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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, University of Leeds, England, 1978 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF CHEMISTRY We accept t h i s thesis as conforming to the-^eODired standaitfJ THE UNIVERSITY OF BRITISH COLUMBIA June 1985 © Kim Andrew Sharp, 1985 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by h i s or her representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of Oh^.yv\\<^Ofl  The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date k ^\)c« \<\%5 DE-6 (3/81) Abstract - i i -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 their interface. The behaviour of human erythrocytes i n such two phase systems was studied i n order to characterize some of the physico-chemical interactions important i n determining c e l l p a r t i t i o n . Two aspects were studied: the role of e l e c t r o s t a t i c and a f f i n i t y ligand effects in 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 relationship of th i s r e l a t i v e a f f i n i t y to the c e l l p a r t i t i o n . The potential difference produced by the unequal a f f i n i t y of the buffer cations and anions for each phase was related to the s a l t p a r t i t i o n by a thermodynamic model, which agreed with experimental results obtained i n single and mixed s a l t systems. A thermodynamic theory for the effects of an a f f i n i t y ligand on the c e l l surface free energy difference between the phases was derived, and found to agree Quantitatively with experimental results using the a f f i n i t y ligand PEG-palmitate. The change in c e l l surface free energy difference as a function of potential and ligand concentration was determined by contact angle measurements. This change was very small, based either 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 attributed to p a r t i a l exclusion of the phases from the c e l l glycocalyx. C e l l p a r t i t i o n into the upper PEG r i c h phase increased as th i s phase was made more positive with respect to the lower phase, or as the amount of an a f f i n i t y ligand, PEG-palmitate, i n the system was increased. Contact angle measurements were used to determine the energy of erythrocyte attachment to the interface 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 far 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 difference between the phases. This and other results led to the hypothesis that droplet coalescence i s the primary process by which large p a r t i c l e s (>1 i^m dia.) such as c e l l s are distributed between the interface and one of the phases. - i v-Contents Page T i t l e Page i Abstract i i Contents i v L i s t of Tables i x L i s t of Figures x Acknowledgements x i i Dedication x i i i Chapter One. Introduction A. General Background and Objectives 1 B. H i s t o r i c a l Outline 10 C. Theoretical Aspects of P a r t i t i o n 17 i ) Physical Chemistry of Phase Separation 17 i i ) Properties of the Phase System 25 i i i ) Theory of Molecular P a r t i t i o n i n g 38 i v ) Theory of P a r t i c l e P a r t i t i o n i n g 43 D. The Erythrocyte 65 i ) Morphology and Erythrogenesis 65 i i ) Biochemistry of the Erythrocyte Membrane 67 Chapter Two. Materials and Methods 71 A. General Methods 71 -V-Contents continued Page Chapter Two. Materials and Methods B. Preparation and Characterization of Phase Systems 72 i ) Polymer Properties 72 i i ) 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 Potential Difference 80 C. P a r t i t i o n of Solutes i n the Phase System 82 i ) General Methods 82 i i ) P a r t i t i o n Coefficients 83 i i i ) PEG-palmitate C r i t i c a l Micelle 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 88 i i ) PEG 8000-palmitate Adsorption 91 i i i ) Desorption of PEG and PEG-palmitate 93 G. Contact Angle Measurements 94 i ) Apparatus 94 i i ) Preparation of Pipettes 96 i i i ) Experimental Procedure 96 iv) Image Analysis 97 H. Treatment of Results and Experimental Uncertainties 99 Contents continued - v i -Page Chapter Three. Theoretical Results 101 A. Potential Difference i n Single Salt Systems 101 B. Potential Difference i n Mixed Salt Systems 103 C. Polyelectrolyte 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 Effects and the C e l l Surface Free Energy Difference 121 A. Introduction 121 B. Effects of Buffer Composition on Phase System Properties 122 i ) Effect of Phosphate on the Binodial 122 i i ) Effect of Buffer on I n t e r f a c i a l Tension 124 i i i ) Discussion 125 C. Potential and Salt P a r t i t i o n 127 i ) Salt Bridge Effects 127 i i ) Single Salt Systems 129 i i i ) Phosphate Concentration Effects 134 i v ) Mixed Salt 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 Salt Composition 142 i i ) C e l l Surface Free Energy Difference and Potential 145 i i i ) Discussion 149 Contents continued - v i i - Page Chapter Five. PEG-palmitate and the C e l l Surface Free Energy Difference 154 A. Introduction 154 B. Effect of PEG-palmitate on.the Phase System 155 i ) Compositional and E l e c t r o s t a t i c Effects 155 i i ) Effect of Ester on Tension 156 i i i ) Discussion 157 C. Behaviour of PEG-palmitate i n the phase system 157 i ) PEG-Palmitate P a r t i t i o n 157 i i ) PEG-Palmitate C r i t i c a l Micelle Concentrations 159 i i i ) Discussion 160 D. PEG-palmitate/Erythrocyte interactions 165 i ) C e l l P a r t i t i o n 165 i i ) Binding Studies 167 i i i ) PEG-palmitate and the C e l l Surface Free Energy Difference 177 iv) Discussion 179 Chapter Six. 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 i i ) Polymer Composition and Contact Angle 191 i i i ) C e l l P a r t i t i o n and the Cell/Interface Interaction 195 Contents Continued - v i i i - Page Chapter Six. Factors Determining C e l l P a r t i t i o n B. Determinants of C e l l P a r t i t i o n i v ) Discussion 198 C. Mechanisms of C e l l P a r t i t i o n 204 i ) C e l l P a r t i t i o n , Phase Density and Volume Ratio 204 i i ) Discussion and Proposal of a Mechanism for C e l l P a r t i t i o n 209 Chapter Seven. General Discussion and Summary 220 A. Overview 220 B. Statement of New Results and Suggestions for Future Research 227 C. Summary 230 Glossary of Symbols and Abbreviations 235 Appendices 239 A. The Minimum Force Necessary to P u l l a Spherical P a r t i c l e o f f a Liauid Interface 239 B. Mechanisms of C e l l P a r t i t i o n 240 Bibliography 247 - i x -L i s t of Tables Page 2.1 Description of Dextran Lots 73 2.2 Selected Physical Properties of the Phase Polymers 7A 4.1 Effect of Phase Composition on I n t e r f a c i a l Tension 125 4.2 Effect of Salt Concentration and Electrode Bridge Type on Potential 128 4.3 Salt P a r t i t i o n and Potential i n Single Salt Systems. I 130 4.4 Salt P a r t i t i o n and Potential i n Single Salt Systems. II 131 4.5 Salt P a r t i t i o n and Potential i n Single Salt Systems. I l l 132 4.6 Effect of Phosphate Concentration on Potential 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- Effect of Potential and Ionic Strength 147 5.1 Effect of Ester on Phase Compositions 155 5.2 Effect 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 Micelle Concentrations 160 5.4 Summary of Ester Binding Data from Scatchard Plots 177 5.5 Erythrocyte P a r t i t i o n and Contact Angle- Effect of Ester 178 6.1 Erythrocyte P a r t i t i o n and Contact Angle- Effect of Tension 193 6.2 Dimensionless Numbers Characterising Fluid Flow Regimes for Phase System Droplets 211 - X -L i s t of Figures " Page 1.1 General Phase Diagram For a Two Polymer/Solvent System 18 1.2 Interaction of a Spherical 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 Potential and Salt 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 Effect of A f f i n i t y Ligand on C e l l Surface Free Energies 120 4.1 Effect of Salts on the Phase Diagram 123 4.2 Comparison of Theoretical and Experimental Potentials 133 4.3 Effect of Salt Composition on Erythrocyte P a r t i t i o n 144 4.4 Effect of Potential 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- Effect 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 Plots of Ester Binding Data 176 - x i -* L i s t of Figures continued Page 5.9 Effect of Ester on C e l l Surface Free Energies-Comparison 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 Plots for Erythrocytes 194 6.3 Dependence of Erythrocyte P a r t i t i o n Coefficient on the Cell/Interface Interaction Energy 196 6.4 Dependence of Percent Erythrocyte P a r t i t i o n on the Detachment Force 197 6.5 Effect 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-Microscopic View 208 7.1 Schematic Outline of the Process of C e l l P a r t i t i o n 228 - x i i -Acknowledgements I t i s a great pleasure for me to be able to formally thank a l l the many people who combined to provide me with a context for t h i s thesis: In the lab, p a r t i c u l a r l y Jim Van Alstine and Tim Webber, for introducing me to 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 for introducing me to column chromatography; Rob Snoek, on whom I could r e l y for his broad knowledge of the erythrocyte; Evan Evans for showing me how to measure contact angles with his elegant apparatus; Barbara Kukan, for help with the contact angle measurements. I would especially l i k e to thank my supervisor, Don Brooks, from whom I learnt much about the method, p o s s i b i l i t i e s and excitement of research, and who always treated me as a friend. This thesis benefited greatly from his generous flow of support, suggestions and advice. Outside the lab, I would l i k e to thank a l l my other friends, who provided me with the kind of support that made everything so much easier, and the balance that I believe i s necessary to good science, and who made Vancouver such a wonderful place for me. In p a r t i c u l a r , Cynthia, Sandra and Rob for t h e i r music; Timmie for introducing me to the New Age; Judy and Ree, good t r a v e l l i n g companions; Evelyn and Rob, for days on the beach. I am grateful to 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 to 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. - x i i i -This thesis i s dedicated to those who gave me l i f e -1-Chapter One. Introduction Those who f a l l i n love with practice 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 certain 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 le a f pigments'*" (hence the term chromatography). A crude centrifugation process had been used to separate tung o i l as long ago as the tenth century, although the centrifuge as a sophisticated a n a l y t i c a l tool did not exist 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 centrifuges by Svedburg and coworkers'''. Continuous improvements of, and developments from, these two techniques, plus the addition of others such as electrophoresis (which was f i r s t developed by T i s e l i u s i n the ^O's"*"), gave researchers increasingly sharp and discriminating biochemical scalpels with which to dissect 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 state of any area i n biochemistry today depends to a great degree on the sophistication of the separation techniques available. Encyclopaedia Britannica, 1968 Edn. -2-I t i s a sine qua non that any separation method must discriminate between different elements or properties of a mixture while a l t e r i n g the material as l i t t l e as possible: the separation method must be compatible with the material. As a rule the larger and more complex the material, the more stringent these requirements become. Thus while there are many methods for separating proteins, carbohydrates and l i p i d s , there are fewer methods that can deal with complexes of proteins, membranes, and c e l l organelles, and there i s a paucity of methods for separating intact viable c e l l s (for a review see e.g. Catsimpoolas, 1977). This thesis i s concerned with p a r t i t i o n i n aqueous polymer two-phase systems (APTS) as a method of c e l l separation and analysis i n biochemistry and biophysics. While many classes of two and multi-phase systems e x i s t , the only type used to any degree for separating or analysing c e l l s i s that formed from two incompatible neutral polymers i n aqueous solution. I f a solution i s made of two polymers i n a common solvent, and the energy of interaction between segments of the different polymers i s unfavourable, then at some condition 