e r i e s of flame sealed quenched standards  (Beckman Instruments, Palo A l t o , Ca.).  -85-  i i i ) PEG E s t e r C r i t i c a l M i c e l l e  Concentrations  C r i t i c a l m i c e l l e concentrations (cmc's) were measured by the method o f fluorescence enhancement, whereby the quantum y i e l d o f a fluorescent probe i s increased on p a r t i t i o n i n g from the aqueous phase i n t o the hydrophobic i n t e r i o r o f a m i c e l l e (Tong e t a l . , 1965). Solutions o f 3 pm 6-propionyl-2-dimethylamino naphthalene (PRODAN) or 7 p i l-anilino-8-naphthalene sulphonic a c i d (1-8-ANS) (Molecular Probes, Piano, Texas) were made up i n d i s t i l l e d water or e i t h e r phase o f a (5,4)10,130,0 system. PEG ester was added t o the probe s o l u t i o n t o give an i n i t i a l concentration o f 20CjpM. The fluorescence was measured at 385/485nm. The ester s o l u t i o n was then s e q u e n t i a l l y d i l u t e d with the probe s o l u t i o n , the probe concentration thus remaining constant, and the fluorescence i n t e n s i t y measured. The cmc was estimated as the e s t e r concentration at the break i n a , p l o t o f fluorescence i n t e n s i t y against concentration ( f o r a t y p i c a l p l o t see F i g . 5.1). The method was checked by measuring the cmc o f sodium dodecyl sulphate. Both probes gave values i n the range o f 0.7 to 1.3 mg/ml, somewhat lower than the l i t e r a t u r e value o f 1.4-2.6 mg/ml (Mukerjhee and Mysel, 1971), probably due to the mixed m i c e l l e e f f e c t o f the probe.  D. Preparation of Erythrocytes  Human blood was obtained by venipuncture o f the c u b i t a l vein o f the author, or other healthy volunteers. Rabbit blood was obtained from the ear  -86-  v e i n . Blood was c o l l e c t e d i n t o sodium c i t r a t e anticoagulant (1 ml of  3.8%  c i t r a t e , pH7.16 per 9 ml of whole blood), and then washed three times with ten volumes of PBS, to remove the plasma, buffy coat and any lysed erythrocytes. Erythrocytes were used fresh the same day.  C e l l concentrations were determined by two methods.  f  a) Haematocrit measurements. The c e l l suspension was drawn up ir. o an uncoated glass c a p i l l a r y , i . d . 0.1 mm,  and one end plugged with c l a y . The  tube was spun at 11,000 rpm for 5 min i n a microhaematocrit  centrifuge  ( I n t e r n a t i o n a l Equipment Corporation). The volume percentage of c e l l s (haematocrit) was determined by measuring the r e l a t i v e heights of the columns of c e l l s and supernatant. P r e c i s i o n was +0.5% e r r o r ) . Haematocrits  (absolute  could be converted to number of c e l l s / m l using a human 5  erythrocyte volume, i n i s o t o n i c media, of 90 j-im", or to a weight f r a c t i o n using a c e l l density of 1.09  g/ml  (Wintrobe, 1974).  a) Impedence c e l l counting. An Electrozone Celloscope ( P a r t i c l e Data Inc.) f i t t e d with a 0.1 ml J-tube and a 70 jjm d i a . o r i f i c e , was used to determine c e l l concentrations below 5% haematocrit. Providing the c e l l 5  suspension was d i l u t e d to below lxlO* c e l l s / m l , the counts were l i n e a r with c e l l concentration, p r e c i s i o n 5%, and agreed with the  haematocrit  method to w i t h i n 5%. For the c e l l concentrations u s u a l l y used f o r p a r t i t i o n 40 pi  of system was d i l u t e d i n t o 10 ml of counting b u f f e r .  -87-  E. Erythrocyte P a r t i t i o n  Washed packed erythrocytes were resuspended i n a small volume o f upper phase to give a haematocrit o f about 50%. Small a l i q u o t s of t h i s c e l l suspension were added to the top phase u n t i l the required concentration was achieved (for most experiments t h i s was around 2x10  cells/ml).  One or two ml of the upper phase plus c e l l s was added to an equal volume o f 2 lower phase i n 1 cm xlO cm g l a s s c u l t u r e tubes ( r e f e r r e d to subsequently as 1+1 or 2+2 ml r e s p e c t i v e l y ) . The phases were mixed by i n v e r t i n g the tubes twenty times. At t h i s stage a d d i t i o n a l solutes such as a f f i n i t y ligands were added i f necessary. The tubes were again mixed by i n v e r s i o n , and the phases allowed to s e t t l e f o r 15 min f o r the 1 ml volumes, or 30 min f o r the 2 ml volumes. The top phase was sampled by automatic p i p e t t o r from the middle of the  phase, taking care not to d i s t u r b or a s p i r a t e the i n t e r f a c e  The c e l l  concentration was determined by c e l l counting. The percentage of the c e l l s added that returned to the top phase was c a l c u l a t e d (%P), or was expressed as a p a r t i t i o n c o e f f i c i e n t , K= (number of c e l l s i n top phase/number of c e l l s at the i n t e r f a c e ) =%P/(100-%P). P a r t i t i o n s were u s u a l l y reproducible to w i t h i n 2-5% (absolute e r r o r ) . In some experiments c e l l s were suspended i n , or sampled from the lower phase.  Phase volume r a t i o s were a l s o varied w i t h i n t h i s general p r o t o c o l .  Isopycnic systems were allowed t o separate f o r one hour, and the inner and outer phases c a r e f u l l y sampled.  -88-  F. Polymer Adsorption to C e l l s  i ) Adsorption of PEG  Polymers such as dextran and PEG adsorb to erythrocytes extremely weakly, therefore the binding cannot be measured by the disappearance o f l a b e l l e d polymer from s o l u t i o n on adding c e l l s (Janzen, 1985). In a d d i t i o n the  amount of trapped polymer i n the c e l l p e l l e t i s comparable to the amount  adsorbed. Markers f o r trapped volume must f i r s t be shown to bind to the c e l l at l e a s t an order of magnitude more weakly than the polymer i t s e l f , and are thus not very u s e f u l . The f o l l o w i n g protocol was adapted from Brooks et a l . (1980; see Janzen, 1985 f o r a more d e t a i l e d a n a l y s i s ) , to enable trapped and bound material to be d i s t i n g u i s h e d .  4  *C  l a b e l l e d PEG 8000 ( 3 X 1 0  12  Bq/mmole, Amersham Radiochemicals) was  mixed with unlabelled PEG to give a f i n a l s p e c i f i c a c t i v i t y of 10** Bq/mmole. Solutions of l a b e l l e d PEG were made up i n b u f f e r or e i t h e r phase of a (5,A) system as appropriate. Washed erythrocytes were p e l l e t e d at 165,000g f o r 15 min i n a 13 mm xlOO mm polyallomer tube (Beckman Instruments  model LS-65 u l t r a c e n t r i f u g e , 35,000 rpm with a SWAl swinging  bucket r o t o r ) . About one gram of packed c e l l s was added to each 1ml sample of PEG s o l u t i o n by puncturing the bottom of the polyallomer tube and e x p e l l i n g the c e l l s with p o s i t i v e pressure. The c e l l suspensions were mixed gently by i n v e r s i o n f o r one hour. Each tube was then f i l l e d t o w i t h i n 2 mm o f the  top (to prevent the tube c o l l a p s i n g during u l t r a c e n t r i f u g a t i o n ) with an  i n e r t o i l intermediate i n density between the b u f f e r and c e l l s (1:3.5  w/w  -89-  cottonseed o i l r b e n z o y l benzoate, density 1.078  g/ml), and c e n t r i f u g e d at  165,000g for one hour. This enabled the high s p e c i f i c a c t i v i t y  supernatant  to be c l e a n l y separated from the p e l l e t , and a l s o produced a very compact p e l l e t , thus reducing the amount of unbound l a b e l associated with the p e l l e t to a minimum.  The supernatant and o i l were removed and t h e i r a c t i v i t i e s determined  (1  ml samples i n t o 10 ml Atomlight, NEN, counted on a P h i l l i p s PW4~00 s c i n t i l l a t i o n counter). The o i l always contained l e s s than 0.1% of the a c t i v i t y . The surface of the c e l l p e l l e t was swabbed free of o i l , and the p e l l e t a c t i v i t y determined as f o l l o w s (adapted from the Beckman |_SC A p p l i c a t i o n s Handbook): T r i p l i c a t e samples of p e l l e t about lOmg were accurately weighed i n t o glass s c i n t i l l a t i o n v i a l s f i t t e d with p l a s t i c l i n e d caps. The c e l l s were digested by adding 0.5 ml of P r o t o s o l t i s s u e s o l u b i l i z e r (NEN) plus 0.5 ml ethanol and incubating  the t i g h t l y sealed  v i a l s at 60° for one hour. The v i a l s were cooled and 0.5 ml 30% hydrogen peroxide was added to bleach the digested haemoglobin, with continuous vortexing so as to prevent excessive foaming  The v i a l s were loosely capped  and incubated at 60° f o r 30 min to remove excess hydrogen peroxide which could cause quenching. Atomlight (15 ml) was added, and the c o c k t a i l  was  a c i d i f i e d by the a d d i t i o n of 0.5 ml 0.5 N HC1 to reduce quenching by the basic quaternary amines i n the t i s s u e s o l u b i l i z e r . The f i n a l s o l u t i o n was a pale yellow, and produced l i t t l e quenching. Counting e f f i c i e n c i e s were determined  from the counter i n t e r n a l standard, which had previously been 14  c a l i b r a t e d with flame sealed quenched  C standards (Packard Instruments).  -90-  The r e s t of the c e l l p e l l e t was accurately weighed i n t o a 15mm  xlOOmm  polycarbonate tube as before by puncturing the bottom of the c e n t r i f u g e tube and e x p e l l i n g the p e l l e t with p o s i t i v e pressure. Eight volumes of buffer were added, the c e l l s resuspended by i n v e r s i o n f o r f i f t e e n minutes and p e l l e t e d at 500g f o r 5 min. Ninety percent of the b u f f e r was removed, counted and replaced with fresh b u f f e r . This washing and a n a l y s i s procedure was repeated s i x to eight times. The f i n a l c e l l p e l l e t was sampled, digested and counted as before. Using t h i s method the trapped l a b e l coul'j be distinguished from bound l a b e l , as f o l l o w s , since i t was r a p i d l y d i l u t e d out and only contributed to the a c t i v i t y of the i n i t i a l p e l l e t . The a c t i v i t y of the p e l l e t a f t e r each wash was c a l c u l a t e d from the a c t i v i t y of the i n i t i a l p e l l e t by s u b t r a c t i n g the t o t a l amount of l a b e l released i n t o the wash b u f f e r s . The decrease i n c e l l p e l l e t a c t i v i t y a f t e r each wash could be w e l l f i t t e d by the sum of two decaying exponentials. The e x t r a p o l a t i o n of t h i s double exponential back to the i n i t i a l p e l l e t always gave a smaller a c t i v i t y than the measured value. In t h i s study the d i f f e r e n c e between the two  values  was assumed to be trapped m a t e r i a l , which could then be corrected f o r , to obtain the amount bound. The apparent trapped m a t e r i a l v a r i e d from 30 to 50% of the t o t a l p e l l e t a c t i v i t y , and thus represented a s i z a b l e c o r r e c t i o n . F i t t i n g of the data to the exponential function was done by means of a four parameter non-linear regression program w r i t t e n i n Fortran, using the damped Newton-Raphason method ( F l e t c h e r , 1965).  -91-  i i ) PEG 8000-palmitate Adsorption  Ester adsorption was measured by three methods.  a) Disappearance of l a b e l l e d ester from s o l u t i o n . One ml volumes of 14 C l a b e l l e d ester s o l u t i o n s of the required concentrations were made up i n b u f f e r or e i t h e r phase. Two 0.1 ml samples were taken and the a c t i v i t y determined. Washed erythrocytes were adjusted to between 50 and 00% haematocrit i n the same b u f f e r or phase, and the haematocrit accurately determined. The c e l l suspension was accurately weighed i n t o the ester s o l u t i o n s to give the required f i n a l c e l l concentration. The c e l l suspension was mixed gently by i n v e r s i o n f o r 30 min and the c e l l s p e l l e t e d at 10,000 rpm f o r 1 min (1.2 ml volume polypropylene micro tubes i n an Eppendorf 3200 micro c e n t r i f u g e ) . The supernatant was sampled and the a c t i v i t y determined. The amount of bound ester was determined from the decrease i n s o l u t i o n a c t i v i t y , a f t e r c o r r e c t i n g f o r d i l u t i o n due to the added buffer i n the o r i g i n a l c e l l suspension. Except f o r experiments where the e f f e c t s of c e l l concentration were being s t u d i e d , the f i n a l haematocrit was adjusted to between 2.5 and h%,  since t h i s r e s u l t e d i n approximately equal amounts of  ester being bound and f r e e , thus minimizing the e f f e c t s of uncertainty i n sampling and a c t i v i t y determination. • b) C e l l p e l l e t a n a l y s i s . The second method d i f f e r e d from the f i r s t method i n that the c e l l p e l l e t produced by c e n t r i f u g a t i o n was analysed d i r e c t l y , a f t e r removing 95% of the supernatant. The c e l l p e l l e t was weighed, digested and counted as above. Since the ester binding was much  -92-  stronger than the PEG binding, the p e l l e t a c t i v i t y could be corrected f o r trapped and remaining b u f f e r by using the d i f f e r e n c e i n f i n a l and i n i t i a l c e l l p e l l e t weights.  c) Binding from a complete phase system ( i n phase binding). This method, although more d i f f i c u l t and l e s s accurate, was developed so that the ester binding could be measured from both phases simultaneously, under the conditions used f o r c e l l p a r t i t i o n . C e l l s were added to 2+2 ml of 'jhase system, the concentration determined and r a d i o l a b e l e d ester added, a l l as described f o r c e l l p a r t i t i o n (section E  above), using d u p l i c a t e sets of  tubes. The phases were mixed by i n v e r s i o n and allowed to s e t t l e f o r 30 min. For  one set of d u p l i c a t e s , the c e l l concentrations i n the top phase were  measured by c e l l counting, two 0.8ml samples removed to Eppendorf microtubes, 0.4ml of intermediate density o i l added and the c e l l s p e l l e t e d at 11,000 rpm f o r one min. A l l the supernatant and most of the o i l was removed, and t h e i r a c t i v i t i e s determined. Again l e s s than 1% of the a c t i v i t y appeared i n the o i l . The c e l l p e l l e t s were resuspended i n 0.2ml b u f f e r , divided i n t o three samples, digested and counted. The lower phase remaining i n the tubes was sampled and the a c t i v i t y determined, to enable the ester p a r t i t i o n c o e f f i c i e n t to be c a l c u l a t e d .  The other set of d u p l i c a t e tubes  was centrifuged l i g h t l y (200 g f o r  5 min) to p e l l e t a l l the c e l l s i n t o the lower phase. The top phase was removed and the a c t i v i t y determined to provide another estimate of the ester p a r t i t i o n c o e f f i c i e n t . The c e l l s were gently resuspended i n the lower phase by mixing f o r f i f t e e n minutes, to allow the binding to r e - e q u i l i b r a t e , and  -93-  the c e l l concentrations determined by c e l l counting. F i n a l l y 0.8 ml of the lower phase was t r a n s f e r r e d to Eppendorf microtubes and the binding determined as f o r the upper phase.  The intermediate density o i l was used not because trapping was a problem, but because without i t the small c e l l concentrations used f o r partition  (around 2 x l 0  7  c e l l s / m l , or 2-4 mg/tube) make i t very d i f f i c u l t  to avoid a s p i r a t i n g a l o t of the c e l l s when removing the supernatant before digestion.  i i i ) Desorption o f PEG and PEG-palmitate  Desorption of the ester from the c e l l surface was analysed by means o f sequential washes. A f t e r the binding was measured, between 80 and 90% of the b u f f e r was removed and i t s a c t i v i t y determined. The same weight of fresh b u f f e r or phase  was added, the c e l l s resuspended by gentle mixing for ten  minutes, and the c e l l s r e - p e l l e t e d by c e n t r i f u g a t i o n (10,000 rpm f o r 1 min). This wash procedure was repeated as many times as necessary. In some experiments the c e l l s were lysed by washing with hypotonic buffer (10 mM sodium phosphate b u f f e r , pH 8 ) . In these experiments c o n t r o l s were washed with b u f f e r o f the same i o n i c strength made i s o t o n i c with s o r b i t o l .  -94-  G. Contact Angle Measurements  i ) Apparatus  Contact angles formed between the two phase i n t e r f a c e and the c e l l surface were measured using the micro-pipette a s p i r a t i o n and micromanipulation  apparatus o f Evans (1980). A diagram of the measurement  chamber i s given i n F i g . 2.1. An inverted microscope ( L e i t z Diavert, Wetzlar, FDR) was mounted on a 10x50x60cm granite slab supported by f i f t e e n pressureless tennis b a l l s f o r v i b r a t i o n i n s u l a t i o n . The microscope was f i t t e d with a beam s p l i t t e r and video camera (MTI 65), the output of which was d i r e c t e d t o a high r e s o l u t i o n black and white monitor (RCA, Lancaster, Pa). The time was a l s o displayed on the screen. The microscope magnification was xl250, with a f i n a l screen magnification of xl0,000. Depth of f i e l d was ca. 0.35 jjm. The video output was a l s o  recorded on a video cassette  recorder (Sony VO-5600 VCR) f o r o f f - l i n e a n a l y s i s . A s t a i n l e s s s t e e l frame mounted on the specimen stage held two p a i r s of g l a s s cover s l i p s 2mm apart (Fig.  2.1a). The cover s l i p s were held t o the frame and sealed by vacuum  grease. The spaces between the c o v e r s l i p s could then be f i l l e d with l i a u i d , which was held by c a p i l l a r y a c t i o n . Two f l u i d f i l l e d chambers were thus formed, open at both s i d e s , and separated by a 3mm a i r gap, i n t o which micropipettes could be i n s e r t e d . Two custom made a i r p i s t o n driven micromanipulators  could be used t o p o s i t i o n and c o n t r o l two micropipettes to  a r e s o l u t i o n of l e s s than one micron. The pressure w i t h i n the p i p e t t e s could be c o n t r o l l e d by mouth s u c t i o n or by a micrometer driven h y d r o s t a t i c pressure head.  Figure 2.1 Measurement of Contact Angles, a) Apparatus, b) Analysis o f image. Symbols defined i n the t e x t .  -96-  i i ) Preparation of P i p e t t e s  P i p e t t e s were drawn on a v e r t i c a l p i p e t t e p u l l e r from 0.4 mm i . d . sodium glass tubing. The p i p e t t e opening was trimmed to the required i n s i d e diameter using an e l e c t r i c a l l y heated loop o f nichrome wire mounted on a three dimensional micromanipulator, viewed with a stereomicroscope. Each experiment required one small p i p e t t e , 1-1.5 ym i . d . for c e l l a s p i r a t i o n , and one large p i p e t t e , 20-50 pm i . d . f o r c e l l t r a n s f e r . The small pipette was f i l l e d with 150 mOsm b u f f e r (10 mM phosphate b u f f e r , 60 mM NaCl) by b o i l i n g i t i n the buffer under reduced pressure f o r 30 min. The l a r g e r p i p e t t e was p a r t i a l l y f i l l e d , t o w i t h i n ca. 20 jjm oil  o f the t i p , with an i n e r t  by c a p i l l a r y a c t i o n , so as t o eliminate any f l u i d flow w i t h i n i t during  the experiments.  i i i ) Experimental Procedure  A l l experiments were done with phase systems and b u f f e r s of 150m0sm, approximately h a l f i s o t o n i c , t o s w e l l the erythrocytes.  This did not a f f e c t  the p a r t i t i o n c o e f f i c i e n t o f the c e l l s . Thus when a c e l l was aspirated i n t o the small p i p e t t e , as large an area as p o s s i b l e of the c e l l was l e f t exposed for contact with the phase system drops, making the contact angle measurements e a s i e r . About I J J I of blood from a f i n g e r p r i c k was d i l u t e d i n 5ml o f b u f f e r . This b u f f e r , (but not the phase systems) contained 0.1 % human serum albumin, t o prevent adherence of the c e l l s to the small p i p e t t e . 5  The extremely low concentration o f c e l l s (about 10^ c e l l s / m l or 1 0 ~ %  -97-  haematocrit) made washing of the c e l l s unnecessary. One chamber was f i l l e d with t h i s c e l l suspension, the other with top phase (which always contains some small drops of the lower phase). An erythrocyte was aspirated i n t o the small p i p e t t e u n t i l a r i g i d s p h e r i c a l surface was produced ( F i g . 2.2). The t i p o f the p i p e t t e was i n s e r t e d about f o r t y microns i n t o the buffer f i l l e d mouth of the large p i p e t t e . The c e l l was then t r a n s f e r r e d t o the chamber containing the phase system by t r a n s l a t i n g the stage holding the chambers, r e l a t i v e t o the p i p e t t e s . The small p i p e t t e holding the c e l l was then withdrawn from the mouth o f the large p i p e t t e . The c e l l was manoeuvered i n t o contact with a droplet o f the lower phase so that i t wetted the c e l l surface and formed a contact angle ( F i g 2.2). The c e l l and drop were oriented so that t h e i r o u t l i n e s were simultaneously i n focus, thus ensuring that t h e i r centres l a y i n the same o p t i c a l plane, perpendicular to the o p t i c a l a x i s . An a d d i t i o n a l check on the alignment was t o ensure that the contact c i r c l e (Figs.  2.1b and 2.2) appeared as a s t r a i g h t l i n e , and was thus l y i n g i n a  plane p a r a l l e l to the o p t i c a l a x i s . The image was then videotaped f o r subsequent a n a l y s i s . In some experiments the c e l l s were incubated i n buffer then the lower phase before making the measurements.  i v ) Image Analysis  Linear dimensions were measured d i r e c t l y from s t i l l frame images on the monitor using an e l e c t r o n i c video c a l i p e r (Model 305, V i s t a E l e c t r o n i c , La Mesa, Ca.). The video c a l i p e r s were c a l i b r a t e d i n the x and y d i r e c t i o n s from microscope images o f a stage mounted micrometer. Measurements o f several diameters of both c e l l s and drops confirmed that they were indeed  -98-  Figure 2.2. Photograph of Cell/Drop Contact Angle. Photo was taken from a s t i l l image on the TV monitor. The c e l l was aspirated i n t o a p i p e t t e a t l e f t , and i s wetted by a drop o f lower phase suspended i n upper phase. Time and frame number are displayed at top r i g h t . White l i n e s are produced by the video c a l i p e r s , and show the measurement of the diameter o f the contact c i r c l e , which appears as a s t r a i g h t l i n e i n t h i s o r i e n t a t i o n .  -99-  s p h e r i c a l , as expected. The contact angle could thus be obtained t r i g o n o m e t r i c a l l y from the two diameters, 2 a and 2 a , and the diameter p  d  of the c i r c l e o f three phase contact, 2 a , ( F i g . 2.1b) using: c  0 = sin (a /a ) + sin (a /a ) _ 1  _ 1  c  p  c  [2.5]  d  In p r i n c i p l e any diameters o f the c e l l and drop images could be used. However with regard to o p t i c a l e r r o r s there are two p a r t i c u l a r l y u s e f u l diameters- those p a r a l l e l to the contact c i r c l e , f o r which the r a t i o of diameters i s unaffected by l i n e a r screen d i s t o r t i o n .  C a l c u l a t i o n of the  angle was found to be more o b j e c t i v e and precise than d i r e c t angle measurements with a p r o t r a c t o r . As a check on the measurements the height o f the drop from the contact l i n e , 1^, was back-calculated from the contact l i n e length and the diameters, using:  l  d =  ( a  a  d - c  ) 1 / 2  +  a  d  ^  Only when the c a l c u l a t e d and measured values of t h i s length agreed to w i t h i n 5% were the r e s u l t s used. The average angle was taken from measurements on at l e a s t f i v e c e l l s , using three d i f f e r e n t drops per c e l l . Angles greater than 20° could be measured to w i t h i n 2-3°.  H. Treatment of Results and Determination of Experimental U n c e r t a i n t i e s  Measurement u n c e r t a i n t i e s were determined from the p r e c i s i o n of the  -100-  relevant instruments. A l l measurements w i t h i n experiments were c a r r i e d out at l e a s t i n d u p l i c a t e . Most experiments were repeated at l e a s t once. Standard deviations i n f i n a l q u a n t i t i e s were determined e i t h e r from v a r i a t i o n s between experiments i f p o s s i b l e , from v a r i a t i o n s between r e p l i c a t e s w i t h i n an experiment, or from regression a n a l y s i s as appropriate.  Where l i n e a r regression was used, estimates o f the standard d e v i a t i o n i n the slope,  a , and i n t e r c e p t , g  o\, were c a l c u l a t e d from the  following formulae (Mendenhall and Schaeffer, 1973):  2  c r = SSE/(n-l)V  v  [2.7]  [2.8]  where SSE i s the sum o f the squared e r r o r s , n i s the number of data, and V  x  i s the variance of the independent v a r i a b l e s , x^. Error bars on  f i g u r e s and error l i m i t s i n t a b l e s are t y p i c a l f o r that data set unless otherwise i n d i c a t e d .  -101-  Chapter Three.  Theoretical Results  Empiricism may serve to accumulate f a c t s , but i t w i l l never b u i l d science. The experimenter who does not know what he i s looking for w i l l not understand what he f i n d s - Claude Bernard  A. P o t e n t i a l Difference  i n Single S a l t Systems  The difference i n inner or Galvani p o t e n t i a l s between two phases i s not d i r e c t l y measurable, as was discussed i n Chapter One. considerations  General thermodynamic  (Adamson, 1976, Ch. 8) suggest that the p o t e n t i a l difference  that i s measured, A ty , i s the p o t e n t i a l d i f f e r e n c e between the phases, m  ^  D  US a  tb' '''  ^  e r m  a r  s  * *  n q  ^  r o m  ne  *- chemical work performed on moving the  t e s t charge(s) between the phases  A | i ^ . Thus:  [3.1]  In the experimental s e t up described i n t h i s work the t e s t ions could be K , CI  +  (and Na , S0~, HPO^ or H P0~, depending on the b u f f e r ) . The 2  phase system at e q u i l i b r i u m can provide no work, so the measured p o t e n t i a l must a r i s e from the d i f f e r e n c e i n (phase) j u n c t i o n p o t e n t i a l s , ^ J " i ^ ,  generated at the boundary between the s a l t bridges and each phase.  These could i n p r i n c i p l e be c a l c u l a t e d by i n t e g r a t i n g the equation f o r the d i f f u s i o n p o t e n t i a l across the j u n c t i o n zones (Kortlim, 1965, pp 291-2):  [3.2]  -102-  where a^, n^, i t h ion.  are the a c t i v i t y , transport number and valence of the  Determining  difficult.  n and a, which vary with p o s i t i o n , would be  extremely  However changes i n the p o t e n t i a l d i f f e r e n c e between the phases  can be measured d i r e c t l y .  An expression for t h i s quantity i s now  derived.  At e q u i l i b r i u m the chemical p o t e n t i a l of every species i s the same i n both phases. Thus f o r the K  +  ion ( s u b s c r i p t k) i n a system containing for  example only KC1 (subcript c) we have:  H \c  kTln c  0 t +  H  fc  ^ e vli* = K,c k,c c +  o b  V  +  kTln c  b  V  f  5 +  Kc  ei|J  [3.3]  b Y  c  Where the s u p e r s c r i p t s t and b r e f e r to the upper and lower phases, c i s the ion concentration, f i s the ion a c t i v i t y .  - Ap° = kTln K  t  k  c  + kTln r  k  c  Rearranging:  + e Aty  b  Where K=c /c i s the p a r t i t i o n c o e f f i c i e n t , t  activity coefficients, for the K  0  -Au,  +  b  Ai|>= i|#- i p , and  T=f^/f^  Ap=  i s the r a t i o of  \£-  b  u. . S i m i l a r l y  i o n i n a system c o n t a i n i n g only IC^SO^ (subscript s ) :  = kTln K. K  KS  [3.4]  Q  + kTln r. i  b  K  »  + eAdj  [3.5]  b  b  Each phase i s e l e c t r i c a l l y n e u t r a l , hence for s i n g l e s a l t systems the p a r t i t i o n c o e f f i c i e n t of the potassium ion i s equal to that of the r e s p e c t i v e counterion, K  or K CjC  = K  = K , and K. CjC  C  KjS  = K  r e s p e c t i v e l y . Hence K. SjS  = K . Subtracting [3.4] and SjS  S  KyC  [3.5]  -103-  (eg. Davis and R i d e a l , 1961) g i v e s :  AI}J  S  -  AV)J  c  k j i n ( K / K ) + kTln ( r / r ) e e  =  c  +  (Au°  k>c  s  -  c  A^  ) S  [3.6]  s  )/e  Now the l a s t term on the r i g h t hand s i d e i s not measurable. However f o r two systems having very s i m i l a r upper and lower phase compositions, and hence very s i m i l a r t i e l i n e lengths i t can be assumed that:  K,s  -  K,c  [ 3  -  7 1  leaving only measurable q u a n t i t i e s .  B. P o t e n t i a l Difference i n Mixed S a l t Systems  The approach and n o t a t i o n used f o r s i n g l e s a l t systems can be generalized t o deal with systems containing two s a l t s with a common"ion. +  Consider a system containing a mixture of the two s a l t s K +C1~ and +  2  zK +S ~, ( s u b s c r i p t m), where z i s the net charge o f the second anion. An expression i s required r e l a t i n g the p o t e n t i a l i n the mixed system t o those i n the two s i n g l e s a l t systems, as a function o f i t s s a l t composition. For the two systems containing only KC1 and K S, [3.4] and [3.5] apply. 2  For the mixed system we have:  " V A  kTln  +  k T l n  r  M  +  [ 3  -  8 ]  -104-  •Aii° = kTln K + kTln r - eAiJJ cm c,m c,m m m  [3.9]  T  Ai? = kTln K + kTln r - zeAiiJ sjn s,m s,m m m  [3.10]  T  and f o r the anions i n the s i n g l e s a l t systems, the complementary  equations  to [3.4] and [3.5] are  .A£  = kTln K SS  - zeAib  + kTln r  i>, i>  o, s  [3.11] b  • Au° = kTln K „ + kTln r - eAtb c.c c,c c,c c n  r  Electroneutrality  K  c  z  k,m = ^ = Cs,m  +  c  m  c  zc k W )  s,m  gives:  zK  c  c,m = s,m s,m  Vf  n  Vr  +  c  [3.12]  Y  +  K  c  c,m c,m  V»  2C  c,m  [3.13]  V  c  s,m + c,m  The bulk concentration o f an i o n i can be w r i t t e n : i,m  c  c  (K  r  = i,m i,m v  +  ^  /  (  r  +  v  1 }  ^3.14]  3  where r sv^/v* i s the r a t i o o f upper t o lower phase volumes, and a parameter r , the r a t i o of bulk concentrations o f the two s a l t s i n an s  equal volume system can be defined as:  = cs,m = cs.m (Kc • m v .m^Cjm^^v c,m r  For r  [3.15]  1)  = 1, the appropriate value o f r  can be obtained using  -105-  [3.14-5]. Equation 3.13 can then be w r i t t e n :  K  z K  k,m =  K  s , n A s + c.m *s m K +l zrr£ 1 s,m 1 c,m 1 +1  n m  K  +  K  [3.16] •  +  Again i t i s assumed that the phase compositions o f the three systems are very s i m i l a r . Hence  V, k  =  c  k  = &,m  s  [3.17]  Vs.m  ^s,s= A  A  V,  £,c =  A  ^,m  ^3.19]  Now neglecting a c t i v i t y c o e f f i c i e n t s , and e l i m i n a t i n g 4 using [3.12] and A u ^ f r o m  kTln K - z e A ^ = kTln K s  Au. from [3.10] s,m  [3.9] using [3.11] gives  g  m  - ze A ^  [3.20]  m  kTln K - eAlk = kTln k - e A i | ) c t c,m m  [3.21]  B  o  Au.  can be eliminated from [3.08] using [3.05] (or [3.04]), to give:  kTln K  s  + eA^ = kTln s  + eA+  At t h i s point i t i s convenient  [3.22]  m  to introduce a dimensionless function of  the p o t e n t i a l , AV)J. with respect t o some reference p o t e n t i a l , Avp . Let Q  v  i = exp(e(A^  -b%)/kl)  [3.23]  -106-  Choosing A4<  0  as A ^  gives V = 1. This function serves two c  purposes. I t enables [3.20-22] t o be expressed i n product form, f a c i l i t a t i n g a l g e b r a i c manipulation. Also a l l p o t e n t i a l s appear as d i f f e r e n c e s , which are the only q u a n t i t i e s that can be measured (Section A above). Using [3.6] equations [3.20-22] become  s,m s =  /K  K  c,m c = m  /K  K  C3  <VV  K  V  V  K  '  C 3  V  K  C 3  k,m m = s s = c  '  -  2A]  2 5 ]  2 6 ]  These equations are e s s e n t i a l l y the same as those derived by Kortum (1965, pp 407-10) which a l s o r e l a t e the p a r t i t i o n c o e f f i c i e n t s and p o t e n t i a l d i f f e r e n c e s i n mixed s a l t systems. Equation [3.16] can a l s o be w r i t t e n as;  z r  ( K  K  s k , m - s m> f  Kcs,m + 1 m  +  (K  K  k,m ~ c,m  )  =°  3  '  2 7 ]  c,m+ 1 m  E l i m i n a t i n g the ion p a r t i t i o n c o e f f i c i e n t s of the mixed s a l t system using [3.2A-6] and rearranging gives:  zr A + B = 0 g  where  [3.28]  -107-  A = (l-(V /V ) m  Z + 1  s  Z  )/(l (V /V ) 'K /V ) +  m  s  c  [3.29]  s  B = (l-V^)/(l K V ) +  c  [3.30]  m  where [3.28] i s a polynomial i n V , the reauired Quantity. Now O ^ r ^ O O , which may be inconvenient to deal with, so r  g  may be  r e w r i t t e n i n terms of the mole f r a c t i o n , f , of the t o t a l s a l t , which v a r i e s between one and zero:  f  s  = c / ( c + c ) = r / ( r + 1) s,m s,m c,m s s m  [3.31]  m  In the l i m i t s o f f = 0 and 1 ( r = 0, 0 0 ), [3.28] gives the s i n g l e s a l t p o t e n t i a l s Ai|> =  and A ^  m  s  r e s p e c t i v e l y : I f f = 0 then g  then [3.28] gives B = 0. Using [3.30] t h i s i m p l i e s that V = 1, or that m  AS|J= A<K  I f f = 1, [3.30] gives A= 0, and [3.29] i m p l i e s that V  m  = V  s  or that Alp = Alp. m c Equation [3.28] can be generalized to systems containing a s i n g l e c a t i o n , and n anions, each with valence z^, and present at a mole r a t i o o f r ^ :  J  1  V i^VV' ^ (l+^/V.^O^/V.)  2  !)  [3  =o  1 =1  Where V-^ and r ^ = 1 by d e f i n i t i o n .  From [3.26] i t may be noted that  to solve [3.32] e i t h e r the p a r t i t i o n c o e f f i c i e n t or the p o t e n t i a l i s required from each s i n g l e s a l t system.  -  32]  -108-  S i m i l a r expressions to [3.32] can be obtained f o r systems with a common anion. The e f f e c t s o f n o n - i d e a l i t y can be incorporated by r e p l a c i n g the p a r t i t i o n c o e f f i c i e n t s i n [3.24-3.26] by the r a t i o o f a c t i v i t i e s . Some c h a r a c t e r i s t i c s o f [3.28] are i l l u s t r a t e d i n F i g . 3.1, f o r various values o f K /K g  f  c  and z. A l l the curves o f p o t e n t i a l pass through Ai|> and s  at  = 1,0 r e s p e c t i v e l y , f o r any parameter values. The curvature depends on  the r e l a t i v e s a l t p a r t i t i o n s and the valence o f the second anion. I f z=»l, or K >K , then the l i n e i s curved towards  (A,B,C). I f z«=l, or  K «= K , then the l i n e curves the other way, towards Au)  (E,F). The  l i n e i s only s t r a i g h t , i e . the p o t e n t i a l s are a d d i t i v e , for p a r t i c u l a r values o f the parameters, i n p a r t i c u l a r when both s a l t s have the same p a r t i t i o n c o e f f i c i e n t and anion valence (D). The more u n l i k e the anions are, i n e i t h e r p a r t i t i o n or valence, the more curved the p l o t s become.  