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 into 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 isotonic and (providing the polymers have no deleterious effects) otherwise made compatible with sensitive b i o l o g i c a l material. Such two phase systems, p a r t i c u l a r l y those containing dextran and poly(ethylene glycol) (PEG), can be used i n a manner that I w i l l outline shortly, 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 for amino-acids, proteins, nucleic acids, 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 certain other separation methods. The simplest application i s the single step p a r t i t i o n : the material of interest (for convenience referred to hereafter as the solute, although i t may also be an insoluble 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 dist r i b u t e d , or partitioned, between the two phases and t h e i r mutual interface. For soluble material especially, t h i s i s analogous to solvent extraction, 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 single 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 resolution 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 discrete analogue of chromatography, where either of the phases can be considered as the stationary phase. I t i s an interesting h i s t o r i c a l note that CCD i n fact 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 proteins. Not obtaining s u f f i c i e n t resolution, they Encyclopaedia Britannica, 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 of p a r t i t i o n chromatography. Continuous l i q u i d - l i a u i d extraction procedures such as the c o i l planet centrifuge and continuous flow-through centrifuges have also been adapted to APTS, making the s i m i l a r i t y with chromatography even closer. By contrast, when c e l l s or p a r t i c l e s are being partitioned the method has closer 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 extraction or chromatography: after the phases are mixed, and while they are separating, the p a r t i c l e s are interacting with a dense emulsion of droplets which are either f l o a t i n g or sedimenting to 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 to 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 to thei 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 introduction. Both phases consist primarily 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 addition of any s a l t s , factors etc. required by parti c u l a r solutes. In addition 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 factors r e s u l t i n g i n a benign environment for sensitive solutes. The i n t e r f a c i a l tension between the phases i s extremely low -4 2 (10 -10 dynes/cm), thus reducing the chance of denaturing solutes adsorbed at the interface. A very important aspect of p a r t i t i o n i s that i t separates by means of differences i n surface properties- except under parti 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 solute. This feature i s an advantage when trying to separate, for example, a mixture of c e l l s that have different functions, and hence which might be expected a p r i o r i to d i f f e r i n surface properties, but not i n density or s i z e . P a r t i t i o n i s extremely sensitive, depending, as w i l l be seen shortly, on roughly the exponential of the relevant solute properties. Moreover, what these relevant properties are, i . e . the particular surface characteristics 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 ioni c composition of the phases, or by the addition of certain ligands. By adding such a f f i n i t y ligands, whose mode of action w i l l be outlined l a t e r i n t h i s introduction, the p a r t i t i o n can be made to depend primarily on the nature of the ligand/solute interaction. This adds the p o s s i b i l i t y of much greater control 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 size from angstroms to microns. The upper size 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, either to the interface or the bottom of the container. The lower size l i m i t i s p r i n c i p a l l y determined by the fact 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 practice both these size l i m i t s manifest themselves as loss of resolution or separating power. Within these l i m i t s APTS has been used for solutes of an almost continuous size 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 equilibrium conditions, or at least i n a time independent manner, which can simplify the analysis 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 physical chemistry of the phase systems, or, more importantly the separation process i t s e l f . L i t t l e i s known about which of the solute surface properties 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 diffuse l i k e soluble material, are actually distributed between the two phases and the interface are unclear. While t h i s separation method i s very sensitive to the surface properties of the solute, the separations obtained are generally based on b i o l o g i c a l l y non-specific differences. 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 resolution, can be obtained by a f f i n i t y methods, as i n other separation techniques such as chromatography, by using antibodies, cofactors, ligands etc. However although these have been applied to protein, nucleic acid and membrane receptor p u r i f i c a t i o n s i n APTS, so far 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 detailed 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 also needed. Lack of such knowledge and techniques hampers the r a t i o n a l application of APTS to many d i f f i c u l t separation problems. This i s compounded by the fact that there are many variables which may be altered i n making up two phase systems, such as the type, molecular weight and concentrations of both polymers, i o n i c composition etc. This provides great v e r s a t i l i t y . I t also makes selection of a suitable system largely an empirical procedure, however. The great s e n s i t i v i t y of the systems i s also a double-edged sword, since reproducible results may be d i f f i c u l t to obtain, p a r t i c u l a r l y with larger p a r t i c l e s , unless experimental conditions, such as -7-temperature, phase s e t t l i n g time etc. are c a r e f u l l y controlled. This problem i s exacerbated by polydispersity 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 differences 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 , especially i f the polymers cannot be recycled after 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 to, or i n other ways cause unwanted alterations to the solute. 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 suitable 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 for separating and studying c e l l s based on surface properties, and furthermore, that l i t t l e Quantitative information i s available regarding the surface properties that are important, or how such separations are achieved. These considerations motivated t h i s study. This thesis investigates 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. I t considers two auestions: 1). What role do phase system and c e l l surface properties have i n determining the interaction 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 for each phase? Two aspects of t h i s interaction are studied: e l e c t r o s t a t i c effects -8-and a f f i n i t y ligand effects. 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 interaction? To examine these questions i t was also necessary to study the i n t e r -relationships of some of the system properties themselves. To pursue these objectives the p a r t i t i o n of human erythrocytes i n two phase systems composed of dextran T500 and PEG 8000 was studied. This p a r t i c u l a r polymer combination was chosen because i t i s by far the most widely used, especially 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 detailed knowledge available on t h e i r surface structure (section D below). Outline of Thesis The remainder of t h i s introduction consists of three parts: -A b r i e f history of the subject. -A detailed summary of the theory relevant to c e l l p a r t i t i o n . This section also gives more detailed explanations of terms such as surface properties, surface interactions, e l e c t r o s t a t i c interactions and a f f i n i t y ligand i n the context of p a r t i t i o n . -A b r i e f description 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 heoretical 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 Six contain the experimental r e s u l t s , with Four and Five dealing primarily with the f i r s t question posed i n the objective, and Chapter Six treating the second'. Each chapter has a b r i e f introduction outlining the approach to the problem. Chapter Seven i s a general discussion chapter i n which I t i e together the previous work and attempt to put i t i n perspective. The appendices contain some material related to the discussion on c e l l p a r t i t i o n mechanisms. A glossary of symbols and abbreviations i s given after Chapter Seven. -10-B. H i s t o r i c a l Outline The history 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 applications. The phenomenon of phase separation i n a three component, polymer/polymer solvent system was f i r s t reported i n 1896 (Beijerinck) for gelatin/starch solutions. Flory (1941) and Huggins (1941) independently worked out a successful theory for the thermodynamics of concentrated solutions of f l e x i b l e polymers. This was extended by Scott (1949) to describe phase separation phenomena i n solutions 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 for separating b i o l o g i c a l material was performed by Albertsson during his doctoral thesis, and the f i r s t paper on t h i s application was published i n 1958 (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 his thesis (Albertsson, 1960). Albertsson and his co-workers subsequently pioneered the application of APTS to a wide range of b i o l o g i c a l materials. With the publication 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 revised e d i t i o n . i n 1971 (Albertsson, 1971) other workers became interested i n t h i s technique. The f i r s t publications concerned protein separations. The study of immunological reactions was another early application (Albertsson and Philipson, 1960), as was the extension to larger molecules and p a r t i c l e s (Albertsson, 1961). DNA was partitioned i n 1962, (Frick and L i f ) , and the f i r s t c e l l organelles, chloroplasts, were studied i n 1963 (Albertsson and -11-Baltescheffsky). Viruses were f i r s t studied i n APTS i n 1963 (Bengtsson and Philipson). Many other types of solutes, 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 , including liposomes (Dahlgren et a l . , 1977, Eriksson et a l . , 1978). In 1965 Albertsson described a new type of thin layer CCD apparatus s p e c i a l l y designed to minimize the long separation times due to the small density difference and high v i s c o s i t i e s of the phase systems. Although other types of apparatus for multistep p a r t i t i o n were described by Albertsson (Albertsson, 1971; Blomquist and Albertsson, 1972), there were no extensive applications of new apparatus u n t i l 1978, when Sutherland and Ito described the use of the toroidal' c o i l centrifuge for p a r t i t i o n i n g c e l l s and organelles, and i n d u s t r i a l scale l i q u i d / l i q u i d extraction was applied to protein separation by APTS (Hustedt et a l . , 1978). Another technical 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 Baird (1962) described the f i r s t application to c e l l s early on i n the development of APTS. With the separation of young and old 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 partitioned, including lymphocytes and leukocytes (Walter et a l . , 1969), hepatocytes (Walter et a l . , 1973a), pl 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 ligand 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 ligand, PEG-TMA, for protein p a r t i t i o n . A t h i r d type of ligand, PEG-fatty acid esters, also known c o l l e c t i v e l y as hydrophobic a f f i n i t y ligands, was introduced by Shanbhag and Johansson (1974) for protein p a r t i t i o n . This type of ligand 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 studies. 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 protein i s o e l e c t r i c points of proteins by a technique known as cross-partition (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 (Ericson, 1974; Horie et a l . , 1979; Akerlund et a l . , 1979). Antibody/antigen interactions (Albertsson and Philipson, 1960), protein/ligand interactions (Gray and Chamberlain, 1971), protein/protein interactions (Backman et a l . , 1977) and c e l l / c e l l interactions (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 of alterations i n a r t e r i a l tissue 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 etting, 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 ligand assay (PALA) (Mattiason, 1980), and as a possible test for multiple s c l e r o s i s (Van Alstine and Brooks, 1984). There were few early commercial applications for APTS (eg. virus 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-series of papers was published by Kula and her colleagues on a biotechnological application- the large scale p u r i f i c a t i o n of enzymes. Other applications include alcoholic 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 fastest growing areas of research i n APTS (Mattiason, 1983). Although there have been many applications 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 less rapid. The work of Albertsson and Nyns i n 1961 on the effects of s a l t s on protein p a r t i t i o n represented the f i r s t step towards understanding what physicochemical factors affect 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 interface provided l i t t l e resistance to the d i f f u s i o n of proteins between the phases. Albertsson had predicted that certain s a l t s could give r i s e to Donnan type potentials between the phases, and t h i s was confirmed by direct measurements i n 1973 (Reitherman et a l . , ) . Johansson (1974b) also measured these potentials i n d i r e c t l y by protein p a r t i t i o n . However i t was not u n t i l recently that a f u l l thermodynamic relationship between the potential 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 and confirmed experimentally (Brooks et a l . , 1984). A contribution to the understanding of e l e c t r o s t a t i c e ffects i n protein p a r t i t i o n was made by deLigny and Gelsema (1982) who put the relationship between s a l t and protein -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 theoretical footing. The effects of polymer type and concentration were also investigated. Albertsson measured phase compositions for several polymer types and molecular weights, and many of the resulting phase diagrams are given i n his book (Albertsson, 1971). Albertsson also gives a treatment of the theoretical framework of par t i t i o n i n g i n t h i s book. Ryden and Albertsson (1971) investigated the relationship 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 investigated the role of 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 parti c u l a r they related 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 difference i n polymer concentrations between the phases, and established the fourth power dependence of the tension on t h i s difference. The determinants of c e l l p a r t i t i o n was also a subject of some in t e r e s t . Walter and Coyle (1968) used enzymatic modification of erythrocyte surfaces to investigate t h i s aspect. Walter et a l . , (1968b) also looked at the other side of the problem by investigating the effects of 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 correlated with electrophoretic mobility, one of 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 effects of aldehyde f i x a t i o n on erythrocyte p a r t i t i o n were also 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 to 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 of 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 to 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 role of non-electrostatic effects i n c e l l p a r t i t i o n was studied by Walter et a l . , (1976) who correlated erythrocyte p a r t i t i o n with membrane l i p i d composition. Eriksson et a l . , (1976) also found a sim i l a r correlation 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 elucidate the role of bilayer 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 series of papers containing some controversial work on the role of io n i c composition, ionic strength and hydrophobicity i n c e l l p a r t i t i o n . This prompted a dicussion on the the meaning and role of hydrophobic effects i n p a r t i t i o n (Walter and Anderson, 1981). 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 distributed i n the phase system, i n the absence of a d i f f u s i o n mechanism have long been recognized. Gerson (1980) and Gerson and Akit (1980) have used contact angle measurements, and Raymond and Fisher (1980) have observed the role of cel l / d r o p l e t interactions i n systems of low polymer concentration, i n attempts to understand t h i s problem better. There remains much to be discovered about the d e t a i l s of c e l l p a r t i t i o n . In retrospect many of the theoretical studies outlined 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 of the phase system or solute surface independently of the others, and some studies often f a i l e d to account for the fact that more than one factor was being varied 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 properties, and the determinants of solute and c e l l p a r t i t i o n . Increased interest i n APTS resulted i n the f i r s t conference on par t i t i o n i n g being held i n Los Angeles i n 1979. Work on the various applications of APTS continues at an increasing rate. A complete computerized bibliography of the l i t e r a t u r e was started after 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 publications. 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 of the leading reasearchers i n the f i e l d i s i n press (Walter et a l . , 1985), with the aim of being published i n time for the fourth international 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 to the f i r s t e dition of Albertsson's book, i n 1960, seems to 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 offer 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. Theoretical Aspects of P a r t i t i o n i ) Physical Chemistry of Phase Separation a) The Phase Diagram. A discussion 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 hesis, the most useful type i s the compositional phase diagram, constructed at a constant temperature, pressure, pH, polymer molecular weights, and s a l t composition. (Fig. 1.1). This phase diagram contains two pieces of information. I t indicates which compositions form one phase, and which separate to form two phases. I t also 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 subtraction. 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 for convenience. From a theoretical point of view the most useful concentration units are mole or volume fractions, but for p r a c t i c a l reasons weight/weight percentages are usually used for polymer systems. The binodial 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 binodial w i l l -18-POLYMER A Figure 1.1 General Phase Diagram for a Two Polymer/Solvent system -19-phase separate u n t i l i t just forms two stable phases. Hence these phases are represented by two points, F and G, that l i e on the bi n o d i a l . The binodial can be divided into two parts, 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 abscissa. The c r i t i c a l or p l a i t point, 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 phases, c*\ c b , weighted by the amounts of each phase, a \ a*3, thus: where the superscripts t and b refer to the top and bottom phases respectively (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 t i e l i n e also s a t i s f y [1.1], with different values of a*", a*3. 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 different r e l a t i v e amounts. From [1.1] and the figure i t can be seen that the weight r a t i o of phases i s given by ' , t t b bv ./ t b x c x = (a c + a c )/(a +a ) Cl.l] a t / a b = FE/GE [1.2] I f the densities of the phases are p and p then the volume r a t i o r y i s given by r y = p tFE/ p bGE [1.3] which i s approximately FE/GE i f the densities 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 binodial to the axes i n Fig. 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 point, and increasing with increasing polymer concentrations. An expression for t-^ i s eas i l y obtained by geometry, being the orthogonal mean of the polymer concentration differences: h = ( c a " c a ) + ( V c b ) I t turns out that the t i e l i n e i s an extremely useful c h a r a c t e r i s t i c of a phase system, which can be used to relate and predict i t s various properties. b) Theory of Phase Separation. Several classes of phase separation phenomena can occur. Many of these have been described by Flory (1953). Two phases w i l l occur i n polymer/salt/water systems i f the polymer strongly -21-rejects one of the s a l t ions (Albertsson, 1971). This type of phase system has been used widely for b i o l o g i c a l separations, most notably for large scale protein 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 for our purposes i s that formed from two incompatible polymers i n aqueous solution. This type of phase separation can be successfully treated using the Flory-Huggins theory for concentrated polymer solutions (Scott, 1949, Tanford, 1961)), which i s outlined below. This theory i s also applicable to the p a r t i t i o n of certain solutes themselves i n the phase system, since the solute i s of course just another component of the system. The free energy of formation of a solution from i t s pure components, known as the free energy of mixing, i s given by: AG m = AH -T AS [1.5] m m m where AH m and AS m are the enthalpy and entropy of mixing respectively. The chemical potential of the i ^ component, u.^ , i n t h i s solution i s given by the p a r t i a l molar free energy of mixing for that component H A - ^° = dAGm 9n ; [1.6] where the derivative 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 potential i n some reference state, i e . the standard state chemical potent i a l . Now the conditions that must be s a t i s f i e d simultaneously for the formation of two stable phases i n thermodynamic equilibrium from a mixture of components are: i ) the overall free energy of mixing must be minimized. -i i ) the chemical potential 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, results i n a decrease i n entropy, therefore i f AG i s to be decreased, AH must also decrease. This w i l l occur i f the enthalpy of interaction between unlike polymer segments i s unfavourable, or p o s i t i v e , since t h i s interaction i s decreased on phase separation. On a mole basis, 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 contribution from the polymer conformation). Thus for high molecular weight polymers one would expect that even very small positive enthalpies per segment can become important. This i s demonstrated by the fact that polymer incompatability i s the rule rather than the exception (Dobry and Boyer-Kawenoki, 1947). Such effects are also referred to as excluded volume e f f e c t s . In the Flory-Huggins theory, the solution i s envisaged as consisting of -23-a l a t t i c e - i e . molecules or polymer segments are confined to a regular array of i d e n t i c a l positions, 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, for a hexagonal close 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 ef f e c t i v e volume, and that no volume changes occur on mixing, AVm=0. The term segment as used here i s thus an operational 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 necessarily refer to the repeating monomer unit. This theory gives the free energy of mixing of an m component solution as: f r a c t i o n , i t s number of segments, and X ^ j i s the Flory Huggins interaction parameter describing the enthalpy of interaction between segments of compnents i and j . Component one i s the solvent, hence P^ = 1. The Flory-Huggins interaction parameter can be interpreted as the maximum change i n interaction energy, i n units of kT, occuring when a segment of the i t h component i