C. P o l y e l e c t r o l y t e P a r t i t i o n  A further g e n e r a l i z a t i o n o f the treatment o f e l e c t r o s t a t i c e f f e c t s i n phase systems can be made f o r the case where a multivalent i o n , or a p o l y e l e c t r o l y t e such as a p r o t e i n , i s present with a s a l t . Previous treatments o f the e f f e c t o f s a l t on protein p a r t i t i o n were summarized i n the i n t r o d u c t i o n , Chapter One, s e c t i o n C . i i i . The l i m i t a t i o n s o f these treatments were discussed, and the approach o f deLigny and Gelsema (1982) mentioned. A general expression i s now derived, using the formalism o f  -109-  Figure 3.1 P o t e n t i a l and S a l t Composition. Theoretical Curves o f p o t e n t i a l as a function o f the mole f r a c t i o n o f one o f the s a l t s i n a mixed s a l t system, c a l c u l a t e d from Eqn.3.32- K s / K c = o.75, z=3 (A), K / K = l , z=3 (B), K /K =2, z=l (C), K / K = l , z=l and K /K =1.12, z=0.5 (D), K / K = l , z=0.5 ( E ) , K /K =0.3, z=l (F). A^ =2mV, =0 f o r a l l curves. s  s  s  c  c  s  s  c  c  s  c  s  c  -110-  s e c t i o n A, and r e l a t e d to t h e i r expression.  I t i s convenient t o s t a r t with  [1.16], v a l i d f o r any concentration r a t i o of s a l t t o (anionic) p r o t e i n :  In K  = -AfjJ/kT - In r  M  z^/kl  m +  [3.33]  An i d e n t i c a l equation can be w r i t t e n down (using primed symbols) f o r a system containing the p r o t e i n and another uni-univalent s a l t with with the same cation and pH:  In K = -Au*/kT - In r m  \ z eAi|j/kT  [3.34]  m  subtracting [3.33] and [3.34], and assuming that  In HL/K = (Au* - AU-'VkT - In r ' / r T  n  m  r  m  m  z m  =  z m  gives:  [3.35]  m m  + z e(Aij/-A4!>/kT m  An expression  f o r the d i f f e r e n c e i n p o t e n t i a l s between two systems with  a common cation (subscript +) has already been derived i n section A ( [ 3 . 6 ] ) , and can be s u b s t i t u t e d i n t o y i e l d :  in  (K /K ) M  M  = (Au; - Au )/kT - i n ( r > > m  +  v  l n (  K  +  /K;  [3.36]  m  }  +  v  l n  (r +  /;  }  r  + z (AH° - A!4 ')/kT m  +  Now i f the two systems have i d e n t i c a l phase compositions, i e . the two s a l t s have a n e g l i g i b l e e f f e c t on the phase separation, or the same e f f e c t ,  -Ill-  then the difference i n standard state chemical p o t e n t i a l s o f both the p r o t e i n and the c a t i o n w i l l be the same i n both phases. With these assumptions,  In  (K'/K  mm  [3.36]  becomes:  ) = - In ( r ' / r j + z . l n m m m m  (K  , ' ) +/K  [3.37]  +  + z . l n ( r ') m +/r +  A s i m i l a r expression can be obtained f o r systems with a common anion. I f the s a l t s i n the two systems do not have a common i o n , then the difference i n p o t e n t i a l s i n [ 3 . 3 5 ] can be expressed as  Ai|/  - Aip  =  ( Ail/ -  A<JJ")  -  (Aip  -  Ai|>")  [3.38]  it where  AIJJ  i s the p o t e n t i a l d i f f e r e n c e i n a system containing a common  c a t i o n with the f i r s t (unprimed) system, and a common anion (subscript -) with the second (primed) system, or v i c e versa. Two s u b s t i t u t i o n s of the form o f [ 3 . 6 ] can be made, and with the same assumption that the d i f f e r e n c e i n standard state chemical p o t e n t i a l f o r any species common to two systems i s equal, we obtain: In  (K /K) M  mm  = - In  (r / r )  mm  + z.ln  m  (K K /K K  +-+-  )  [3.39]  + z .In (r* r' / r r') m + - +-  I f the s a l t i s i n excess, then  K = K =K +  f o r a l l three systems, and i f  a l l the a c t i v i t y c o e f f i c i e n t s are neglected,  [3.39]  becomes  -112-  (K'/K  ln  m  m  )=  z ..In m  (K" /K.K)  [3.40]  2  which i s the expression of deLigny and Gelsema (1982). However i t must be noted that the assumption that the s a l t i s i n excess, and that the phase compositions are unaffected by the type of s a l t added, are u n l i k e l y t o be v a l i d simultaneously. coefficients  This, combined with the neglect of a c t i v i t y  may be s u f f i c i e n t t o account f o r t h e i r i n c o r r e c t p r e d i c t i o n of  protein partition coefficients  at the i s o e l e c t r i c p o i n t .  The treatment of s e c t i o n B also a p p l i e s t o a p o l y e l e c t r o l y t e , where the charge z on the i o n S i s l a r g e . Equations [3.24-26] correspond t o [3.36] i n the l i m i t i n g case where one o f the systems contains only the p r o t e i n and i t s counterion. This can be seen by e l i m i n a t i n g V /V m  [3.26].  K  s,m  g  from [3.24] using  Equation [3.24] then becomes  = K (K /K.  s  s  k,m  )  Z  C  3  which i s i d e n t i c a l t o [3.37] (neglecting a c t i v i t y c o e f f i c i e n t s ) since K = G  K  k s  = K  w n e r e  s s'  ^  n e  primed system i s equivalent t o the s a l t plus  protein system (subscript m) and the unprimed system contains only the p r o t e i n (subscript s)  '  4  1  ]  -113-  D. Ligand Binding and P a r t i c l e P a r t i t i o n  An expression for the e f f e c t of an a f f i n i t y l i g a n d on the surface free energy d i f f e r e n c e , A y , may  be obtained by i n t e g r a t i n g the Gibbs equation^":  [3.42]  where  r \ i s the surface excess of the i t h conponent, and 6\l^  change i n chemical p o t e n t i a l of the i t h component.  I t may  i s the  be noted that  the  change i n the chemical p o t e n t i a l of any component at a surface w i l l equal the change i n chemical p o t e n t i a l of that component i n the s o l u t i o n , since at e q u i l i b r i u m the chemical p o t e n t i a l i s the same everywhere.  Equation [3.42]  applies i n both the upper and lower phases, so that the change i n Ay  may  be  w r i t t e n as:  dAy  =  £T  b  dn  b  -  £  d|i*  [3.43]  where the superscripts t and b r e f e r to the upper and lower phases respectively.  To f i n d the t o t a l change i n A y  on adding a ligand to the  phase system, [3.43] must be integrated from zero to the required concentration.  ligand  This equation can be s i m p l i f i e d by a number of  approximations: f i r s t l y , that the ligand on binding to the surface does not s i g n i f i c a n t l y a l t e r the p a r t i c l e area, and hence also does not a l t e r the  •'•The author would l i k e to thank Dr. C.P.5. Taylor f o r suggesting t h i s approach.  -114-  surface concentration of any f i x e d surface components.  Secondly, that the  only component that makes a s i g n i f i c a n t c o n t r i b u t i o n to the i n t e g r a l of [3.43] i s the l i g a n d .  This w i l l be a good approximation  f o r low  concentrations of l i g a n d , since the change i n the chemical p o t e n t i a l s of the other components i n s o l u t i o n w i l l be small.  Also at low surface coverage by  the l i g a n d , the surface excesses of the other components w i l l not change much with l i g a n d concentration. Thus under these conditions the T^.d u.^ terms to the i n t e g r a l w i l l be small  c o n t r i b u t i o n s of the other  compared to that of the l i g a n d . With these approximations,  [3.43] may  be  wri tten as:  dAv  =  T  b  du 1 1  b  -  ^ d ^ I I  [3.44]  where the s u b s c r i p t 1 r e f e r s to the l i g a n d . The chemical p o t e n t i a l of the l i g a n d i n the upper phase i s  ^  =  u  011  + kT In c  1  [3.45]  the d i f f e r e n t i a l of t h i s i s  d \i = kT dcVc* l  [3.46]  The surface excess of the l i g a n d i n the upper phase i s the amount of l i g a n d bound per u n i t area.  This i s some function of the s o l u t i o n chemical  p o t e n t i a l of the l i g a n d i n the upper phase, termed the binding isotherm. The simplest isotherm, the Langmuir isotherm, assumes that there are  -115-  n i d e a l l i g a n d binding s i t e s per u n i t area.  The term i d e a l r e f e r s to the  f a c t that the binding s i t e s are independent (no cooperative e f f e c t s ) and i d e n t i c a l (the same binding energy per molecule).  This i s equivalent to  the statement that the equation of s t a t e f o r the bound l i g a n d obeys a two dimensional form o f the gas law  TT = n V r  where n  1  [3.47]  i s the number of ligands bound per u n i t area, and TT i s the  spreading pressure, equal to the decrease i n the surface  tension.  The  Langmuir isotherm i n the upper phase can be w r i t t e n  n  fc  where  = n cVlk  1  + c-)  [3.48]  i s the d i s s o c i a t i o n constant f o r the binding.  The i n t e g r a l of  the second term i n [3.44] i s  nkT.dgt <t + c t )  [3.49]  Performing the i n t e g r a t i o n gives  yf _ y I  t =  n k T  l n  [3.501  ( t t > Ic*  0  Evaluating the l i m i t s ,  k  +  c  0  -116-  -  Y  [3.51]  1  = nkT.ln (k* + c ) /  fc  Integrating the corresponding equation f o r the lower phase gives  Y  b  t  -  Y  b  b  = nkT.ln ( k + c ) / k  b  [3.52]  b  o  Subtracting [3.51] from [3.52] gives  AYi -  AY  0  =  n  k  T  l  n  fk  j? +  fo-k*  (kt +  [3.53]  c ).kP l  From the form of the Langmuir isotherm,  (k  b  b  b  + c ) = n.c /n  [3.54]  b  S u b s t i t u t i n g t h i s and the corresponding expression f o r the upper phase i n t o [ 3 . 5 3 ] , and noting that c V c  b  = K-^, the l i g a n d p a r t i t i o n c o e f f i c i e n t ,  we obtain:  AY  2  -  A Y = nkT In n L k t rPj<P. Ki  Since AG° = -kT.ln K , and A G ±  AY  X  -AY  0  = n(  [3.55]  0  AG  o t  -  AG  o b  +  0 1  = kT.ln k , [3.55] can be w r i t t e n 1  AG° + kT.ln nVn ) b  [3.56]  which i s i d e n t i c a l t o the free energy of t r a n s f e r of a s o l u t e of u n i t area between the phases, [ 1 . 3 9 ] , Chapter One.  -117-  Several l i m i t i n g cases o f [3.56] are o f i n t e r e s t , and there are p a r a l l e l s with the case o f i n t e r a c t i n g s o l u t e s i n phase systems, discussed by Albertsson  (1983).  °t a) A c o v a l e n t l y bound l i g a n d . Let AG ,  «b t b AG-*oo , thus n = n.= n  giving  AV  -  X  AY  Q  = n AG°  [3.57]  b) A l i g a n d that i s completely hidden from the phase system on binding. From F i g . 3.2, using the f a c t that the free energy i s a s t a t e f u n c t i o n , A G ^ - A G ^ - A G ^ = A G * , the free energy o f t r a n f e r r i n g the bound b  o l i g a n d between the phases, while bound. I f the l i g a n d i s hidden A G ^ = 0 *b  <t  and thus AG  -  AG  o = AG^. Also from the form o f the Langmuir  isotherm, [3.48], n^= n must hold, since c V c b  3  =  = k^/k^.  This y i e l d s AY  - AY  1  Q  = 0  [3.58]  which i s expected i n t u i t i v e l y .  o o °t *b c) A completely exposed l i g a n d . A G = AG^ and thus AG = AG , lb  giving  AY  2  . AY  Q  s  n (  A G^  +  kT.ln n t b ) / n  [ 3  .  5 9 ]  -118-  Top phase  Bottom phase  1 ^ AG  T  I  1  AG  B  Figure 3.2 Theory of P a r t i c l e A f f i n i t y Ligand P a r t i t i o n : E f f e c t of complex surface on the e f f e c t of a l i g a n d on the p a r t i c l e surface free energy d i f f e r e n c e . A l l symbols are defined i n the t e x t .  119-  In p r a c t i c e the l i g a n d could never be completely exposed to the phase system, since at l e a s t some small p o r t i o n must be involved i n the binding i n t e r a c t i o n , such as the palmitate t a i l o f the PEG-ester.  Eauation [3.59] gives the dependence o f the surface free energy d i f f e r e n c e on l i g a n d concentration i m p l i c i t l y . Using the equations f o r the b  Langmuir isotherms ([3.48]) t o eliminate n*" and n , and expressing everything i n terms o f c AY - A Y = n( A G X  o t  0  -  b  gives  AG  0 D  +  b  A G i + kT.ln ( k + c^) (r + c )  [3.60]  D  k  where r ^ k v K } . Some c h a r a c t e r i s t i c s o f [3.60] are i l l u s t r a t e d i n F i g . 3.3 for various b  values o f n, k \ k , and K^. A l l the curves have the same general form: the surface free energy d i f f e r e n c e increases i n a sigmoidal fashion with l i g a n d concentration, and f i n a l l y the curve reaches a plateau at a value determined by ( k V k K ^ ) b  n  when the binding i n both phases  saturates. This i s s i m i l a r t o a cooperative binding curve (Mustacic and Weber, 1978).  Considering F i g . 3.3a, i f the r a t i o k V l ^ K ^ 1, which  i s equivalent to the case where the ligand i s completely hidden, the curve i s f l a t , with no free energy increase (A). As K i s increased, the curves 1  t  b  r i s e more steeply and reach a greater maximum (B,D). For k /k constant, the curve r i s e s more steeply as k V k  b  increases (B,C and D,E).  For a constant r a t i o o f k^/k K^, the curves r i s e more steeply as the b  d i s s o c i a t i o n constants are decreased (D,F). Referring to F i g . 3.3b, decreasing n decreases the e f f e c t o f the l i g a n d , but does not a l t e r the concentration dependence (A,C,E). The e f f e c t of changing with n (A,B and E,F).  also decreases  -120a  9 8 7 6 5 4 u 3 \ CO 2 CD CH 1 LU •>—' 0 ...-L. -1 00 0.1 _  •  A 1 _l l i i i n  -1  l l i in  L_  —1  1 1 1 I.I.XJ-I  10  i  i  100  i i  11II  1000  1 10 100 LIGAND CONCENTRATION ( M)  1000  P  Figure 3.3 P a r t i c l e A f f i n i t y Ligand P a r t i t i o n , a) E f f e c t o f l i g a n d binding strength and p a r t i t i o n c o e f f i c i e n t . k t / k = i , Kj=l (A), k V k = i Ki=1.02 (B), kVk =1.5, K 1.53 (C), k t , k = 3, K 1.03 (D), k*= 3, k =2, K 1.545 ( E ) , kt= 1, k = 0.33, K 3.09 ( F ) . n = 7 xlO molecules/cm f o r a l l curves, b) E f f e c t o f number o f binding s i t e s and phase volume r a t i o . kfyk =3 f o r a l l curves, n = 7 x i o l l molecules/cm , (A,B), n = 3.5 x l O , (C,D), n = 7 x l O * (E,F). K]=3.06 (A,C,E), Kl=3.09 (B,D,F). b  b  b  b  1=  1=  b  b  1=  1 2  1=  2  b  2  1 2  2  f  -121Chapter Four. E l e c t r o s t a t i c E f f e c t s and the C e l l Surface Free Energy Difference  Seek s i m p l i c i t y and d i s t r u s t i t - A l f r e d North Whitehead  A. Introduction  The importance of e l e c t r o s t a t i c e f f e c t s i n c e l l p a r t i t i o n i s i l l u s t r a t e d by the fact that c e l l surface charge has been widely discussed i n the l i t e r a t u r e as a major determinant o f p a r t i t i o n (Albertsson, 1971; Walter, 1977; F i s h e r , 1981).  In a d d i t i o n b i o l o g i c a l l y s p e c i f i c c e l l separations  have been a t t r i b u t e d to d i f f e r e n c e s i n c e l l surface charge density (eg. Walter et a l . , 1980).  The e f f e c t s of charge on the p a r t i t i o n have been  assumed to r e s u l t from the p o t e n t i a l d i f f e r e n c e between the phases. Another reason f o r studying such e l e c t r o s t a t i c e f f e c t s i s that they are experimentally a c c e s s i b l e by standard electrochemical techniques. A number of problems are examined i n t h i s chapter. The f i r s t i s whether i t i s p o s s i b l e to manipulate the p o t e n t i a l independently of other phase system properties.  Prompted by the t h e o r e t i c a l treatment of Chapter Three, another  question considered i s under what conditions can such p o t e n t i a l s be measured, and do such measurements agree with the theory? This forms the necessary background f o r a study of the e f f e c t of p o t e n t i a l on the c e l l surface free energy d i f f e r e n c e , and c e l l p a r t i t i o n .  The e f f e c t on the  former i s of p a r t i c u l a r i n t e r e s t since t h i s quantity can be measured at thermodynamic e q u i l i b r i u m v i a contact angle measurements.  -122B. E f f e c t s of Buffer Composition on Phase System P r o p e r t i e s  i ) E f f e c t of Phosphate on the B i n o d i a l  In phase systems that do not contain charged polymers, the p o t e n t i a l i s c o n t r o l l e d by the buffer composition,  often by a l t e r i n g the r a t i o of  phosphate to c h l o r i d e . The b u f f e r s used i n t h i s study contained sodium c h l o r i d e and sodium phosphate b u f f e r , pH 7.16.  sorbitol,  The b i n o d i a l l i n e of  phase systems containing a phosphate r i c h buffer 110,0,0 (also known i n the l i t e r a t u r e as charge s e n s i t i v e systems), and a c h l o r i d e r i c h buffer 10,130,0 (charge i n s e n s i t i v e ) were determined by polarimetry and refractometry.  The  lower sections of the two b i n o d i a l s are shown i n F i g . 4.1. Except at high polymer concentrations the three points representing the compositions of each phase and the bulk composition of each system are c o l i n e a r w i t h i n the e r r o r of the measurements, i n d i c a t i n g that the assumption of equal s a l t p a r t i t i o n between the phases leads to l i t t l e e r r o r i n these Increasing the phosphate/chloride  determinations.  concentration r a t i o increases the degree  of phase separation, lengthening the t i e l i n e s of the phase systems, and s h i f t i n g the b i n o d i a l towards lower concentrations. Thus systems j u s t below the b i n o d i a l that w i l l not phase separate with sodium c h l o r i d e r i c h buffer w i l l form two phases with 110 mM phosphate. The e f f e c t of phosphate on the composition decreases i n systems f u r t h e r from the p l a i t p o i n t , since the  two  b i n o d i a l s converge at higher concentrations. A l t e r i n g the sodium c h l o r i d e / s o r b i t o l r a t i o has l i t t l e e f f e c t on the phase composition (data not shown).  -123-  0  L  1  0  2  '  4  J  6 % DEXTRAN  '  8  1  10  Figure 4.1 E f f e c t of S a l t s on the Phase Diagram. Lower parts of the b i n o d i a l s are drawn together to show the e f f e c t of i n c r e a s i n g the phosphate concentration from 10mM ( s o l i d l i n e ) to llOmMM (dotted l i n e ) while decreasing the c h l o r i d e concentration from 130 to 0 mM.  -124i i ) E f f e c t of Buffer on I n t e r f a c i a l Tension  The e f f e c t s on the i n t e r f a c i a l tension of a l t e r i n g the r a t i o of c h l o r i d e to phosphate, the phosphate concentration and polymer concentration are summarized i n Table 4.1. The tensions were measured by the r o t a t i n g drop method, and the t i e l i n e lengths were obtained from the polymer  compositions  of each phase as determined by polarimetry and refractometry. In a system containing 10 mM phosphate the concentrations of sodium c h l o r i d e and s o r b i t o l have l i t t l e e f f e c t on the tension, the l a r g e s t change being about 10% when 130 mM sodium c h l o r i d e i s replaced by 100 mM s o r b i t o l .  Halving the  t o n i c i t y of a (5,4) system by changing the buffer from 10,130,0 to 5,60,0, which i s necessary  f o r the contact angle measurements, has l i t t l e e f f e c t on  the tension. Increasing the phosphate concentration from 10 to 110 mM at constant polymer concentration has a large e f f e c t on the tension, i n c r e a s i n g i t by 30 to 50%, the e f f e c t being greater f o r systems c l o s e r to the c r i t i c a l point. The tension, Y ^ > was found to have a power law dependence on the t i e l i n e length, t , , expressed  by  [4.1]  where the values of a and b are given i n Table 4.1 f o r the b u f f e r compositions 110,0,0 and 10,0,100.  -125-  TABLE 4.1 EFFECT OF PHASE COMPOSITION ON INTERFACIAL TENSION  System  Tie Line Length (%)  (5,4)10,130,0 (5,4)5,60,0 (5,4)10,16,68 (5,4)10,0,100 (6,4)10,0,100 (7,4.4)10,0,100 (5,4)110,0,0 (6,4)110,0,0 (7,4.4)110,0,0  11.85+0.2 12.3 12.0 12.2 14.0 16.8 12.7 14.3 17.0+0.4  TensionxHp erg/cm 2  5.73+0.2 6.37 6.45 6.31 10.3 21.3 9.11 13.9 26.8+0.5  The tension as a function of t i e l i n e length was f i t t e d to the equation_ln Y = a + b . l n tj_ where a was -7.3+0.8, -7.22+0.2 , b was 3.67+0.3, 3.71+01, and r = 0.997, 0.998 for tf7e b u f f e r s 10,0,100 and 110,0,0 r e s p e c t i v e l y tb  i i i ) Discussion  The e f f e c t s of phosphate on the b i n o d i a l ( F i g . 4.1) are s i m i l a r to those found f o r dextran T40/PEG 8000 systems (Bamberger et a l . , 1984a). In the published study the e f f e c t s were shown to be due to the unequal p a r t i t i o n o f phosphate between the phases. The phosphate p a r t i t i o n e d more i n t o the dextran r i c h phase, t h i s tendency i n c r e a s i n g with the t i e l i n e length. Unequal p a r t i t i o n o f a s a l t can be due e i t h e r to e x c l u s i o n o f the s a l t by one o f the polymers, an a s s o c i a t i o n with the other polymer, or a combination of both. In a d d i t i o n both polymers may exclude or associate with both the co- and counter-ions, but to d i f f e r e n t extents, g i v i n g the same r e s u l t .  For  -126the case of phosphate, Bamberger et a l . showed by e q u i l i b r i u m d i a l y s i s that the e f f e c t was due almost e n t i r e l y to phosphate exclusion by the PEG, phosphate p a r t i t i o n depending only on the d i f f e r e n c e i n PEG  the  concentrations,  i r r e s p e c t i v e of i t s molecular weight or the presence of the dextran. In fact at high enough s a l t concentrations, two phase systems can be formed with  PEG  and sodium phosphate alone (Albertsson, 1971). Such a mechanism i s undoubtedly responsible f o r the e f f e c t s i n Dx 500/PEG 8000 systems as w e l l .  Sodium c h l o r i d e was found to p a r t i t i o n evenly between the phases, being s l i g h t l y excluded by both polymers. S o r b i t o l a l s o p a r t i t i o n s evenly i n Dx 500/PEG 8000 systems (Brooks et a l . , 1984), which explains the small e f f e c t of these solutes on the phase compositions.  In systems c l o s e r to the  c r i t i c a l point the s a l t s have more e f f e c t on the t i e l i n e length.  This i s  because the t i e l i n e s meet the b i n o d i a l at a smaller angle i n t h i s region of the phase diagram, thus small s h i f t s i n the p o s i t i o n of the b i n o d i a l r e s u l t i n l a r g e r changes i n the t i e l i n e length.  In a d d i t i o n the s a l t forms a  l a r g e r f r a c t i o n of the t o t a l solute close to the c r i t i c a l point.  A consequence of these salt-induced t i e l i n e length changes i s that other properties of the phase system may be s i g n i f i c a n t l y a l t e r e d , a f f e c t i n g p a r t i t i o n and other measurements.  Important e f f e c t s are l i k e l y to be due to  changes i n tension, since t h i s depends roughly on the fourth power of the t i e l i n e length.  However the above r e s u l t s i n d i c a t e that provided  the  concentrations of phosphate, s o r b i t o l and c h l o r i d e do not exceed 10,  100,  and 130 mM r e s p e c t i v e l y , the phase compositions and tension are e f f e c t i v e l y independent of the buffer composition.  This allowed for s u f f i c i e n t  -127v a r i a t i o n i n the p o t e n t i a l , i o n i c strength and t o n i c i t y for t h i s work. These upper l i m i t s apply to (5,A) systems, and could be r a i s e d or lowered for systems f a r t h e r from,or c l o s e r to,the c r i t i c a l p o i n t .  Since i n most systems used by other workers f o r c e l l separation work the s a l t i s always a small f r a c t i o n of the t o t a l polymer weight, composition changes have often been overlooked. In p a r t i c u l a r the phosphate concentration (and the c h l o r i d e concentration) i s u s u a l l y a l t e r e d to change the p o t e n t i a l , which changes the phase compositions as w e l l , and while t h i s i s not important f o r q u a l i t a t i v e separation work, i t can i n v a l i d a t e the i n t e r p r e t a t i o n of more q u a n t i t a t i v e s t u d i e s , such as those of Reithermen et a l . (1973), and Zaslavsky et a l . (1982).  C. P o t e n t i a l and S a l t P a r t i t i o n  i ) S a l t Bridge E f f e c t s  In Chapter Three i t was pointed out that no work could be obtained from a phase system at e q u i l i b r i u m , and that the measured p o t e n t i a l must r e s u l t from the d i f f e r e n c e i n p o t e n t i a l s at the e l e c t r o d e / s a l t bridge phase j u n c t i o n s . To give meaningful information about the phase system, the measured p o t e n t i a l s should not depend on the nature of the e l e c t r o d e / s a l t bridge.  To i n v e s t i g a t e t h i s the KC1 s a l t concentration i n the s a l t bridges  was changed by a factor of four. This has l i t t l e e f f e c t on the measured p o t e n t i a l ( f i r s t three l i n e s of Table 4.2). However the s a l t bridges used by other workers for such measurements (eg. Reitherman et a l . , 1973;  and  -128Zaslavsky et a l . 1982) commonly contain 2% agar t o reduce leakage o f KC1. Comparison of the p o t e n t i a l s obtained i n potassium sulphate containing systems using s a l t bridges with and without 2% agar g e l show that as the s a l t concentration o f the phase system i s increased, the p o t e n t i a l s measured with the agar bridges drop by 1.3mV, and are 0.6 t o 1.8mV l e s s than the p o t e n t i a l s obtained using bridges without agar. Measurements obtained using bridges without agar did not change with sulphate concentration. With sodium phosphate containing systems, the p o t e n t i a l s with agar were 0.3 to 0.6 mV lower than without agar.  TABLE A.2 EFFECT OF SALT CONCENTRATION AND ELECTRODE BRIDGE TYPE ON POTENTIAL System  (7,A.4) it II  (5,4) II  ti II II  (5,4) (5,4) a  Salt  S a l t bridge concentration (M)  110,0,0 II II  1 mM K 10 mM 100 mM 200 mM 300 mM 110,0,0 96,50,0  2  S0 " " " "  nd: not determined.  4  0.5 1.0 2.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0  P o t e n t i a l (mV) bridge type: microcapillary  agar a  nd nd nd 1.79+0.1 1.11+0.06 0.55+0.05 0.51+0.05 0.50+0.05 2.40+0.16 1.67+0.1  2.5A+0.0A 2.A3+0.0A 2.57+0.07 2.35+0.1 2.32+0.2 2.26+0.05 2.19+0.06 2.30+0.03 1.80+0.1 1.35+0.1  -129i i ) S i n g l e S a l t Systems  In Chapter 3A i t was suggested that the d i f f e r e n c e i n p o t e n t i a l s between two systems,  AI^-AIJJ.,  could be measured under conditions where the common  ion standard state chemical p o t e n t i a l terms, Au,  f  were the same f o r both  systems. Therefore a t e s t was made o f the expression r e l a t i n g the d i f f e r e n c e i n p o t e n t i a l s t o the s a l t p a r t i t i o n s f o r two systems containing a common i o n , [3.6].  Ai|> _ Ai}> = k j l n ( K / K ) + kTln ( r / r ) e e s  c  c  +  (Au°  k>c  s  c  s  [3.6]  - Au° )/e k>s  The d i f f e r e n c e i n the standard s t a t e chemical p o t e n t i a l terms for the two systems i s not d i r e c t l y measurable. However by d e f i n i t i o n the standard s t a t e chemical p o t e n t i a l depends only on the polymer and water composition o f each phase a t constant temperature and pressure. Therefore t h i s term would vanish i f the two systems had i d e n t i c a l phase compositions. This s i t u a t i o n was approximated experimentally by comparing systems with the same t i e l i n e length. In c o l l a b o r a t i o n with Stephan Bamberger o f the Oregon Health Sciences Center, P o r t l a n d , a t e s t o f t h i s equation was made. The p o t e n t i a l s , s a l t p a r t i t i o n c o e f f i c i e n t s and phase compositions were measured i n systems containing e i t h e r potassium c h l o r i d e or potassium sulphate. Although these s a l t s are not generally used f o r c e l l b u f f e r s , they were chosen f o r t h e i r good s o l u b i l i t y , and to avoid complications due t o b u f f e r e q u i l i b r i u m . The potassium i o n a c t i v i t y c o e f f i c i e n t s , f, i n each phase were c a l c u l a t e d from the Debye Huckel expression (Robinson and Stokes, 1959):  -130-  A/  L/  £  log f = -AI V(l+BaI- ' )  where A=0.5115 (1/mole)  [4.2]  , B=0.3291 r ' V ( m o l e A), I i s the i o n i c  strength, c a l c u l a t e d from the s a l t concentration i n the phase. The parameter a, the e f f e c t i v e hydrated i o n diameter, was chosen so as to give the best f i t o f [4.1] to the measured a c t i v i t y c o e f f i c i e n t s i n Robinson and Stokes, o  r e s u l t i n g i n a = 3.11 and 4.25 A f o r the sulphate and c h l o r i d e systems respectively.  The data are summarized i n Tables 4.3 and 4.4, and the  predicted and measured p o t e n t i a l s f o r the sulphate systems p l o t t e d against the t i e l i n e length i n F i g . 4.2. TABLE 4.3 SALT PARTITION AND POTENTIAL IN SINGLE SALT SYSTEMS. I . POTASSIUM CHLORIDE CONTAINING SYSTEMS 3  Salt Cone. (mM) 1 3 10 30 100 200 300 400 a  Partition Tie Line Length (%) C o e f f i c i e n t  b  nd nd 10.5+0.1 10.45 10.25 10.0 10.1 9.95  0.952+0.01 nd 0.973 0.956 0.964 0.950 0.961 0.955  A c t i v i t y Coeffi c i e n t Ratio nd nd 1.001 1.002 1.004 1.006 1.006 1.007  Measured P o t e n t i a l (mV)  0.51+0.1 0.20 0.11 nd 0.08 0.07 0.05 nd  A l l systems contained potassium c h l o r i d e and had a bulk polymer composition o f (5,4). Tie l i n e lengths and p a r t i t i o n c o e f f i c i e n t s were measured by Dr. Stephan Bamberger. Errors quoted f o r these systems were t y p i c a l f o r a l l data i n Tables 4.3-4.5. n d : not determined D  -131-  TABLE A. A SALT PARTITION AND POTENTIAL IN SINGLE SALT SYSTEMS. I I . THE EFFECT OF SULPHATE 3  Partition Activity Tie Line Salt Ratio Cone. (mM) Length (%) C o e f f i c i e n t  1 3 10 30 100 200 300 AOO  nd nd nd 10. A 11.1 11.25 11.5 12.0  0.888 0.883 0.880 0.879 0.8A1 0.815 0.790 0.760  Coefficient  1.003 1.007 1.010 1.015 1.025 1.031 1.037 1.0A5  0  Potential (mV) Measured Calculated  2.27 2.25 2.25 2.25 2.30 2.39 2.52 2.92  2.39 2.15 2.A8 1.95 3.05 3.36 A.30 5.03  a  Systems contained potassium sulphate and had a bulk polymer composition of (5,A). Tie l i n e lengths and s a l t p a r t i t i o n s were measured by Dr. Stephan Bamberger. D  C a l c u l a t e d p o t e n t i a l s i n Tables A.A-A.5 were obtained using [3.6] and the potassium c h l o r i d e system with the most s i m i l a r t i e l i n e length from Table A.3  -132-  TABLE 4.5 SALT PARTITION AND POTENTIAL IN SINGLE SALT SYSTEMS. I I I . THE EFFECT OF TIE LINE LENGTH 3  System Composition  (5,4)30 (4.85,3.88)100 (4.63,3.7)200 (4.27,3.42)300 (4.44,3.52)400  Tie Line Length (%)  10.7 10.5 10.0 9.25 9.85  Partition Coefficient  0.870 0.856 0.881 0.910 0.880  P o t e n t i a l (mV) A c t i v i t y Coeff. Measured Calculated Ratio  1.015 1.029 1.020 1.014 1.020  2.17 1.82 1.42 1.14 1.47  2.21+0.3 2.29 1.79 1.08 1.80  a  Systems i n t h i s t a b l e were obtained from those i n Table 4.4 above by d i l u t i n g with the appropriate concentration of potassium sulphate to give systems with s i m i l a r t i e l i n e lengths to those i n Table 4.3.  The c h l o r i d e concentration has l i t t l e e f f e c t on the t i e l i n e length, s a l t p a r t i t i o n c o e f f i c i e n t or the p o t e n t i a l (Table 4.4). However as the sulphate concentration i s increased, the t i e l i n e length and the p o t e n t i a l both increase, while the s a l t p a r t i t i o n c o e f f i c i e n t becomes more unequal (Table 4.5). The increase i n t i e l i n e length due to the sulphate probably occurs by the same mechanism as f o r phosphate i n s e c t i o n B, i e . exclusion of sulphate by PEG,  since PEG/I^SO^ mixtures can a l s o form two phase systems  (Albertsson, 1971). The data i n Table 4.5 were obtained by d i l u t i n g the systems of Table 4.4 with potassium sulphate s o l u t i o n s , so as to keep the s a l t concentrations the same, while decreasing the polymer concentrations. The phase compositions were thereby kept c l o s e to those of the c h l o r i d e systems, thus s a t i s f y i n g the assumptions used i n d e r i v i n g [3.6]. As long as the t i e l i n e length of the sulphate systems are s i m i l a r  MOLE FRACTION OF PHOSPHATE Figure A.2 Comparison of T h e o r e t i c a l and Experimental P o t e n t i a l s , a) S i n g l e s a l t systems containing 0.001 to O.AM potassium sulphate (Tables A.3-5). E f f e c t of t i e l i n e changes on measured (o) and predicted (*) p o t e n t i a l s from [3.6]. b) Mixed s a l t systems, composition (5,A), containing sodium phosphate b u f f e r and sodium c h l o r i d e . Measured (o). Predicted (*), using [3.28] with z=1.735, K =0.938, AiV =2.65mV,A4i =0.0AmV. Data from Reitherman et a l . , 1973 ( 0 ) , B a l l a r d et a l . , 1979 (+). c  s  c  -134to those i n the c h l o r i d e systems, there i s good agreement between the predicted and measured p o t e n t i a l s a t a l l sulphate concentrations.  i i i ) Phosphate Concentration E f f e c t s  The r e s u l t s of s e c t i o n i i i n d i c a t e that the s a l t concentration can a f f e c t the p o t e n t i a l v i a phase composition a l t e r a t i o n s , but that there i s no i n t r i n s i c dependence on concentration up t o 400 mM. The e f f e c t on the p o t e n t i a l o f a l t e r i n g the phosphate b u f f e r concentration i s shown i n Table 4.6 f o r a system c l o s e t o the c r i t i c a l point (5,3.8), which i s expected t o be s e n s i t i v e t o changes i n s a l t concentration, and f o r two systems f u r t h e r away, (5,4) and (7,4.4). In each case the p o t e n t i a l i s approximately constant, with perhaps a small decrease of 0.2 t o 0.3 mV below 20 mM.  TABLE 4.6 EFFECT OF PHOSPHATE CONCENTRATION ON POTENTIAL System  (5,3.8) II  it (5,4) ti ti II  (7,4.4) II  it ti  a  Phosphate Concentration (mM)  10 40 110 5 10 30 110 10 20 30 110  3  Potential (mV)  1.84+0 2.06 1.99 2.42 2.65 2.72 2.60 2.97 3.34 3.30 3.35  system b u f f e r s contained only phosphate b u f f e r , pH 7.16  -135iv) Mixed S a l t Systems  Phase systems used f o r work with c e l l s generally require a pH around 7, and so contain a buffer ( t y p i c a l l y phosphate), and often contain a d d i t i o n a l s a l t s . I t i s therefore of p r a c t i c a l use t o extend the theory of p o t e n t i a l s to deal with such mixed s a l t systems, p a r t i c u l a r l y t o a i d the i n t e r p r e t a t i o n of the experiments i n s e c t i o n D below.  