s transferred 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 teraction i s unfavourable, X j j > 0 which can r e s u l t i n an unfavourable enthalpy of mixing. m m [1.8] where n^ i s the number of moles of the i t h component, <tK i t s volume For monodisperse polymers the conditions for phase separation and the form of 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 solving the m+1 simultaneous equations implied by conditions i ) and i i ) . For the special case of two polymers with the same molecular weight and s o l u b i l i t y , P 2=Pj a n c l ^12=*13* T ^ e c r i t i c a l molecular weight and concentration conditions for phase separation to occur are <t>2 = <t>3 = 1 / P 2 X 2 3 [1.9] It may be noted that the only interaction parameter that appears i s the polymer/polymer interaction parameter. In other words, providing X 2-j i s posit i v e , however small, 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 to 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 for d i s s i m i l a r polymers, since incompatibility i s the rule rather than the exception (Dobry and Boyer-Kawenoki, 1947). For the special case the phase diagram i s symmetrical, and can eas i l y be predicted i f X 2 3 i s known. In practice predicting phase diagrams i s extremely d i f f i c u l t for unlike, polydisperse polymers, such as dextran T500 and PEG 8000. For t h i s polymer pair the phase diagrams are assymmetrical, due partly to the difference 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 prediction of phase diagrams i s that those systems used for b i o l o g i c a l applications nearly always contain s a l t s or other small solutes, some of which interact with the polymers. -25-i i ) Properties of the Phase System a) B i o l o g i c a l effects 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 linked polymer of glucose, (ca. 5% branching), obtained from a b a c t e r i a l c e l l wall (Leuconostoc mesenteroides), with an approximate weight average molecular weight of 500,000 g/mole; polyethylene glycol 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 synthetic, highly 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 quantities (Reynolds, 1982). Most studies on c e l l p a r t i t i o n have demonstrated no deleterious effects due to the phase polymers. For example lymphocytes are f u l l y viable after p a r t i t i o n , as determined by a variety of biochemical assays, such as complement binding and rosette formation (Walter et a l . , 1979). In fact the polymers often have a protective 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 also attest to t h e i r b i o l o g i c a l inertness. Dextran has successfully been used.for many years as a plasma expander. F i c o l l gradients are used routinely for density centrifugation 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 of p a r t i t i o n , and the fact that viable 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 effects that these polymers -26-generally have i s to aggregate or disaggregate c e l l s . While t h i s may inter 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 non-specific, i s f u l l y reversible when the c e l l s are washed with polymer free buffer, and can be i n h i b i t e d by using lower i o n i c strength buffers 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 section 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 length, t ^ , raised 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) also show the same dependence although these authors o r i g i n a l l y interpreted the dependence as an exponential function 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 point, 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 for various systems are given i n Walter et a l . (1985, Ch. 3). No theoretical explanation for 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 difference between the l i q u i d and i t s vapor (MacLeod, 1923). -27-Sodium chloride has l i t t l e effect on the tension. However increasing concentrations of phosphate, up to 0.22 M increase the tension dramatically, up to 300% for systems close to the c r i t i c a l point, and less further from the c r i t i c a l point. A large part of t h i s dependence i s due to the effect of phosphate i n increasing 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 to the phosphate gradient across the interface (Bamberger et a l . , 1984b). From these results some general remarks may be made about the effect of additives 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 resu l t from two effects - the gradient of the substance i t s e l f across the interface, and the increase i n the extent of phase separation, and hence t i e l i n e length, due to the unequal interaction of the substance with each of the phase polymers. i i ) Conversely a substance that p a r t i t i o n s equally between the phases, such as sodium chloride, w i l l have l i t t l e e f fect on the tension. i i i ) A substance that adsorbs at the interface w i l l lower the tension, an effect deducible from Gibbs equation (for example see Adamson, 1976). iv ) The effect of an unequally distributed substance w i l l be greater the closer the system i s to the c r i t i c a l point, and the larger the fraction of t o t a l solute 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 cation of a s a l t have different r e l a t i v e a f f i n i t i e s for each phase, the requirement of electroneutrality i n -28-each phase results i n a Donnan-type e l e c t r o s t a t i c potential difference (Galvani or inner potential difference), between the phases. This potential difference i s an important parameter to be considered i n choosing suitable phases systems, and has a large effect 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 potential differences 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 interpreted 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 potential difference, no e l e c t r o s t a t i c potential difference or even an e l e c t r o s t a t i c potential difference of opposite sign, by investigators p a r t i t i o n i n g different material or using different 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 potential of about lmV (Zaslavsky et a l . , 1979 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 potential, while potassium sulphate systems had a negligible p o t e n t i a l , whereas the opposite resu l t was obtained by Brooks et al.,(1984). This confusion has arisen because i t was not recognized that any test ion (often chloride) or charged molecule which i s used to measure the potential i s a physical e n t i t y . Therefore the measured potential contains an unknown contribution from the difference i n standard state chemical potential of that ion or molecule between the phases, i . e . Galvani or inner potentials are not d i r e c t l y measurable (Kortiim, 1965, Adamson, 1976). In addition i f one wants to predict the e l e c t r o s t a t i c potential 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 state chemical potential differences of the potential determining ions. Such standard state chemical -29-potentials are not d i r e c t l y measurable. A way to 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 theoretical section of t h i s thesis. Another point that has not been given adequate attention i s that when a s a l t p a r t i t i o n s unequally there i s a difference i n io 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 possible that such ionic strength differences, as well as the e l e c t r o s t a t i c potential difference, may be important i n the p a r t i t i o n of charged material. Such i o n i c strength effects are proportional to the square of the net charge and would favour p a r t i t i o n into the phase with the highest s a l t concentration. They could thus either augment or diminish the effect of the e l e c t r o s t a t i c potential 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 potential difference i n phase systems, s t a r t i n g with the fundamental conditions that the chemical potential 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 , neutral. Thus for a s a l t A z +B z~, where the superscripts t and b refer to the upper and lower phases, and the subscripts + and - refer to the cation and anion respectively, he obtained: (z + z )Ail>= (kT/e)ln r / r + ( A u ° - Au°)/e [1.11] + — — + — * + + (kT/e)ln K where the superscripts t and b refer to the upper and lower phases. -30-e = the electron charge r = f * 7 f b , the r a t i o of ion a c t i v i t y c o e f f i c i e n t s A = i ^ - ^ * 3 , the difference i n galvani potentials A |A° = \i0^- H ° b , the difference i n standard state chemical potentials. K = c V c b , the r a t i o of 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 electroneutrality reauirements of each phase i e . K = K+= K_) Thus there w i l l be a potential i f the ions have dif f e r e n t r e l a t i v e a f f i n i t i e s for each phase, as expressed by differences i n the standard state chemical potential 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 ion 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 ion p a r t i t i o n s i n the absence of potential (these differences i n formalism are discussed more f u l l y i n section i i i below). His notation tended to obscure the fact that the main contribution to the ion 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 potential generated i s smaller for higher valence ions, providing the other terms are constant. In practice however, larger multivalent inorganic ions often p a r t i t i o n more unequally, giving r i s e to larger potentials than monovalent ions (Johansson, 1974a, 1974b, Reitherman et a l . , 1973). Polyelectrolytes such as proteins or dextran-DEAE would however be expected to generate very small potentials. 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 potentials 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 quantitatively for the reasons given above. Two basic methods of measuring the potential have been used; i ) Determination via the p a r t i t i o n of a solute of known and variable charge, for example a protein. i i ) Direct measurement using reversible, 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 of a protein, determined previously by t i t r a t i o n , was altered by varying the pH. The e l e c t r o s t a t i c potential difference was then determined from the slope of a plot of log (protein p a r t i t i o n ) measured i n a series of systems with different pH, against net protein charge. However t h i s method requires several systems of varying pH to be made up i n order to measure the potential of one system. In addition the method assumes that the protein standard state chemical potentials 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 ion binding to the protein occur. Some of these assumptions are examined i n Chapter Three. Most measurements of the el e c t r o s t a t i c potential difference have used s i l v e r / s i l v e r chloride electrodes, (Reitherman et a l . , 1973, Zaslavsky et_ a l . , 1982, Brooks et a l . , 1984) although the calomel electrode has also been used (Ballard et a l . , 1979), the electrodes i n each case being connected to the phase system by s a l t bridges, which are usually f i l l e d with agar or other polymer gel to reduce leakage. Johansson (1974a) used electrodes connected by s a l t bridges containing 12% PEG saturated with KC1 to the top phases of two different systems, which i n turn had th e i r lower phases connected by a 20% Dx/0.5M N H4N03 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 for various ions, and successfully predicted the potentials of some systems. An advantage of t h i s arrangement for measuring potentials i s that i t yields the differences i n potentials between the two systems d i r e c t l y , although t h i s method has not been exploited further. Reitherman et a l . (1973) showed that the measured potential was independent of the s a l t concentration i n t h e i r agar f i l l e d bridges, indicating that junction potentials due to the s a l t were neg l i g i b l e . However junction potential effects may arise from the gel i n the s a l t bridge (Brooks et a l . , 1984), another complication of potential measurements that was not known i n e a r l i e r studies. The most commonly used way to manipulate the potential has been to a l t e r the r a t i o of phosphate to chloride ions i n the phase system. The potential 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), for t i e l i n e lengths from 8 to 17%, although i t i s not known whether such a proportionality i s generally true for other polymer/salt systems. The measured e l e c t r o s t a t i c potential difference 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 Ballard 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 potential difference as the concentration was increased, which they attributed to differences i n polymer l o t s , but t h i s may also 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 potential difference 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 variation of potential with ion type i s complex, and direct measurements of the e l e c t r o s t a t i c potential difference 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 several 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 relationship between the s a l t p a r t i t i o n and potentials for KC1 and potassium sulphate, some general trends may be inferred: 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 chloride and so w i l l give a larger potential. For the a l k a l i halide s a l t s , the potential would be expected to increase for the series K +, Na +, L i + , and for 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 into the lower phase than the di-basic ion (Johansson, 1970), and i n fact the potential was shown to be less negative for the mono-basic s a l t (Zaslavsky et a l . , 1982). I t has been pointed out that the potential effects of two s a l t s are not additive (Zaslavsky et a l . , 1982), and so must be determined either by direct measurements or from a theoretical approach such as that developed i n Chapter Three of t h i s thesis. No systematic studies of the effect on the e l e c t r o s t a t i c potential difference 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 certain 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 potential OA-differences. Zaslavsky et a l . , (1982) found larger potentials 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 did not affect the e l e c t r o s t a t i c potential difference i n KC1 containing systems. The inclusion of charged polymers such as DEAE-dextran (Walter et a l . , 1968a, Reitherman et al.,1973) and trimethylamino-PEG (Johansson, 1978) may also be used to produce e l e c t r o s t a t i c potential differences, although the effect of 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) Viscosity i s an important property of polymer solutions, which increases rapidly 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 effects 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 requiring 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 difference between the phases increases with t i e l i n e length. The time required for phase separation may therefore be minimized by judicious choice of these factors. The phase v i s c o s i t i e s are also important i n the flow processes believed to play a role i n c e l l p a r t i t i o n i n g (Raymond and Fisher 1980; Chapter Six, below), i n i n d u s t r i a l scale applications 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 to r o i d a l c o i l (Sutherland and Ito, -35-1980) , where effec t i v e mass transfer between the phases and e f f i c i e n t retention of the stationary phase are essential i n order to take advantage of the very high theoretical 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 effect 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 th e i r polymer and s a l t compositions, that there would be a difference i n the hydrophobicity of the two phases. 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 into one of the phases, which could then be labelled as the more hydrophobic of the two. This, i n fact, 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 series of surfactants i n a variety of phase systems, Zaslavsky et a l . , (1978a, 1981) found a li n e a r relationship between the log 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 of 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 calculate the hydrophobicity difference, AG™, , which was between 16 and 30 cal/mole, twenty to forty times lower than t y p i c a l values for 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 difference was greater for charge sensitive systems (containing 110 mM phosphate), and for increasing concentrations of KC1. In spite of t h i s work, the question of whether the hydrophobicity difference 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 of more complex solutes, p a r t i c l e s and c e l l s i s not at a l l clear. In the f i r s t place the phenomenon of phase separation i s governed primarily by the incompatibility between the two polymers, as discussed i n section i above, and does not p a r t i c u l a r l y depend either on the nature of the solvent, 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 difference i n hydrophobicity between the phases. Secondly the interactions that govern the p a r t i t i o n of a molecule are s i m i l a r to those that determine phase separation, as i s discussed below i n section i i i . Therefore the predominant interactions would be expected to be between the solute and the two polymers rather than between the solvent and the solute. This i s made more evident by a consideration of the phase diagram and [1.14] of section i i i below, since the r e l a t i v e difference i n water concentrations between the phases w i l l generally be small compared with the polymer concentration differences, and could even be zero. Similar considerations apply to the surface free energy differences 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 clear a p r i o r i that the main determinant of surfactant p a r t i t i o n w i l l be the hydrophobicity difference between the phases, and t h i s applies even more strongly when such conclusions are being extended to other solutes, 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 transfer between phases i s unlikely 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 rule of p a r t i t i o n postulating hydrophobic factors 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 extrapolation from solutes to p a r t i c l e s , which p a r t i t i o n between the interface and one of the phases, i s r i s k y . In addition they noted that several phase system parameters such as the e l e c t r o s t a t i c potential difference and the i n t e r f a c i a l tension were also being varied along with the hydrophobicity difference. I t may also be noted that the measured differences i n erythrocyte hydrophobicity (Zaslavsky et a l . , 1979) were of -22 the order of 10 moles/cell, which combined with a hydrophobicity difference, AGq H , of 16-30 cal/mole results i n surface free energy differences many orders of magnitude smaller than 10 to 10 2 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 res u l t i n measureable p a r t i t i o n differences. 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 factor affecting 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 correct chemically speaking, and i n fact I believe that t h i s has led to a number of erroneous conclusions i n the past. -38-i i i ) Theory of 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 neutral molecules. The p a r t i t i o n behaviour of any molecule, m, i s governed by the same thermodynamic pr i n c i p l e s as the phase separation phenomenon i t s e l f . At equilibrium, therefore, condition i i ) of section i holds, namely that the chemical potential of the species i s the same i n both phases. Thus: \L0t + kTln f V = R 0 b + kTln Ah [1.12] or rearranging: In K = -In f f c / f b - ( n 0 t - H°b)/kT = -In r f - An°/kT [1.13] Neglecting a c t i v i t y coefficents for the moment, i t can be seen that the p a r t i t i o n i s determined by the difference i n standard state chemical potential between the phases. Now the standard state chemical potential i n [1.12] i s the term that contains a l l the interactions 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 units 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 contributions from interactions with the other solute molecules. Thus by d e f i n i t i o n f** and f*3 tend to one i n the low concentration l i m i t . Albertsson (1971) however has viewed the relationship of p a r t i t i o n to the chemical potential d i f f e r e n t l y . He assumed that the standard state chemical potential of the solute i n both phases was the same -39-(presumably taking the pure solute as his 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 interactions of solute and polymers. This i s incorrect 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 also makes i t more d i f f i c u l t to separate out the contribution of solute/solute interactions to the chemical potential. Now the interaction of a solute such as a neutral 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 an expression for the solute p a r t i t i o n c o e f f i c i e n t , K.: where A<t>^  = <t>^ - <t>^ , second order terms i n $ were neglected, and i t was assumed that <J>oc<J>^, 4> 2 , Q^. The exponent of [1.14] can be equated with Au.°/kT i n [1.13], giving some insight into what molecular interactions 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 . [1.14] a) The p a r t i t i o n depends exponentially on the solute molecular weight, becoming more one sided as i t increases. This effect has been observed experimentally (Albertsson, 1971) -40-b) The p a r t i t i o n depends exponentially on the difference i n the standard state chemical p o t e n t i a l . c) The standard state chemical potential difference depends on the difference i n concentrations of a l l three phase system components, and on the interaction of the solute with a l l three components. d) As the interaction between the solute and one of the phase components increases, i e . as X ^ becomes more positive,- p a r t i t i o n into 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 difference 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 into 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 of section i i i a above can be extended to charged molecules as w e l l , since the electrochemical potential of a molecule with net charge z m can be written as: pi = |A° + kTln fc + z e [1.15] nm m m and hence -41-l n K = -In TP - 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 po t e n t i a l , i f a l l the other terms are constant. This i s the basis of Johansson's method of measuring potentials- by a l t e r i n g the pH of the system, and therefore z m of a charged protein, 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 state chemical potentials were constant, one can determine the potential of the system. I f the s a l t i s i n excess over the solute, then i t i s the main determinant of the potent i a l . From the electroneutrality condition the p a r t i t i o n c o e f f i c i e n t s of the two s a l t ions w i l l be eaual, to a good approximation, so that [1.11] of section i i b can be used to eliminate Avjj i n [1.16] to give: In K = -In r - A u!/kT - z m (Au .