In t h i s work the p o t e n t i a l i s  c o n t r o l l e d by the concentration r a t i o of phosphate t o c h l o r i d e . The common ion H  i n t h i s case i s sodium, and the anions present are c h l o r i d e , HPO^ and  2 "V P I  T b e  a  r  r  a  e  PP °P i- t equation to t e s t would therefore be [3.32] with n  = 3. The i n i t i a l bulk concentration r a t i o o f mono and d i v a l e n t phosphate i s 2.8, which gives a pH of 7.16. However the a n a l y s i s i s complicated by the fact that the concentration of these two ions i n each phase i s not f i x e d , but depends on the pH, which i s not quite the same i n each phase since the hydrogen ion p a r t i t i o n c o e f f i c i e n t i s not one (or a l t e r n a t i v e l y the two phosphate ions have d i f f e r e n t p a r t i t i o n c o e f f i c i e n t s , see Johansson, 1970b). Moreover the hydrogen i o n p a r t i t i o n c o e f f i c i e n t w i l l vary with the p o t e n t i a l (as given by, f o r example, [3.26]). In other words  and r ^ ,  although  not independent, cannot be obtained d i r e c t l y from the i n i t i a l phosphate i o n r a t i o i n the buffer stock used to make up the systems, but they vary with p o t e n t i a l i n some manner, subject t o the c o n d i t i o n that the t o t a l phosphate concentration i s f i x e d .  This amounts to the f a c t that the s a l t  composition  of the phase system depends on the p o t e n t i a l .  Fortunately, i n dealing with t h i s problem, some s i m p l i f y i n g approximations  can be made, without knowing the p r e c i s e manner i n which r  ?  -136and r ^ vary.  These can be j u s t i f i e d by showing that f o r the conditions  used i n t h i s work the p o t e n t i a l i s f a i r l y i n s e n s i t i v e t o the change i n the ratio r / r 2  3  that could occur i n these systems.  F i r s t l y i t may be noted that at pH 7.16, the concentrations of hydrogen, hydroxide, t r i b a s i c phosphate ions and phosphoric acid are very s m a l l . Except f o r t h e i r e f f e c t on the e q u i l i b r i u m between mono- and d i - b a s i c phosphate i o n s , t h e i r c o n t r i b u t i o n t o the p o t e n t i a l w i l l therefore be small.  Only the mono- and d i - b a s i c phosphate ions need t o be considered.  Secondly i t i s assumed that the e f f e c t s o f phosphate on the p o t e n t i a l i n these systems can be described by the behaviour of a h y p o t h e t i c a l 'average phosphate i o n ' , whose charge and p a r t i t i o n c o e f f i c i e n t are intermediate between those of HPO^ and H P0^, and whose concentration i s equal t o 2  the t o t a l phosphate concentration.  This i s achieved by using equation  [3.28] with an i o n of non i n t e g r a l charge.  I n i t i a l l y , z = 1.74 was chosen,  since t h i s i s the average charge on the phosphate i o n i n a 2.8:1 mixture o f d i b a s i c and monobasic phosphate.  To c a l c u l a t e V , the p o t e n t i a l i n a g  system with 10,0,100 b u f f e r , pH 7.16, (2.65 mV) was used, which o f course i s already an 'average' determined by both ions.  The p o t e n t i a l and s a l t  p a r t i t i o n c o e f f i c i e n t i n a pure c h l o r i d e system are 0.04 mV, and 0.938. Using these data the predicted p o t e n t i a l s were c a l c u l a t e d using [3.28], where r  g  was the r a t i o o f t o t a l phosphate t o c h l o r i d e ions.  F i n a l l y , the maximum probable e r r o r a r i s i n g from not considering the two phosphate ions e x p l i c i t l y was estimated. The p o t e n t i a l s i n system  -137containing 10 mM of e i t h e r the mono or d i basic phosphate (pH 4.5 and 9 r e s p e c t i v e l y ) were measured as 1.5 and 2.9 mV. [3.32] for a three s a l t system.  These data were put i n t o  The r a t i o of the two phosphate ion  concentrations was then changed from 1.5 to 4, which i s equivalent to a pH change of 0.4.  The predicted p o t e n t i a l changed by about 0.2 mV.  c a l c u l a t e d for a phosphate/chloride l a r g e s t (based on Figure 3.1).  This  was  r a t i o of one, where the e f f e c t s would be  This i n d i c a t e s that the e r r o r introduced  by  averaging the e f f e c t s of the two phosphate ions i s c e r t a i n l y not much l a r g e r than the p r e c i s i o n of the measurements. Since [3.28] and [3.32] a l s o neglect the e f f e c t s of a c t i v i t y c o e f f i c i e n t s , e x p l i c i t consideration of the buffer e q u i l i b r i u m i s thus not warranted.  This s i m p l i f i c a t i o n , which i s of  pragmatic rather than t h e o r e t i c a l value, a p p l i e s only to these system, i n the l i m i t e d range of s a l t compositions used here.  A d d i t i o n a l confirmation  that t h i s approximation i s reasonable comes from the f a c t that the t o t a l phosphate ion p a r t i t i o n c o e f f i c i e n t predicted from [3.26] i s 0.837, which i s very close to the value of 0.835 predicted using the PEG  concentration  d i f f e r e n c e between the phases of 4.3 %, and the p l o t of phosphate p a r t i t i o n against PEG concentration d i f f e r e n c e given i n Bamberger et a l . (1984a).  Systems containing 10 mM phosphate buffer with i n c r e a s i n g amounts of c h l o r i d e were made up, with s o r b i t o l being added to keep the t o n i c i t y at  150  mOsm. The r e s u l t s of s e c t i o n B i n d i c a t e d that the polymer compositions of these systems were e s s e n t i a l l y i d e n t i c a l .  Based on the r e s u l t s of s e c t i o n  i i , i t was assumed that the i o n standard s t a t e chemical p o t e n t i a l d i f f e r e n c e s were thus unchanged.  The p o t e n t i a l s i n these systems were  measured with m i c r o c a p i l l a r y electrodes. The t h e o r e t i c a l and  experimental  -138curves of p o t e n t i a l against percentage phosphate are p l o t t e d i n F i g . 4.2b, showing good agreement.  The data o f Reitherman e t a l . (1973), measured with  agar s a l t bridges, and B a l l a r d e t a l . (1979) are shown for comparison.  v) Discussion  From fundamental considerations, the inner or Galvani p o t e n t i a l d i f f e r e n c e between two phases i s not measurable (Section 3A): the p o t e n t i a l that i s i n fact measured, A i p , i s the sum o f the Galvani p o t e n t i a l m  d i f f e r e n c e , Alp ( = i p - i y ) and the d i f f e r e n c e i n standard s t a t e chemical p o t e n t i a l s of the p o t e n t i a l determining i o n ( s ) .  The e f f e c t o f changing the  c h l o r i d e concentration shows that there i s no j u n c t i o n p o t e n t i a l due t o the s a l t i n the bridges. In F i g . 4.2a,  the agreement between t h e o r e t i c a l  p o t e n t i a l s and those measured with m i c r o c a p i l l a r y electrodes without agar i s confirmed. However the d i f f e r e n t p o t e n t i a l s obtained with and without agar (Table 4.2) i n d i c a t e that i f there i s agar present there i s a polymer induced j u n c t i o n p o t e n t i a l which depends on the s a l t concentration i n the phase system. At 0.1M s a l t the p o t e n t i a l s obtained using the two bridge types d i f f e r by 1.7mV for the sulphate system, but only by 0.4mV f o r the phosphate system, suggesting that t h i s a r t i f a c t also depends on the s a l t type. These r e s u l t s imply that measurements made by other workers (Zaslavsky et a l . , 1981; Reitherman e t a l . , 1973) are too low, and show too strong a dependence on the phase system s a l t concentration.  In t e s t i n g the equation r e l a t i n g the s a l t p a r t i t i o n c o e f f i c i e n t s t o the p o t e n t i a l , i t i s found that the sulphate-induced  t i e l i n e length increases  -139give r i s e to an increasing discrepancy between the predicted and measured p o t e n t i a l s (Table 4.4), as the d i f f e r e n c e between the t i e l i n e lengths of the sulphate and c h l o r i d e systems increases. This e f f e c t i s l i k e l y to be due to changes i n the standard s t a t e chemical p o t e n t i a l terms, since d i l u t i n g the systems so as to keep the t i e l i n e lengths more s i m i l a r removes the discrepancy  (Table 4.5).  In p r a c t i c a l terms, systems with t i e  l i n e lengths that do not d i f f e r by more than 0.5 % e f f e c t i v e l y s a t i s f y the assumption of constant i o n standard s t a t e chemical p o t e n t i a l d i f f e r e n c e s , given the s i z e of the p o t e n t i a l s u s u a l l y encountered and the p r e c i s i o n to which they can be measured.  The e f f e c t o f phosphate concentration on p o t e n t i a l i s o f i n t e r e s t both t h e o r e t i c a l l y , and f o r studies i n which the i o n i c strength of the system i s varied (section D below).  The small decrease i n p o t e n t i a l below 20mM s a l t ,  Table 4.6, may be due to a small decrease i n t i e l i n e length. B a l l a r d et a l . (1979) a l s o found a s i m i l a r decrease f o r (5,5) systems. Both B a l l a r d et a l . and Zaslavsky et a l . (1982) found a decrease i n p o t e n t i a l with i n c r e a s i n g phosphate concentration, although t h i s could be due to the e f f e c t s o f using agar f i l l e d s a l t bridges. The e f f e c t o f phosphate on the t i e l i n e length was not considered i n e i t h e r of these s t u d i e s .  I t seems f a i r to conclude that  i n the absence o f t i e l i n e length changes the p o t e n t i a l i s independent o f s a l t concentration, at l e a s t up t o 400 mM.  The approach to p r e d i c t i n g p o t e n t i a l s from s a l t p a r t i t i o n s used i n s e c t i o n 3A was generalized to deal with mixtures o f two or more s a l t s , p a r t i c u l a r l y the commonly used phosphate/chloride  mixtures. The r e s u l t s of  -140F i g . 4.2b  show good agreement between the theory and experiment, despite  the device used to account f o r the two forms of phosphate ion present.  These measurements were done at low phosphate concentration, since although [3.28] has no e x p l i c i t dependence on s a l t concentration, changes i n the t i e l i n e length would i n v a l i d a t e the assumptions used i n i t s d e r i v a t i o n . The r e s u l t of such e f f e c t s i s i n d i c a t e d by the shape of the curve obtained when the phosphate concentration was increased from 10 to HOmM, redrawn from Reitherman et a l . (1973), who used agar f i l l e d s a l t bridges.  Tils  curve does not have the same general shape as the t h e o r e t i c a l curve, while the data of B a l l a r d et a l . (1979), where the phosphate concentrations were kept below 10 mM,  does show the c o r r e c t t h e o r e t i c a l shape. The fact that the  t h e o r e t i c a l curve i s not s t r a i g h t a l s o i l l u s t r a t e s the fact that the p o t e n t i a l s are not a d d i t i v e . This was a l s o demonstrated experimentally f o r mono and d i - b a s i c phosphate containing systems by Zaslavsky et a l . (1982).  As w e l l as v e r i f y i n g that the measured p o t e n t i a l s i n the mixed s a l t systems were c o r r e c t , another important Quantity could be obtained from the equations i n s e c t i o n 3B: the d i f f e r e n c e i n i o n i c strength between the two phases.  This could be obtained from the t o t a l ion concentrations and the  p o t e n t i a l using the ion p a r t i t i o n c o e f f i c i e n t s c a l c u l a t e d from [3.24-3.26]. I t was pointed out i n the Introduction that the free energy of a charged surface depends on the i o n i c strength of the medium, and that t h i s e f f e c t has not previously been considered.  Zaslavsky et a l . (1978b, 1982), Walter  et a l . (1968b) studied the e f f e c t of the bulk i o n i c strength on c e l l partition.  However they d i d not consider the fact that i t i s only  -Ind i f f e r e n c e s i n i o n i c strength between the phases that c o n t r i b u t e to A y . An expression f o r the t o t a l e l e c t r o s t a t i c c o n t r i b u t i o n t o the c e l l surface free energy d i f f e r e n c e ,  A \  , i s e a s i l y obtained from equations 13 and 23 o f  Verwey and Overbeek (1948) (see Brooks et a l . , 1985):  Ay  = 2TT0- (l/x 2  e l  D  - 1/X )/E  t  +  where cr i s the surface charge d e n s i t y ,  Aipa  e  [4.3]  i s the d i e l e c t r i c constant o f the  phase system (assumed to be the same i n both phases), Atp i s the p o t e n t i a l d i f f e r e n c e , and H ^ ' K  d  are the Debye-Huckel parameters i n the upper and  lower phases r e s p e c t i v e l y , which are p r o p o r t i o n a l to the square roots of the i o n i c strengths. Now f o r phosphate/chloride systems, both s a l t s p a r t i t i o n i n t o the lower phase, so the f i r s t term i s p o s i t i v e . Since a i s negative for c e l l s and Alp i s p o s i t i v e , the second term i s negative.  Ifi t i s  assumed that the s a l t p a r t i t i o n s and the p o t e n t i a l are independent of the t o t a l s a l t concentration ( t h i s i s true at low concentrations since the phase compositions are also unchanged), then [4.3] can be w r i t t e n :  Ay  e l  = B a r (K~ 2  1/2  1/2  - 1) +  Aipcr  [4.4]  where B i s a constant, I i s the lower phase i o n i c strength, and K i s the g  net  s a l t p a r t i t i o n ( i e the r a t i o of the sum of the concentrations of a l l  s a l t s i n the upper phase to the sum of those i n the lower phase). This describes the v a r i a t i o n o f A Y ^ with the bulk i o n i c strength at constant e  potential.  -142Although the p o t e n t i a l undoubtedly increases with t i e l i n e length (Tables 4.4,  4.6),  because the phase compositions, and hence the  ion  standard state chemical p o t e n t i a l s , are being considerably a l t e r e d ,  the  absolute s i z e s of the p o t e n t i a l s cannot be compared with each other.  This  d i f f i c u l t y applies to any i n t e r p r e t a t i o n of the observations of Johansson (1978), who  found that the measured p o t e n t i a l i n potassium c h l o r i d e systems  depended l i n e a r l y on t i e l i n e length.  The r e s u l t s of sections B and C show that for these systems the p o t e n t i a l can be varied independently, and that changes i n the measured p o t e n t i a l agree with the p r e d i c t i o n s of theory, providing length of the system i s not a l t e r e d by more than about  the t i e l i n e 0.5%.  D. E l e c t r o s t a t i c Interactions and the Erythrocyte  i ) P a r t i t i o n and S a l t Composition  Chapter Six deals more f u l l y with the question of what determines c e l l partition.  However, a n t i c i p a t i n g the connection between the c e l l surface  free energy difference and p a r t i t i o n , some e f f e c t s of s a l t composition on erythrocyte p a r t i t i o n are presented i n t h i s s e c t i o n . These r e s u l t s show that the changes i n p o t e n t i a l described i n section C above do a f f e c t c e l l p a r t i t i o n , and they also a i d i n the i n t e r p r e t a t i o n of i o n i c strength e f f e c t s on the c e l l surface free energy d i f f e r e n c e . The e f f e c t of s a l t composition i n phosphate- and chloride-containing  systems i s shown i n F i g . 4.3a.  The  c e l l p a r t i t i o n increases r a p i d l y with increasing phosphate, the rate of  -143increase being greater at high and low p a r t i t i o n s . F i g . 4.3b shows the p a r t i t i o n as a function of p o t e n t i a l . The p a r t i t i o n increases with p o t e n t i a l , more r a p i d l y when the p o t e n t i a l i s above 2 mV. Changing the phosphate concentration from 30 to 10 mM has l i t t l e e f f e c t on e i t h e r the p o t e n t i a l (Table 4.6), or the p a r t i t i o n . When the phosphate concentration i s lowered to 5 mM, the p a r t i t i o n decreases, but l i e s on the same curve as the other points i n F i g . 4.3b since the p o t e n t i a l a l s o decreases (Table 4.6, section C i i i ) . The e f f e c t o f i o n i c strength i s shown more e x p l i c i t l y i n Table 4.7.  TABLE 4.7 ERYTHROCYTE PARTITION AND IONIC STRENGTH  3  Buffer  5,0,114 10,0,100 20,0,73 30,0,45 a  Ionic Strength (mM) 12.4 24.7 49.4 74.1  Potential (mV)  Partition (%)  2.42+0.05 46+3 2.65 82 2.72 85 2.60 87.5  Polymer composition of a l l systems was (5,4)  -144-  LU  0. It  >—i  C_J  g0. 01  0  0  0. 5 MOLE FRACTION OF PHOSPHATE  1 POTENTIAL  1. 0  2 (mV)  Figure 4.3 E f f e c t o f S a l t Composition on Erythrocyte P a r t i t i o n , a) P a r t i t i o n as a function o f mole f r a c t i o n of phosphate, b) P a r t i t i o n as a function o f p o t e n t i a l . Buffer: 5,0,114 ( + ), 10,0,100 (*), 20,0,73 ( o ) , 30,0,45 (<».  -145I t can be seen that a s i x f o l d change i n i o n i c strength has no e f f e c t on the p a r t i t i o n other than that expected from the concomitant change i n p o t e n t i a l .  i i ) C e l l Surface Free Energy Difference and P o t e n t i a l  The c e l l s u r f a c e / i n t e r f a c e contact angle was measured i n a s e r i e s of systems with d i f f e r e n t r e l a t i v e amounts of phosphate and c h l o r i d e ions. F i g . 2.2 i s a photo taken from the video monitor during an experiment, showing the s p h e r i c a l c e l l , drop, and the contact l i n e .  The c e l l surface tree  energy d i f f e r e n c e was c a l c u l a t e d from Young's eauation, [1.23], and the energy of c e l l / i n t e r f a c e i n t e r a c t i o n was c a l c u l a t e d from equation [1.28], using the tensions measured i n Table 4.1:  yt  A  E  _ y  ti  =  = Ay = -  D  T T a  pY  ( 1 t b  -  [1.23]  C 0 S  9  )  [1.28]  2  The c e l l p a r t i t i o n was a l s o measured i n these system, and these q u a n t i t i e s are tabulated i n Table 4.8 ( a c t u a l l y the i n t e n s i v e quantity A E 2 E  /  ^ ti '  T T a  p *  s  9^  v e n  *  n  obtained from F i g . 4.2.  t°*  s  table).  U  =  Data f o r the p o t e n t i a l s were  The p a r t i t i o n c o e f f i c i e n t s of the sodium, c h l o r i d e  and phosphate ions were c a l c u l a t e d from the p o t e n t i a l using [3.24-3.26]. From these c o e f f i c i e n t s and the t o t a l s a l t concentrations the i o n i c strength and Debye-Huckel parameter i n each phase were c a l c u l a t e d .  These data were  used to c a l c u l a t e A (column seven of Table 4.8), the parameter c h a r a c t e r i z i n g the i o n i c strength c o n t r i b u t i o n to Ay  , ([4.3]):  -146-  b  A = 2 TTU/X* - l / V . ) / e  [4.5]  When measuring contact angles, the c e l l s were u s u a l l y added to the upper phase f i r s t . I f the c e l l s were added to the lower phase f i r s t , the contact angle d i d not change s i g n i f i c a n t l y ( t t e s t , p>30%). contact angles were a l s o the same. contact angle was being measured.  Advancing and receding  This i n d i c a t e d that the e q u i l i b r i u m The drop diameter was v a r i e d from 5 to 50  pm, and there was no c o r r e l a t i o n of contact angle with drop s i z e ( c h i squared t e s t , p>10%)^  As the phosphate percentage i s increased, the p o t e n t i a l and c e l l p a r t i t i o n increase, while the c e l l surface free energy d i f f e r e n c e , the contact angle and c e l l / i n t e r f a c e i n t e r a c t i o n energy decrease. The c e l l surface free energy d i f f e r e n c e i s p l o t t e d against the p o t e n t i a l i n F i g . 4.4. This p l o t was found to be l i n e a r (r=0.982) with a slope o f -553+100 2 esu/cm . The i o n i c strength parameter, A, decreases with i n c r e a s i n g i o n i c strength, and i n c r e a s i n g c h l o r i d e percentage.  The surface charge density  ( l a s t two columns) was c a l c u l a t e d from the p o s i t i v e and negative roots of [4.1].  A l l the values given by the p o s i t i v e root f a l l w i t h i n 10% of t h e i r  mean, while the v a r i a t i o n i n the values given by the negative root i s much  1 The v a r i a t i o n o f contact angle with drop s i z e i s described by cos 9 = AY/ Y t b ^c t i s the l i n e tension, and a i s the radius of the contact c i r c l e (e.g. Schulze, 1984, p 160). With an i n t e r f a c i a l tension of 6 x l O dynes/cm, and a p r e c i s i o n of 2-3° i n measuring the angles, t h i s puts an upper l i m i t o f around 10" dynes for the l i n e tension i n t h i s system. +  T  a  w n e r e  c  - 3  6  TABLE 4.8 ERYTHROCYTE PARTITION AND CONTACT ANGLE. THE EFFECT OF POTENTIAL AND IONIC STRENGTH  Buffer  10,0,110 10,4,92 10,8,84 10,12,76 10,16,68 5,0,114 10,0,100 10,130,0 5,0,94° 10,0,85 c  a  Potential (mV)  Contact Angle («)  2.65+0.1 2.3 2.0 1.7 1.6 2.4 2.75 0.1 2.3 2.5  46.5+3 52 58 63.5 67.5 53 45 90.5 69 60  AE AY x-1 (ergs/cm^) x H r  a  t i  44.5+2 40 34.5 29 25 38 44 -1 33 47  6+2 9 14 20 25 10 5.5 65.5+7 39 23  Partition (%) 79.5+4 25 16 13.5 10 46 82 2+1 12 30  A xlO (erg cm esu~2)  1 0  2  13.9+1 12.4 11.1 10.0 9.2 19.6 13.9 2,9 26.3 18.6  Charge Density (esu/cm ) x - l 0  2  552+60 582 576 582 519 543 521  5803+500 5550 5400 4950 5169 3573 6074  536 640  2330 3888  C a l c u l a t e d from eauation [4.5]. °Values obtained from the p o s i t i v e and negative roots of [4.3] r e s p e c t i v e l y (5.5,4) systems.  c  -148-  Figure 4.4 E f f e c t of P o t e n t i a l on the C e l l Surface Free Energy Difference. B u f f e r : 10,x,y (*), 5,x,y ( o ) , x and y given i n Table 4.8.  -149l a r g e r , some o f the values d i f f e r i n g by a f a c t o r of two. Values obtained with 5 mM instead o f 10 mM phosphate give very s i m i l a r r e s u l t s , the slope i n Fig.  4.4 being about 5% smaller.  i i i ) Discussion  The increase i n c e l l p a r t i t i o n on i n c r e a s i n g the phosphate t o c h l o r i d e r a t i o has been w e l l documented (Albertsson, 1971; Walter et a l . 1968b, Reitherman et a l . , 1973). The p a r t i t i o n i n high phosphate systems t v s been shown t o depend on the c e l l surface charge (Brooks e t a l . , 1971). This i n t e r p r e t a t i o n i s supported by the f a c t that the e l e c t r o s t a t i c p o t e n t i a l increases with phosphate percentage (Section C), and that the p a r t i t i o n c o r r e l a t e s w e l l with the p o t e n t i a l ( F i g . 4.3).  The c e l l surface free energy  d i f f e r e n c e i s p r o p o r t i o n a l to the p o t e n t i a l ( F i g . 4.4) again supporting the idea of c e l l charge as the major determinant of p a r t i t i o n i n these systems. However the surface charge density c a l c u l a t e d from t h i s p l o t (ignoring i o n i c 2 strength e f f e c t s , vide i n f r a ) i s around -553 esu/cm , compared with estimates of the amount of charge on s i a l i c a c i d derived from chemical or enzymic assays of -10,600 esu/cm  (Cook, 1976).  This twentyfold  discrepancy i s p u z z l i n g , and s e v e r a l p o s s i b l e explanations were considered: a) The change i n c e l l surface free energy i s not due t o the change i n p o t e n t i a l , but due t o some other concomitant change i n the phase system p r o p e r t i e s , such as ion binding. This i s believed t o be u n l i k e l y , since i f the e f f e c t i s due t o a s p e c i f i c i n t e r a c t i o n with the phosphate (eg. an e x c l u s i o n o f phosphate from the c e l l surface, r e s u l t i n g i n increased  -150p a r t i t i o n i n t o the upper, phosphate poor phase), then the a d d i t i o n of a small amount of c h l o r i d e , which on i t s own has no e f f e c t on c e l l p a r t i t i o n , would not be expected to a l t e r the c e l l surface free energy d i f f e r e n c e to the extent i t does.  Also changing the phosphate concentration has no e f f e c t  on the dependence of e i t h e r the p a r t i t i o n or Ay on the p o t e n t i a l .  b) Since the free energy of a charged surface depends on the i o n i c strength the d i f f e r e n c e i n i o n i c strengths between the phases might be important. This d i f f e r e n c e decreases as the percentage phosphate decreases, since c h l o r i d e p a r t i t i o n s more evenly than phosphate, as expressed by the decrease i n the parameter A i n Table A.8. I t i s therefore possible that the two terms i n [4.3] could be of s i m i l a r s i z e , and thus that the dependence of Ayon  Alp could be s m a l l , even though a i s l a r g e .  From [4.4], i f the  f i r s t term i s important, then Ay and hence the p a r t i t i o n should vary with the i o n i c strength at constant p o t e n t i a l . This i s not supported by the data i n Table 4.7,  i n the case where the phosphate concentration i s changed from  10 to 30mM. The change i n p a r t i t i o n from 5 to lOmM seems to be due e n t i r e l y to the p o t e n t i a l change ( F i g . 4.3). Equation 4.3. i s quadratic i n the surface charge density, therefore two roots were obtained i n Table 4.8.  The l a r g e r  root represents the case where the i o n i c strength term i s l a r g e and comparable to the p o t e n t i a l term. The smaller root a r i s e s from the case where the i o n i c strength term i s n e g l i g i b l e , and the second term small. The l a t t e r give more consistent values, and i s considered to represent the true situation.  c) The t h i r d explanation considered i s that the p o t e n t i a l as measured by  -151the s i l v e r electrodes i s not the a c t u a l p o t e n t i a l between the phases, as 'seen' by the c e l l . However the good agreement between the t h e o r e t i c a l and measured p o t e n t i a l s described i n s e c t i o n AC does not support t h i s possibility.  d)  The a c t u a l net charge on the c e l l surface may be considerably  smaller than that c a l c u l a t e d from the amount of s i a l i c a c i d , due to the presence of other charged groups, p a r t i c u l a r l y on the p r o t e i n s .  No r e l i a b l e  estimates are a v a i l a b l e of the i d e n t i t y and number of other chargeo groups on the c e l l surface (Seaman, 1975).  However the i n t r i n s i c membrane proteins  almost c e r t a i n l y have b o t h . p o s i t i v e l y charged amine groups and negatively charged c a r b o x y l i c a c i d groups.  Thus while the net charge may w e l l be l e s s  2  than 10,600 esu/cm , i t i s u n l i k e l y that there would be a s u f f i c i e n t excess of p o s i t i v e l y charged groups to give a net charge one twentieth as small.  This e f f e c t could not completely account f o r the above r e s u l t s .  e) The f i n a l explanation i s that most of the charge i s hidden from the phase system, i n the sense that t h i s charge w i l l not come i n t o contact w i t h , and c r o s s , the i n t e r f a c e i f the c e l l i s moved between the phases. The concept of hidden charge has commonly been invoked to explain erythrocyte e l e c t r o k i n e t i c data (Seaman, 1975). Mathematical d e s c r i p t i o n s of t h i s e f f e c t i n e l e c t r o p h o r e s i s have been published (Donath and Pastushenko, 1979; Levine et a l . , 1983, Sharp and Brooks, 1985). In these studies the s i g n i f i c a n t features are that the c e l l surface charge i s borne by the glycocalyx, which has a thickness of 50-100 A, and that the charge appears to be d i s t r i b u t e d through t h i s l a y e r over some depth normal to the surface. I f neither of the  -152phases f u l l y penetrates the glycocalyx, then only the charge that experiences the i o n i c m i l i e u of both phases w i l l contribute to the c e l l surface free energy d i f f e r e n c e .  This hypothesis i s consistent with the r e s u l t s o f t h i s work, and the nature of the c e l l surface, although there i s no d i r e c t evidence that the phases are excluded from t h i s glycocalyx. That other molecules can be excluded i s i n d i c a t e d by the c r y p t i c i t y o f c e r t a i n erythrocyte g l y c o l i p i d s to antibodies r a i s e d against the p u r i f i e d antigen (Hakamori, 1981), increased p r o t e o l y t i c d i g e s t i o n o f membrane proteins a f t e r removal of the s i a l i c a c i d (Marchesi, 1976), and the i n a b i l i t y of antibodies to bind to Band 3 u n t i l a f t e r enzymatic removal o f some o f the glycocalyx (Kay and Goodman, 1984). The amount of dextran bound to the erythrocyte at a constant weight concentration decreases at high molecular weight (Brooks, 1973), which could a l s o be a t t r i b u t e d to e x c l u s i o n . To t e s t t h i s hypothesis, smooth p a r t i c l e s of a known surface charge density (McDaniel et a l . , 198A), such as charged l i p i d v e s i c l e s , could be used for s i m i l a r contact angle measurements.  Ionic strength e f f e c t s would a l s o be expected to be  s i g n i f i c a n t f o r smooth p a r t i c l e s with charge d e n s i t i e s comparable t o that of the erythrocyte.  The importance of other charged groups on the c e l l surface  could be estimated by measuring the change i n A y removed by enzymic treatment.  as the s i a l i c a c i d i s  I f the other charges were n e g l i g i b l e , A y  would be l i n e a r l y r e l a t e d to the amount o f s i a l i c a c i d l e f t on the surface.  Other studies i n the l i t e r a t u r e on the r o l e of c e l l surface charge i n p a r t i t i o n give no clue as to whether the phases can be excluded i n t h i s  -153manner. However i f t h i s i s the case, then the observed p a r t i t i o n d i f f e r e n c e s i n charge s e n s i t i v e systems (Brooks et a l . , 1971) may r e f l e c t changes i n only a small f r a c t i o n of the surface charge.  Another p o s s i b i l i t y i s that  such changes may be due to conformational changes that expose more or l e s s charge to the phase system, while the amount of t o t a l charge remains unchanged.  In conclusion, the r e s u l t s of t h i s chapter show that the p o t e n t i a l d i f f e r e n c e between the phases can be c o n t r o l l e d independently, concentrations of the ions are s u f f i c i e n t l y low.  providing the  This w i l l depend on the  phase systems and s a l t s used, but f o r (5,A) systems, conditions where the t i e l i n e changes by l e s s than 0.5% are s u f f i c i e n t .  Under the same  c o n d i t i o n s , d i f f e r e n c e s i n p o t e n t i a l can be measured, and are consistent with those predicted from the s a l t p a r t i t i o n c o e f f i c i e n t s i n s i n g l e and mixed s a l t systems.  The p a r t i t i o n of c e l l s i n t o the upper phase increases  as t h i s phase i s made more p o s i t i v e with respect to the lower phase.  The  c e l l surface free energy d i f f e r e n c e i s l i n e a r l y r e l a t e d to the p o t e n t i a l . However the e f f e c t o f the p o t e n t i a l i s smaller than predicted based on the surface charge density estimated from the amount of s i a l i c a c i d on the cell.  This i s a t t r i b u t e d p r i m a r i l y to an exclusion of the phases from much  of the charged region of the glycocalyx.  -154-  Chapter Five. PEG-palmitate and the C e l l Surface Free Energy Difference  When I examine myself and my methods of thought, I come to the conclusion that the g i f t of fantasy has meant more to me than my t a l e n t for absorbing p o s i t i v e knowledge- A l b e r t E i n s t e i n  A. Introduction  A f f i n i t y p a r t i t i o n i s a method by which the experimenter can make the p a r t i t i o n of a c e l l depend on one p a r t i c u l a r surface property- the a b i l i t y of the surface to bind the l i g a n d . higher r e s o l u t i o n separations.  This can r e s u l t i n more s p e c i f i c and  S p e c i f i c a f f i n i t y ligands have been used to  separate p r o t e i n s , n u c l e i c acids and membrane r e c p t o r s , but are only j u s t being developed f o r c e l l s (Sharp et a l . 1985).  A theory for solute a f f i n i t y  p a r t i t i o n has previously been developed, but most o f the admittedly  few  t e s t s that have been made do not confirm t h i s theory.  In Chapter Three a theory was developed to describe the e f f e c t of an a f f i n i t y l i g a n d on the c e l l surface free energy d i f f e r e n c e .  This chapter i s  concerned with studying the e f f e c t of PEG-palmitate ester (ester) a f f i n i t y l i g a n d , and determining  the a p p l i c a b i l i t y of the theory. This l i g a n d was  chosen because i t has previously been used for c e l l p a r t i t i o n studies (Eriksson et a l 1976, concentrations.  Van A l s t i n e , 1984), and i s e f f e c t i v e at low  Following the general experimental  strategy of t r y i n g to  a l t e r only one s i g n i f i c a n t property of the phase system at a time, the e f f e c t s of changing the ester concentration on several phase system p r o p e r t i e s are f i r s t examined. phase system i s then studied.  The behaviour of the ester i t s e l f i n the F i n a l l y the e f f e c t of ester on the c e l l  -155-  surface free energy d i f f e r e n c e and i t s i n t e r a c t i o n with the c e l l surface are measured.  These are then r e l a t e d by the theory o f Section 3D.  B. E f f e c t o f PEG-palmitate on the Phase System  i ) Compositional and E l e c t r o s t a t i c E f f e c t s  Because o f i t s PEG head group, the ester i s expected t o p a r t i t i o n predominantly i n t o the PEG r i c h phase, and t h i s unequal p a r t i t i o n could appreciably a f f e c t the phase separation i n a manner analogous t o phosphate (Chapter Four). The e f f e c t s on the phase system are summarized i n Table 5.1.  TABLE 5.1 EFFECT OF ESTER ON PHASE COMPOSITIONS  3  Additive  Phase Compositions (%) Top Bottom  0.1 ml water 125 J J M PEG 20 uM ester _c 20 JJM e s t e r  0  (0.76,6.0) (0.96,5.71) (0.75,5.94) (0.88,5.84) nd nd  Tie l i n e Length (%)  (9.85,1.61) (9.83,1.50) (9.86,1.64) (9.87,1.63) nd nd  10.1+0.5 9.8 10.1 9.9 nd nd  Potential (mV) nd° 0.24+0.10 nd 0.18 1.82 1.80  3  system was (5,3.8)10,130,0 °not determined system was (5,3.8)10,0,220 c  Within the error of measurement, the ester has no more e f f e c t on the phase composition than that due t o e i t h e r the same amount of u n e s t e r i f i e d PEG, or the c a r r i e r buffer added with the e s t e r , even at concentrations of 20 JJM, four times the maximum amount generally used. The p o t e n t i a l between  -156-  the phases i s a l s o unchanged.  i i ) E f f e c t o f Ester on I n t e r f a c i a l Tension  Given that the tension depends roughly on the fourth power of the t i e l i n e length (Table 4 . 1 ) , i t i s a very s e n s i t i v e measure of changes i n the phase composition, as w e l l as being very important f o r c e l l p a r t i t i o n .  