° -Au° + kTln r / r ) • m m rm m r - r+ - + [1.17] (z ++z_).kT which can be written as: l n K m = l n K m - Z m . ( A t i ; - A ^ + kT.ln r . / r + ) (z ++z_).kT [1.18] -42-where has been interpreted by Johansson (1974) and Albertsson as the protein p a r t i t i o n i n the absence of a potential. Note that usually z(1pc»z+,z , so the protein p a r t i t i o n would be expected (through the O 0 standard state chemical potential differences A U , , Ap. i n [1.17]) t o be very + — sensitive to the s a l t type added to the phase system. This has i n fact been well documented (Sasakawa and Walter, 1972; Johansson, 1970a; Albertsson, 1961). I f the (p o s i t i v e l y charged) protein i s i n excess then the other main ionic species i s the protein counterion. I f the counterion i s univalent, we have by analogy with [1.13]: In K_ = -In r_ - A J A V R T + eA+AT [1.19] Eliminating AI|J from [1.19] and [1.13], and noting from the electroneutrality conditions that K M =K , we have: In = l / ( z m + l ) [ l n ( l / r f m r + ) - A ^ / k T - z ^ V k T J [1.20] 0 Again the protein p a r t i t i o n depends greatly on the s a l t type since A H _ i s multiplied by z m which i s often large. Note that as z m increases the protein 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 for the difference i n formalism. Unfortunately neither [1.18] nor [1.20] can be tested, 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 polyelectrolytes are non-ideal solutes even at concentrations less than 1M (Tanford, 1961; -43-Robinson and Stokes, 1959), so r i s not necessarily unity. deLigny and Gelsema (1982) proposed a way around the f i r s t problem by comparing the protein p a r t i t i o n s i n two systems containing di f f e r e n t s a l t s , K M and K M » For the s a l t i n excess, and neglecting a c t i v i t y c o e f f i c i e n t s , they obtained the expression i n K ' / K = z l n K " 2 / K K' [1.21 m m m s s s, where « S , K G 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 K S i s the p a r t i t i o n c o e f f i c i e n t of a s a l t containing a common cation with the f i r s t system, and a common anion with the second system, or vice versa. When they reanalysed the data of Johansson using t h i s eauation, they obtained l i n e a r plots of the log of the r a t i o of the two protein partion co e f f i c i e n t s versus protein charge, as expected, but the equation incorrectly predicted the p a r t i t i o n of the uncharged protein. This may be due to the assumptions inherently made i n deriving [1.21]. These assumptions are examined, and a f u l l equation derived i n Chapter Three of th i s thesis. i v ) Theory of P a r t i c l e P a r t i t i o n i n g a) Relationship of p a r t i t i o n to 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 for the discussion of the theoretical aspects of p a r t i c l e p a r t i t i o n i s the Boltzmann equation. This expression relates the number (n^,n 2) or concentration (c-pO,) of pa 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 of a p a r t i c l e being i n either compartment (see, e.g., -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 'characteristic energy*. (The term compartments i n t h i s case refers both to the two phases and the interface 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 x/n 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 diffuses f r e e l y , i . e . , that i t i s being distributed 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 potential 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 clear 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, especially 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 interface and one of the phases, which i s usually the case for c e l l s . Albertsson and Baird (1962) found that the number of small bacteria 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 interface i s one of the char a c t e r i s t i c s that distinguishes 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 arises from the fact that p a r t i c l e s generally seem to be p a r t i a l l y wetted by both phases, i e . that the p a r t i c l e surface/two phase interface 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 fact that p a r t i t i o n i s a stochastic process, i . e . , a p a r t i c l e has a certain probability of being i n a par t i c u l a r compartment. This i s i l l u s t r a t e d by the fact that i f a homogeneous population of p a r t i c l e s i s partitioned, and the p a r t i c l e s i n one of the compartments are collected and repartitioned, 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 fraction 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 spite of the reservations 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 transfer between the two phases and the interface w i l l be important i n determining p a r t i t i o n behavior. The appropriate relationships for an idealized spherical p a r t i c l e of 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 interface and the p a r t i c l e surface i s used. This approach i s algebraically simpler and also 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 well as indicating the role 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 interface i s characterized by an i n t e r f a c i a l free energy Y * or Y B respectively. Assume that the spherical p a r t i c l e , experiencing no net force, i s at equilibrium at a phase interface (Figure 1.2a). Then Young's equation (Adamson, 1976) relates the i n t e r f a c i a l tension, Y T B , the surface -46-free energies,Y \ Y B , and the contact angle, 9: Y T - Y B = A Y = " Y t b c o s 9 [1.23] I f the p a r t i c l e has equal a f f i n i t y for either phase, i . e . , each phase wets the p a r t i c l e surface equally, then the surface free energy difference, 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 interface at equilibrium. This i s the condition for p a r t i c l e adsorption. I f |AY| > Y U then the contact angle i s either 0 or 180°, depending on the sign 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. At equilibrium i t w i l l be i n either the top or the bottom phase. The work of moving the p a r t i c l e from the interface into the top phase A E ^ i s the sum of two components: i ) the transfer of part of the p a r t i c l e surface of area A b from the bottom phase to the top phase, with a net energy change of A B A Y ; i i ) the increase i n surface area of the interface by A^, with a net energy change of A ^ y ^ . T n u s : AE t. =AYA b + Y t b A t b [1.24] Expressions for A^b and A b are eas i l y obtained by trigonometry from the contact angle. A b i s given by the area of a spherical cap of height h, as: 2 2TTho p= 2TTaJ(l-cos 0 ) [1.25] -47-Fiqure 1.2 Interaction of a Spherical P a r t i c l e With the Interface, a) _ P a r t i c l e at equilibrium, experiencing no net force, forming an equilibrium contact angle 9 with the interface, b) P a r t i c l e experiences a net force f displacing i t to the l e f t , r e s u l t i n g i n a curved interface -48-\b * s 9^-ven b v *-ne a r e a of the c i r c l e of cross section of the sphere as: T T a 2sin9 [1.26] Substituting [1.25] and [1.26] into [1.24] gives A E t i = T r a 2(2(l-cos 6 ) AY + Y t b s i n 2 6 ) [1.27] Substituting for AY using [1.23], and reducing gives: A E t i = ^ a 2 Y t b d - c o s 6 ) 2 " [1.28] The energy of transfer to the bottom phase, A E D T , can be obtained 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 Fig. 1.2a that the role of top and bottom phases i s interchanged i f the complementary angle 9 = 180 - 9 i s used. Noting that cos (180 - 0 ) = - cos 9 , we obtain: E b i = TTa 2 Y t bd+cos 9 ) 2 [1.29] The energy of transfer from the bottom phase to the top phase, AE^ b, i s obtained simply by subtracting [1.29] from [1.28] which gives A E t b = 4 TT a 2 AY [1.30] which i s just AY times the t o t a l p a r t i c l e area. Note that [1.30] does not -49-involve the tension. Equations 1.28 and 1.29 were derived for a planar interface, although i n practice p a r t i c l e s can interact with droplets of many sizes during p a r t i t i o n . In t h i s case the energy of pa 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 substituted into [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 interface and the top phase. In logarithmic form t h i s expression i s I f cos © i s replaced using [1.23] then the expression of Albertsson (1971) i s obtained. I f [1.30] i s substituted into [1.22] instead, we obtain where now K = n /n . I f kT i s replaced by an empirical parameter and a constant added, the expression of Gerson (1980) for 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 to spherical 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 spherical, the same type of arguments w i l l hold, so that these equations are adequate for a discussion of the parameters important i n p a r t i t i o n . [1.31] [1.32] t/J) Theoretical expressions for p a r t i c l e p a r t i t i o n have also been derived by a s l i g h t l y d ifferent approach by Gerson (1980). His st a r t i n g point i s the -50-equality of the chemical potential of a c e l l i n each phase. However, the use of a chemical potential for c e l l s i s problematical, as a c t i v i t y c o e f f i c i e n t s and standard state chemical potentials are defined for solutes, but not for 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 substituting i n some t y p i c a l values. Letting Y T B = 0.006 erg/cm 2, a = 3 [p and 9= 45° i n [1.28] we obtain AE^ = 1.5 x 10" ergs. This i s four orders of magnitude -14 larger 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 into the top phase. However, appreciable p a r t i t i o n i n g of p a r t i c l e s of t h i s s i z e , (e.g., c e l l s ) i n systems with tensions of t h i s magnitude, does occur. This point w i l l be discussed further i n section b) below. The measurement of p a r t i c l e surface free energy differences by means of contact angles (section d below) enables the relationships between the surface properties, phase system properties and the p a r t i t i o n , which were developed above, to be tested. As noted above, the relationship 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 problematical, because to obtain a p a r t i t i o n the phase system must be mixed and allowed to coalesce and separate. The p a r t i c l e s w i l l not diffuse to t h e i r equilibrium p a r t i t i o n however long the systems are l e f t , unlike solutes. Gerson (1980, and Gerson and A k i t , 1980) tested the a p p l i c a b i l i t y of [1.22] to the p a r t i t i o n of c e l l s , using [1.30], and found a linea r -51-relationship between log ( p a r t i t i o n c o e f f i c i e n t ) and cos 9 for a number of different 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 properties. However as a test 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 interface and one of the phases, so [1.30] i s not applicable. 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 to s e t t l e for four hours and then centrifuged. This may have allowed c e l l s to sediment into the lower phase, leading to the conclusion that the c e l l s were par 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 theoretical treatment of section a) does not account for some other important char a c t e r i s t i c s of the p a r t i t i o n of large (>1 jjm dia.) c e l l s . When the phases are f i r s t mixed, the c e l l s are uniformly distributed 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 . ) . The phases then separate by a combination of coalescence and s e t t l i n g . In systems containing erythrocytes, which are easy to observe due to thei r colour, the difference between a system where a l l the c e l l s p a r t i t i o n to the interface, 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 large enough to see (Chapter Six; Van A l s t i n e , 1984), which indicates that c e l l p a r t i t i o n i s determined early on i n phase separation, as suggested by Van A l s t i n e , and Albertsson (1971, p 134). I f the phases separate s u f f i c i e n t l y rapidly compared to the rate of c e l l -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 usually being taken somewhere on the plateau. The p a r t i t i o n also 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 after 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 horizontal 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 potentials, almost a l l c e l l s are attached to the interface, even i f i t i s i n the form of small drops, irrespective of th 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 th e i r thermodynamic equilibrium position, as predicted from [1.31]. However i n spite of t h i s different species' erythrocytes s t i l l have different p a r t i t i o n c o e f f i c i e n t s . Ignoring for the moment these e f f e c t s , [1.31] does make some useful q u a l i t a t i v e predictions 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 to 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 tension, re 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 properties. 