Adding 0 . 3 _uM ester apparently decreases the tension by about 5 % (Table 5.2),  but the tension increases as more ester i s added, and at 6 JJM i s about  8% higher.  However at 1 . 2 JJM, which i s the maximum concentration generally  used for the work with c e l l s , there i s no s i g n i f i c a n t change.  The apparent  decrease below t h i s concentration probably r e s u l t s from experimental uncertainty.  TABLE 5 . 2 EFFECT OF PHASE COMPOSITION ON INTERFACIAL TENSION  System  (5,4)10,130,0 (5,4)10,130,0+0.3 (5,4)10,130,0+1.2 (5,4)10,130,0+3.0 (5,4)10,130,0+6.0  a  n d : not determined  Tie Line Length (%) 11.85+0.2  nd nd nd nd  a  TensionxlO erg/cm  3  2  5.73+0.2 5.45 5.69 5.92 6.14  -157-  i i i ) Discussion  The a d d i t i o n of the e s t e r has l i t t l e e f f e c t on the phase composition, even though i t p a r t i t i o n s predominantly  i n t o the PEG r i c h phase, probably  as  a r e s u l t of the low concentrations used. Since the p o t e n t i a l i s also unaffected, presumably the i o n d i s t r i b u t i o n s are a l s o unchanged by the e s t e r . This l i g a n d a l s o has l i t t l e e f f e c t on the tension.  I t i s therefore  assumed that providing the e s t e r concentration i s kept below 6 JJM,  i t has no  s i g n i f i c a n t e f f e c t s on the phase system p r o p e r t i e s . This makes i t a convenient model l i g a n d f o r d e t a i l e d study.  C. Behaviour of PEG-palmitate i n the phase system  i) Partition  The percent p a r t i t i o n of PEG-palmitate i n t o the upper phase of a (5,4)10,130,0 system as a f u n c t i o n of ester concentration i s shown i n Fig.  5.1a.  The r e s u l t s are the average of seven experiments varying s l i g h t l y  i n experimental  d e t a i l s . The r e s u l t s from measurements made during a  p a r t i t i o n / b i n d i n g experiment with erythrocytes i n the phase system (Section D i i below) are also shown. The f i r s t set of data shows a s i g n i f i c a n t increase i n ester p a r t i t i o n with concentration. The l a t t e r s e t , measured simultaneously with c e l l p a r t i t i o n , show s i m i l a r p a r t i t i o n c o e f f i c i e n t s . Experiments where the t o t a l amount of ester was measured simultaneously show that l i t t l e ester was adsorbed at the l i q u i d - l i q u i d i n t e r f a c e , and that t h i s  -158-  100  0. 01 160  0.1 1.0 ESTER CONCENTRATION  10 CuM)  200 ESTER  CONCENTRATION  (>JM>  Figure 5.1 Behaviour o f Ester i n the Phase System, a) Ester p a r t i t i o n c o e f f i c i e n t i n a (5,4)10,130,0 system as a function o f concentration (o). Measured simultaneously with ester binding to erythrocytes (*). Apparent percentage o f ester at the i n t e r f a c e , xlO (+). b) Example o f fluorescence p l o t f o r determining the cmc. Data for the ester i n water containing PRODAN, cmc i s given by the break i n the p l o t at approximately 35 J J M .  -159-  amount has no meaningful dependence on concentration ( F i g . 5.1a). Experiments where the area of tube c r o s s e c t i o n , and hence the i n t e r f a c i a l area, was v a r i e d by a f a c t o r o f four gave e s s e n t i a l l y the same r e s u l t s . Loss of e s t e r by adsorption to the sampling p i p e t t e s was found to be l e s s than 0.5% by assaying an a l i q u o t of r a d i o - l a b e l l e d ester before and a f t e r ten sequential samplings with fresh p i p e t t e s . This could not therefore account for the observed r e s u l t s . Volume r a t i o changes were a l s o r u l e d out by d i r e c t measurements before and a f t e r the experiment.  i i ) PEG-Palmitate C r i t i c a l M i c e l l e Concentrations  Both the ester p a r t i t i o n r e s u l t s of s e c t i o n i above, and the i n t e r p r e t a t i o n of the ester binding to erythrocytes and i t s e f f e c t on t h e i r p a r t i t i o n (Section D), required that the c r i t i c a l m i c e l l e concentration (cmc) of the ester i n each phase be measured. A v a r i e t y of methods to measure cmc's e x i s t , such as i n t e r f a c i a l tension and c o n d u c t i v i t y measurements (Mukerjhee and Mysels, 1971), but almost a l l of these are i n a p p l i c a b l e to a non-ionic amphiphile i n the presence of a high concentration of polymers and s a l t s . The method of fluorescence enhancement v i s l e s s a f f e c t e d by these problems, and so was used to measure the ester cmc's. A t y p i c a l p l o t of fluorescence against ester concentration i s shown i n F i g . 5.1b, and the r e s u l t s are summarized i n Table 5.3.  -160-  TABLE 5.3 PEG ESTER CRITICAL MICELLE CONCENTRATIONS  Solvent Water Water (5,4)10,130,0 Top (5,4)10,130,0,Bottom 13% PEG i n water  Probe PRODAN ANS ANS ANS ANS  cmc (uM) 37+5 42+5 20+5 10+5 62+8  I t must be stressed that the values i n t h i s table are lower l i m i t s , since the mixed m i c e l l e e f f e c t of the probes, which themselves are hydrophobic, tends t o lower the apparent cmc (see d i s c u s s i o n below). The cmc i n both phases appears t o be w e l l above the range o f concentrations where the p a r t i t i o n increase i s seen i n F i g . 5.1a, and the t y p i c a l concentrations used f o r c e l l p a r t i t i o n . The cmc decreases by about 10 JJM when the solvent i s changed from water to the PEG r i c h phase and t o the dextran r i c h phase, showing the large e f f e c t o f the polymers.  i i i ) Discussion  The increase i n ester p a r t i t i o n with concentration i s unexpected and p u z z l i n g ( F i g . 4.4a). The p a r t i t i o n increases from 65 t o 81%, which when expressed as a p a r t i t i o n c o e f f i c i e n t , increases from 1.86 t o 4.26, a very s i g n i f i c a n t change. I t i s a l s o s u r p r i s i n g that the ester p a r t i t i o n i s l e s s than the PEG p a r t i t i o n i t s e l f (3.9), except at very high concentration,  -161-  since t h e o r e t i c a l l y the p a r t i t i o n would be expected to be about equal to the product of the p a l m i t i c a c i d and PEG p a r t i t i o n c o e f f i c i e n t s (See Chapter Three, s e c t i o n D), i e about A.3.  Various c o n t r o l experiments eliminated  p o s s i b l e systematic e r r o r s associated with sampling, incomplete s e t t l i n g of the phases, phase volume changes and adsorption at the i n t e r f a c e . The ester has l i t t l e e f f e c t on the tension, which a l s o i n d i c a t e s that l i t t l e adsorption i s occurring at the i n t e r f a c e , although t h i s might be expected because of the ester's amphiphilic and detergent p r o p e r t i e s . This i s probably because both the p a l m i t i c a c i d t a i l , and the PEG head group separately p a r t i t i o n i n t o the PEG r i c h phase (K = 1.16 respectively).  and  3.9  Therefore there would be no free energy decrease for an  ester molecule adsorbed at the i n t e r f a c e . The p a r t i t i o n c o e f f i c i e n t of a solute such as the ester might be expected to depend exponentially on the t-^ (see s e c t i o n l C . i i i ) . Thus a very small increase i n t i e l i n e length, implied by the small tension increase at high ester concentration, could i n p r i n c i p a l cause a p a r t i t i o n c o e f f i c i e n t increase. However the p a r t i t i o n increases more r a p i d l y at low ester concentration, where the ester has l i t t l e e f f e c t on the tension, and increases l e s s r a p i d l y at higher concentration, where i t would be expected to have the most e f f e c t , so t h i s seems u n l i k e l y to be the explanation.  Another explanation f o r t h i s e f f e c t could be that the free energy o f e s t e r t r a n s f e r between the phases, given by the d i f f e r e n c e i n standard s t a t e chemical p o t e n t i a l s , remains constant, but the r e l a t i v e ester a c t i v i t y c o e f f i c i e n t s i n the two phases a l t e r s with concentration, and hence the p a r t i t i o n c o e f f i c i e n t changes (see [1.13]). One way the a c t i v i t y c o e f f i c i e n t  -162-  of an amphiphile could change i s by aggregation, or m i c e l l e formation. The formation of m i c e l l e s i s expected i n the l i g h t of the commercial a p p l i c a t i o n of t h i s type of ester as detergents (Rosen, 1978). The cmc's o f a number o f PEG f a t t y a c i d e s t e r s , and the analogous PEG f a t t y a c i d ethers, with smaller head groups have previously been measured (Elsworthy and MacFarlane, 1962). For the palmitate s e r i e s the cmc (expressed as m o l e s / l i t r e ) was found to be r e l a t e d to the number of ethylene u n i t s i n the head group, n, by  cmc = -5.93 + 0.0245n  [5.1]  for n = 6-21. E x t r a p o l a t i o n o f t h i s equation to a head group molecular weight of 6650 g/mole (n = 120) gives a cmc i n the m i l l i m o l a r range, w e l l above the concentration range i n F i g . 5.1a. However such a f i g u r e cannot be used u n c r i t i c a l l y since i t i s based on a considerable e x t r a p o l a t i o n , and i t also takes no acount of the system polymers. The r e s u l t s i n Table 5.3 i n d i c a t e that the actual cmc's i n the phase system are much lower, although s t i l l considerably higher than the region of i n t e r e s t . These data must be considered as semi-ouantitative i n view of the u n c e r t a i n t i e s i n d e f i n i n g and measuring the cmc, e s p e c i a l l y f o r polydisperse. m a t e r i a l . The lower values are not s u r p r i s i n g since the e f f e c t o f each a d d i t i o n a l ethylene head group i n i n c r e a s i n g the cmc would be expected to decrease as the head group becomes l a r g e r , and conforms more to the random c o i l c o n f i g u r a t i o n .  The phases decrease the apparent cmc. This e f f e c t appears to be due mainly to the dextran, since the e f f e c t i s greater i n the lower phase, and  -163-  13% PEG alone increases the cmc. Such an e f f e c t i s understandable i f m i c e l l e formation i s viewed as a form of phase separation (Tanford, 1976), the e f f e c t o f the polymers on m i c e l l e formation being the same as t h e i r e f f e c t on p a r t i t i o n i n g the ester between the phases. The onset o f m i c e l l e  formation  would be expected to increase the net ester p a r t i t i o n since a m i c e l l e would be expected t o have a l a r g e r p a r t i t i o n c o e f f i c i e n t i n t o the PEG r i c h phase than an ester monomer (This can be seen from [1.38], i f the m i c e l l e i s modelled as a molecule with a p a r t i t i o n c o e f f i c i e n t of one bearing n bound ester molecules).  Johansson and Shanbhag (1984) a l s o found an increase i n  ester p a r t i t i o n at higher concentrations  (0.1-1 mM) which they a t t r i b u t e d t o  m i c e l l e formation. The p a r t i t i o n was close t o that o f the PEG i t s e l f below 1 mM, and increased, as expected i f m i c e l l e s were forming, t o f o r t y times the PEG p a r t i t i o n .  I f the phase separation model o f m i c e l l e formation i s used then the chemical p o t e n t i a l of the e s t e r i n the free and m i c e l l e form are equal, leading t o (Tanford, 1976):  H°e " H ow where  u. , g  =  k T l n  ^e "  k T  /n  l n ( X  T  / n )  [ 5  '  2 ]  oh u. are the standard s t a t e chemical p o t e n t i a l s of the ester g  i n aqueous and hydrocarbon solvent ( i e . the m i c e l l e i n t e r i o r ) , X^,  X™  are the mole f r a c t i o n s of e s t e r i n monomeric and m i c e l l a r form, and n i s the number of ester molecules per m i c e l l e (assumed constant). The l e f t hand side i s constant, and [5.2] can be r e - w r i t t e n as  -164-  Xg/(Xg)  1 / n  = const.  [5.3]  w For reasonably large m i t can be seen that X w m total  amount of e s t e r , X  e  + X » e  ?  changes very slowly as the  increases. Such behaviour i s  behind the concept of a cmc. A p o s s i b l e a r t i f a c t of cmc measurements made by means of hydrophobic probes, the so c a l l e d mixed m i c e l l e e f f e c t , r e s u l t s from the f a c t that the probe i t s e l f w i l l p a r t i t i o n p r e f e r e n t i a l l y i n t o the hydrophobic m i c e l l e i n t e r i o r , thus d r i v i n g m i c e l l e formation. From [5.2] i t can be shown that the cmc w i l l be lowered by a f a c t o r 1 -  X  , where P  Xp i s the mole f r a c t i o n concentration of probe i n the m i c e l l e . Thus the a c t u a l cmc's are l i k e l y to be higher than those i n Table 5.3. Although the cmc's would therefore seem to be too high to account f o r the observed p a r t i t i o n changes, another d i f f i c u l t y  must be mentioned. The d r i v e  for m i c e l l e formation i s the hydrophobic e f f e c t , which operates when water i s excluded from contact with the hydrophobic t a i l groups o f the amphiphiles i n the m i c e l l e i n t e r i o r . Such an exclusion of water presupposes a c e r t a i n a b i l i t y to pack the ester molecules together t i g h t l y . However the PEG head o  group, with a radius o f g y r a t i o n of about 25 A (Cabanes, 1982) i s much l a r g e r than the p a l m i t i c a c i d t a i l (with a c r o s s e c t i o n a l area around 50 A , Elsworthy and MacFarlane, 1962), so that i t i s d i f f i c u l t to v i s u a l i z e more than four or f i v e such molecules forming a m i c e l l e . Bearing i n mind the i m p l i c a t i o n s of [5.3], the s i g n i f i c a n c e of the apparent cmc's measured with the fluorescent probes i s not c l e a r .  -165-  I t i s possible that the apparent cmc's measured here are an a r t i f a c t  due  t o the presence of the probe i t s e l f , which allows l a r g e r m i c e l l e s to form, and that the p a r t i t i o n e f f e c t s are due to small aggregates or 'proto-micelies' which occur at lower concentrations, and which cannot be detected by the fluorescent probe.  M i c e l l e s of SDS have been shown to  adsorb to PEG molecules i n aqueous s o l u t i o n (Cabanes, 1982).  A s i m i l a r type  of a s s o c i a t i o n between PEG and the ester 'micelles' could provide explanation for the complex behaviour seen here.  an  Whatever the reason, these  r e s u l t s e f f e c t i v e l y l i m i t the experimentally a c c e s s i b l e range of ester concentrations, and make p r e c i s e determination  of the free energy of ester  t r a n s f e r between the phases d i f f i c u l t .  D. PEG-palmitate/Erythrocyte  interactions  i) Cell Partition  Before studying the e f f e c t of ester on the c e l l surface free energy d i f f e r e n c e , the range of concentrations over which the ester a f f e c t e d the c e l l p a r t i t i o n was determined ( F i g . 5.2a).  The ester increases the c e l l  p a r t i t i o n d r a m a t i c a l l y , even i n the micro-molar concentration range. The p l o t of l o g K against concentration i s sigmoidal i n shape, being steeper at high and low p a r t i t i o n s . Both the synthesized r a d i o l a b e l e d ester and  the  commercially obtained u n l a b e l l e d ester used f o r the work i n t h i s t h e s i s have polydisperse PEG head groups.  They a l s o d i f f e r i n t h e i r p u r i t y , the  commercial ester containing 84% u n e s t e r i f i e d PEG, containing l e s s than 1%.  the r a d i o l a b e l e d ester  However ester from both sources has the same  -166-  0. 01  0  0.5  1.0  1.5  *  100 b  o  80  /  Q 60 2 40 ct: «<  Q_  J ...  0  i  1 ESTER  i_  2  i  3  CONCENTRATION  4 (>JM)  Figure 5.2 Erythrocyte P a r t i t i o n and Ester Concentration, a) C e l l s p a r t i t i o n e d i n a (5,4)10,130,0 system. Ester expressed as bulk concentration f o r an equivolume system, b) Comparison o f commercial (*) and ^ C l a b e l l e d (o) e s t e r .  -167-  e f f e c t on c e l l p a r t i t i o n on a mole basis ( F i g . 5.2b), which i s a s e n s i t i v e i n d i c a t i o n that there i s no s i g n i f i c a n t d i f f e r e n c e between them.  i i ) Binding Studies  The i n t e r a c t i o n of the e s t e r with the c e l l s was i n v e s t i g a t e d by means of a number of binding experiments.  a) PEG  Adsorption  The binding of PEG, which forms the ester head group, was studied i n i t i a l l y as a c o n t r o l , and a l s o to give some idea of how strongly the phase polymers bound to the c e l l surface.  The PEG binding isotherm i s shown i n  F i g . 5.3, and can be seen to be e s s e n t i a l l y l i n e a r up to 6% PEG, f o r binding from the upper phase. Binding i n b u f f e r i s l i n e a r up to 4%, and then appears to l e v e l o f f somewhat at 6%, although with only one p o i n t , and given the weakness of the binding and the consequent large e r r o r s , i t i s d i f f i c u l t to draw a d e f i n i t e conclusion. The binding from 110,0,0 and 10,130,0 buffers i s very s i m i l a r . The phase-forming polymers appear to have l i t t l e e f f e c t on the binding since the points from the upper and lower phases l i e on the same l i n e as the other p o i n t s .  b) PEG-palmitate Adsorption  The ester binding isotherms  f o r binding from both phases of a  (5,4)10,130,0 system are shown i n F i g . 5.4a. Ester concentrations i n d i c a t e d  -168-  Figure 5.3 Adsorption of PEG 8000 to Erythrocytes. Incubation medium: PBS (*), 110,0,0 b u f f e r (+), top (o), and bottom (0) phase of a (5,4)10,130,0 system.  -169-  ixi  CO  cn s  10c  LU  »—  CO LU Q  ID O CD  0. \ 0. 1  1 ESTER CONCENTRATION  10 (pM)  Figure 5.4 Ester Binding t o Erythrocytes. The E f f e c t o f the Phases and C e l l Concentration, a) E f f e c t o f incubation medium. Top (o) and bottom (*) o f a (5,4)10,130,0 system, a t 3% haematocrit. b) E f f e c t o f c e l l concentration. 3% haematocrit ( o ) , other haematocrits given on the f i g u r e (*).  -170-  are e q u i l i b r i u m concentrations. Both isotherms appear to be l i n e a r at low concentration, and saturate at higher concentration. The binding i s stronger from the lower phase. Several c o n t r o l experiments were done f o r the e s t e r binding, to check the r e s u l t s shown i n F i g . 5.4a.  Most of the studies were o  done at a haematocrit of around 3%, equivalent to 3x10 Increasing the haematocrit  cells/ml.  from 2 to 40% lowers the e q u i l i b r i u m ester  concentration, but does not a f f e c t the isotherm ( F i g . 5.4b).  Binding  was  measured e i t h e r by disappearance of l a b e l from s o l u t i o n on adding the c e l l s , or by analysing the c e l l p e l l e t .  Both methods gave the same r e s u l t s w i t h i n  experimental e r r o r , i n d i c a t i n g that a l l the r a d i o l a b e l could be accounted for  (data not shown).  Studies on the time course of e s t e r binding and  desorption i n d i c a t e d that the binding reaches e q u i l i b r i u m w i t h i n three minutes (the shortest f e a s i b l e sampling time), and does not change for up to two hours ( r e s u l t s not shown).  The binding of PEG, dextran and ester i s compared i n F i g . 5.5.  The  concentration and approximate amounts bound of PEG and dextran i n the upper phase, and of ester s u f f i c i e n t to give a c e l l p a r t i t i o n of 50% i n a  (5,4)  system are i n d i c a t e d on t h i s f i g u r e .  c) Desorption  Studies  Many studies have shown that when the polymer concentration i n a medium i n e q u i l i b r i u m with a surface i s lowered, desorption of polymer from the surface reaches e q u i l i b r i u m very slowly (eg. see Adamson, 1976). been shown f o r dextran and f i b r i n o g e n adsorption to erythrocytes  This has  -171-  POLYMER CONCENTRATION <%> Figure 5.5 Comparison o f PEG 8000, Dextran T500 and Ester Binding. Incubation medium: PBS f o r PEG ($) and Dextran ( o ) , top (5,4)10,130,0 f o r PEG-palmitate (*). Dextran data from Joe Charalambous, personal communication. Dotted l i n e s indicated estimated amounts o f these three components bound i n a (5,4) system with a c e l l p a r t i t i o n o f 50%.  -172-  (Brooks et a l ^ , 1980).  Since PEG, dextran and ester are unequally  d i s t r i b u t e d i n the phase system, slow desorption e f f e c t s could i n p r i n c i p l e be important when the c e l l i s t r a n s f e r r e d from one phase t o the other.  The  desorption o f PEG and ester were i n v e s t i g a t e d by wash o f f s t u d i e s . The r e s u l t s o f washing adsorbed PEG o f f the c e l l s with PBS, top phase or bottom phase of a (5,4)10,130,0 system are shown i n F i g . 5.6a. The semi-log p l o t s of the f r a c t i o n o f PEG l e f t a f t e r each wash are nonlinear i n a l l three cases, p r o p o r t i o n a l l y l e s s m a t e r i a l again being removed with each wash." Washing with the upper phase removes more bound PEG, by a f a c t o r o f f i v e , than does washing with the lower phase or PBS.  The desorption of the ester was studied by washing the c e l l s with various buffers ( F i g . 5.6b). A l l o f the semi-log p l o t s are non-linear, with the exception o f that f o r the upper phase, p r o p o r t i o n a l l y l e s s material being removed with each wash. The amount o f m a t e r i a l removed per wash increases i n the order: lower phase, PBS (high i o n i c strength b u f f e r ) , phosphate buffer (low i o n i c strength), upper phase. The p o s s i b i l i t y that the ester i s entering the c e l l s was studied by l y s i n g the c e l l p e l l e t with hypotonic b u f f e r . When the c e l l s are lysed a f t e r three washes, the amount o f ester released i s equal to that f o r the c o n t r o l buffer o f the same i o n i c strength. When the c e l l s are lysed on the f i r s t wash, the amount o f ester released i s l e s s than with the c o n t r o l . In f a c t about twice as much ester i s associated with the membrane a f t e r l y s i n g .  This i s i n t e r p r e t e d as material  released from the outer surface by the l y s i n g b u f f e r , which was being re-bound on the previously unexposed inner membrane surface. therefore assumed that PEG can not cross the membrane.  It i s  -173-  100*  -J <  on UJ  o o_ ZD  O CD  Figure 5.6 Desorption of PEG and Ester from Erythocytes. a) Desorption o f PEG. b) Desorption o f e s t e r . C e l l s were washed with PBS (*>), top (o) and bottom (*) phases of a (5,4)10,130,0 system, or 10,0,220 (+). F i l l e d symbols represent washes where the c e l l s were lysed with 10,0,0 b u f f e r , pH 8, and the c e l l membranes p e l l e t e d a t 15,000g f o r 15min.  -174-  For the experiments where the c e l l s were washed with the phases, the amount of ester bound a f t e r each wash was p l o t t e d against the e q u i l i b r i u m ester concentration i n the wash, and compared with the binding isotherms ( F i g . 5.7). For the top phase, the points f o r the wash o f f l i e i n a f a i r l y s t r a i g h t l i n e passing through the o r i g i n , with a slope about 25 to 30% greater than the isotherm. The points for the wash o f f i n the lower phase l i e above the isotherm, and appear to gradually diverge from i t , not passing through the o r i g i n .  d) Estimation of Ester Binding Energies  The data of F i g . 5.4 are r e p l o t t e d on a Scatchard p l o t i n F i g . 5.8a.  The  binding from both phases give l i n e a r p l o t s (r=0.966, 0.886, for the upper and lower phases r e s p e c t i v e l y ) , with very s i m i l a r i n t e r c e p t s on the abscissa. The data from the lower phase has a slope j u s t over three times as large.  The binding from each phase measured i n the complete phase system i s analysed by Scatchard p l o t s i n F i g . 5.8b,  and has the same general features  as the binding from the separated phases.  Both isotherms again give l i n e a r  p l o t s , with very s i m i l a r i n t e r c e p t s . The t o t a l number of binding s i t e s , and the binding energy i n each phase, determined by l i n e a r regression a n a l y s i s of the Scatchard p l o t s , i s summarized i n Table 5.4. Good c o r r e l a t i o n c o e f f i c i e n t s are obtained f o r a l l p l o t s . The t o t a l number of binding s i t e s estimated from the separated phases i s about 18% lower than f o r the complete  -175-  1. 0  0. 1 ESTER  0. 2  0. 3  CONCENTRATION  0. 4 (>JM)  Figure 5.7 Comparison o f Ester Adsorption and Desorption. C e l l s incubated and washed with top (•) or bottom (*) phase o f a (5,4)10,130,0 system. Numbers r e f e r to the wash number, zero being the o r i g i n a l amount bound. S o l i d l i n e s i n d i c a t e isotherms from F i g 5.4  -176-  0  l  0 BOUND ESTER  (10  -4  8  10  g/g CELLS)  Figure 5.8 Scatchard P l o t s of Ester Binding, a) Data from binding i n separate phases (Fig.6.6). b) Data from complete phase system. Binding measured i n the upper (0) or lower (*) phase of a (5,4)10,130,0 system.  -177-  system, while the corresponding binding energy estimate f o r the upper phase i s about 0.2 kT lower. The lower phase binding energy estimate i s very s i m i l a r f o r both methods.  TABLE 5. A SUMMARY OF ESTER BINDING DATA FROM SCATCHARD PLOTS  Phase  Binding S i t e s 10 /cell 6  Top Bottom Top Bottoms 3  a  Dissociation Constant JJM  8.A8+0.3 8.68+0.6 10.9+1 10.3+1.5  3.3+0.3 0.85+0.2 2.82+0.3 0.90+0.3  Binding Energy kT/molecule  Regression Coefficient  -16.6+0.2 -18.0+0.4 -16.8+0.A -17.9+0.A  0.966 0.886 0.887 0.950  measured i n a complete system.  i i i ) PEG-palmitate and the C e l l Surface Free Energy Difference  A s e r i e s of (5,A)10,130,0 systems containing i n c r e a s i n g amounts o f ester were made up. The c e l l p a r t i t i o n and contact angle were measured i n each system.  The c e l l surface free energy d i f f e r e n c e and c e l l / i n t e r f a c e  attachment energy were c a l c u l a t e d from the contact angle and the i n t e r f a c i a l tension (Table 5.2), using [1.23] and [1.28] as i n Chapter Four. are  l i s t e d i n Table 5.5 (as before, the i n t e n s i v e v a r i a b l e  AE  These data  fci  i s a c t u a l l y tabulated). The amount of ester bound per u n i t surface area o f the  c e l l i n each phase was c a l c u l a t e d from the bulk ester composition, the  ester p a r t i t i o n c o e f f i c i e n t ( F i g .  5.1) and the isotherm parameters derived  -178-  from binding studies i n complete phase systems (second set of data, Table 5.A).  Only the number bound i n the upper phase i s given i n the t a b l e ,  although the data from the lower phase were very s i m i l a r , the values being about 10% smaller. increases.  The contact angle decreases as the e s t e r concentration  There i s a concomitant increase i n c e l l p a r t i t i o n and a decrease  i n c e l l / i n t e r f a c e i n t e r a c t i o n energy. The c e l l surface free energy d i f f e r e n c e i s e s s e n t i a l l y zero i n the absence of e s t e r , and increases l i n e a r l y with the amount of ester bound ( r = 0.976), with a slope of -0.061+0.02 kT/molecule.  TABLE 5.5 ERYTHROCYTE PARTITION AND CONTACT ANGLE. EFFECT OF ESTER 0  Ester Contact Cone. (JJM) Angle (°) 0 0 0.2 0.3 O.A 0.5 0.6 0.7 0.8 1.0 1.2 3  92+3 90 86 80 78.5 76 6A.5 62 60.2 A7.5+3 AA.5  Ay _ AEti (erg/cm )xl0 2  2+3 -0.3 -A.5 -11 -13 -15.5 -27 -30 -31.7 -A3+2 -A5.5  5  68+6 63 55 A3.5 Al 37 21 18 16.1 6.5+: 1.5 5  System composition: (5,A)10,130,0 °bulk concentration Measured i n the upper phase. c  Partition (%) 0.5+1 3.5 10.5 13 16.5 19 2A.5 29 3A.5 51.5+3 70  Bound E s t e r / 1 0 molecules/cm ) 2  c  0 0 0.7 1.1 1.3 1.5 1.75 2.0 2.2 2.5+0.3 2.8  3  12  -179-  The dependence of c e l l surface free energy d i f f e r e n c e , Ay , on the e s t e r concentration i s shown i n F i g . 5.9, along with some t h e o r e t i c a l curves c a l c u l a t e d from [3.57] using the binding data i n Table 5.4.  The ester  p a r t i t i o n c o e f f i c i e n t was v a r i e d w i t h i n the l i m i t s of the data i n F i g . 5.1a for the ' i n phase' experiment, to obtain the best f i t . This occurred when the p a r t i t i o n c o e f f i c i e n t was allowed to increase s l i g h t l y from 3.18 as the ester concentration was increased from 0 to 1.2  to  3.28  (bulk  concentration for equal volumes of each phase).  i v ) Discussion  Studies of the e f f e c t of ester on the p o t e n t i a l , phase composition  and  i n t e r f a c i a l tension show that at low concentrations i t has l i t t l e e f f e c t on the d i s t r i b u t i o n of any other phase system component. PEG ester increases c e l l p a r t i t i o n d r a m a t i c a l l y from 2% to 100% over a concentration range of 0 to 2 JJM. Therefore the ester must exert i t s e f f e c t on c e l l p a r t i t i o n p r i m a r i l y by i t s i n t e r a c t i o n with the c e l l surface. This made i t s u i t a b l e for a d e t a i l e d study of the the e f f e c t of an a f f i n i t y l i g a n d on the c e l l surface free energy d i f f e r e n c e .  To study the i n t e r a c t i o n of the l i g a n d with the c e l l surface, several types of binding s t u d i e s were c a r r i e d  out.  The binding i s more than three  times as strong from the lower phase as from the upper phase ( F i g 5.4a), which i s consistent with the general r u l e that binding i s increased from a poorer solvent (Adamson, 1976). For t h i s type of e f f e c t to occur, the bound  -180-  BULK  ESTER CONCENTRATION  (JJM)  Figure 5.9 E f f e c t o f Ester on C e l l Surface Free Energy. Comparison with Theory. Experimental (*), t h e o r e t i c a l ( ) c a l c u l a t e d from [3.60] with n=10.9xl0 molecules per c e l l , k =2.82 uM, k =0;898 JJM. given on the f i g u r e . Ester i s expressed as bulk concentration f o r an equivolume system. 6  t  D  -18 im-  material must be at l e a s t p a r t i a l l y removed from contact with the s o l v e n t , otherwise there i s no d r i v i n g force for such an e f f e c t . The i m p l i c a t i o n s of t h i s w i l l be c l e a r e r when the r e l a t i v e binding strengths are discussed i n more d e t a i l below.  Desorption of e s t e r was studied by removing the ester from the c e l l s by a s e r i e s of washes. Figure 5.6b  summarizes several experiments.  The amount  of m a t e r i a l removed per wash v a r i e s with the wash medium. More i s removed by the top phase than the bottom phase since the former i s a b e t t e r solvent f o r the e s t e r . The lower phase excludes PEG and the e s t e r , so tends to remove l i t t l e . The top phase removes ester b e t t e r than the b u f f e r . This i s probably due to the high PEG concentration.  At any point on the isotherm, at  e q u i l i b r i u m i n the presence of the polymer i n s o l u t i o n , the rates of binding and desorption must j u s t balance each other. However polymer desorption often reaches e q u i l i b r i u m extremely slowly when the free polymer concentration i s lowered, due to the fact that i t attaches to the surface at several points ( S i l b e r b e r g , 1962). This m u l t i - p o i n t attachment considerably slows the k i n e t i c s of desorption, and i s reduced i f there i s a high concentration of free polymer (such as PEG) i n s o l u t i o n which competes for the attachment s i t e s . Such non-equilibrium desorption behaviour i s i n d i c a t e d by the non-linear semi-log wash o f f curves f o r both PEG and the ester i n the absence of the top phase. The i m p l i c a t i o n here i s that the PEG head group of the ester slows the k i n e t i c s of desorption down by forming m u l t i p l e attachments, and that the high concentration of PEG i n the upper phase competes for these attachment s i t e s . S i m i l a r slow desorption behaviour  was  a l s o seen f o r dextran and f i b r i n o g e n binding to erythrocytes (Brooks et a l . ,  -182-  1980).  The reason the low i o n i c strength buffer removes more ester than PBS  i s p u z z l i n g , since the binding i s not i o n i c i n nature. This may be due to a l t e r a t i o n s i n the c e l l glycocalyx at low i o n i c strength (Wolf and G i n g e l l , 1983) that f a c i l i t a t e the release of the e s t e r .  Desorption of ester i n the upper phase seems to reach the same e q u i l i b r i u m as the binding, as i n d i c a t e d by the s i m i l a r i t y of the isotherms i n F i g . 5.7.  two  This i s not the case for the lower phase.  The binding of dextran T500, PEG 8000 and the e s t e r are compared i n F i g . 5.5.  I t can be seen that the e s t e r binding i s three to four orders of  magnitude stronger than the binding of e i t h e r of the phase polymers. However the amount of m a t e r i a l bound a t , say, 0.5 jjm ester i n a (5,4) system (with a c e l l p a r t i t i o n of about 50%), i s comparable, since the concentrations of the phase polymers are so high. This f i g u r e a l s o i l l u s t r a t e s the fact that ester binding i s p r i n c i p a l l y driven by the palmitate t a i l , since the binding i s so much stronger than f o r PEG.  In a d d i t i o n the nature, and perhaps the l o c a t i o n , of the ester and binding appear to be d i f f e r e n t , for a number of reasons. F i r s t l y the  PEG PEG  binding appears not t o . s a t u r a t e , or at l e a s t does so at a much higher surface concentration than does the e s t e r . This i n d i c a t e s thay are not binding to the same ' s i t e s ' . Secondly the binding strength of the PEG i s very s i m i l a r i n each phase ( F i g . 5.3), i n d i c a t i n g that i t i s not  excluded  from the lower phase on binding to the extent that the ester i s . F i n a l l y a l a r g e r f r a c t i o n of PEG i s removed per wash ( F i g . 5.6), again i n d i c a t i n g a  -183-  greater a c c e s s i b i l i t y to the phase system. The l i g a n d binding i n both phases showed the c l a s s i c Langmuir isotherm shape ( F i g . 5.4a). The e s t e r binding data were therefore analysed by Scatchard p l o t s ( F i g . 5.8). P l o t s f o r both the phases are q u i t e l i n e a r , although there i s more s c a t t e r f o r binding data from the lower phase. This could be due to the higher v i s c o s i t y of the lower phase or to dextran induced aggregation, with consequent mixing problems. The estimates of the number of binding s i t e s from both phases were very s i m i l a r , again supporting the i n t e r p r e t a t i o n i n terms of the Langmuir isotherm. A value of 8.5 m i l l i o n molecules per c e l l gives an average distance between molecules of around o  o  45A, compared with an estimated radius of g y r a t i o n f o r PEG 6000 of 25 A (Cabane, 1985). The binding energies were estimated from these p l o t s as -16.6+0.3 and -17.9+0.3 kT/molecule i n the upper and lower phases r e s p e c t i v e l y . The free energy of t r a n s f e r of p a l m i t i c acid from an aqueous to a hydrocarbon solvent i s estimated to be around -14.4 kT/molecule, of which +7 kT i s due to the c a r b o x y l i c a c i d head group (Tanford, 1976). These f i g u r e s are comparable, and support the proposed mechanism of PEG-palmitate a c t i o n (Eriksson and Albertsson, 1978, Van A l s t i n e , 1984), whereby the palmitate t a i l i n t e r c a l a t e s i n t o the l i p i d b i l a y e r - a hydrophobic interaction. The low l i g a n d concentrations needed to produce p a r t i t i o n e f f e c t s , the fact that the binding appears to be of the Langmuir type, and the r e l a t i v e l y low surface coverage of the l i g a n d (about one t h i r d of the s a t u r a t i o n value at 100% p a r t i t i o n , estimated from F i g . 5.2b and the data i n Table 5.5), suggest that the theory developed i n Chapter 3D can be a p p l i e d to t h i s data. Another estimate of the binding energy can be obtained without using  -184-  Scatchard p l o t s and the Langmuir model i m p l i c i t i n them. In t h i s case i t i s assumed that the palmitate t a i l i s e f f e c t i v e l y p a r t i t i o n i n g between the s o l u t i o n and the l i p i d b i l a y e r , which i s treated as having  the  c h a r a c t e r i s t i c s of a two dimensional hydrocarbon solvent. Then  we have  (Tanford, 1976):  AG  where  0  = kT In  X^,  X /"X 1  [5.4]  b  X^ are the mole f r a c t i o n concentrations of l i g a n d i n  s o l u t i o n and i n the b i l a y e r r e s p e c t i v e l y . An estimate of the t o t a l number of l i p i d s can be obtained from the l i t e r a t u r e (Van Deenan and G i e r , 1974) g 5 xlO  as  molecules per c e l l . The r a t i o of mole f r a c t i o n s of free and bound  ester i s then obtained from the i n i t i a l slope of the isotherm i n the upper phase as 3.6 x l O  - 6  g i v i n g an estimate of the binding energy as  -12.5  kT/molecule, which i s somewhat smaller than that obtained from the  Scatchard  p l o t s . However the d i f f e r e n c e i n binding energies i n each phase i s given d i r e c t l y from the logarithm of the r a t i o of i n i t i a l isotherm slopes, f o r e i t h e r method of a n a l y s i s , providing the number of binding s i t e s i s the same i n each phase. These binding data thus allow some reasonable  estimates  of  the-ester binding energies, and p a r t i c u l a r l y t h e i r d i f f e r e n c e , to be made. Binding experiments were a l s o done i n complete phase systems i n order to more c l o s e l y d u p l i c a t e the conditions of c e l l p a r t i t i o n .  The estimate of  the number of s i t e s i s again very c l o s e i n each phase, i n d i c a t i n g the i n t e r n a l consistency of the measurements ( F i g 5.8b). The apparent number of binding s i t e s , and the binding energy i n the upper phase are s l i g h t l y higher  -185-  using t h i s method. This probably r e f l e c t s the d i f f i c u l t y i n measuring such low c e l l concentrations accurately during the binding measurements. An a d d i t i o n a l complication i s that at low ester concentrations the c e l l s a l l accumulate-at the i n t e r f a c e . The binding energy i n the lower phase i s the same i n the two experiments, i n d i c a t i n g that there i s no d i f f e r e n c e i n binding when the c e l l s are e i t h e r added t o the lower phase d i r e c t l y , or added f i r s t to the upper phase then t r a n s f e r r e d to the lower phase. The ester p a r t i t i o n c o e f f i c i e n t s measured simultaneously give very s i m i l a r r e s u l t s to those measured i n separate experiments ( F i g 5.1a).  The dependence of the c e l l surface energy d i f f e r e n c e on the number of ester molecules bound was obtained by contact angle measurements i n the presence o f various ester concentrations (Table 5.5). The c e l l surface free energy d i f f e r e n c e , Ay decreases by  -0.06 kT/molecule bound, which i s  extremely small compared with the ester binding energies or the energy of ester t r a n s f e r between the phases. A t e s t o f [3.60] was made by s u b s t i t u t i n g i n the values of n, k^, k  D  experiments and determining  obtained from the ' i n phase' binding Ay as a function of concentration. The r a t e o f  increase o f Ay given by [3.60] was very s e n s i t i v e t o the values of binding energies, and of the ester p a r t i t i o n c o e f f i c i e n t used ( F i g . 5.9), since t h i s equation was derived from [3.56] which contains the d i f f e r e n c e s i n three l a r g e , s i m i l a r l y s i z e d terms. I t was not p o s s i b l e to f i t the data e x a c t l y with one value, which probably r e f l e c t s the f a c t that the ester p a r t i t i o n c o e f f i c i e n t varied with concentration. The p a r t i t i o n c o e f f i c i e n t was therefore adjusted t o give the best f i t , by i n c r e a s i n g i t s l i g h t l y from 3.145  t o 3.16 over the range 0 t o 2 JJM. These values l a y w i t h i n the range  -186-  determined experimentally i n F i g . 5.1. I f the binding data from the separated phases were used i n s t e a d , a good f i t was obtained with a s l i g h t l y higher ester p a r t i t i o n , 3.95  to  4.1.  The binding and contact angle data are thus i n q u a n t i t a t i v e agreement with the theory of the e f f e c t of an a f f i n i t y l i g a n d on the c e l l surface free energy d i f f e r e n c e proposed i n Chapter Three. One of the features of t h i s model i s that i t explains the d i f f e r e n t e f f e c t s of the ester and  PEG.  Because the ester binding energy i s high, i t has an appreciable e f f e c t on the c e l l surface free energy, even though the ester may  only contribute a  f r a c t i o n of the t o t a l PEG bound to the c e l l surface ( F i g . 5.5). The model also explains the small increase i n c e l l surface free energy per bound ester molecule. The p h y s i c a l basis f o r t h i s i s that the l i g a n d i s p a r t i a l l y hidden from the phase system, an i n t e r p r e t a t i o n consistent with the d i f f e r e n c e i n binding energies i n each phase. This can be seen more c l e a r l y with reference to F i g . 3.2, and the l i m i t i n g cases discussed i n Chapter Three. In the extreme case a l i g a n d not exposed to the phase system at a l l would have no e f f e c t , and the d i f f e r e n c e i n binding energies would be j u s t equal to the energy of l i g a n d t r a n s f e r between the phases, which v a r i e s from -0.69 -1.21  kT i n the range 0 to 1 jjm  to  (Curve A, F i g . 3.4b). By c o n t r a s t , a bound  l i g a n d that i s completely exposed to the phases would have the same binding energy i n both phases.  The a c t u a l data f o r the ester shows that the type of  binding i s c l o s e r to the f i r s t case. The idea of a hidden l i g a n d again invokes the concept of e x c l u s i o n of the phase polymers which was encountered i n s e c t i o n 4D.  A d d i t i o n a l support f o r t h i s e f f e c t comes from the d i f f e r e n c e  i n PEG and ester binding behavior. The model of ester binding by i n s e r t i o n  -187-  of the palmitate t a i l group i n t o the l i p i d b i l a y e r locates the molecule deeply i n the glycocalyx. The head group, which would be around 50 A d i a . based on a random c o i l conformation (Cabanes, 1982;  Tanford, 1961)  could  w e l l be p a r t i a l l y i n a c c e s s i b l e i f the glycocalyx were 70 A t h i c k (Levine et a l . , 1983). At the same time the binding energy argument and d i f f e r e n c e s i n wash o f f behaviour suggest that PEG binds to the outer part of the glycocalyx. Since dextran i s more than t h i r t y times as l a r g e as PEG, i t would also be expected to bind to the outer  regions.  Of course the a n a l y s i s of the model of a f f i n i t y l i g a n d e f f e c t s assumes that the l i g a n d binding i s at e q u i l i b r i u m i n both phases, and of the Langmuir type. The binding energy estimates from the Scatchard p l o t s a l s o use t h i s assumption. While these p l o t s are l i n e a r , the ester wash o f f studies i n the lower phase suggest that the binding might not come to e q u i l i b r i u m under a l l c o n d i t i o n s . This could a f f e c t the a p p l i c a b i l i t y of [3.57], although i t i s d i f f i c u l t to incorporate such e f f e c t s i n t o t h i s theory.  The e f f e c t of ester on Ay tensions i n phase systems. (Fig.  E x t r a p o l a t i n g to higher ester concentration  i t can be seen that Ay  5.9)  tension, Y  has some i m p l i c a t i o n s for measuring c r i t i c a l  T  (6.3 xlO  B  3  would become numerically equal to the  dynes/cm) at around 2 JJM (3.5 xlO  12  2 molecules/cm  bound). At t h i s point the contact angle would be zero.  However the surface free energy i n the upper phase w i l l continue to decrease 12 as the ester binding increases to the s a t u r a t i o n value of 6 xlO 2 t molecules/cm , so e i t h e r the surface free energy Y becomes negative,  -188-  which i s u n l i k e l y , or i t i s not zero at the c r i t i c a l tension. The s i t u a t i o n implies that Y  B  i s not equal to  latter  at the c r i t i c a l tension  i n these systems. Therefore the concept of c r i t i c a l spreading tension, and the equation of s t a t e of Neumann et a l . (1974) do not appear to be a p p l i c a b l e to these two phase systems.  To summarize, a number of i n t e r e s t i n g conclusions can be drawn from the r e s u l t s i n t h i s chapter.  At low concentrations, the ester has l i t t l e e f f e c t  on the phase system, but increases c e l l p a r t i t i o n d r a m a t i c a l l y .  The  effect  on the p a r t i t i o n i s due to the strong binding of the ester to the c e l l surface.  The c e l l surface free energy d i f f e r e n c e i s decreased by the bound  e s t e r , but the e f f e c t per molecule i s quite small. This i s a t t r i b u t e d to exclusion of the phases from the glycocalyx, which e f f e c t i v e l y hides the bound e s t e r .  This hypothesis  i s consistent with the f a c t that the  d i f f e r e n c e i n binding energies i n each phase i s s i m i l a r to the energy of ester t r a n s f e r between the phases.  Desorption studies showed that bound PEG  i s more accessible to the upper phase than i s the e s t e r , which again i s consistent with the exclusion hypothesis.  The ester did not appear to reach  desorption e q u i l i b r i u m i n the lower phase, but did so i n the upper.  However  for the present study t h i s probably has l i t t l e consequence for attainment of e q u i l i b r i u m during p a r t i t i o n , since the amount of ester bound i n both phases at e q u i l i b r i u m i s s i m i l a r .  The amount the c e l l surface free energy  d i f f e r e n c e changes per ester molecule bound i s consistent with the  theory  developed i n Chapter Three, using the experimentally determined .binding energies and p a r t i t i o n c o e f f i c i e n t of the e s t e r .  The theory p r e d i c t s that  the binding energy of the l i g a n d i s important, and thus that small changes  -189-  i n the amounts of PEG and dextran bound to the surface would have comparatively  l i t t l e e f f e c t since these polymers bind very weakly.  However  a more extensive t e s t of the theory with t h i s l i g a n d i s not possible f o r a number of reasons.  The ester p a r t i t i o n c o e f f i c i e n t increases with  concentration, and m i c e l l e s form at concentrations greater than 10 J J M . Therefore i t i s not p o s s i b l e to get a good estimate of the energy of ester t r a n s f e r between the phases, a quantity required to t e s t the theory.  This  a l s o means that the high ester concentration range i s experimentally inaccessible.  As a consequence i t i s not possible to t e s t the p r e d i c t i o n  that the e f f e c t of ester should reach a maximum and then decrease to a plateau,value  ( F i g . 3.3).  However i t i s p o s s i b l e that t h i s maximum (plus  the e f f e c t s of m i c e l l e formation) i s responsible f o r the plateau i n c e l l p a r t i t i o n at l e s s than 100% seen by Van A l s t i n e (1984) i n many systems containing various PEG-alkyl e s t e r s .  -190-  Chapter S i x . Factors Determining C e l l P a r t i t i o n  True science however, cannot e x i s t without an a e s t h e t i c appreciation of the objects examined- M i k h a i l Vol'kenshtein  A. Introduction  The previous two chapters are concerned p r i n c i p a l l y with the f i r s t question posed i n the Introduction- what i s the r e l a t i o n s h i p between the phase system p r o p e r t i e s , the c e l l surface p r o p e r t i e s and the r e l a t i v e a f f i n i t y of the c e l l f o r e i t h e r phase?  These e f f e c t s are expressed  thermodynamically i n a s i n g l e q u a n t i t y , the c e l l surface free energy difference, Ay .  This quantity can be determined at e q u i l i b r i u m by means of  contact angle measurements.  This chapter deals with the second question-  what determines the p a r t i t i o n of c e l l s ?  F i r s t , the e f f e c t of the other  thermodynamic quantity involved i n measuring A y , namely the i n t e r f a c i a l tension between the phases, i s studied. and  Ay to partition i s investigated.  Then the r e l a t i o n s h i p of tension Since the p a r t i t i o n i s not determined  completely by these two parameters, the l a s t s e c t i o n looks at the mechanism of c e l l p a r t i t i o n , although i n a more q u a l i t a t i v e way.  B. Determinants o f C e l l P a r t i t i o n  i ) P a r t i t i o n and I n t e r f a c i a l Tension  The e f f e c t s of a l t e r i n g the polymer concentration, and hence the i n t e r f a c i a l tension between the phases, on c e l l p a r t i t i o n were examined.  -191-  Systems containing e i t h e r 10,0,110 or 110,0,0 buffer with i n c r e a s i n g polymer concentrations were made up. The tensions of s e v e r a l systems were measured (Table 4.1), and the r e s t c a l c u l a t e d from t h e i r t i e l i n e lengths using the r e l a t i o n s given i n the Table. Increasing the tension reduces the c e l l p a r t i t i o n dramatically ( F i g . 6.1). Log K decreases l i n e a r l y with i n c r e a s i n g tension down to about K = 0.2, and then decreases l e s s r a p i d l y . Systems with 10 and 110 mM phosphate give e s s e n t i a l l y ' t h e same r e s u l t s .  As the polymer  concentrations are increased, the v i s c o s i t i e s of the phases a l s o increase, p a r t i c u l a r l y that, of the lower phase.  This could r e s u l t i n anomalously high  p a r t i t i o n measurements at high tensions due t o incomplete s e t t l i n g of c e l l / d r o p l e t aggregates from the upper phase.  This was checked by  p a r t i t i o n i n g c e l l s i n two systems containing 10,130,0 b u f f e r , which have s i m i l a r tensions and v i s c o s i t i e s , but l e s s p o s i t i v e p o t e n t i a l s . These c o n t r o l systems give much lower p a r t i t i o n s , i n d i c a t i n g that the r e l a t i v e l y high p a r t i t i o n s at high tensions are not a r t i f a c t s due to incomplete settling.  Data f o r the microorganism Acholeplasma l a i d l a w i , of around 1 jjm  diameter, taken from Van A l s t i n e (198A), are shown f o r comparison.  i i ) Polymer Composition and Contact Angle  The e f f e c t of polymer concentration on the c e l l surface free energy d i f f e r e n c e was a l s o examined by making contact angle measurements on c e l l s i n the 10,0,110 b u f f e r systems of s e c t i o n i ) .  The r e s u l t s are shown i n  Table 6.1. As the tension of the phase systems increases, the contact angle approaches ninety degrees, while the c e l l p a r t i t i o n decreases. The  -192-  Figure 6.1 Erythrocyte P a r t i t i o n and I n t e r f a c i a l Tension. Erythrocytes i n systems containing 10,0,110 buffer (o), 110,0,0 buffer (*), 10,130,0 buffer (•). Acoleplasma l a i d l a w i i p a r t i t i o n e d with 10,130,0 buffer (^), data taken from Van A l s t i n e , 1984.  -193-  normalised c e l l / i n t e r f a c e i n t e r a c t i o n energy, k E ^ / i r a ^ increases at a p r o p o r t i o n a l l y greater r a t e than the tension.  The c e l l surface free  energy d i f f e r e n c e , A y , does not have a simple dependence on the tension, but appears t o show two small maxima over t h i s range.  TABLE 6.1 ERYTHROCYTE PARTITION AND CONTACT ANGLE. EFFECT OF TENSION  System  Contact Tension AE^i Angle (°) — (erg/cm )x!0 — 2  (5,3.8) (5,4) . (6,4) (7,4) (7,4.4) 3  37+3 52+4 69 70 78  42 63+2 102 145 213+5  A  -33.5+2 -39 -37 -49.5 -43  1.7+0.5 9.2 42.0 63 135+15  Partition (%) 89.5+5 73 16.5 8.5 3+1  3  V ~ (cm/erg / ) th  1/2  1  2  15.4+0.2 12.6 9.9 8.3 6.9+0.2  A11 systems contained 10,0,110 b u f f e r  Schurch e t a l . (1981) suggested that the concept of c r i t i c a l wetting, which has been used i n c l a s s i c a l surface chemistry t o estimate surface free energies (Zisman, 1964, G i r i f a l c o and Good, 1957), could be used i n a s i m i l a r fashion i n phase systems.  A p l o t o f cos 6  against  square root of the tension (A Good-Girifalco p l o t ) was l i n e a r (Fig.  (r=0.990)  6.2). An e x t r a p o l a t i o n of t h i s p l o t t o cos 6= 1 gives an estimate of -3  3.0+0.4 xlO the  the r e c i p r o c a l  2 ergs/cm  f o r the c r i t i c a l spreading tension, and hence f o r  c e l l / l o w e r phase i n t e r f a c e free energy. The data of Schurch et a l .  (1981) f o r very s i m i l a r systems are a l s o p l o t t e d on F i g . 6.2 f o r comparison, and have slopes of the opposite s i g n , g i v i n g an estimate f o r the cell/upper phase free energy, with a value four times smaller.  -194-  Figure 6.2 G o o d - G i r i f a l c o P l o t s f o r Erythrocytes. (x,y)10,0,110 systems, Table 6.1 (•). Dx T500/PEG 8000 (o) and .Dx T500/PEG 20000 (*) systems containing Ringers, data taken from Schurch et a l . , 1981  -195-  i i i ) C e l l P a r t i t i o n and the Energy of C e l l / I n t e r f a c e I n t e r a c t i o n s  The theory o f p a r t i c l e p a r t i t i o n proposed by Albertsson (1971), based on the Bronsted equation, r e l a t e s the p a r t i t i o n c o e f f i c i e n t to the energy necessary to remove the c e l l from the i n t e r f a c e i n t o the top phase,  A  E  ti  =  a  p  T T  tb  ( 1  "  c  o  s  e  )  AE^  2  In K = - AE /kT  [1.22]  ti  Figure 6.3 shows the dependence of p a r t i t i o n on t h i s parameter.  The  p a r t i t i o n data and values f o r the normalized attachment energies were taken from Tables 4.8, 5.5 and 6.1, and a radius of 3.5 pm used f o r the c e l l . The p a r t i t i o n i n these three sets o f curves was manipulated by varying e i t h e r the p o t e n t i a l , the t e n s i o n , or the l i g a n d concentration. In a l l cases the ordinate i n t e r c e p t s are around 10 to 15. The i n i t i a l slopes are s i m i l a r and g i v e , using [1.22], values of around 2x10^ k T / c e l l f o r the c h a r a c t e r i s t i c energy ( E ) o f p a r t i t i o n . The slopes decrease i n a l l three c  4 curves, t o give around 4x10  5 and 2x10  kT/cell respectively for E  c >  Because of the experimental s c a t t e r , the p l o t f o r the a f f i n i t y l i g a n d could perhaps be i n t e r p r e t e d as being l i n e a r (r=0.960).  The data from F i g . 6.3  were a l s o expressed as percent p a r t i t i o n as a f u n c t i o n of the minimum force required to remove a c e l l from a plane i n t e r f a c e , estimated from [A4] of Appendix A, and t h i s i s shown i n F i g . 6.16. In a l l three cases the p l o t s resemble step f u n c t i o n s , the one f o r the tension showing a more gradual  -196-  0. 01  0 AE  t |  xl0  9  (ERGS)  Figure 6.3 Dependence o f Erythrocyte P a r t i t i o n C o e f f i c i e n t on the C e l l / I n t e r f a c e I n t e r a c t i o n Energy. Data taken from Tables 4.8, 5.5 and 6.1, where the p o t e n t i a l (+), the phase composition (tension) (G), or ester concentration (*) were v a r i e d .  -197-  0  5 DETACHMENT FORCE  10  15  (10" DYNES) 6  Figure 6.4 Dependence of Percent Erythrocyte P a r t i t i o n on the Detachment Force. The minimum force necessary t o detach a c e l l from a plane i n t e r f a c e was c a l c u l a t e d from the data i n Tables 4.8, 5.5 and 6.1 using [A4]. Tension (o), p o t e n t i a l (*), or ester concentration (+) was v a r i e d .  -198-  decrease i n p a r t i t i o n as the force i s increased.  iv)  Discussion Since the p a r t i t i o n decreases with i n c r e a s i n g tension (Fig 6.1),  p r e d i c t i o n of the Br^nsted equation  the  ( i n the form on [1.31]) of the r o l e of  i n t e r f a c i a l tension i s perhaps borne out i n a q u a l i t a t i v e way.  However the  Br^nsted equation p r e d i c t s that the dependence of log K on tension would be more l i n e a r , since  Y i n [1.28] increases with the fourth power of the t i e  l i n e length, while AY  i s a weaker function of tension (Table 6.1).  course when the polymer compositions  Of  are a l t e r e d , v i r t u a l l y every other  property of the phase system i s a l s o a l t e r e d , i n d i c a t i n g here that other f a c t o r s are involved i n p a r t i t i o n .  In a d d i t i o n t h i s equation p r e d i c t s that  p a r t i t i o n to the i n t e r f a c e should increase exponentially with area, and that the dependence of p a r t i t i o n on the tension should increase r a p i d l y with area. Figure 6.1 shows that these p r e d i c t i o n s are not borne out. Although the area of A. l a i d l a w i i i s more than a hundred times smaller than that of an erythrocyte, the dependence of p a r t i t i o n on tension i s very s i m i l a r . P a r t i t i o n can be c a r r i e d out on solutes over an enormous s i z e range, where i t i s expected that the s i z e of the A y  terms would not vary by more than  an order of magnitude. These observations i n d i c a t e that the p a r t i t i o n i s a c t u a l l y a weak function of the p a r t i c l e area.  The v a r i a t i o n of the c e l l  p a r t t i o n c o e f f i c i e n t on the energy of c e l l / i n t e r f a c e attachment, however, shows that there are more serious objections to the use of the equation f o r d e s c r i b i n g c e l l p a r t i t i o n (vide i n f r a ) .  Br^nsted  -199-  There i s a s t r i k i n g d i f f e r e n c e i n the Good-Girifalco p l o t s seen i n F i g . 6.2  f o r the same c e l l type i n very s i m i l a r phase systems.  The contact angle  as a function of tension changes i n opposite d i r e c t i o n s i n the c h l o r i d e r i c h systems of Schurch et_ a l . (1981) and the phosphate r i c h systems of Table 6.1.  Since the systems i n Table 6.1 contain only phosphate and  sorbitol,  the r e s u l t s of Chapter Four, s e c t i o n D i n d i c a t e that the p o t e n t i a l contributes s i g n i f i c a n t l y to AY . Since the p o t e n t i a l increases with t i e l i n e length (and therefore with t e n s i o n ) , then the weak dependence of AY t ^ must be due to an i n c r e a s i n g l y p o s i t i v e c o n t r i b u t i o n to AY terms, such as polymer i n t e r a c t i o n s . Introduction that AY  on  from other  This emphasises the point made i n the  i s a r e s u l t a n t of several e f f e c t s , and the dependence  of t h i s parameter on the polymer composition of the phase system i s l i k e l y to be complex. The r e s u l t s i n F i g . 6.2  show that AY  can increase or  decrease with tension, depending on the precise composition of the phase system, and hence on the r e l a t i v e importance of the various factors that contribute to AY . Also the large d i f f e r e n c e i n estimates for the c e l l 3  surface free energy, Y*  obtained from the c r i t i c a l spreading  tension  obtained i n the d i f f e r e n t systems show that t h i s quantity i s a r e l a t i v e  one,  which a p p l i e s only to the surface i n the phase that wets i t at that c r i t i c a l tension. that  y  t  Thus the l i n e a r i t y of such Good-Girifalco p l o t s need i n d i c a t e only and  Y  i n d i c a t i n g that  b  vary i n an orderly fashion with Y  t  Y , tb  rather than  = 0 at the c r i t i c a l tension, since t h i s treatment of  surface energies and c r i t i c a l tensions ( G i r i f a l c o and Good, 1957)  has  not  been v e r i f i e d t h e o r e t i c a l l y f o r phase systems, and i s i n f a c t i n c o n s i s t e n t with the e f f e c t s of ester on  AY (Section 5D).  -200-  On the other hand the contact angle and the tension can be used to obtain two other important q u a n t i t i e s , the energy of c e l l - i n t e r f a c e attachment, A E ^ ,  and the minimum force necessary to detach the c e l l from  the i n t e r f a c e , f . E i t h e r of these parameters could be considered to be the important quantity with respect to p a r t i t i o n , depending on the mechanism by which the c e l l s are d i s t r i b u t e d . The r e l a t i o n s h i p s between the c e l l p a r t i t i o n and the c e l l i n t e r f a c e attachment energy, A E ^ , detachment f o r c e , f  Now E  ^ ti'  are shown i n F i g s . 6.3  and the  and 6.A r e s p e c t i v e l y .  i n the Br0nsted theory the p a r t i t i o n i s determined s o l e l y by w n  *  c n  *  s  1  i  n e a I  ' l y r e l a t e d to the l o g of the p a r t i t i o n c o e f f i c i e n t ,  with an inverse slope of kT. I t can be seen that the exponential r e l a t i o n s h i p between p a r t i t i o n and the attachment energy i s not confirmed  strictly  for erythrocytes. The work of Gerson (Gerson, 1980, Gerson and  A k i t , 1980) was not a s a t i s f a c t o r y t e s t of the Brc/>nsted r e l a t i o n f o r reasons given i n the Introduction. The slopes of the p l o t s i n F i g . 6.3, however, are four to f i v e orders of magnitude smaller than predicted from [1.22], g i v i n g c h a r a c t e r i s t i c p a r t i t i o n energies of 2-20  xlO  kT/cell.  I t i s c l e a r that  c e l l p a r t i t i o n i s not a thermodynamic e q u i l i b r i u m process driven only by thermal energies, since i n systems where a f i n i t e p a r t i t i o n i s observed the free energy w i l l be minimised when a l l the c e l l s are at the i n t e r f a c e .  At t h i s point i t must be noted that other workers have used the term non-equilibrium i n a d i f f e r e n t sense, r e f e r r i n g to the time dependence of p a r t i t i o n (eg. Raymond and F i s h e r , 1981; Fisher and Walter, 1984; section l C . i v ) .  see  For t y p i c a l p a r t i t i o n experiments and systems used i n t h i s  -201-  work, the plateau period f o r c e l l p a r t i t i o n extended from about twenty t o f i f t y minutes a f t e r mixing the phases, so the p a r t i t i o n was e s s e n t i a l l y time independent i n t h i s period. However depending on the systems, t h e i r volumes, and the c e l l s i z e , there may be no plateau period at a l l , or i t may l a s t indefinitely.  The curvature o f the p l o t s i n F i g . 6.3 could be i n t e r p r e t e d as changes i n the c h a r a c t e r i s t i c energy o f p a r t i t i o n , as the appropriate parameter of the system, such as the tension or p o t e n t i a l i s v a r i e d . C e r t a i n l y as the tension of the system i s increased by i n c r e a s i n g the polymer concentrations, almost every other property of the system i s being a l t e r e d , so the n o n - l i n e a r i t y of t h i s p l o t i s not s u r p r i s i n g . A l t e r n a t i v e l y the curvature may r e f l e c t the i n a p p l i c a b i l i t y o f even the exponential form o f the p a r t i t i o n equations. The exponential form a r i s e s , however, from quite general considerations of the s t o c h a s t i c nature of such d i s t r i b u t i o n processes, such as the Boltzmann d i s t r i b u t i o n , or p a r t i t i o n (eg. see Guggenheim, 1959), so i n the absence of a p a r t i c u l a r model or further data i t i s d i f f i c u l t to suggest a p l a u s i b l e a l t e r n a t i v e .  P a r t i t i o n may a l s o be viewed as a mechanical, force driven process: c e l l s are attached t o droplets of the phases, as they s e t t l e and coalesce. These processes cause complex f l u i d flows, which r e s u l t i n c o n t i n u a l l y varying drag forces on the c e l l s . These forces can p o t e n t i a l l y remove c e l l s from the i n t e r f a c e , p a r t i t i o n i n g them. At some point i n the separation process, the c e l l s encounter some maximum drag force. The average maximum drag force experienced by the c e l l s ( f ) i s thus important i n determining a  -202-  whether c e l l s can be removed from the i n t e r f a c e , i e . whether the p a r t i t i o n i s greater than zero.  The minimum force necessary t o detach a s p h e r i c a l p a r t i c l e from a plane i n t e r f a c e , f , can be estimated from the contact angle and equation [A3]. The p a r t i t i o n / f o r c e curves i n F i g . 6.4 have the same general form, a type o f step function, the p a r t i t i o n decreasing r e l a t i v e l y q u i c k l y as f i s increased.  However assignment of a p h y s i c a l i n t e r p r e t a t i o n to a  c h a r a c t e r i s t i c force obtained from the curves i n the t h i s model i s d i f f i c u l t . The force at 50% p a r t i t i o n could perhaps represent the f that the c e l l population experiences i n that p a r t i c u l a r system. I f c e l l p a r t i t i o n were not random, i e . i f a l l the c e l l s were attached t o the same s i z e drops, and the phases separated out i n a completely uniform way, a l l c e l l s would experience exactly the same maximum force, f , and the curves of F i g . 6.4 would be p e r f e c t l y sharp step functions. There would be a c r i t i c a l r e t a i n i n g force, f , below which a l l the c e l l s would be detached, and the p a r t i t i o n would be a hundred percent (also assuming no reattachment i n t h i s i d e a l case). Above t h i s force, no c e l l s would be detached, and the p a r t i t i o n would be zero. The sharpness of the step can therefore be thought o f as 1  representing the ' d i s p e r s i t y , or randomness of the p a r t i t i o n process. The curve where the tension i s v a r i e d has the greatest d i s p e r s i t y , since not only i s the necessary detachment force ( f ) being a l t e r e d , but the separation of the phases, and consequently the forces applied t o the c e l l s are a l s o being a l t e r e d as the polymer concentrations are increased.  -203-  The force view a l s o may p a r t i c l e p a r t i t i o n on area.  make i t easier to explain the weak dependence of Such behaviour could be explained by the  p l a u s i b l e assumption that the forces experienced by the p a r t i c l e s which tend to remove them from the i n t e r f a c e decrease as t h e i r area decreases, u n t i l u l t i m a t e l y they could be d i s t r i b u t e d by d i f f u s i o n alone.  To conclude t h i s s e c t i o n , the r e s u l t s show that erythrocyte p a r t i t i o n i s not a thermodynamic e q u i l i b r i u m process.  However, f o r a system of given  polymer composition, under i d e n t i c a l conditions f o r p a r t i t i o n ( i e . s e t t l i n g time, tube geometry e t c . ) , the p a r t i t i o n i s determined by the  cell/interface  attachment energy, a thermodynamic quantity r e l a t e d to the tension and r e l a t i v e a f f i n i t y of the c e l l f o r each phase.  the  As t h i s quantity (or a  r e l a t e d quantity, the minimum force of detachment) i s decreased, by  altering  the p o t e n t i a l or adding an a f f i n i t y l i g a n d f o r example, the p a r t i t i o n i n t o the upper phase increases.  In other words differences i n p a r t i t i o n r e f l e c t  d i f f e r e n c e s i n the cell/phase system i n t e r a c t i o n . In cases where the system parameters are held constant, d i f f e r e n c e s i n p a r t i t i o n therefore r e f l e c t d i f f e r e n c e s i n c e l l surface p r o p e r t i e s .  P a r t i t i o n has a weak dependence on  the c e l l area, shape (hypertonic s w e l l i n g of the c e l l s has l i t t l e e f f e c t ) , or density (providing p a r t i t i o n i s measured before the c e l l s s e t t l e out of the system).  -204-  C. Mechanisms of C e l l P a r t i t i o n  i)  C e l l P a r t i t i o n , Phase Density and Volume Ratio  The r e s u l t s of the previous s e c t i o n i n d i c a t e that c e l l s are not d i s t r i b u t e d by thermal motion, i n the manner of s o l u t e s , and that the p a r t i t i o n i s not completely characterised by Y  t b  and A Y .  Other  properties of the system are thus important. The e f f e c t s of two o f these, volume r a t i o and phase density d i f f e r e n c e , were examined.  a) Phase Volume Ratio  The e f f e c t of changing the phase volume r a t i o i s shown i n F i g . 6.5a. Four (5,4)10,130,0 systems were made up with varying amounts of e s t e r , so as to give a range o f c e l l p a r t i t i o n s from 20 t o 90%.  P a r t i t i o n experiments  were performed with e i t h e r the top or t o t a l volumes held constant, with e s s e n t i a l l y the same r e s u l t s .  The p a r t i t i o n decreases as the volume r a t i o  i s increased or decreased, being maximum at one. This e f f e c t i s most noticeable at lower p a r t i t i o n s .  b) Phase Density Difference  Three dextran/PEG/Ficoll systems (7,0,12), (7,0.3,12), and (7,0.6,12)10,130,0  were made up, where the f i r s t system has a more dense  F i c o l l r i c h phase, the second system has no density d i f f e r e n c e between the phases, and the t h i r d system has a more dense dextran r i c h phase. The e f f e c t  -205-  of e s t e r on c e l l p a r t i t i o n i n a l l three systems i s shown i n F i g . 