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, either 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 interface i f < Y T B , or otherwise to one of 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-interface should increase, t h i s increase being larger for bigger p a r t i c l e s . c) The p a r t i c l e surface free energy difference, Ay , i s probably of great importance i n a theoretical understanding of p a r t i t i o n , since t h i s term contains a l l the contributions of the p a r t i c l e surface properties and t h e i r interaction with the phase system. The a b i l i t y of phase systems to separate different p a r t i c l e s , or to detect alterations i n surface properties, depends en t i r e l y on differences 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 direct 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 differences occurring with i d e n t i c a l p a r t i c l e s of different areas, although t h i s point has not been examined experimentally. The difference i n p a r t i c l e surface free energy depends on the net effect of a l l the factors contributing to p a r t i c l e surface energy, i . e . , on the sum of the interactions between the surface and the components of the phase system. The interactions 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 b a t t r a c t i v e , decreasing Y or Y )» or unfavorable. Some of these are considered i n further d e t a i l i n the appropriate sections below. i ) van der Waals interactions, or dispersion forces - These are nonspecific, almost always a t t r a c t i v e and of very short range. i i ) Hydrogen bonding - Again the interaction 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^ g r o u p s < i i i ) Hydration - This i s an enthalpically favorable int e r a c t i o n , the -54-binding of water to polar surface groups. iv ) Hydrophobic interaction - In a sense t h i s i s the converse of hydration - the entropically unfavorable structuring of water around non-polar groups. v) E l e c t r o s t a t i c interactions - These are long range and can be favorable or unfavorable. They depend on the r e l a t i v e potential of the phase and the charge density of the surface. Since the free energy of a charged surface i s also decreased by increasing 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 repulsion - The interaction of either of the polymers or ions with the surface, which may be mediated by any of the s p e c i f i c interactions l i s t e d here. Binding or adsorption w i l l decrease the surface free energy, repulsion w i l l increase i t . I t must be stressed that the net effect on A-y depends on the difference i n the resultant of these effects i n each of the phases. Also the d i v i s i o n of 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 effects cannot a l l be i s o l a t e d , either i n p r i n c i p l e or experimentally, and the i r effects are not necessarily additive. For example, the removal of charge-bearing s i a l i c acids from erythrocytes has opposite effects on the p a r t i t i o n i n charge sensitive and non-charge sensitive phase systems (Walter et a l . , 1976). Probably the most experimentally accessible contribution to A Y i s the e l e c t r o s t a t i c dependence. The potential difference between the phases can affect 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 for example be increased by increasing the r a t i o of phosphate to chloride 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 fact that removal of negatively charged s i a l i c acid, 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 contributions to Ay are much more d i f f i c u l t to i d e n t i f y and measure independently. The role of hydrophobicity has already been discussed i n section i i . The other most c l e a r l y defined contribution to Ay comes from polymer adsorption. For a two component system, Gibbs derived the following expression for the surface free energy (e.g., Adamson, 1976): -dy = Tsdu.s [1.33] where i s the surface excess of solute, i e . the amount bound per unit area of surface, and du.& i s the change i n solute chemical potential i n the bulk solution. This equation states 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 for 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 different polymers are l i k e l y to adsorb to the p a r t i c l e surface i n different amounts, the contribution of polymer adsorption to the surface free energy w i l l be different i n each phase, res u l t i n g i n a contribution to Ay. This -56-effect 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 quantitative theories available that relate 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 surface (Brooks et a l . , 1980; 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 sensitive systems and found correlations with the l i p i d compositions of the membranes. These were interpreted as differences i n interaction of the phase polymers, p a r t i c u l a r l y PEG, with the membrane surfaces. Support for t h i s idea comes from work on l i p i d bilayer phase tra n s i t i o n s . Both PEG (Tilcock and Fisher, 1979) and simple sugars such as sucrose (Crowe et a l . , 1984) 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 , indicating that interactions between these solutes and l i p i d do occur. d) Contact Angles. Direct measurements of contact angles are useful for two reasons: i ) t h e o r e t i c a l , as the equations i n section a) indicate, 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 properties, such as surface charge density, and on the phase system properties, such as the e l e c t r o s t a t i c potential difference 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 difference between the phases i s of direct i n t e r e s t , for example as a measure of the differences i n -57-c e l l or tissue properties. Gerson (1980, and Gerson and Akit , 1980) developed the ' c e l l lawn' method for measuring contact angles on c e l l s . This can be extended to surfaces as well 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 of the dense phase i n the l i g h t e r phase resting on a layer of c e l l s 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 factors must also be considered i n the a n a l y t i c a l use of contact angle measurements: f i r s t l y , the surface properties are almost certainly altered upon contact with the phases, p a r t i c u l a r l y since both dextran and PEG adsorb to c e l l surfaces (Brooks, 1973, vide i n f r a ) . In addition, when the concentration of polymer i n the solution i s lowered, the desorption of these polymers i s slow. Secondly, the cha 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 structure and thickness. Mclver and Schurch (1982) have shown that the chara 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 bilayer the interface with the phase system was. Inspite of t h i s , two polymer phase systems are uniquely suited to study changes i n the properties of b i o l o g i c a l surfaces since the 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 results can be obtained, with the provisos that (a) the b i o l o g i c a l significance of the changes i n the absence of the phase polymers, and (b) the assignment of the effects 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 Akit (1980). They correlated 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 the i r adherence to hydrophobic test surfaces, interpreting the results as r e f l e c t i n g changes i n hydrophobic and van der Waals interactions. Also Boyce et a l . , (1983) determined the surface free energy differences of rabbit aorta endothelium by means of contact angle measurements i n DxT2000/PEG 20000 systems. Controlled damage to the endothelium to expose the subendothelial layer was used to simulate changes i n atherogenesis. The damaged surface was wetted more strongly by the dextran-rich phase, which was interpreted as a decrease i n the apparent hydrophobicity of the surface, although t h e i r results could also 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 difference 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 several attempts, based on models and empirical r e l a t i o n s , to obtain expressions for either 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 solid/liquid/vapour systems where only dispersion 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 either 0 or 180°. Thus extrapolation of cos 6 (as a l i n e a r function of tension -* 7' 2) 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 for 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. plots have been found for several c e l l types under a variety of to conditions, including lymphocytes (Gerson, 1980), erythrocytes and macrophages (Schurch et a l . , 1981) i n Dx T500/PEG 20000 systems, and erythrocytes i n Dx T500/PEG 6000 systems (Schurch et a l . , 1981). However some results i n t h i s thesis show that large differences i n estimates of the c e l l surface free energy can occur with small changes i n buffer type, indicating the r e l a t i v e nature of such estimates. The second approach involves estimating ory ^ from an empirical equation of state. An expression, applicable 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-Five), results obtained by a l t e r i n g the cell/two phase contact angle at constant i n t e r f a c i a l tension by means of PEG-palmitate imply that t h i s equation of state cannot be applied to two phase systems. Mclver and Schurch (1982), and Boyce (1984) also came to t h i s conclusion. Gerson (1983) has also used an empirically derived expression, s i m i l a r to that of Good and G i r i f a l c o (1957). In interpreting these surface free energies, i t must be remembered that-the results obtained refer to the surface i n the phase system at which the c r i t i c a l tension occurs, or at which the equation of state was applied. The surface energy therefore may be different i n other systems due to al t e r a t i o n s , possibly i r r e v e r s i b l e , on exposure to the phase system resulting for example from polymer adsorption. One approach to minimizing these d i f f i c u l t i e s i s to estimate y^ or y^ in'various phase systems to obtain an empirical dependence on the polymer concentrations and extrapolate the results back to 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 of phase components i s important i s a f f i n i t y p a r t i t i o n . A f f i n i t y ligands are usually molecules that are linked to one of the phase polymers and thus p a r t i t i o n unequally, and which also bind to the p a r t i c l e surface. When the ligand 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 of the polymers, increasing i t s p a r t i t i o n into the phase r i c h i n that polymer. The most common ligand 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 of liposomes i n a manner dependent mainly on the l i p i d head group, and to a lesser extent on the degree of unsaturation of the a l k y l chain t a i l group (Eriksson and Albertsson, 1978, Van Al s t i n e , 1984). The p a r t i t i o n of -61-erythrocytes i n the presence of PEG-palmitate has also been correlated 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 also very sensitive to the chain length and degree of unsaturation of PEG-fatty acid esters (Van A l s t i n e , 1984), erythrocytes from individuals suffering from multiple s c l e r o s i s being distinguishable from controls on the basis of part i t i o n i n g induced by such ligands (Van Alstine and Brooks, 1984). To date the effects of such ligands have only been studied semi-quantitatively. Eriksson (1976) found that PEG palmitate was more effect i v e than the oleate, l i n o l e a t e , linolenate, or deoxycholate forms, while Van Alstine (1984) correlated the effectiveness of PEG-fatty acid esters with the hydrophobicity of the fatty acid t a i l . The more hydrophobic fatty acids were more ef 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 larger change i n Ay. Other a f f i n i t y ligands used for c e l l p a r t i t i o n included DEAE-dextran (Walter et a l . , 1968a) and trimethylamino-PEG (TMA-PEG) (Johansson, 1970a). These are both charged ligands, and so t h e i r effects would be complicated by the effects of the ion composition and potential of the phase system. In order to study c e l l / l i g a n d interactions Reitherman et al_. (1973) measured the p a r t i t i o n of DEAE-dextran i n a charge sensitive phase system, i t s binding to 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 partitioned into the PEG r i c h phase when there was no pot e n t i a l , and into the negatively charged lower phase when there was a detectable potential difference. 