6.5b. In the absence of e s t e r , the c e l l s p a r t i t i o n mostly t o the i n t e r f a c e , but the p a r t i t i o n i n t o the F i c o l l  r i c h phase increases with e s t e r concentration. A l l  three systems give very s i m i l a r curves, with the isopycnic system having a s l i g h t l y higher p a r t i t i o n at the highest ester concentration. The p a r t i t i o n i s l e s s s e n s i t i v e to ester concentration than i n PEG/dextran systems.  c) V i s u a l D e s c r i p t i o n of P a r t i t i o n  Other workers (Albertsson, 1971, ppl34-6; Van A l s t i n e , 1984) have observed that c e l l p a r t i t i o n i s apparently determined e a r l y on i n the separation of the phases a f t e r mixing.  The time at which the p a r t i t i o n i s  determined i s important i n a consideration o f p o s s i b l e mechanisms of c e l l p a r t i t i o n (section i i i below).  Therefore t h i s point was studied by means of  v i s u a l and stereomicroscopic examination o f phase systems during p a r t i t i o n . Figures 6.6 and 6.7 show the appearance o f c e l l p a r t i t i o n i n isopycnic Dx/PEG/Fi systems. The appearance o f c e l l p a r t i t i o n i n Dx/PEG systems was s i m i l a r , but because of the r a p i d flow of the phases due to the density d i f f e r e n c e , they could not e a s i l y be photographed.  The r a t e of phase  separation by coalescence i s f a i r l y r a p i d , the phases being  completely  separated a f t e r 15 min ( F i g . 6.6d). At one minute the. d i f f e r e n c e between high and low p a r t i t i o n i s already evident, the i n t e r f a c e i n the low p a r t i t i o n system ( l e f t hand cuvette, %P = 0) being much more defined due to the accumulation  o f c e l l s there, compared to the r i g h t hand one (%P = 100).  This i s more apparent i n the magnified view ( F i g . 6.7). Comparing photos a) (%P = 0) and b) (%P = 100) the d i f f e r e n c e between the high and low  -206-  2  r  0  0.2  0.4  0.6  0.8  1  FRACTIONAL TOP PHASE VOLUME  < CL  LU  ESTER CONCENTRATION (juM) Figure 6.5 E f f e c t of Phase Volume Ratio and Density Difference on Erythrocyte P a r t i t i o n , a) E f f e c t of volume r a t i o . System: (5,4)10,130,0 plus 0.5 (A,B); 0.7 (C); 0.9 (D); 1.5 (E) uM e s t e r . Total volume 2ml ( o ) , top phase volume 1ml (*), top phase volume 2ml (+). b) E f f e c t o f density d i f f e r e n c e . (7,0,12), with more dense F i c o l l p h a s e , ^ = 0.006 g/ml (*), (7,0.3,12), isopycnic system ( o ) , (7,0.6,12), with more dense dextran phase, = 0.006 g/ml ( 0 ) . C e l l s p a r t i t i o n e d i n t o the F i c o l l r i c h phase. A l l systems contained 10,130,0 b u f f e r .  -207-  Figure 6.6. Appearance of C e l l P a r t i t i o n i n Isopycnic Systems. System used was a (7,0.3,12)10,130,0 as i n F i g . 6.5b, with from l e f t to r i g h t : 0,2,3,8 JJM e s t e r . Systems were mixed by i n v e r s i o n twenty times and allowed to s e t t l e for 3 ( a ) , 6 (b), 9 ( c ) , 15 (d) minutes. Dextran r i c h phase i s i n the centre i n ( d ) . Magnification x l . 5 .  -208  Figure 6.7. C e l l P a r t i t i o n i n Isopycnic Systems- Microscopic View. System was (7, 0.3, 12)10,130,0. In b) and d) 8 JJM ester was added to the system. Photos were taken 45 sec (a, b) and 3 min ( c , d) a f t e r mixing. Magnification x50.  -209-  p a r t i t i o n i n g systems i s apparent only 45 sec a f t e r mixing, and i s s t r i k i n g a f t e r 3 min o f separation. The c e l l s appear as small dark dots about 0.3 mm dia.  Small drops («c50j_im dia.) are not resolved c l e a r l y due to the low  r e f r a c t i v e index d i f f e r e n c e between the phases and the density of the emulsion, but are apparent from the mottled appearance.  i i ) Discussion and Proposal of a Mechanism f o r C e l l P a r t i t i o n  a) Background  Since thermal energies, i e . d i f f u s i o n processes, are not s u f f i c i e n t l y energetic to d i s t r i b u t e large (=>1 pm dia.) c e l l s between the i n t e r f a c e and the phases, the question a r i s e s as to what process does p a r t i t i o n the cells.  A model based on forces a r i s i n g during the separation of the phases  has already been alluded to i n s e c t i o n B i i i above.  Before considering t h i s  question f u r t h e r , i t w i l l be h e l p f u l to summarize a number of pertinent observations, which are based mainly on the behaviour of erythrocytes i n Dx/PEG systems of the type considered i n t h i s work.  P a r t i t i o n of erythrocytes i s a s t o c h a s t i c process with a c h a r a c t e r i s t i c energy ( E ) ranging from 2 to 20 xlO k T / c e l l . c  P a r t i t i o n o f erythrocytes i s independent o f c e l l concentration a t l e a s t 6  8  i n the range 1 0 - 1 0 c e l l s / m l (Van A l s t i n e , 198A). P a r t i t i o n depends weakly on the p a r t i c l e area. P a r t i t i o n i s i n s e n s i t i v e t o the density d i f f e r e n c e between the phases, i n the range +0.006 g/ml.  -210-  P a r t i t i o n increases as the a f f i n i t y o f the c e l l f o r the upper phase i s increased, and as i t s a f f i n i t y f o r the i n t e r f a c e i s decreased C e l l p a r t i t i o n i s increased as the height o f the phases i s reduced (Walter, 1985) P a r t i t i o n i s maximum when the phase volumes are equal. P a r t i t i o n i s determined e a r l y on i n phase separation (within a minute)  Studying the mechanism o f p a r t i t i o n i s extremely d i f f i c u l t , due to the time dependent nature of p a r t i t i o n and the d i f f i c u l t y o f looking at c e l l s and drops during the p a r t i t i o n process.  However i t i s p o s s i b l e t o propose  several d i s t i n c t p a r t i t i o n mechanisms, not n e c e s s a r i l y mutually e x c l u s i v e . By a consideration o f q u a l i t a t i v e and semi-quantitative arguments  (Appendix  B), the a b i l i t y o f these mechanisms t o account for the observed features o f c e l l p a r t i t i o n can be discussed. Three types o f arguments can be considered: energy arguments, force arguments and q u a l i t a t i v e explanations o f the features l i s t e d above.  In a d d i t i o n the s i m i l a r i t i e s between p a r t i c l e  p a r t i t i o n and foam f l o t a t i o n i n ore processing have already been noted (Albertsson, 1971, and s e c t i o n 1A).  Some o f the r e s u l t s obtained i n the  theory o f foam f l o t a t i o n (eg. Clarke and Wilson, 1983; Schulze, 1984) are thus d i r e c t l y a p p l i c a b l e t o c e l l p a r t i t i o n , d i f f e r i n g only i n the scale o f parameters such as density d i f f e r e n c e , v i s c o s i t y and p a r t i c l e s i z e .  b) A Proposed Mechanism f o r C e l l P a r t i t i o n  The p r i n c i p a l model o f p a r t i t i o n that w i l l be considered here i s the coalescence model. When the phase system i s shaken up, a very f i n e emulsion  -211-  i s formed, c o n s i s t i n g of a l a r g e number of small drops o f both phases. The i n t e r f a c i a l area i s extremely large at t h i s point. As the phases separate, the drops coalesce and become l a r g e r , the area decreasing u n t i l i t i s f i n a l l y equal to the tube c r o s s e c t i o n a l area. This decrease i n area r e s u l t s i n a d i s s i p a t i o n o f the energy associated with the i n t e r f a c e . In t h i s model the relevant forces a r i s e from f l u i d flows generated when drops coalesce. Quite high v e l o c i t i e s can be generated compared to sedimentation,  although  these are more t r a n s i t o r y , being q u i c k l y damped by the high v i s c o s i t i e s . That the i n t e r f a c i a l forces are l a r g e compared to the g r a v i t a t i o n a l forces i s evident from the small Eotvos number (Table 6.2). This t a b l e a l s o i n d i c a t e s that f o r small drops viscous and i n e r t i a l forces are a l s o small. For l a r g e r drops (>100 pm dia.) g r a v i t a t i o n a l forces dominate, while viscous and tension forces are comparable.  TABLE 6.2 DIMENSIONLESS NUMBERS CHARACTERISING FLUID FLOW REGIMES FOR PHASE SYSTEM DROPLETS 3  Dimensionless Number  Ratio of Forces  Eotvos (Eo) Reynolds (Re) Weber (We) C a p i l l a r y (Ca)  gravity/tension inertial/viscous inertial/tension viscous/tension  Formula  2  l Apg/y 1 Apu/ri 1 Apt^/Y Tiu/Y  3  10  Drop d i a . , 1 (pm) 100 1000 3  6xl0" 1x10-6 6xl0" 6xl0" 9  3  0.65  65  1x10-2 6xl06xl0"  6 2  lxlO"  2  6xl0~ 0.6  3  D a t a f o r a lower phase drop i n the upper phase of a (5,4) system: g = 980.9cm/s , TI=4 cpoise, Y = 6 x l 0 dynes/cm,Ap=0.04 g/ml. Several of the dimensionless numbers require a c h a r a c t e r i s t i c v e l o c i t y . For the purposes of i l l u s t r a t i o n , a v e l o c i t y of one drop diameter per second was used. 2  _3  -212-  I f two drops of equal radius (a^) fuse, then the radius of the new drop (a.') i s :  [6.1]  and the change i n area i s  4 7Ta (2-2 2  2/3  )  = 5.18a  2  [6.2]  The energy released on the coalescence of two drops, 0.01 and 0.1 mm d i a . 5 i s 2x10  7 and 2x10  kT r e s p e c t i v e l y , which i s considerably l a r g e r than  the corresponding energies a v a i l a b l e from sedimentation (Appendix B), and l a r g e r than E  c  f o r c e l l p a r t i t i o n i n these systems. Coalescence i s thus a  s u f f i c i e n t l y energetic process to p a r t i t i o n the c e l l s , i n p r i n c i p l e .  It i s  a l s o more l i k e l y to dominate the p a r t i t i o n process e a r l y on i n the separation, where coalescence i s r a p i d , but the small drops are not s e t t l i n g appreciably. However estimates of the forces generated by coalescence are d i f f i c u l t to make because the geometry of the flow i s complex. These are not steady s t a t e flows, but s t a r t suddenly, and are q u i c k l y damped, so i n e r t i a l e f f e c t s may a l s o be important. Probably the strongest d i r e c t evidence f o r the importance of coalescence i s the independence of p a r t i t i o n from the density d i f f e r e n c e .  In the  i s o p y c n i c system coalescence phenomena must be responsible f o r p a r t i t i o n , since no s e t t l i n g occurs.  By i n f e r e n c e , i t i s a l s o the dominant process  even i n the presence of s e t t l i n g . Now i t may be argued that t h i s process may  -213-  not be important i n other systems with d i f f e r e n t tensions, v i s c o s i t i e s and d e n s i t i e s , such as the Dx/PEG systems. However t h i s would require the ad hoc i n t r o d u c t i o n of a second mechanism. In a d d i t i o n since the v i s c o s i t i e s are lower, and the tensions higher i n Dx/PEG systems, the c a p i l l a r y number i s lower i n Dx/PEG systems, so coalescence driven flows would be greater i n these systems.  To summarize the points made i n t h i s d i s c u s s i o n and Appendix B, f i v e possible mechanisms of c e l l p a r t i t i o n were considered. P a r t i t i o n driven by the mixing o f the phases was r u l e d out because o f the r e p r o d u c i b i l i t y of p a r t i t i o n . The re-attachment mechanism could not account f o r the s e l e c t i v i t y of p a r t i t i o n . Both these mechanisms were a l s o r u l e d out because the i n i t i a l drop separation distance i s o f the same order as the c e l l s i z e . Sedimentation driven processes were considered unimportant except as a possible secondary e f f e c t l a t e r i n separation, because of i n s u f f i c i e n t l o c a l energy a v a i l a b l e , and the small forces generated. In p a r t i c u l a r the capping process was r u l e d out because o f the independence o f p a r t i t i o n on c e l l concentration. P a r t i t i o n by coalescence driven flows was thus considered to be the dominant mechanism. This conclusion was based p a r t l y on energy arguments, but mainly on the fact that c e l l p a r t i t i o n was e s s e n t i a l l y unchanged by the presence or absence of s e t t l i n g .  c) Consistency o f the Coalescence Model  To show that t h i s hypothesis i s consistent with the observations l i s t e d above i t i s h e l p f u l to consider a more d e t a i l e d q u a l i t a t i v e d e s c r i p t i o n of  -214-  p a r t i t i o n suggested by t h i s model. Some terms are now defined to c l a r i f y t h i s d e s c r i p t i o n : the measured p a r t i t i o n i s the percentage o f c e l l s i n the upper phase, as determined by counting a sample drawn a t a c e r t a i n time from the upper bulk phase (which may contain s i g n i f i c a n t amounts o f lower phase, depending on the time o f sampling). The true p a r t i t i o n i s defined as the percentage o f c e l l s not attached t o the i n t e r f a c e i n any form ( i e . the bulk i n t e r f a c e or drops). The plateau p a r t i t i o n i s the percentage o f c e l l s i n the upper bulk phase a f t e r a time long enough f o r a plane i n t e r f a c e between the bulk phases to form.  When the phase system i s shaken up a very f i n e emulsion o f droplets i s formed since the i n t e r f a c i a l tension i s so low. The average drop s i z e would t y p i c a l l y be l e s s than the c e l l diameter, ie. l e s s than 5 JM. For a one t o one volume r a t i o , the average distance between drops would be o f the order of 0.3 or l e s s o f the drop r a d i u s , forming an extremely close packed emulsion. The c e l l s would a l l be i n contact with the i n t e r f a c e . Because o f the close packing, Brownian motion and r e s i d u a l motion from the mixing cause c o l l i s i o n s and r a p i d coalescence o f the drops. L i t t l e s e t t l i n g occurs a t t h i s stage because o f the small s i z e o f the drops. Coalescence r e s u l t s i n a d i s s i p a t i o n o f energy, which has two e f f e c t s . The c e l l s are d i s t r i b u t e d between one o f the phases and the i n t e r f a c e . In a d d i t i o n the f l u i d motions due t o drop f u s i o n , combined with the random arrangement o f close packed drops generates a random Brownian-like motion which causes continual c o l l i s i o n s and coalescence, even as the drops become too large to d i f f u s e ( s e l f s t i r r i n g ) . At t h i s stage the true p a r t i t i o n i s determined p r i m a r i l y by the s i z e o f the c e l l / i n t e r f a c e attachment energy, A E ^  o r  attachment  -215-  f o r c e , f . Because of the random d i s t r i b u t i o n of c e l l s and statistically  drops,  speaking some c e l l s w i l l encounter s u f f i c i e n t force to remove  them from the i n t e r f a c e , while some w i l l not. Obviously for a given system the chances of a c e l l encountering s u f f i c i e n t f o r c e , f , and hence also the true p a r t i t i o n , increase as the c e l l / i n t e r f a c e attachment, f , i s decreased.  Also the force experienced by a c e l l increases with i t s s i z e .  The measured p a r t i t i o n i s not defined at t h i s stage since there i s no bulk upper phase to sample. However as soon as the drops become v i s i b l e , the d i f f e r e n c e between systems with a high and a low erythrocyte p a r t i t i o n i s apparent, the system with a lower p a r t i t i o n having a more granular appearance because the c e l l s at the i n t e r f a c e give the drops more v i s u a l d e f i n i t i o n (See F i g . 6.7). As the drops increase i n s i z e they s t a r t to s e t t l e . This increases the c o l l i s i o n and fusion r a t e as d i f f e r e n t s i z e drops s e t t l e at d i f f e r e n t r a t e s . Coalescence continues to d i s t r i b u t e the c e l l s .  At  the same time s e t t l i n g drops tend to reduce the true p a r t i t i o n by c o l l e c t i n g free c e l l s and t r a n s p o r t i n g them to the bulk i n t e r f a c e . As separation continues, s e t t l i n g of the l a r g e r drops can also shear c e l l s o f f the i n t e r f a c e , thus i n c r e a s i n g the true p a r t i t i o n somewhat. The low tensions and large drop s i z e s (E , C ^ l ) r e s u l t i n the formation of m i l l i m e t e r long o a 0  streams of each phase, flowing past each other at v e l o c i t i e s of 0.001 mm/s.  to 0.1  Eventually most of the phases have s e t t l e d . Numerous smaller drops  remain i n both phases, e s p e c i a l l y i n the more viscous lower phase. These escaped coalescence i n the e a r l i e r stages of separation, and now  coalesce  extremely slowly due to t h e i r low volume concentration, and the small number of r e s u l t a n t c o l l i s i o n s . At t h i s stage coalescence, and hence c e l l  -216-  d i s t r i b u t i o n , i s e s s e n t i a l l y over, and the plateau p a r t i t i o n i s reached.  As some of the remaining small drops s e t t l e they reattach to c e l l s free i n the upper phase. Thus at t h i s stage the true p a r t i t i o n can only decrease, perhaps even to zero, and i n a n o n - s p e c i f i c manner. The measured p a r t i t i o n at t h i s time, however, w i l l more c l o s e l y r e f l e c t the true p a r t i t i o n at the time the c e l l s were a c t i v e l y being d i s t r i b u t e d , although i t w i l l i t s e l f decrease as the drops s e t t l e to the i n t e r f a c e , and c l e a r the upper phase of cells.  This i s because c e l l s that remain i n the upper phase at t h i s time,  whether or not they are attached to drops, represent c e l l s that were removed from the i n t e r f a c e  i n the e a r l i e r stages by coalescence, and were therefore  not c a r r i e d to the i n t e r f a c e  i n the rapid s e t t l i n g stage. F i n a l l y the  plateau p a r t i t i o n decreases to zero as the c e l l s themselves s e t t l e . Whether there i s a true plateau period i n the measured p a r t i t i o n , and how c l o s e l y i t r e f l e c t s the true d i s t r i b u t i o n p a r t i t i o n , depends on the r a t e at which the coalescence, re-attachment, and f i n a l s e t t l i n g processes occur.  In isopycnic systems no s e t t l i n g occurs. I f the volume r a t i o i s c l o s e to one however, coalescence continues at a s u r p r i s i n g l y  rapid r a t e u n t i l the  bulk phase that b e t t e r wets the container completely surrounds the other phase ( F i g . 6.6). Coalescence continues even as the drops become l a r g e since they remain close packed ( o i 0 . 3 r a d i i apart) i r r e s p e c t i v e of the change i n scale. At the same time both the energy d i s s i p a t i o n per fusion,  ([6.2]) and  the energy expended to move a drop a distance of one radius at constant v e l o c i t y both increase as  ajj. The Brownian l i k e motion therefore  continues, and to a f i r s t approximation, the coalescence phenomenon i n the  -217-  absence of s e t t l i n g i s s c a l e i n v a r i a n t .  The observation that i n systems close to the c r i t i c a l point a l l the c e l l s appear to be attached to drops, whatever t h e i r p a r t i t i o n c o e f f i c i e n t (Raymond and F i s h e r , 1980), i s probably a r e s u l t of secondary reattachment, and i s not relevant to the primary p a r t i t i o n i n g process, since f u r t h e r from the c r i t i c a l point most c e l l s i n the upper phase are not attached to droplets.  C e l l p a r t i t i o n i n t h i s model i s c l e a r l y a s t o c h a s t i c process.  In  a d d i t i o n the independence of p a r t i t i o n on c e l l concentration and area i s e a s i l y r a t i o n a l i z e d i n the coalescence model of p a r t i t i o n . At higher concentrations the c e l l s can however decrease the coalescence  rate by  coating the drops, yet increase t h e i r s e t t l i n g r a t e by aggregating them (Raymond, 1981). This would decrease the p a r t i t i o n . The capacity of the i n t e r f a c e could a l s o be exceeded i n t h i s s i t u a t i o n . C e l l s would then be squeezed o f f the i n t e r f a c e as coalescence decreases the a v a i l a b l e surface area, increasing the p a r t i t i o n .  The e f f e c t s of a l t e r i n g the height of the phases or the phase volume r a t i o can be a t t r i b u t e d to changes i n the r e l a t i v e r a t e s of  coalescence,  s e t t l i n g and drop clearance. As the height i s decreased most-of the phases s e t t l e q u i c k l y i n the e a r l y r a p i d coalescing stage of separation, l e a v i n g l e s s droplets to s e t t l e slowly and c l e a r the upper phase of c e l l s .  The  p a r t i t i o n i s thus higher. A l t e r i n g the volume r a t i o has two e f f e c t s . i n i t i a l coalescence  The  r a t e drops sharply as the r a t i o i s made smaller or  -218-  l a r g e r than one (Van A l s t i n e et a l . , 1984), since the volume concentration of drops i s lower. At the same time the s e t t l i n g process i s a l t e r e d . As expected the f i r s t e f f e c t decreases the p a r t i t i o n , since the chance o f a c e l l being transported to the bulk i n t e r f a c e by a drop before encountering s u f f i c i e n t coalescence-generated force t o remove i t increases as the coalescence r a t e decreases.  This e f f e c t occurs i r r e s p e c t i v e of whether the  height of the upper phase i s a l t e r e d on not, the p a r t i t i o n being maximum at r = 1 f o r both constant top phase and t o t a l phase volumes ( F i g . 6.b). v  d) Tests o f the Model  One t e s t of the coalescence model has already been made by e l i m i n a t i n g s e t t l i n g e f f e c t s using an i s o p y c n i c system. are needed.  However other c r i t i c a l t e s t s  E s s e n t i a l l y these would i n v o l v e an i n v e s t i g a t i o n of the  c o r r e l a t i o n of p a r t i t i o n with the r a t e and energy d i s s i p a t i o n of coalescence.  Unfortunately, despite many years of work on emulsions,  coalescence i s s t i l l a poorly understood phenomenon.  This i s i l l u s t r a t e d by  a quote from a recent monograph concerning emulsion s t a b i l i t y  (Carroll,  1976):  "...and i t i s s t i l l very true to say that the problem remains one o f the betes n o i r e s o f c o l l o i d chemistry. This quandary a r i s e s i n part from the d i f f i c u l t y o f studying any o f the various f a c t o r s t o the e x c l u s i o n o f the others i n r e a l systems..." Nevertheless i t i s c l e a r that coalescence depends on the drop s i z e d i s t r i b u t i o n , the drop concentration, the density d i f f e r e n c e , the i n t e r f a c i a l tension, the v i s c o s i t y o f both phases, and any i n t e r d r o p forces  -219-  that may  exist.  The experiment i n which the volume r a t i o was a l t e r e d was a preliminary i n v e s t i g a t i o n of the e f f e c t of drop concentration, the r e s u l t s of which were consistent with t h i s hypothesis, i e . that coalescence, decreases with drop concentration. Sutherland and I t o , 1980) may  and hence p a r t i t i o n ,  Continuous flow apparatus (eg.  permit steady s t a t e conditions to be  i n v e s t i g a t e d where the d i s p e r s i t y and concentration of drops could ce controlled better.  D i r e c t examination of coalescing systems to see whether  fusing drops can remove c e l l s from the i n t e r f a c e would also be valuable. The d i f f i c u l t i e s here would be i n imaging the c e l l / d r o p l e t aggregates i n these dense emulsions w e l l enough i n the e a r l y stages of separation, and i n demonstrating that t h i s mechanism i s not only p o s s i b l e , but dominant.  The i n t e r f a c i a l tension and phase v i s c o s i t i e s cannot be varied independently i n the isopycnic system since the density d i f f e r e n c e i s e f f e c t i v e l y zero only at a number of defined compositions. g r a v i t y experiments (Brooks et a l . , 1984;  However zero  Van A l s t i n e et a l . , 1984)  are  c u r r e n t l y underway i n which these two parameters can be v a r i e d independently i n the absence of s e t t l i n g e f f e c t s . A p r e d i c t i o n of t h i s hypothesis  i s that  for constant c e l l i n t e r f a c e attachment energy and phase v i s c o s i t i e s , the p a r t i t i o n should increase with tension, since the energy d i s s i p a t i o n on coalescence would be greater.  -220-  Chapter Seven. General Discussion and Summary  Connect, always connect- A l b e r t E i n s t e i n  A. Overview  This t h e s i s i s an attempt to apply a p h y s i c a l chemical approach to a complex c e l l separation method i n order to b e t t e r understand the f a c t o r s involved.  The problem n a t u r a l l y d i v i d e s i n t o two p a r t s , e q u i l i b r i u m and  non-equilibrium  phenomena. The f i r s t part i s concerned p r i n c i p a l l y with the  r e l a t i v e a f f i n i t y of the c e l l for the two phases, and i t s r e l a t i o n s h i p to the c e l l and system p r o p e r t i e s .  Here several w e l l established thermodynamic  p r i n c i p l e s can be applied to the a n a l y s i s .  The power of thermodynamic  methods i s that they deal with the r e l a t i o n s h i p between general q u a n t i t i e s , such as free energy and i n t e r f a c i a l tension, e t c . without r e q u i r i n g knowledge of what p a r t i c u l a r f a c t o r s and mechanism give r i s e to these quantities.  This i s valuable when studying a complex process such as  partition.  At e q u i l i b r i u m the free energy of the system must be at a minimum, and the chemical p o t e n t i a l of each component must be the same i n both phases. Using the e q u a l i t y of chemical p o t e n t i a l s , a new  expression r e l a t i n g the  e l e c t r o s t a t i c p o t e n t i a l d i f f e r e n c e to the s a l t p a r t i t i o n i s derived i n sections 3A-B.  Since thermodynamics concerns i t s e l f with measurable  q u a n t i t i e s , the conditions under which these p o t e n t i a l s can be measured i s also derived from t h e o r e t i c a l considerations, and examined experimentally  in  -221-  section AB-C.  I t i s shown that only d i f f e r e n c e s or changes i n the p o t e n t i a l  can be measured, and these only i n systems with very s i m i l a r compositions. These r e s t r i c t i o n s were not recognized i n previous studies of p o t e n t i a l s i n two phase systems.  The e f f e c t s of phase composition changes can be  looked  at from another view point: with respect to the s a l t i o n s , the 'solvent' i s the water plus both polymers, since these determine the ion standard chemical p o t e n t i a l s .  state  Hence the 'solvents', which are the two phases, are  not f i x e d , as they would be i n a water/benzene two phase system for example. Large changes i n the polymer compositions of the phases, which can be brought about by the s a l t ions themselves, thus e f f e c t i v e l y changing the 'solvents'.  However the p o t e n t i a l can be manipulated under conditions of  e f f e c t i v e l y constant polymer composition by keeping the s a l t  concentrations  s u f f i c i e n t l y low, since the p o t e n t i a l , and i t s e f f e c t on the c e l l s , depend only on the composition,  not the concentration, of the b u f f e r .  In s e c t i o n 3D the concept of a thermodynamic s t a t e function i s used to derive a theory f o r the e f f e c t of an a f f i n i t y l i g a n d on the surface free energy d i f f e r e n c e of a p a r t i c l e , AY  .  Previous theories of a f f i n i t y  p a r t i t i o n applied only to s o l u t e s , which d i s t r i b u t e between the two phases. These theories a l s o assumed that p a r t i t i o n i s at thermodynamic e q u i l i b r i u m . Neither of these conditions apply to erythrocyte p a r t i t i o n , so a new had to be developed. compositions,  theory  This theory a l s o applies only at constant phase  l i k e that f o r the p o t e n t i a l s . Composition changes not only  change the 'solvents' as noted above, but have a large e f f e c t on the tension between the phases, since t h i s depends roughly on the fourth power dependence on the t i e l i n e length. Because the c e l l s d i s t r i b u t e between one  -222-  of the phases and the i n t e r f a c e , t h e i r p a r t i t i o n i s s e n s i t i v e t o the tension, as i s shown i n s e c t i o n 6B. The r e s u l t s of s e c t i o n 5B demonstrate that s u i t a b l e conditions for the a n a l y s i s of a f f i n i t y l i g a n d e f f e c t s on AY can be obtained i n the concentration range where the l i g a n d a f f e c t s c e l l p a r t i t i o n , since the p a r t i c u l a r l i g a n d chosen f o r study, PEG-palmitate, i s e f f e c t i v e at very low concentrations.  Young's equation, which i s a statement o f thermodynamic e q u i l i b r i u m at a three phase boundary, i s used t o determine the c e l l surface free energy difference by means o f contact angle measurements i n sections 4D and 5D. The e f f e c t of p o t e n t i a l and a f f i n i t y ligand can thus be studied under e q u i l i b r i u m c o n d i t i o n s . The v a r i a t i o n of the c e l l surface free energy d i f f e r e n c e with changes i n these two parameters i s s u r p r i s i n g l y small.  The  conclusion drawn from t h i s i s that the phase system i s excluded to a large degree from the region of the c e l l surface where the a f f i n i t y ligand i s binding, and from where much of the surface charge i s located.  This  i n t e r p r e t a t i o n i s supported by an argument based on the d i f f e r e n c e i n l i g a n d binding energies i n the two phases, again using the concept of a thermodynamic s t a t e f u n c t i o n .  This appears t o be the f i r s t evidence that  exclusion o f the phases by the c e l l glycocalyx occurs i n these two phase systems.  The surface region of the erythrocyte i s complex, having s i g n i f i c a n t thickness, and t h i s i s consistent with the r e s u l t s i n d i c a t i n g exclusion of the phases from the glycocalyx.  Phase exclusion complicates the  i n t e r p r e t a t i o n of changes i n c e l l p a r t i t i o n i n a way that has not previously  -223-  been considered.  For example i t i m p l i e s that p a r t i t i o n i n these phase  systems may only be s e n s i t i v e to a small part of the c e l l surface.  The  depth to which the phases penetrate may a l s o depend on the phase system, p a r t i c u l a r l y on the polymer molecular weights and concentrations.  The  l a t t e r p o s s i b i l i t y provides another reason f o r keeping the phase compositions constant i n p h y s i c a l studies of t h i s type.  Changes i n the  extent of phase exclusion with composition may also play a r o l e i n the weak dependence of c e l l surface free energy on tension ( s e c t i o n 6B).  Mclver  and  Schurch (1982) noted that the apparent surface free energy of complex surfaces of t h i s type decreased with the distance from the b i l a y e r at which the e f f e c t i v e outer surface occurred. They a l s o commented that there i s no unique answer to the question of what i s the c e l l surface free energy. This view of the cell/phase i n t e r f a c e a l s o suggests that conformational changes can contribute to the surface free energy, by a l t e r i n g the exposure of surface groups or binding s i t e s to the phase system.  The i n a p p l i c a b i l i t y of Neumann's equation of s t a t e to these systems, which i s shown by the r e s u l t s of Boyce (1984) and the r e s u l t s of s e c t i o n 5D, i s not s u r p r i s i n g , since i t was developed f o r a two component system. Another concept from c l a s s i c a l surface chemistry, estimation of surface energies from c r i t i c a l wetting, a l s o does not apply to these complex systems (section 6B). Again t h i s i s not s u r p r i s i n g , since t h i s approach was derived for solid/liquidA'apour systems with fewer components, no adsorption, and non-polar, non-hydrogen bonding solvents.  Young's equation can be used  s u c c e s s f u l l y since i t deals with the r e l a t i o n s h i p between general thermodynamic q u a n t i t i e s , but the equation of s t a t e , and c r i t i c a l wetting,  -224-  which i n v o l v e non-thermodynamic assumptions, cannot.  The other side of the  coin i s that Young's equation gives no clue as to what parameters contribute to the c e l l surface free energy d i f f e r e n c e . Few treatments of t h i s problem appear i n the l i t e r a t u r e , with the notable exceptions of the work s t a r t e d by G i r i f a l c o and Good (1957), and Fowkes (1963), who considered two component systems where d i s p e r s i v e i n t e r a c t i o n s dominated.  The work of Chapters Four  and Five represents a f i r s t attempt to r e l a t e the contact angle i n a complex system to p a r t i c u l a r surface i n t e r a c t i o n s .  Complications i n t h i s study of two phase systems arose from a number of sources.  F i r s t l y the p r o p e r t i e s of the phase system are a l l r e l a t e d to some  extent, which has to be taken i n t o account when one i s t r y i n g to a l t e r only one parameter of the system at a time.  Examples of t h i s d i f f i c u l t y are the  composition and tension changes, which have been discussed above.  Secondly, non-ideal s o l u t e behaviour often occurs.  In s i n g l e s a l t  systems, i o n a c t i v i t y c o e f f i c i e n t s were considered when c a l c u l a t i n g the p o t e n t i a l (section 4C).  In the mixed s a l t p o t e n t i a l study the agreement  with theory i s remarkably good although the a c t i v i t y c o e f f i c i e n t s of the ions were neglected.  This probably i n d i c a t e s that i n t h i s case the r a t i o s  of a c t i v i t y c o e f f i c i e n t s between the phases are c l o s e to one.  However i n  the a f f i n i t y l i g a n d study, the p a r t i t i o n c o e f f i c i e n t of the ester i s found to be concentration dependent, which i s a t t r i b u t e d to changes i n the activity coefficient. JJM.  The ester a l s o appears to form m i c e l l e s above  Both these f a c t o r s r e s t r i c t the t e s t of the l i g a n d theory.  10-20  -225-  F i n a l l y , the phase system i s a complex mixture of components, and i d e a l l y the e f f e c t of a l l of them should be considered together.  This can  make the study of such systems very d i f f i c u l t , unless the problem can s i m p l i f i e d by neglecting some of the components.  be  For example i n the study  of p o t e n t i a l s i n mixed s a l t systems several components are involved i n the buffer e q u i l i b r i u m .  However i t i s shown that  under the conditions used  here, only one of these components needs to be considered e x p l i c i t l y . second example i s i n the l i g a n d study.  A  Binding experiments show that both  the phase polymers, as w e l l as the a f f i n i t y l i g a n d , adsorb to the c e l l surface.  However the a f f i n i t y l i g a n d theory developed here suggests one  s i m p l i f i c a t i o n , since i t p r e d i c t s that the e f f e c t of an adsorbed component at constant surface concentration increases with i t s binding energy.  Thus  since the phase polymers bind much more weakly than an a f f i n i t y l i g a n d , t h e i r c o n t r i b u t i o n to changes i n c e l l surface free energy can be compared to t h a t  neglected,  of the l i g a n d .  The r e s u l t s of s e c t i o n 6B c l e a r l y show that erythrocyte p a r t i t i o n i s not a thermodynamic e q u i l i b r i u m process- the e q u i l i b r i u m p o s i t i o n for a l l c e l l s i s e i t h e r at the i n t e r f a c e or the bottom of the tube.  Non-equilibrium  e f f e c t s thus lead to the second question: what determines the c e l l p a r t i t i o n , and how phases?  i s i t r e l a t e d to the c e l l ' s r e l a t i v e a f f i n i t y f o r the  The large c h a r a c t e r i s t i c energies of p a r t i t i o n , ( l O ^ - l Q  two  5  k T / c e l l , s e c t i o n 6B), mean that d i f f u s i o n i s not energetic enough to d i s t r i b u t e the c e l l s .  However t h i s does not mean that the e q u i l i b r i u m  thermodynamic e f f e c t s discussed above are not important.  I f the other  non  thermodynamic f a c t o r s are held constant, then p a r t i t i o n w i l l be determined  -226-  by the surface properties o f the c e l l , v i a t h e i r i n t e r a c t i o n with the system as expressed through the c e l l surface free energy d i f f e r e n c e .  The statement  that p a r t i t i o n i s exponentially r e l a t e d to the c e l l surface p r o p e r t i e s , which occurs widely i n the l i t e r a t u r e , i s shown to be an approximation. I t does however serve to bring out the f a c t that p a r t i t i o n i s s e n s i t i v e to the c e l l surface p r o p e r t i e s .  The non-thermodynamic e f f e c t s i n p a r t i t i o n are a consequence o f the large s i z e of the 'solute', which n a t u r a l l y leads t o a more mechanical, hydrodynamic view of p a r t i t i o n .  In section 6C a t t e n t i o n i s focussed on  other physico-chemical processes, such as s e t t l i n g and coalescence. The c o n t r i b u t i o n o f thermodynamics i n t h i s view i s brought i n through e i t h e r the energy or the force needed to detach the c e l l from the i n t e r f a c e , which i s determined by the contact angle and tension.  P a r t i t i o n requires an input o f  energy, since the c e l l s are not at thermodynamic e q u i l i b r i u m , and t h i s i s achieved by mixing the systems.  Energy can now be d i s s i p a t e d broadly i n two  ways, by s e t t l i n g , which d i s s i p a t e s g r a v i t a t i o n a l p o t e n t i a l energy, and by coalescence, which d i s s i p a t e s i n t e r f a c i a l free energy.  By studying  isopycnic systems, the f i r s t mode o f d i s s i p a t i o n i s e l i m i n a t e d , with l i t t l e e f f e c t on c e l l p a r t i t i o n .  This r e s u l t and a number o f other arguments l e d  to a new hypothesis concerning the mechanism of c e l l p a r t i t i o n : coalescence i s the p r i n c i p a l process that d i s t r i b u t e s l a r g e r c e l l s such as erythrocytes.  However as the p a r t i c l e s i z e i s reduced d i f f u s i o n , and  perhaps s e t t l i n g processes, would gradually become more important. In a d i f f u s i o n dominated process p a r t i t i o n would a l s o be a t e q u i l i b r i u m .  -227-  F i n a l l y , i n order t o show the r e l a t i o n s h i p between the important p h y s i c a l and chemical aspects o f p a r t i t i o n covered i n t h i s t h e s i s , I have viewed c e l l p a r t i t i o n as a network o f r e l a t e d properties and processes, which are presented i n the form o f a flow chart i n F i g . 7.1.  B. Statement of New Results and Suggestions  f o r Future Work  The l i t e r a t u r e contains very few studies of p a r t i t i o n , p a r t i c u l a r l y of c e l l p a r t i t i o n , from the p h y s i c a l chemical point o f view that was used here.  Thus much of the work i n t h i s area i s p r e l i m i n a r y .  Three types of  new r e s u l t s were obtained i n t h i s t h e s i s : t h e o r e t i c a l r e s u l t s ,  experimental  r e s u l t s , and conclusions based on these with regard t o the behaviour of c e l l s i n two phase systems. The most s i g n i f i c a n t of these were as f o l l o w s :  A new theory r e l a t i n g the p o t e n t i a l to the s a l t p a r t i t i o n was derived. The conditions under which t h i s theory i s a p p l i c a b l e and can be experimentally tested were suggested.  P o t e n t i a l and s a l t p a r t i t i o n  measurements i n agreement with t h i s theory were obtained. has been published previously (Brooks et a l . , 1984).  Part of t h i s work  A new theory f o r the  e f f e c t of an a f f i n i t y l i g a n d on the surface free energy d i f f e r e n c e of a p a r t i c l e was derived.  This theory was tested experimentally by means of  binding experiments using erythrocytes and PEG-palmitate.  I t was found that  there was a large d i f f e r e n c e i n l i g a n d binding energy i n the two phases.  The c e l l surface free energy d i f f e r e n c e as a f u n c t i o n of p o t e n t i a l and  -228-  2. Surface p r o p e r t i e s of the c e l l or p a r t i c l e such as charge density  1. Physico-chemical p r o p e r t i e s of the polymers and other phase system components  4. V i s c o s i t y 3. Density difference  5. Tension  6. P o t e n t i a l difference  7. I n t e r a c t i o n of polymers and other components with the c e l l surface  Surface free energy r e l a t i o n s h i p s  Droplet formation, coalescence and s e t t l i n g behaviour  10. W e t t a b i l i t y of the c e l l surfaceContact angle formation.  11. Extent and r a t e of c e l l / d r o p l e t i n t e r a c t i o n s , such as s e t t l i n g , attachment, detachment and droplet fusion  12. D i s t r i b u t i o n of the c e l l s between the two phases and t h e i r i n t e r f a c e , i . e . the p a r t i t i o n c o e f f i c i e n t  Figure 7.1. Schematic Outline of the Process of C e l l P a r t i t i o n  -229-  a f f i n i t y l i g a n d concentration was obtained by means of contact angle measurements on s i n g l e c e l l s .  These two parameters had a small e f f e c t on  t h i s free energy d i f f e r e n c e which, combined with the r e s u l t s obtained from binding experiments,  suggested that the phases can be excluded from the  glycocalyx of the c e l l . This i s the f i r s t d i r e c t experimental such an e f f e c t .  evidence of  This exclusion a l s o suggests a way i n which conformational  changes at the c e l l surface could a f f e c t c e l l p a r t i t i o n .  The dependence of  the contact angle on the amount of PEG-palmitate bound to the erythrocyte surface implies that the technique of c r i t i c a l wetting cannot be used to obtain the cell/phase surface free energy i n these systems.  Erythrocyte p a r t i t i o n was shown to be a non-thermodynamic e q u i l i b r i u m process, with a c h a r a c t e r i s t i c energy s e v e r a l thousand f o l d times that of thermal energies.  A new mechanism by which l a r g e p a r t i c l e s are p a r t i t i o n e d ,  by means of the energy d i s s i p a t e d by coalescence of the emulsion droplets formed on mixing the phase systems, was o u t l i n e d .  Some of the p r i n c i p a l d i r e c t i o n s suggested by t h i s work are o u t l i n e d here b r i e f l y .  Further t e s t s of the theory of p o t e n t i a l s , p a r t i c u l a r l y i n the commonly used mixed s a l t systems, would be of value.  For example chloride/sulphate  systems, which were studied here as s i n g l e s a l t systems, would be convenient.  These would not have the complications of pH e q u i l i b r i a .  However since most systems used f o r b i o l o g i c a l m a t e r i a l are buffered, a study of the pH, p o t e n t i a l , and s a l t p a r t i t i o n , p a r t i c u l a r l y i n pure  -230-  phosphate systems, would a l s o be required.  An extensive t e s t of the l i g a n d theory could be made using PEG-alkyl e s t e r s , since these are a v a i l a b l e with a v a r i e t y of head group s i z e s , and f a t t y a c i d t a i l s , and i n a d d i t i o n t h e i r p a r t i t i o n e f f e c t s have a l s o been studied by other workers (Eriksson and Albertsson, 1978, Van A l s t i n e , 1984). A t e s t with a l i g a n d that had a constant p a r t i t i o n , and that did not form m i c e l l e s , i n order to i n v e s t i g a t e the high concentration range would also be valuable. The p r e d i c t i o n that a l i g a n d binding to the outer part of the glycocalyx would have a l a r g e r e f f e c t than one  binding  to the inner  regions could perhaps be tested using PEG modified sugar binding proteins (ie. lectins).  Tests of the e f f e c t of both p o t e n t i a l and a f f i n i t y ligands using p a r t i c l e s with smooth surfaces, such as l i p i d v e s i c l e s , would be i n v e r i f y i n g the e x c l u s i o n hypothesis.  important  These studies could be extended by  incorporating g l y c o l i p i d s and glycoproteins i n t o the v e s i c l e s , i n order to produce model erythrocyte surfaces with more defined p r o p e r t i e s .  I f the the exclusion hypothesis i s accepted, then studying the p a r t i t i o n c o e f f i c i e n t of various molecules i n r e l a t i o n to the d i f f e r e n c e i n t h e i r binding to the c e l l surface i n each phase could be u s e f u l .  This may  provide  a method of probing the a b i l i t y of such molecules to penetrate i n t o the glycocalyx, and provide u s e f u l information about the conformation glycocalyx.  of the  -231-  Studies to i n v e s t i g a t e the r o l e o f coalescence i n p a r t i t i o n , by varying the tension, drop concentration,  g r a v i t y , phase v i s c o s i t i e s , have already  been mentioned i n s e c t i o n 6C.  C. Summary  The p r i n c i p a l r e s u l t o f t h i s t h e s i s i s that i t i n d i c a t e s that p h y s i c a l chemical methods can be used s u c c e s s f u l l y to study c e l l p a r t i t i o n i n aaueous polymer two phase systems, and to gain new information on what f a c t o r s are important.  I t i s expected that the r e s u l t s summarised below can be applied  to improve the a b i l i t y of such phase systems to separate and analyse not only c e l l s , but other b i o l o g i c a l m a t e r i a l .  This t h e s i s dealt with two aspects o f c e l l p a r t i t i o n . The f i r s t was the r o l e of e l e c t r o s t a t i c and a f f i n i t y l i g a n d e f f e c t s i n determining the r e l a t i v e a f f i n i t y o f a c e l l for each phase.  The r e l a t i o n s h i p between s a l t p a r t i t i o n and p o t e n t i a l was i n v e s t i g a t e d . Phosphate and sulphate s a l t s produce p o t e n t i a l d i f f e r e n c e s between the phases which are several m i l l i v o l t s more p o s i t i v e than c h l o r i d e s a l t s . These p o t e n t i a l s a r i s e due to the unequal a f f i n i t y of the c a t i o n and anion f o r each phase, as Albertsson  (1971) f i r s t suggested. A thermodynamic treatment  was derived to r e l a t e the p o t e n t i a l s and s a l t p a r t i t i o n s .  This agreed w e l l  with experimental data for s i n g l e and mixed s a l t systems. Theoretical considerations  showed that only d i f f e r e n c e s i n p o t e n t i a l s between two  systems can be measured, subject to the condition that the d i f f e r e n c e i n  -232-  standard s t a t e chemical p o t e n t i a l between the phases i n both systems i s the same f o r any i o n . In p r a c t i c e t h i s means comparing systems with the same phase compositions, or at l e a s t with the same t i e l i n e length. I t i s a l s o suggested that t h i s should be a general c o n d i t i o n s a t i s f i e d i n any s i m i l a r physico-chemical study of two phase systems.  The p o t e n t i a l theory was extended t o deal with the behaviour of p o l y e l e c t r o l y t e s i n the presence of s a l t . The r e s u l t was compared with a previous treatment i n the l i t e r a t u r e , again demonstrating the importance o f using p a i r s o f systems with the same polymer compositions.  The e f f e c t of the p o t e n t i a l on the c e l l surface free energy was then studied by means o f contact angle measurements on s i n g l e erythrocytes. The free energy d i f f e r e n c e increases l i n e a r l y with the p o t e n t i a l , but i s twenty f o l d smaller than expected based on the best estimates f o r the c e l l surface charge density. The hypothesis presented t o account for t h i s i s that the phase system i s excluded from most o f the charged region of the g l y c o c a l y x .  The e f f e c t of an a f f i n i t y l i g a n d on c e l l p a r t i t i o n and i t s i n t e r a c t i o n with the c e l l surface were studied from a t h e o r e t i c a l and experimental point of view.  A thermodynamic theory f o r the e f f e c t s of an a f f i n i t y l i g a n d on  the c e l l surface free energy d i f f e r e n c e was derived. In t h i s theory the change i n t h i s parameter depends on the number o f ligands bound and the binding energy i n each phase, as w e l l as the ligand p a r t i t i o n c o e f f i c i e n t .  Experimental s t u d i e s were c a r r i e d out using PEG-palmitate, a hydrophobic  -233-  a f f i n i t y ligand.  This l i g a n d has l i t t l e e f f e c t on the phase compositions,  i n t e r f a c i a l tension and p o t e n t i a l i n the range used for c e l l p a r t i t i o n . C e l l p a r t i t i o n increases as the amount of PEG-palmitate i s increased. This i s due to the i n t e r a c t i o n o f t h i s l i g a n d with the membrane l i p i d b i l a y e r .  The ester p a r t i t i o n c o e f f i c i e n t increases with concentration below 10 uM. The reason f o r t h i s e f f e c t i s unclear, since the e s t e r does not form m i c e l l e s i n t h i s concentration range, although the formation of small aggregates i s not r u l e d out.  The i n t e r a c t i o n of the ester with the c e l l surface was studied by means of adsorption experiments.  Binding of the ester to the c e l l surface  saturates at 8-10 m i l l i o n molecules per c e l l . The binding i s strong, with d i s s o c i a t i o n constants i n the micromolar range, consistent with a hydrophobic i n t e r a c t i o n . The binding i s more than three times as strong from the dextran r i c h phase compared with the PEG r i c h phase.  The e f f e c t o f the ester on the c e l l surface free energy d i f f e r e n c e , again determined by means o f contact angle measurements, was found t o be very small per molecule bound. The l i g a n d theory agrees Q u a n t i t a t i v e l y with the experimental r e s u l t s f o r the erythrocyte/ester system. In t h i s theory, the small e f f e c t of the l i g a n d i s a l s o due to exclusion of the phases from the region where the l i g a n d i s bound.  PEG and the ester appear to be bound t o the c e l l surface d i f f e r e n t l y , based on the t o t a l number o f binding s i t e s , the e f f e c t of the phases on the  -234-  binding strength, and the desorption behaviour.  These r e s u l t s suggest that  the ester i s bound more deeply w i t h i n the glycocalyx, supporting the hypothesis that the phases are p a r t i a l l y excluded from the glycocalyx.  The second aspect of p a r t i t i o n that was looked at was the r e l a t i o n s h i p between the c e l l ' s p a r t i t i o n and i t s r e l a t i v e a f f i n i t y f o r the two phases. The r o l e of other f a c t o r s important i n c e l l p a r t i t i o n , such as the i n t e r f a c i a l tension, phase volume r a t i o and phase density d i f f e r e n c e , was a l s o studied.  The dependence of c e l l p a r t i t i o n on the c e l l / i n t e r f a c e  attachment energy showed that the c h a r a c t e r i s t i c energy of p a r t i t i o n i s several orders of magnitude greater than thermal energies. This i n d i c a t e s that erythrocyte p a r t i t i o n i s not a thermodynamic e q u i l i b r i u m process i . e . the c e l l s are not d i s t r i b u t e d by d i f f u s i o n . However i f non-thermodynamic f a c t o r s are held constant, the p a r t i t i o n depends only on the tension and the c e l l surface free energy d i f f e r e n c e . Although p a r t i t i o n i s s e n s i t i v e to the c e l l surface p r o p e r t i e s , i t does not depend on them i n an exponential fashion.  The p a r t i t i o n i s not a f f e c t e d by the density d i f f e r e n c e between the phases i n the range +0.006 g/ml, and i s maximum when the phase volumes are eaual.  These r e s u l t s , and semi-quantitative c a l c u l a t i o n s o f the energies  and forces involved i n c e l l p a r t i t i o n l e d t o the proposal of a mechanism f o r partition.  I t i s suggested droplet coalescence, rather than droplet  s e t t l i n g , c e l l capping, or other mechanisms, i s the primary process by which l a r g e p a r t i c l e s (>l-um dia.) such as c e l l s are d i s t r i b u t e d between the i n t e r f a c e and the two phases.  -235-  Glossary of Symbols and  Abbreviations  A l l s u p e r s c r i p t s t and b r e f e r to Quantities i n the upper and lower phases r e s p e c t i v e l y . I f not e x p l i c i t l y mentioned, the subscripts i , j r e f e r to the i t h species i n the j t h system r e s p e c t i v e l y . A l l d i f f e r e n c e s i n , or r a t i o s of a u a n t i t i e s i n , the two phases are expressed as top-bottom or top/bottom respectively.  a  radius of three phase contact  c  ap.a^  ,  line  radius of p a r t i c l e , drop  A  area  c,C  concentration, bulk or average concentration  Ca  c a p i l l a r y number  Dx  dextran  e  e l e c t r o n charge, A.lxlO""'"^ esu.  E  c h a r a c t e r i s t i c energy of p a r t i t i o n  c  Eo  Eotvos number  f. .  molal a c t i v i t y c o e f f i c i e n t  f,f^  f o r c e , drag force  f ,f ID  detachment force, applied force during p a r t i t i o n  3  f  mole f r a c t i o n of s a l t i n a phase system  Fi  Ficoll  g  a c c e l e r a t i o n due to g r a v i t y 980.5 dynes/g  h  height of s p h e r i c a l cap  I  i o n i c strength  -236-  k  Boltzmann's constant, 1.36xl0~* 1  k  6  ergs/molecule.°K  a s s o c i a t i o n constant f o r l i g a n d binding  K,K^  c^/c  3  p a r t i t i o n c o e f f i c i e n t , ligand p a r t i t i o n c o e f f i c i e n t ,  M ,M  number, weight average molecular weight  n  number of binding s i t e s per molecule or per u n i t area,  n  w  transport number n  1  number of molecules bound per u n i t area or per macromolecule  CJ n\  the binomial c o e f f i c i e n t ,  n^  number of drops  n!/((n-i)I.i!)  23 N  g  Avogadro's number, 6.02x10  P  s  surface pressure  P  number of polymer segments  PEG x  poly(ethylene g l y c o l ) , molecular weight approx. x g/mole  r^ j r ,r. s' 1 r  r a t i o of a c t i v i t y c o e f f i c i e n t s i n phase system mole r a t i o of bulk s a l t concentrations  r, k  r a t i o of a s s o c i a t i o n constants  ri  r e f r a c t i v e index r e l a t i v e to water  tj,  t i e l i n e length  T  absolute temperature  u  velocity  v  phase volume r a t i o  v  volume, phase volume  V  dimensionless exponential function of p o t e n t i a l  z + z m  ,z_  ,Zi  valence of c a t i o n , anion valence of macromolecule or p r o t e i n , valence of i ^  h  ion  -237-  surface free energy i n t e r f a c i a l tension between the phases surface excess of solute free energy of p a r t i c l e / i n t e r f a c e attachment 2  =  A E ^ / u a ^ , normalised free energy of attachment  free energy of p a r t i c l e t r a n s f e r between phases binding energy/molecule free energy o f l i g a n d t r a n s f e r between phases per molecule free energy of mixing enthalpy of mixing entropy of mixing surface free energy d i f f e r e n c e between the phases surface free energy d i f f e r e n c e between phases i n the presence, absence of a l i g a n d . d i f f e r e n c e i n standard state chemical p o t e n t i a l s between the phases 2 d i e l e c t r i c constant of water, 78 esu /cm.erg viscosity e a u i l i b r i u m , complementary, displaced contact angle o p t i c a l r o t a t i o n of polymer s o l u t i o n angle subtended at centre of p a r t i c l e , drop maximum cap s i z e on a s p h e r i c a l drop Debye-Huckel parameter standard s t a t e , chemical, electrochemical  potential  density, density d i f f e r e n c e between the phases surface charge density  -238-  <t>  volume f r a c t i o n  X  mole f r a c t i o n  i}j,Aip  Galvani, or inner p o t e n t i a l , p o t e n t i a l d i f f e r e n c e between the phases  [x]  concentration of x  (x,y,z)  phase system containing x% Dx, y% PEG, z% F i ,  p,q,r+s  phase system b u f f e r , c o n s i s t i n g of p mM sodium phosphate b u f f e r , q mM NaCl, r mM s o r b i t o l and s JJM PEG-palmitate.  -239-  Appendices  A. Estimation  of the minimum force necessary to p u l l a s p h e r i c a l p a r t i c l e  off a l i q u i d interface  A d e t a i l e d a n a l y s i s of the i n t e r a c t i o n of a p a r t i c l e with the i n t e r f a c e i s given by Schulze (1984), which includes e f f e c t s due to g r a v i t y and pressure v a r i a t i o n s .  However since these e f f e c t s are generally much smaller  than the tension e f f e c t s , the s i m p l i f i e d a n a l y s i s given here i s s u f f i c i e n t to estimate the necessary force. Consider a s p h e r i c a l p a r t i c l e , radius ap, attached to a plane i n t e r f a c e with tension  Y  t b  and r e s t r a i n e d at i t s  outer edge. Let the e q u i l i b r i u m contact angle be 0 . Now l e t a force f be applied to the p a r t i c l e , d i s p l a c i n g i t to the l e f t , so that the l o c a l contact angle i s s t i l l  0 (Adamson, 1976), at c i r c l e B ( F i g . 1.2b). The  i n t e r f a c e i s now curved, r e s u l t i n g i n a h o r i z o n t a l component of tension  that  balances the applied force. This component i s given by the product of the h o r i z o n t a l component o f the tension and the circumference of c i r c l e B:  f = 2 Tra s i n 0 " . Y . s i n ( 0 tb P  0")  [Al]  D i f f e r e n t i a t i n g and applying the double angle formula:  [A2]  This i s zero at 0 " = 0 / 2 , and hence the maximum force i s  -240-  f  2 T T a  m =  p V b  s i n 2 ( 9 / 2 )  t  a  = * p Y b  ( 1  t  "  c o s  6  [A3]  }  For a p a r t i c l e attached to a drop of radius a , the maximum force w i l l d  be smaller, since the three phase contact l i n e B i s shorter. The a n a l y s i s i s complicated  by the f a c t that the drop does not remain s p h e r i c a l , and i t s  radius decreases as the p a r t i c l e i s withdrawn. Neglecting t h i s change, we obtain  f  = 2 Tra  m  where 6  p  4-K p V'tb  s i n 2  ( 6  p  /2)  [A4]  i s l e s s than the e a u i l i b r i u m contact angle, being the angle  subtended at the p a r t i c l e centre by the e a u i l i b r i u m contact l i n e (eg. F i g 2.1), where  tan 0  and a  d  = s i n 0 /(cos 0 + a /a .)  [A5]  i s the e a u i l i b r i u m drop r a d i u s .  B. Mechanisms of C e l l P a r t i t i o n  This appendix complements the discussion on c e l l p a r t i t i o n mechanisms given i n Chapter S i x . I t l i s t s s e v e r a l mechanisms of c e l l p a r t i t i o n , and considers t h e i r p l a u s i b i l i t y by means of a number of Q u a l i t a t i v e and semi-auantitative arguments.  -241-  a) The shaking mechanism. This hypothesis proposes that the forces that p a r t i t i o n the c e l l s are generated d i r e c t l y by the shaking or mixing of the phase systems. The moment the a g i t a t i o n i s stopped, the p a r t i t i o n i s determined. There i s c e r t a i n l y enough energy put i n t o the system by  shaking  to p a r t i t i o n the c e l l s , and t h i s model i s consistent with the v i s u a l observation that the c e l l s seem to have d i s t r i b u t e d very e a r l y i n the p a r t i t i o n process. The c h i e f argument against t h i s mechanism i s the r e p r o d u c i b i l i t y of p a r t i t i o n . The p a r t i t i o n i s the same whether the phase system i s mixed gently by i n v e r s i o n , or more vigorously by vortexing the s o l u t i o n s . This model i n c o r r e c t l y p r e d i c t s that the p a r t i t i o n i n systems with high tensions, which i s u s u a l l y low, could be increased, u l t i m a t e l y to a hundred percent, i f the system was mixed vigorously enough to detach a l l the c e l l s from the i n t e r f a c e .  b) D i f f e r e n t i a l re-attachment. In t h i s model a l l the c e l l s are removed from the i n t e r f a c e at some e a r l y point i n the process, and p a r t i t i o n i s the process of re-attachment, low p a r t i t i o n being the consequence of more e f f i c i e n t attachment. This model f a i l s ' t o e x p l a i n how small c e l l surface d i f f e r e n c e s could r e s u l t i n d i f f e r e n t p a r t i t i o n c o e f f i c i e n t s . The attachment of the c e l l to the i n t e r f a c e i s a contact phenomenon, there are no long range forces operating here, c e r t a i n l y not on the s c a l e of the c e l l radius. The re-attachment i s therefore c o n t r o l l e d by the c o l l i s i o n r a t e between c e l l s and the i n t e r f a c e of drops, which would be independent of both the c e l l surface p r o p e r t i e s , and phase system properties such as p o t e n t i a l and l i g a n d concentration, and which would instead depend only on the gross  -242-  properties of the system such as the density d i f f e r e n c e and phase viscosities.  Another f a t a l objection to both t h i s and the previous  mechanism i s that given a one to one volume r a t i o , and the f a c t that microscopic observation shows that the drops produced on shaking are at l e a s t as small as the c e l l s themselves, the average distance between the drops i s smaller than the c e l l . Therefore a l l c e l l s must i n i t i a l l y be i n contact with the i n t e r f a c e when mixing stops.  c) Shear forces generated by sedimenting drops. The c e l l s are a l l i n i t i a l l y at the i n t e r f a c e , t h e i r thermodynamic e q u i l i b r i u m p o s i t i o n (except for the s p e c i a l case of very high p a r t i t i o n systems, where 9=0). As the droplets of the upper or lower phase cream to t h e i r respective bulk phases, they experience shear stresses due to f l u i d  flow past the droplet, which  p u l l or push the c e l l s o f f the drop i n t e r f a c e i n t o the upper phase. Consider the t o t a l energy d i s s i p a t e d by a drop with one c e l l attached, as i t s e t t l e s a distance of one c e l l diameter under i t s own weight, and whether t h i s energy i s s u f f i c i e n t to detach the c e l l . The energy d i s s i p a t e d for a drop at constant v e l o c i t y i s the product of the distance and the g r a v i t a t i o n a l force:  3  4 TT/3. Ap a a g  [Bl]  p  For  a (5,4) system the density d i f f e r e n c e i s 0.04 g/ml, and a  p  f o r an  erythrocyte i s about 3.5x10"^ cm. For two representative drop s i z e s of -12 0.01 and 0.1 mm d i a . , 5  t h i s gives 7.2 xlO  -9 and 7.2x10  ergs, or 180 to  1 . 8 x l 0 kT. The l a r g e r f i g u r e i s comparable to the c h a r a c t e r i s t i c energies  -243-  derived from F i g 6.15. However these estimates are upper l i m i t s , since not a l l of the energy would be a v a i l a b l e to remove the c e l l , a l o t being d i s s i p a t e d i n f l u i d flow i n and around the drop. Although the energy depends on the cube of the r a d i u s , the f r a c t i o n expended on the c e l l would decrease the l a r g e r the drop s i z e i s r e l a t i v e to the c e l l , so the dependence of a v a i l a b l e energy on the radius would be l e s s r a p i d . From t h i s one that t h i s process would only occur f o r large drops ( >0.1  concludes  mm d i a . ) , and  would thus become more important as the phases coalesced, while p a r t i t i o n i s already occurring e a r l y on i n the separation, i n the stage before the phases r e a l l y s t a r t s e t t l i n g at an appreciable r a t e and the drops are s m a l l . Another type of argument u s e f u l i n d i s c u s s i n g t h i s model i s based on the probable force experienced by the c e l l i n the s e t t l i n g process. Again t a k i n g a (5,4) system, containing 0.8 uM e s t e r , at 34% p a r t i t i o n , 2 Y^ =  0.0063 ergs/cm  b  6 = 60°,  (Table 5.5). The minimum force to remove the c e l l ,  from [A3], i s about 3 . 5 x l 0 ~  6  dynes, f o r a plane i n t e r f a c e , somewhat l e s s o  for a drop. Using [A5] we have f o r 0.01 and 0.1 mm d i a . drops, 6^= o _g and 56.6 r e s p e c t i v e l y . Using [A4], f i s about 1.3, 3.1 xlO  35.8  d y n e s / c e l l , r e s p e c t i v e l y . An estimate of the drag force experienced by a p a r t i c l e attached to a sedimenting lower phase drop can be obtained from the appropriate equation i n the foam f l o t a t i o n l i t e r a t u r e (Clarke and Wilson, 1983):  2  f = 2 7TApga a g  [B2]  d  —8 This equation gives estimates f o r the net force on the c e l l as 1.5 and 1.5 x l O  - 7  10~  dynes r e s p e c t i v e l y f o r the two drop s i z e s . These forces are  -244-  considerably smaller than those required to remove the c e l l . estimate of f  Using the  f o r a plane i n t e r f a c e and s o l v i n g [A3]  for a^ gives a diameter of 0.12 cm as the minimum drop s i z e where t h i s p a r t i t i o n mechanism could operate. Of course t h i s a n a l y s i s i s only v a l i d f o r an i s o l a t e d drop, not f o r the very dense emulsions formed from phase systems, but the general magnitude of the forces would be s i m i l a r . This a n a l y s i s a l s o assumed that the f l u i d flow around the drop was e s s e n t i a l l y undisturbed by the presence of the c e l l . I f t h i s i s not the case, then the problem i s much more d i f f i c u l t . French and Wilson (1980) solved the exact Navier-Stokes equations f o r the geometry of F i g . 2.1b f o r a p a r t i c l e attached to a bubble. Their conclusion was that the magnitude of the force was s i m i l a r to that i n the above a n a l y s i s , but that i t was d i r e c t e d towards the  centre of the drop. I f t h i s i s the general case during p a r t i t i o n i t  would imply that a c e l l could only be p u l l e d i n t o the upper phase from the i n t e r f a c e of a upper phase drop, not a lower phase drop.  d) C e l l capping. This mechanism of p a r t i t i o n was proposed by French and Wilson (1980) as a mechanism f o r the removal of ore p a r t i c l e s from a i r bubbles during foam f l o t a t i o n (Clarke and Wilson, 1983). cap of c e l l s subtending an angle  In t h i s model a  form on the rear of a sedimenting  drop. Tangential s t r e s s on t h i s cap r e s u l t s from f l u i d flow past the drop, which i s maximum at the cap centre. I f the r e s u l t i n g surface pressure times the  area of drop surface occupied by a c e l l (.~TTB^) i s greater than the  adherence energy, AE^., the c e l l w i l l be popped o f f the drop as the cap buckles. Thus there i s a l i m i t to the s i z e of cap that a given s i z e drop can s u s t a i n . Since the capping mechanism i s driven by s e t t l i n g , the same  -245-  " a v a i l a b l e energy" counter-arguments used with the previous model apply, but with even more f o r c e , since t h i s process requires the removal of more than one c e l l per drop. Making the same assumption about undisturbed flow around the drop as before, the t a n g e n t i a l s t r e s s can be integrated across the cap to obtain an expression f o r the maximum cap s i z e ,  ©  m  (Clarke and Wilson  1983):  e  m  =3AE ./(TraW)  [B3]  t  Taking the same c e l l and system parameters as before, f o r 0.01 and 0.1 mm d i a . drops we obtain  G = 1.21 xKfVa 2 ,, which gives 0 > TT m d' m 3  radians for both drops. In other words the c e l l s could completely cover the drop. No removal of c e l l s i n t o the upper phase could thus occur under these conditions unless the c e l l concentration i s high enough to completely coat the a v a i l a b l e i n t e r f a c e . For t h i s system 0  becomes l e s s than TT f o r m  drops greater than 0.2 mm d i a . Again t h i s mechanism would appear to be too weak at the e a r l y stages of separation, but could become more important l a t e r as the drops increase i n s i z e . For small angles, the cap angle i s 2 p r o p o r t i o n a l to 1/a^, but the cap area for a given angle i s 2 p r o p o r t i o n a l to a^, so the number o f c e l l s per cap, or the drop capacity i s independent of the drop s i z e . The t o t a l capacity of the i n t e r f a c e would thus be p r o p o r t i o n a l to i t s t o t a l area, and would therefore decrease as phase separation progressed. This model e f f e c t i v e l y says that p a r t i t i o n o f c e l l s i n t o the top phase occurs because at some point the t o t a l cap capacity i s exceeded. This i m p l i e s that as the c e l l concentration i s decreased, the d i s t r i b u t i o n would be produced l a t e r i n the s e t t l i n g process,  -246-  and that the p a r t i t i o n would decrease- a f i x e d number of c e l l s would stay at the i n t e r f a c e .  I f the c e l l concentration were further lowered u n t i l the  i n t e r f a c e capacity was not exceeded, the p a r t i t i o n would always be zero. This type of dependence on c e l l concentration i s not seen, which would appear to r u l e out c e l l capping as a s i g n i f i c a n t p a r t i t i o n mechanism, except perhaps at very high c e l l concentrations.  -247-  Adamson, A. W. (1976), " P h y s i c a l Chemistry o f Surfaces." 3rd Ed. John Wiley and Sons, New York, N.Y. Adamson, A. W., and L i n g , I . (1964). The status o f contact angle as a thermodynamic property. In "Contact Angles, W e t t a b i l i t y and Adhesion." Advances i n Chemistry, V o l . 43. Applied P u b l i c a t i o n s ; American Chemical Society, Washington, D.C. Chapter 3. Akerlund, H.-E., Andersson, B., Persson, A., and Albertsson, P.-A. (1979). I s o e l e c t r i c points o f spinach t h y l a k o i d membrane surfaces as determined by cross p a r t i t i o n . Biochem. Biophys. Acta 552, 238.  0 Albertsson, P.-A. (1958a). P a r t i t i o n o f proteins i n l i q u i d polymer-polymer two phase systems. Nature 182, 709.  0 Albertsson, P.-A. (1958b). P a r t i c l e f r a c t i o n a t i o n i n l i q u i d two-phase systems. The composition o f some phase systems and the behavior o f some model p a r t i c l e s i n them. A p p l i c a t i o n t o the i s o l a t i o n o f c e l l w a l l s from microorganisms. Biochim. Biophys. Acta 27, 378-395. Albertsson, P.-A. (1960). " P a r t i t i o n o f C e l l P a r t i c l e s and Macromolecules." Wiley Interscience, New York. Albertsson, P.-A., (1961). F r a c t i o n a t i o n o f p a r t i c l e s and macromolecules i n aqueous two-phase systems. Biochem. Pharmacol. 5, 351. Albertsson, P.-A. (1965a). Biochem. 11, 121.  Thin l a y e r counter current d i s t r i b u t i o n .  Anal.  o  Albertsson, P.-A. (1965b). P a r t i t i o n studies on n u c l e i c acids 1. Influence od e l e c t r o l y t e s , polymer concentration and n u c l e i c a c i d conformation on the p a r t i t i o n i n the dextran-polyethylene g l y c o l system. Biochem. Biophys. Acta 103, 1-12. Albertsson, P.-A. (1971). " P a r t i t i o n o f C e l l P a r t i c l e s and Macromolecules." 2nd. ed., Wiley Interscience, New York. Albertsson, P.-A. (1983). I n t e r a c t i o n between biomolecules studied by phase p a r t i t i o n . Methods o f Biochemical Analysis 29, 1-24. Albertsson, P.-A., and B a i r d , G.D. (1962) Countercurrent d i s t r i b u t i o n o f c e l l s . Exp. C e l l Res. 28, 296-322. Albertsson, P.-A., and Baltescheffsky, H. (1963). Countercurrent d i s t r i b u t i o n of spinach c h l o r o p l a s t s i n an aqueous two phase system. Biochem. Biophys. Res. Comm. 12, 14. Albertsson, P.-A., and Nyns, E.J. (1961). P a r t i t i o n of proteins i n an aqueous phase system o f dextran and polyethylene g l y c o l - i n f l u e n c e o f the e l e c t r o l y t e content. Arkiv Kemi 17, 197.  -248-  Albertsson, P.-A., and Philipson, L. (1960). Antigen-antibody i n l i q u i d two-phase systems; a method f o r studying immunological reactions. Nature 185, 38-40. Albertsson, P.-A., Sasakawa, S., and Walter, H. (1970). Cross p a r t i t i o n and i s o e l e c t r i c points of p r o t e i n s . Nature 228, 1329. Backman, L., Shanbhag, V., and Johansson, G. (1977). A method to detect p r o t e i n - p r o t e i n i n t e r a c t i o n s . Biochem. Soc. Trans. 5, 748. B a i l e y , F.E., and Koleske, J.V. (1976). Poly(ethylene oxide). Academic Press, New York, N.Y. Chapter 4. B a l l a r d , CM., Dickinson, J.P., and Smith, J . J . (1979), C e l l P a r t i t i o n . A study of parameters a f f e c t i n g the p a r t i t i o n phenomenon, Biochim. Biophys. Acta 582, 89-101. Bamberger, S., Seaman, G.V.F., Sharp, K.A., and Brooks, D.E. (1984a). The e f f e c t s of s a l t s on the i n t e r f a c i a l tension of aqueous dextran poly(ethylene g l y c o l ) phase systems. J . C o l l o i d Interface S c i . 99, 194-200. Bamberger, S., Seaman, G.V.F., Brown, J.A., and Brooks, D.E. (1984b). The p a r t i t i o n of sodium phosphate and sodium c h l o r i d e i n aqueous dextran poly(ethylene g l y c o l ) two-phase systems. J . C o l l o i d Interface S c i . 99, 187-193. B e i j e r i n c k , M.W. (1910). Formation of emulsions by mixing water s o l u t i o n s o f c e r t a i n g e l a t i n i z i n g c o l l o i d s . K o l l o i d Z. 7, 16-20. Bengtsson, S., and P h i l i p s o n , L. (1963). Counter-current d i s t r i b u t i o n of p o l i o v i r u s type 1. Virology 20, 176-184. Blomquist, G., and Albertsson, P.-A. (1972). A study of e x t r a c t i o n columns f o r aqueous polymer two-phase systems. J . Chromatogr. 73, 125-133. Boyce, J.F. (1984). Surface P r o p e r t i e s of the A r t e r i a l Wall and t h e i r Relevance to A t h e r o s c l e r o s i s . Ph.D Thesis, U n i v e r s i t y o f Western Ontario. Boyce, J.F., Wong, P.C., Schurch, S., and Roach, M.R. (1983). Rabbit a r t e r i a l endothelium and subendothelium: A change i n i n t e r f a c i a l free energy that may promote i n i t i a l p l a t e l e t adhesion, C i r c u l a t i o n Research 53, 372-377 . Brooks, D. E. (1973). The e f f e c t o f n e u t r a l polymer on the e l e c t r o k i n e t i c p o t e n t i a l o f c e l l s and other charged p a r t i c l e s . I l l Experimental s t u d i e s on the dextran/erythrocyte system. J . C o l l o i d Interface S c i . 43, 700-713. Brooks, D.E., Seaman, G.V.F., and Walter, H. (1971). Detection of d i f f e r e n c e s i n surface-charge-associated properties of c e l l s by p a r t i t i o n i n two-polymer aqueous phase systems. Nature (London) New B i o l . 234, 61-62.  -249-  Brooks, D.E., Greig, R.G., and Janzen, J . (1980). Mechanisms of erythrocyte aggregation. In "Erythrocyte Mechanics and Blood Flow" (Cokelet, G.R., Meiselman, H.J., and Brooks, D.E. eds.), Alan L i s s Inc. New York. Chapter 6. Brooks, D.E., Bamberger, S.B., H a r r i s , J.M., and Van A l s t i n e , J.M. (1984). Rationale f o r two phase polymer systems microgravity separation experiments. Published i n "5th European Symposium- M a t e r i a l Sciences Under M i c r o g r a v i t y . " European Space Agency, P a r i s , pp 315-8. Brooks, D.E., Sharp, K.A., Bamberger, S., Tamblyn, C.H., Seaman, G.V.F., and Walter, H. (1984). E l e c t r o s t a t i c and e l e c t r o k i n e t i c p o t e n t i a l s i n two polymer aaueous phase systems. J . C o l l o i d Interface S c i . 102, 1-13. Brooks, D.E., Sharp, K.A., and F i s h e r , D. (1985). T h e o r e t i c a l aspects of p a r t i t i o n i n g . In " P a r t i t i o n i n g i n Aqueous Two Phase Systems. Theory, Methods, Uses and A p p l i c a t i o n s to Biotechnology." (Walter, H., Brooks, D.E., and F i s h e r , D., eds.) Academic Press, New York. Chapter 3. Cabanes, B. (1982). Organization of s u r f a c t a n t m i c e l l e s adsorbed on a polymer molecule i n water: a neutron s c a t t e r i n g study. J . Physique 43, 1529-1542. C a r r o l l , B.J. (1976). The s t a b i l i t y of emulsions and mechanism of emulsion breakdown. In "Surface and C o l l o i d Science." Volume 9 ( M a t i j e v i c , ed.) John Wiley and Sons, New York. Chapter 1. Catsimpoolas, N. (ed.) (1977). "Methods of C e l l Separation." V o l . 1. Plenum Press, New York. Clark, A.N., York.  and Wilson; D.J. (1983). "Foam F l o t a t i o n . "  C l i f t , R. Grace, J.R., and Weber, M.E. Academic Press, New York. Ch. 3.  Marcel Dekker, New  (1982). "Bubbles, Drops and P a r t i c l e s . "  Cook, G.M.W. (1976). A n a l y s i s of membrane carbohydrates. In "Biochemical A n a l y s i s of Membranes." (Maddy, A.H. ed.) John Wiley and Sons, New York. Cordes, A., F l o s s d o r f , J . , and Kula, M.-R. (1984). A f f i n i t y p a r t i t i o n i n g T h e o r e t i c a l aspects and consequences f o r t e c h n i c a l a p p l i c a t i o n s . European Federation f o r Biotechnology. Proceedings of 3rd European Congress on Biotechnology. V o l . I l l , Verlag chemie, Weinheim, Munchen, FDR Germany, pp. 557-564. Crowe, J.H., Whittam, M.A., Chapman, D., Crowe, L.M. (1984). I n t e r a c t i o n s of phospholipid monolayers with carbohydrates. Biochim. Biophys. Acta 769, 151-159. Dahlgren, C., K i h l s t r o m , E., Magnusson, K.-E., Stendahl, 0., and Tagesson, C. (1977). I n t e r a c t i o n of liposomes with polymorphonuclear leukocytes. I I . Studies of the consequences of i n t e r a c t i o n . Exp. C e l l Res. 108, 175.  -250-  Davis, J.T., and R i d e a l , E.K. (1961). " I n t e r f a c i a l Phenomena." Academic Press, New York. Chapter 2. deLigny, C.L., and Gelsema, W.J. (1982). On the influence o f pH and s a l t composition on the p a r t i t i o n of p o l y e l e c t r o l y t e s i n aqueous polymer two-phase systems, Sepn. S c i . Technol. 17, 375-380. Dobry, A., and Boyer-Kawenoki, F. (1947). Phase separation i n polymer s o l u t i o n s . J . Poly. S c i . 2, 90. Donath, E., and Pastushenko, V. (1979). E l e c t r o p h o r e t i c a l study of c e l l surface properties. The i n f l u e n c e of the surface coat on the e l e c t r i c p o t e n t i a l d i s t r i b u t i o n and on general e l e c t r o k i n e t i c p r o p e r t i e s of animal c e l l s . Bioelectrochem. Bioenergetics 6, 543-554. Elsworthy, P.H., and MacFarlane, C.B. (1962). Surface a c t i v i t y of a s e r i e s of synthetic non-ionic detergents. J . Pharm. Pharmocol. Suppl. 14, 100-102. E r i c s o n , I. (1974). Determination o f the i s o e l e c t r i c point o f r a t l i v e r mitochondria by c r o s s - p a r t i t i o n . Biochem. Biophys. Acta 356, 100. o  Eriksson, E. and Albertsson, P.-A. (1978). The e f f e c t of l i p i d composition on the p a r t i t i o n of liposomes i n aqueous two-phase systems. Biochim. Biophys. Acta 507, 425-432. E r i k s s o n , E., Albertsson, P.-A., and Johansson, G. (1976). Hydrophobic surface properties of erythrocytes studied by a f f i n i t y p a r t i t i o n i n aqueous two-phase systems. Molec. C e l l . Biochem. 10, 123-128. Evans, E. A. (1980). Minimum energy a n a l y s i s o f membrane deformation applied to pipet a s p i r a t i o n and surface adhesion of erythrocytes. Biophys. J . 30, 265. Evans, E.A., and Hochmuth, R.M. (1978). Mechanochemical p r o p e r t i e s o f membranes. In " Current Topics i n Membranes and Transport." Vol X. ( K l e i n z e l l e r , A., and Bronner, F. eds.) Academic Press, New York, N.Y. pp 1-64. F i s h e r , D. (1981). The separation o f c e l l s and organelles by p a r t i t i o n i n g i n two-polymer aqueous phases. Biochemical J . 196, 1 F i s h e r , D. and Walter, H. (1984). C e l l separations and subfractionations by countercurrent d i s t r i b u t i o n i n two-polymer aqueous phase systems depend on non-equilibrium c o n d i t i o n s . Biochim. Biophys. Acta, 801, 106-110. Flanagan, S.D., and Barondes, S.H. (1975). A f f i n i t y p a r t i t i o n i n g . A method for p u r i f i c a t i o n o f p r o t e i n s using s p e c i f i c polymer-ligands i n aqueous polymer two-phase systems. J . B i o l . Chem. 250, 1484-1489. Flanagan, S.D., and Barondes, S.H., and Taylor, P. (1976). Cholinergic receptor c o n t a i n i n g membranes from Torpedo c a l i f o r n i c a . J . B i o l . Chem. 251, 858-865.  -251-  F l e t c h e r , R. (1965). FORTRAN subroutines f o r minimising by quasi-Newton method. Research group r e p o r t , T h e o r e t i c a l Physics D i v i s i o n , Atomic Energy Research Establishment, Harwell, England. F l o r y , P.J. (1941). 9, 660-661.  Thermodynamics o f high polymer s o l u t i o n s .  J . Chem. Phys.  F l o r y , P.J. (1953). " P r i n c i p l e s of Polymer Chemistry". C o r n e l l U n i v e r s i t y Press, Ithaca, N.Y. Chapter 13. Fowkes, F.M. (1963). A d d i t i v i t y o f intermolecular forces at i n t e r f a c e s . I . Determination of the c o n t r i b u t i o n t o surface and i n t e r f a c i a l tensions of d i s p e r s i o n forces i n various l i a u i d s . J . Phys. Chem. 67, 2538-2543. French, R.M. and Wilson, D.J. (1980). F l u i d Mechanics. Foam f l o t a t i o n i n t e r a c t i o n s . Separation Science and Technology 15 1213-1227. F r i c k , G., and L i f , T. (1962). R e l a t i o n between s i z e and d i s t r i b u t i o n of DNA molecules i n a two-phase polymer system. Arch. Biochem. Biophys, Suppl. 1, 271-275. Furthmayr, H. (1978). Glycophorins A,B and C: a family of s i a l o g l y c o p r o t e i n s . I s o l a t i o n and preliminary c h a r a c t e r i z a t i o n of t r y p s i n derived peptides. J . Supramol. S t r u c t . 9, 79-95. Gerson, D.F. (1980). C e l l surface energy, contact angles and phase p a r t i t i o n I. Lymphocyte c e l l l i n e s i n b i p h a s i c aqueous mixtures. Biochim. Biophys. Acta 602, 269-280. Gerson, D. (1983). I n t e r f a c i a l free energy of c e l l s and polymers i n aaueous media. In "Physicochemical Aspects of Polymer Surfaces", V o l . 1. (K. M i t t e l , ed.), Plenum P u b l i s h i n g Corp., New York. pp. 229-240. Gerson, D.F., and A k i t , J . (1980), C e l l surface energy, contact angles and phase p a r t i t i o n . I I . B a c t e r i a l c e l l s i n biphasic aqueous mixtures. Biochim. Biophys. Acta 602, 281-284. Geyer, G., and Makovitzky, J . (1980). Erythrocyte membrane t o p o - o p t i c a l s t a i n i n g r e f l e c t s g l y c o p r o t e i n conformational changes. J . Micros. 119, 407-414. G i r i f a l c o , L.A and Good, R.J. (1957). A theory f o r the estimation of surface and i n t e r f a c i a l energies. I . D e r i v a t i o n and a p p l i c a t i o n to i n t e r f a c i a l tension. J . Phys. Chem. 61, 904-909. Granath, K.A. (1958). "Dextran and i t s Use i n C o l l o i d a l Infusion S o l u t i o n s . " Academic Press, New York, N.Y. Grant, R.A., and Zucker, M.B. (1978). EDTA-induced increase i n p l a t e l e t surface charge associated with l o s s o f a g g r e g a b i l i t y - assessment by p a r t i t i o n i n aqueous two phase polymer systems and e l e c t r o p h o r e t i c m o b i l i t y . Blood 52, 515.  -252-  Gratzer, W.B. (1981). The red blood c e l l membrane and i t s cytoskeleton. Biochem. J . 198, 1-8. Gray, CM., and Chamberlain, M.J. (1971). Measurement of l i g a n d - p r o t e i n binding i n t e r a c t i o n s i n a b i p h a s i c aqueous polymer system. Anal. Biochem. 41, 83-104. Grindrod, J . , and C l i v e r , D.O. (1970). A polymer two phase system adapted to v i r u s detection. Archiv Fur Die Gesamte V i r u s f o r s c h 31, 365 Guggenheim, E.A. (1959). "Thermodynamics." 4th Edn. North Holland P u b l i s h i n g , Amsterdam. Chapter 2. Hahn-Hagerdal, B., Andersson, E., Lopez-Leiva, M., and Mattisson, B. (1981). Membrane biotechnology, co-immobilisation, and aqueous two-phase systems: A l t e r n a t i v e s i n bioconversion of c e l l u l o s e . Biotech. Bioeng. 11, 651. Hakomori, S. (1981). Glycosphingolipids i n c e l l u l a r i n t e r a c t i o n , d i f f e r e n t i a t i o n and oncogenesis. Ann. Rev. Biochem. 50, 733-764. H a r r i s , M.J., Case, M.G., Hovanes, B.A., Van A l s t i n e , J.M., and Brooks, D.E. (1983). P u r i f i c a t i o n of b i o m a t e r i a l s by phase p a r t i t i o n i n g with poly(ethylene g l y c o l ) - a l k y l ethers. Ind. Eng. Chem. Product. Res. Dev. 23, 86. Horie, S., I s h i i , H., Nakazawa, H. Suga, T., and O r i i , H. (1979). Determination of the cross-points of r a t l i v e r peroxisomes, peroxisomal and the core components by cross p a r t i t i o n . Biochem. Biophys. Acta 585, Huggins, M.L. 440.  (1941).  Solutions of long chain compounds.  core 435.  J . Chem. Phys. 9,  Hustedt, H., Kroner, K.H., Menge, U., and Kula, M.-R. (1978). Aqueous two-phase systems for large s c a l e enzyme i s o l a t i o n processes. 1st European Congress on Biotechnology, part 1, Dechema, Frankfurt, pp. 48-51. Janzen, J . (1985). Fibrinogen adsorption to human erythrocytes. Ph.D. U n i v e r s i t y of B r i t i s h Columbia.  thesis,  Johansson, G. (1970a). Studies on aqueous dextran-PEG two-phase systems containing charged PEG 1. P a r t i t i o n of albumins.Biochem. Biophys. Acta 222, 381. Johansson, G. (1970b). P a r t i t i o n of s a l t s and t h e i r e f f e c t s on p a r t i t i o n of proteins i n a dextran-poly(ethylene glycol)-water two-phase system, Biochim. Biophys. Acta 221, 387-390. Johansson, G. (1974a). E f f e c t s of s a l t s on the p a r t i t i o n of proteins i n aqueous polymeric biphasic systems. Acta. Chem. Scand. B 28, 873-882. Johansson, G. (1974b). P a r t i t i o n of proteins and micro-organisms i n aqueous b i p h a s i c systems. Mol. C e l l . Biochem. 4, 169-180.  -253-  Johansson, G. (1976). The e f f e c t of poly(ethylene g l y c o l ) esters on the p a r t i t i o n of proteins and fragmented membranes i n aqueous biphasic systems. Biochim. Biophys. Acta 451, 517-529. Johansson, G. (1978). Comparison o f two aqueous biphasic systems used f o r the p a r t i t i o n of b i o l o g i c a l m a t e r i a l . J . Chromatogr. 150, 63-71. Johansson, G., and Shanbhag, V.P. (1984). A f f i n i t y p a r t i t i o n i n g o f proteins i n aqueous two-phase systems containing polymer-bound f a t t y acids 1. E f f e c t o f polyethylene g l y c o l palmitate on the p a r t i t i o n of human serum albumin and alpha-lactalbumin. J Chromatogr. 284, 63-72. Kay, M.M.B., and Goodman, J.R. (1984). IgG antibodies do not bind to Band 3 i n i n t a c t erythrocytes; enzymatic treatment of c e l l s i s required f o r IgG binding. Biomed. Biochimica Acta 43, 841-846. K e s s e l , D. (1980). C e l l surface a l t e r a t i o n s associated with exposures of leukemia L1210 c e l l s to f l u o r o u r a c i l . Cancer Research 40, 322 Kortum, G. (1965). "Treatise on Electrochemistry." Amsterdam.  Elsevier Publishing,  Kuhn, I. (1980). A l c o h o l i c fermentation i n aqueous two-phase systems. Biotech Bioenq. 22, 2393. Kunda, S.S., Steane, S.M., Bloom, J.E.C., and Marcus, D.M. (1978). Abnormal g l y c o l i p i d composition of erythrocytes with a weak P antigen. Vox Sang. 35, 160-167. Levine, S., Levine, M., Sharp, K. A., and Brooks, D.E. (1983). Theory of the e l e c t r o p h o r e t i c behavior of human erythrocytes. Biophys. J . 42, 127-135. MacLeod, D.B. (1923). Faraday Soc. 19, 38.  R e l a t i o n between surface tension and density.  Trans.  Manning, CD., and Scriven, L.E. (1977). On i n t e r f a c i a l tension measurement with a spinning drop i n g y r o s t a t i c e q u i l i b r i u m . Rev. S c i . Instrum. 48, 1699-1705. Marchesi, V.T., Furthmayr, H., and Tomita, M. (1976). The red c e l l membrane. Ann. Rev. Biochem. 45, 667-698. Mattiasson, B. (1980). P a r t i t i o n a f f i n i t y l i g a n d assay (PALA): Radio-immunoassay o f d i g o x i n . J . Immun. Meth. 35, 137-146. Mattiasson, B. (1983). A p p l i c a t i o n s of aqueous two-phase systems i n biotechnology. Trends i n Biotech. 1, 16. McDaniel, R.V., McLaughlin, A., W i n i s k i , A.P., Eisenberg, M., and McLaughlin, S. (1984). B i l a y e r membranes containing the ganglioside G i'. Models f o r e l e c t r o s t a t i c p o t e n t i a l s adjacent to b i o l o g i c a l membranes. Biochemistry 23, 4618-4623. m  -254-  Mclver, D.J.L., and Schurch, S. (1982), I n t e r f a c i a l free energies of i n t a c t and r e c o n s t i t u t e d erythrocyte, surfaces - i m p l i c a t i o n s for b i o l o g i c a l adhesion, Biochimica et Biophysica Acta 691, 52-60. Mendenhall, W., and Scheaffer, R.L. (1973). "Mathematical S t a t i s t i c s with A p p l i c a t i o n s . " Duxbury Press, North S c i t u a t e , Mass. Miner, K.M., Walter, H., and Nicholson, G.L. (1981). Subfractionation of malignant v a r i a n t s of metastatic murine lymphosarcoma c e l l s by countercurrent d i s t r i b u t i o n i n two-polymer aaueous phases."Biochemistry 20 , 6244. Mueller, W., Schuetz, H.-J., Guerrier-Takada, C , Cole, P.E., and P o t t s , R. (1979). Size f r a c t i o n a t i o n of DNA fragments by l i q u i d - l i q u i d chromatography. Nucleic Acids Res. 7, 483-499. Mukerjee, P., and Mysels, K.3. (1971). " C r i t i c a l M i c e l l e Concentrations of Aqueous Surfactant Systems." National Bureau of Standards. N a t l . Std. Data System. U.S. Dept. of Commerce. V o l . 36. Murphy, J.R. (1973). Influence of temperature and method of c e n t r i f u g a t i o n on the separation of erythrocytes. J . Lab. C l i n . Med. 82, 334-341. Mustacic, R.V., and Weber, G. (1978). Ligand promoted t r a n s f e r of p r o t e i n s between phases: Sponataneous and e l e c t r i c a l l y helped. Proc. N a t l . Acad. S c i . 75, 779-783. Neumann, A.W., Good, R.J., Hope, C.J., S e j p a l , M. (1974). Equation of s t a t e approach to determine surface tensions of low energy surfaces from contact angles. J . C o l l o i d Interface S c i . 49, 291-304. Ponder, E. (1971). "Hemolysis and Related Phenomena." 2nd Edn. Grune and S t r a t t o n , New York, N.Y. pp 275-7. Princen, H.M., Z i a , I.Y.Z., and Mason, S.G. (1967). Measurement of i n t e r f a c i a l tension from the shape of a r o t a t i n g drop. J . C o l l o i d Interface S c i . 23, 99-107. Raymond, F.D. (1981). The P a r t i t i o n of C e l l s i n Two-Polymer Aqueous Phase Systems. Ph.D Thesis, U n i v e r s i t y of London. Raymond, F.D., and Fisher, D. (1980). P a r t i t i o n of r a t erythrocytes i n aqueous polymer two-phase systems, Biochim. Biophys. Acta 596, 445-450. Reitherman, R., Flanagan, S.D., and Barondes, S.H. (1973). Electromotive phenomena i n p a r t i t i o n of erythrocytes i n acqueous two phase systems. Biochim. Biophys. Acta 297, 193-202. Reynolds, J.E. (1982). (Ed.) "Martindale Pharmacopaeia. Pharmacopaeia Press, London.  11  28th Edn.  The  Robinson, R.A. and Stokes, R.H. (1959). " E l e c t r o l y t e S o l u t i o n s . " 2nd Ed., Butterworth, London. Chapter 9.  -255-  Rosen, M.J. (1978). "Surfactants and I n t e r f a c i a l Phenomena." John Wiley and Sons, New York. Ryden, J . , and Albertsson, P.-A. (1971). I n t e r f a c i a l tension o f polyethylene glycol-water two-phase systems. J . C o l l o i d Interface S c i . 37, 219-222. Sasakawa, S., and Walter, H. (1972). P a r t i t i o n behaviour of native proteins i n aqueous dextran- poly(ethylene g l y c o l ) phase systems Biochemistry 11:2760. Schulze, H.J. (1984). "Physico-chemical Elementary Processes i n F l o t a t i o n . " E l s e v i e r , Amsterdam. Ch. 4. Schurch, S., and Mclver, D. J . L. (1981). I n t e r f a c i a l tensions at l i p i d water i n t e r f a c e s . Comparison of equation-of-state p r e d i c t i o n s with d i r e c t experimental measurements. J . C o l l o i d Interface S c i . 83, 301-304. Schurch, S., Gerson, D.F., and Mclver, J.L. (1981). Determination o f cell/medium i n t e r f a c i a l tensions from contact angles i n aqueous polymer systems. Biochim. Biophys. Acta 640, 557-571. S c o t t , R.L. (1949). The thermodynamics of high polymer s o l u t i o n s . IV. Phase e q u i l i b r i a i n the ternary system: polymer 1-polymer 2-solvent. J . Chem. Phys. 17, 268-284. Seaman, G.V.F. (1975). E l e c t r o k i n e t i c behavior of red c e l l s . In "The Red C e l l " (Surgenor, D.M. ed.), V o l . 2, Academic Press, New York. pp. 1135-1229. Shanbhag, V.P. (1971). Rate of transport o f proteins across the i n t e r f a c e between the two aqueous phases i n polyethylene glycol-dextran-water systems. Proceedings of the I n t e r n a t i o n a l Solvent E x t r a c t i o n Conference, The Hague. Society of Chemical I n d u s t r i e s , London. Volume 2, p920. Shanbhag, V.P., and Johansson, G. (1974). S p e c i f i c e x t r a c t i o n of human serum albumin by p a r t i t i o n i n aqueous b i p h a s i c systems containing poly(ethylene glycol)-bound l i g a n d . Biochem. Biophys. Res. Comm. 61, 1141. Sharp, K.A., and Brooks, D.E. (1985). C a l c u l a t i o n of the e l e c t r o p h o r e t i c m o b i l i t y of p a r t i c l e s bearing bound p o l y e l e c t r o l y t e using the non-linear Poisson-Boltzmann Equation. Biophys. J . 47, 563-566 Sharp, K.A., Yalpani, M., Howard, S.J., and Brooks, D.E. (1985). Synthesis and a p p l i c a t i o n of poly(ethylene g l y c o l ) - a n t i b o d y a f f i n i t y l i g a n d for c e l l separation i n aqueous polymer two phase systems. Submitted to Anal. Biochem. S i l b e r b e r g , A. (1962). The adsorption o f f l e x i b l e macromolecules. P a r t 1. The i s o l a t e d macromolecule at a plane i n t e r f a c e . J . Phys. Chem. 66, 1872-1883. Skutelsky, E., Danon, D., Wilchek, M., Boyer, E. (1977). L o c a l i z a t i o n o f s i a l y l residues on c e l l surfaces by a f f i n i t y cytochemistry. J . U l t r a s t r . Res. 61, 325-335.  -256-  Smeds, A.-L., Veide, A., and Enfors, S.-O. (1983). Regeneration of ATP by chromatophores i n aqueous two-phase systems. Enzyme Microbio. Tech. 5, 33-36. Stibenz, D., and Geyer, G. (1980). Conformational c a l c u l a t i o n s of the N-terminal h y d r o p h i l i c segment of human erythrocyte glycophorin. F o l i a Haematol. 107, 787-792. Sutherland, I . , and I t o , Y. (1978). Toroidal c o i l chromatography: A new high-speed, h i g h - r e s o l u t i o n method of separating c e l l s and c e l l organelles on t h e i r d i s t r i b u t i o n i n two-phase polymer systems. J . of High Resolution Chrom. 3, 97. Sutherland, I . , and I t o , Y. (1980). C e l l separation using two phase polymer systems i n a nonsynchronous flow through c o i l planet c e n t r i f u g e . Anal. Biochem. 108, 367-373. Tanford, C. (1961). " P h y s i c a l Chemistry of Macromolecules." John Wiley and Sons, New York, N.Y. Chapter 7. Tanford, C.H. New York.  (1976) "The Hydrophobic E f f e c t . " 2nd Edn. John Wiley and Sons.  T i l c o c k , C.P.S. and F i s h e r , D. (1979). I n t e r a c t i o n of phospholipid membranes with poly(ethylene glycoDs. Biochim. Biophys. Acta 577, 53-61. Tomita, M., Furthmayr, H., and Marchesi, V.T. (1978). Primary structure of human erythrocyte glycophorin A. I s o l a t i o n and c h a r a c t e r i z a t i o n of peptides and complete amino a c i d seauence. Biochemistry 17, 4756-4770. Tong, L.K.J., Reeves, R.L., and Andrus, R.W. (1965). The e f f e c t of s o l u b i l i z a t i o n by s u r f a c t a n t s on the k i n e t i c s of a l k a l i n e decomposition of i n d o - a n i l i n e dyes. J . Phys. Chem. 69, 2357. Topchieva, I. N. (1980). Biochemical a p p l i c a t i o n s of PEG. Translated from Uspekhi Khimi 49, 494-517 i n Russian Chemical Reviews, 49, 260-270. Van A l s t i n e , J.M. (1984). C e l l P a r t i t i o n i n Aaueous Polymer Two Phase Systems. Ph.D. Thesis, U n i v e r s i t y of B r i t i s h Columbia. Van A l s t i n e , J . and Brooks, D.E. (1984). C e l l membrane abnormality detected i n erythrocytes from m u l t i p l e s c l e r o s i s p a t i e n t s by p a r t i t i o n i n two polymer aaueous phase systems. C l i n . Chem. 30, 441-443. Van A l s t i n e , J.M, H a r r i s , J.M., Synder, S, C u r r e r i , P.A., Bamberger, S., and Brooks, D.E. (1984). Separation of aaueous two-phase polymer systems i n microgravity. Published i n "5th European Symposium- M a t e r i a l Sciences Under M i c r o g r a v i t y . " European Space Agency, P a r i s , pp 309-14. Van Deenan, L.L.M. (1981). Topology and dynamics of phospholipids i n membranes. FEBS L e t t . 123, 3-15.  -257-  Van Deenan, L.L.M., and de Gier, J . (1974). L i p i d s of the red c e l l membrane.In "The Red C e l l " (Surgenor, D.M. ed.) V o l . 1. Academic Press, New York. Ch. 4. Van G a s t e l , C , Van den Berg, D., de Gier, J . , and Van Deenan, L.L.M. (1965). Some l i p i d c h a r a c t e r i s t i c s of normal red blood c e l l s of d i f f e r e n t ages. B r i t . J. Haem. 11, 193-198. Van Holde, K.E. (1971). " P h y s i c a l Biochemistry." P r e n t i c e - H a l l , Englewood C l i f f s , New Jersey. Vassar, P.S., Hards, J.M., Brooks, D.E., Hagenberger, B., and Seaman, G.V.F. (1972). Physiochemical e f f e c t s of aldehydes on the human erythrocyte. J . C e l l Biology 53, 809-818. Verwey, E. J . L., and Overbeek, J . Th. G. (1948). "Theory of S t a b i l i t y of Lyophobic C o l l o i d s . " E l s e v i e r P u b l i s h i n g , Amsterdam, New York. Chapter 1. Vonnegut, B. (1942). Rotating bubble method for determination of surface and i n t e r f a c i a l tensions. Rev. S c i . Instrum. 13, 6-9. Walter, H. (1977). P a r t i t i o n of c e l l s i n two-polymer aqueous phases: a surface a f f i n i t y method f o r c e l l separation. In "Methods of C e l l Separation." V o l . 1. (Catsimpoolas, N. ed.). Plenum Press, New York, p 307. Walter, H. (1985). Personal Communication. Walter, H., and Anderson, J.L. (1981), P a r t i t i o n behaviour of c e l l s and soluble substances i n two-polymer aqueous phase systems: comments on Zaslavsky's general r u l e , FEBS L e t t . 131, 73-76. Walter, H., and Coyle, R.P. (1968). E f f e c t of membrane m o d i f i c a t i o n on human erythrocytes by enzyme treatment on t h e i r p a r t i t i o n i n aqueous dextran-polyethylene g l y c o l two-phase systems. Biochem. Biophys. Acta 165, 540. Walter, H., and Selby, F.W. (1966). Counter-current d i s t r i b u t i o n of red c e l l s of s l i g h t l y d i f f e r e n t ages. Biochim. Biophys. Acta 112, 146. Walter, H., and Selby, F.W. (1967). E f f e c t s of DEAE-dextran on the p a r t i t i o n of red blood c e l l s i n aqueous dextran-polyethylene g l y c o l two-phase systems Biochem. Biophys. Acta 148, 517. Walter, H., Selby, F.W., and Brake, J.M. (1964). The separation of young and old red blood c e l l s by counter-current d i s t r i b u t i o n . Biochem. Biophys. Res. Comm. 15, 497. Walter, H., Garza, R., and Coyle, R.P. (1968a). P a r t i t i o n of DEAE-dextran i n aqueous dextran-polyethylene g l y c o l phases and i t s e f f e c t on the p a r t i t i o n of c e l l s i n such systems, Biochim. Biophys. Acta 156, 409-411 . Walter, H., Krob, E.J., and Garza, R. (1968b). Factors i n the p a r t i t i o n of red blood c e l l s i n aqueous dextran-polyethylene g l y c o l two-phase systems. Biochim. Biophys. Acta 165, 507-514.  -258-  Walter, H., Krob, E.J., and Ascher, G.S. (1969). Separation of lymphocytes and polymorphonuclear leukocytes by countercurrent d i s t r i b u t i o n i n aaueous two-polymer phase systems. Exp. C e l l Res. 55, 279. Walter, H., Krob, E.J., Ascher, G.S., and Seaman, G.V.F. (1973a). P a r t i t i o n of rat l i v e r c e l l s i n aaueous dextran-polyethylene g l y c o l phase systems. Exp. C e l l Res. 82, 15. Walter, H., Krob, E.J., Brooks, D.E., and Seaman, G.V.F. (1973b) E f f e c t of acetaldehyde and gluteraldehyde f i x a t i o n on the surface properties of red blood c e l l s as determined by p a r t i t i o n i n aaueous phases. Exp. C e l l Res. 80, 415. Walter, H., Krob, E.J. and Brooks, D.E. (1976). Membrane surface p r o p e r t i e s other than charge involved i n c e l l separation by p a r t i t i o n i n polymer, aaueous two-phase systems. Biochemistry 15, 2959-2965. Walter, H., Krob, E.J., and Moncla, B.J. (1978). C e l l - c e l l a f f i n i t y probed by counter-current d i s t r i b u t i o n in,two-polymer aaueous phase systems. Exp. C e l l Res. 115, 379. Walter, H., Webber, T.J., M i c h a l s k i , J.P., McCombs, C.C. Moncla, B.J., Krob, E.J., and Graham, L.L. (1979). Subfractionation of human p e r i p h e r a l blood lymphocytes on the basis of t h e i r surface p r o p e r t i e s by p a r t i t i o n i n g i n two-polymer aaueous phase systems. J . Immun. 123, 1687. Walter, H., Krob, E.J., Tamblyn, C.H., and Seaman, G.V.F. (1980). Surface a l t e r a t i o n s of erythrocytes with c e l l age: Rat red c e l l i s not a model f o r human red c e l l . Biochem. Biophys. Res. Comm. 97, 107. Walter, H., Brooks, D.E., and F i s h e r , D. (eds.) (1985). " P a r t i t i o n i n g i n Aaueous Two Phase Systems. Theory, Methods, Uses and A p p l i c a t i o n s to Biotechnology." Academic Press, New York. Wintrobe, M.M. (1974). " C l i n i c a l Hematology." Lea and Febiger, P h i l a d e l p h i a , Pa. Chs. 3, 45. Appendix A. Wolf, H., and G i n g e l l , D. (1983). Conformational response o f the glycocalyx to i o n i c strength and i n t e r a c t i o n s with modified glass surfaces: study of l i v e c e l l s by interferometry. J . C e l l S c i . 63, 101-112. Zaslavsky, B.Yu., Miheeva, L.M., and Rogozhin, S.V. (1978a). P o s s i b i l i t y o f a n a l y t i c a l a p p l i c a t i o n o f the p a r t i t i o n i n aaueous biphasic polymeric systems techniaue. Biochim. Biophys. Acta 510, 160-167. Zaslavsky, B.Yu., Miheeva, L.M., Mestechkina, N.M., Pogorelov, V.M., and Rogozhin, S.V. (1978b). General r u l e of p a r t i t i o n behaviour o f c e l l s and s o l u b l e substances i n aaueous two-phase polymeric systems, FEBS L e t t . 94, 77-80.  -259-  Zaslavsky, B.Yu., Miheeva, L.M., and Rogozhin, S.V. (1979). R e l a t i v e hydrophobicity o f surfaces of. erythrocytes from d i f f e r e n t species as measured by p a r t i t i o n i n aaueous two-polymer phase systems. Biochim. Biophys. Acta 588, 89-101. Zaslavsky, B.Yu., Miheeva, L.M., Mestechkina, N.M., Shchyukina, L.G., Chlenov, M.A., Kudrjashov, L . I . , and Rogozhin, S.V. (1980). Use of Solute P a r t i t i o n f o r Comparative C h a r a c t e r i z a t i o n of Several Aqueous Biphasic Polymeric Systems, 3. Chromatogr. 202, 63-73. Zaslavsky, B.Yu., Miheeva, L.M., and Rogozhin, S.V. (1981). Parameterization of Hydrophobic P r o p e r t i e s of Aqueous Polymeric Biphasic Systems and Water-Organic Solvent Systems, J . Chromatogr. 212, 13-22. Zaslavsky, B.Yu., Miheeva, L.M., Mestechkina, N.M., and Rogozhin, S.V. (1982). Physico-chemical Factors Governing P a r t i t i o n Behaviour of Solutes and P a r t i c l e s i n Aqueous Polymeric Biphasic Systems. I I . E f f e c t of Ionic Composition on the Hydration P r o p e r t i e s of the Phases, J . Chromatogr. 253, 149-158 . Zisman, A.W. (1964). R e l a t i o n of e q u i l i b r i u m contact angle to l i q u i d and s o l i d c o n s t i t u t i o n . In "Contact Angles, W e t t a b i l i t y and Adhesion." Advances i n Chemistry, V o l . 43. Applied P u b l i c a t i o n s ; American Chemical Society, Washington, D.C. Chapter 1  

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