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 into the lower phase. Such complications indicate that a quantitative explanation of a f f i n i t y p a r t i t i o n requires complete analysis and measurements of a l l the cell/ligand/system interactions, along the l i n e s suggested i n Chapter Three of t h i s thesis. Flanagan and Barondes (1975) were the f i r s t to treat a f f i n i t y p a r t i t i o n t h e o r e t i c a l l y when they derived an equation for the effect of an a f f i n i t y ligand, v a l i d for molecular p a r t i t i o n i n g at high ligand concentrations, i n connection.with t h e i r use of TMA-PEG as a b i o s p e c i f i c a f f i n i t y ligand for purifying cholinergic 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 for any ligand 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 ligand molecule L, with association constants k*, k*3, i n the upper and lower phases. Then at equilibrium: Top phase: SL i + L- " 5 L ^ + 1 , t Lower phase: SL^ + L " SL^ +^ k b i = 0 . . n - l where -63-kfc = [ S L i + 1 ] t / C S L . ] t [ L ] t [1.34] and k b = [ S L . + 1 ] b / [ S L . ] b [ L ] b [1.35] are the ligand binding association constants. The substrate p a r t i t i o n , K s p i s given by the r a t i o of the t o t a l amounts of S i n each phase: Ks1 = D ^ i ^ = IS] 1 1 p ( K t [ L ] t ) i [1.36] £ CSL.] b [ S ] b E ( - V K b C L ] b ) i where the weighting factor ^ i s due to the number of distinguishable ways of arranging i ligands molecules on n s i t e s . Performing the sums (e.g. Van Holde, 1971) gives K s l = K s ( l + k t [ L ] t ) n / ( l + k b [ L ] b ) n [1.37] where K 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 ligand. Since the binding i s of the Langmuirtype (see [3.54]), [1.37] can also be written as K S L = K s [ ( k V k ^ . C L V ' M n V o ] n c l - 3 8 ] where and n b are the average number of ligands bound per molecule i n the upper and lower phases respectively. Equation 1.38 can also be written ©i i i n terms of standard state free energy changes, where AG = -kTln k , or AG°= -kTln K: -64-AG°, = AG° + n ( A ( ? - AG* + AG, + kTln n V n 3 ) [1.39] At high ligand concentrations, n = n , and [1.38] yields [1.40] which was f i r s t derived by Flanagan and Barondes (1975). Eauation 1.40 indicates that the p a r t i t i o n should be very sensitive to the number of ligands bound. However, tests 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 partly be due to the assumption, made by the above authors, that k*= k b. The implications 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 thesis. -65-D. The Red Blood C e l l i ) Morphology and Erythrogenesis The mature human erythrocyte i n the absence of circu l a t o r y shear forces i s a biconcave disc shaped c e l l , approximately 8.5 jjm i n diameter, maximum thickness 2.4 pm, and minimum thickness, i n the centre, of 1.0 pn. The 2 surface area i s around 145 jjm , with a volume i n plasma or isotonic s a l i n e , of 90 jjm 3, and a density of 1.09 g/ml (Wintrobe, 1974). The erythrocyte thus has about 55% of the volume of a sphere with the same surface, area. Its main function i s to transport oxygen from the lungs to the tissues, and transport carbon dioxide back to the lungs. The structure of the erythrocyte has evolved to optimise t h i s function. 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 solution (ca. 30% by weight of the t o t a l c e l l ) of the oxygen and C0 2 binding protein, haemoglobin. The lack of inte r n a l cytoplasmic structure, and the mechanical properties of the plasma membrane (Evans and Hochmuth, 1978) allow for great c e l l u l a r deformability. This allows the erythrocytes to freely and repeatedly t r a n s i t the microcirculation, where c a p i l l a r i e s can be less than the c e l l diameter. This also results 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 fact that the same volume fraction of r i g i d p a r t i c l e s would "..have the flow properties not unlike those of well matured asphalt (Gratzer, 1981) -66-Erythrocytes arise from hemopoietic stem c e l l s i n the spleen and bone marrow. These stem c e l l s divide to produce erythroblasts, which rapidly synthesis haemoglobin. The nucleus i s extruded to form the reticulocyte, which then enters the c i r c u l a t i o n . A small amount of haemoglobin synthesis continues for about a day. Loss of ribosomes and mitochondria halts haemoglobin synthesis and characterizes 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 for 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 trigger t h e i r removal from c i r c u l a t i o n by erythrophagocytosis i n the reticuloendothelial system. Human red blood c e l l s have several advantages as model c e l l s for p a r t i t i o n studies. They are ea s i l y isolated i n large quantities, washed and p u r i f i e d from other c e l l types by successive centrifugation and re-suspension i n physiological 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 properties. 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 indication 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 , including an apparent decrease i n surface charge, t h i s applies primarily to ra t , not human erythrocytes (Walter et a l . , 1980). -67-i i ) Biochemistry of the Erythrocyte Membrane The most important property of the erythrocyte for p a r t i t i o n i s the composition and structure of the outer plasma membrane, the only part of the c e l l that interacts with the phase system. The plasma membrane consists of a o l i p i d bilayer 50-70 A thick associated with which are two classes of proteins, i n t r i n s i c and e x t r i n s i c (Fig.1.3). Lipids comprise about 44% of the membrane by weight, which can be further 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%, sphingomyelin: 11%, phosphatidylcholine: 17%, phosphatidylethanolamine: 17%, phosphatidylserine: 8% These are not a l l symmetrically distributed i n the two l e a f l e t s of the bil a y e r , the outer layer being enriched i n phosphotidylcholine, a zwitter i o n i c l i p i d , and sphingomyelin, while the inner layer i s enriched i n phosphatidylethanolamine and phosphatidylserine, a negatively charged l i p i d (Van Deenan, 1981). The remaining portion of the membrane consists of 49% protein and 7% carbohydrate, of which 1.2% i s s i a l i c acid. I n t r i n s i c proteins are closely associated with the membrane by hydrophobic interactions, being inserted 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 proteins, such as glycophorin, completely span the b i l a y e r , thus being exposed simultaneously to the cytoplasm and plasma. On the cytoplasmic -68-side of the membrane are the second class of proteins, such as spectrin and ac t i n , known as e x t r i n s i c proteins. These proteins are associated with the membrane primarily by e l e c t r o s t a t i c interactions, and can be extracted under conditions of low ionic strength (Gratzer, 1981). They l i e just beyond the bi l a y e r , attached at certain points to some of 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 barrier to polar molecules, and r e s i s t membrane area changes because of the hydrophobic interactions 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 . Specific l i p i d s may also contribute to certain i n t r i n s i c protein functions. The e x t r i n s i c proteins, and the i n t r i n s i c proteins, to 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 transport, immunological reactions, aggregation and recognition phenomena. The outer surface of the membrane i s thus formed of the outer bilayer 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 gl y c o l i p i d s are glycosphingolipid, globosides and GM^  ganglioside. The main glycoproteins are glycophorins A, B, and C, and the anion transport protein Band 3. An important c h a r a c t e r i s t i c of the outer membrane surface i s that i t has a net negative charge. This i s primarily due to the s i a l i c acid. Enzymatic cleavage and analysis shows that there are about 3.5xl0 7 s i a l i c molecules per c e l l (Cook, 1976), re s u l t i n g i n a net negative charge density of about 1.06xl0 4 esu/cm2. Unfortunately l i t t l e i s known about the r e l a t i v e amounts and type of other charged groups. Less than 5% of the -69-s i a l i c acid i s located on the g l y c o l i p i d s (Kunda et a l . , 1978). Twenty to forty percent of the t o t a l carbohydrate, and forty percent of the s i a l i c 5 acid 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 glycoprotein, contains seven percent of the carbohydrate on 10^ molecules per c e l l . The location of the remaining s i a l i c acid i s not known precisely. The primary structure 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 acid appears to be distributed along the entire e x t r a c e l l u l a r portion. The o v e r a l l picture of the c e l l surface that emerges from the current state of research i s that of a l i p i d bilayer whose outer surface i s composed p r i n c i p a l l y of neutral or z w i t t e r i o n i c head groups. Exterior to t h i s i s a diffuse layer of polyelectrolyte, composed mostly of glycoprotein, with some g l y c o l i p i d head groups. Most of t h i s diffuse layer (ca. 80%) i s carbohydrate distributed throughout which are negatively charged s i a l i c acids. Electrophoretic studies (Donath and Pastushenko, 1978; Levine et a l . , 1983) and cytochemical work (Skutelsky et a l . , 1977) show that t h i s diffuse layer i s between f i f t y and one hundred angstroms thick, that the charge appears to be f a i r l y uniformly distributed throughout the layer, and that ions and water (and probably small molecules) freely penetrate t h i s layer. The volume fra c t i o n of glycoprotein i n t h i s layer 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 Fig. 1.3. 70 Figure 1.3 Schematic Diagram of the Erythrocyte Membrane. Major i n t r i n s i c proteins: Band three (B), glycophorin (G). Major e x t r i n s i c proteins: spectrin (S), a c t i n (Ac), Band 2.1 (ankyrin) (A). L i p i d s : phospholipid bilayer (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 scale, based on current estimates of t h e i r molecular weights, % carbohydrate and amounts per c e l l . -71-Chapter Two. Materials and Methods With accurate experiment and observation to work upon imagination becomes the architect of physical theory- John Tyndall A. General Methods The following materials and methods were used for a l l the work described i n t h i s thesis, unless stated otherwise. Experiments were carried out i n a controlled temperature laboratory at 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, conductivity less than 0.1 pwho/cm was used throughout to make up a l l solutions. A l l buffer solutions and phase systems had a pH of 7.16. In part i c u l a r phosphate buffered s a l i n e , referred to hereafter as PBS, which contained 7.4 mM monosodium phosphate, 2.6 mM disodium phosphate and 130 mM sodium chloride, pH 7.16, was the most commonly used buffer. The term phosphate i s subsequently used to refer to t o t a l phosphate present, unless these two species of phosphate ions are e x p l i c i t l y distinguished. A l l buffers had a t o n i c i t y of 285-300 mOsm, determined by freezing point depression (Osmette II osmometer, Precision 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 to the anomalous freezing c h a r a c t e r i s t i c s of polymer solutions,-and lay between 290 and 305 mOsm. Sodium azide (0.02%) was added to a l l buffers 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 effect on any of -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 solutions, 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 solutions were also 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 referred to as nominal molarities (M). B. Preparation and Characterization of Phase Systems i ) Polymer properties Sentry grade poly(ethylene glycol) 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 anti-oxidants, and f i n a l l y oxidation of the terminal alcohols to carboxylic acid. Dextran T500 was obtained as a spray dried 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) Slight differences 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 differences 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 selected phase system made up with the old and new dextran l o t s before switching to 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 LOTS3 Lot Molecular Weight/1000 Mw/Mn I n t r i n s i c Viscosity Number Mw Mn (g/mole) (ml/g) 7693 485 195.5 2.48 0.54 7830 487 181.5 2.68 0.51 FD16027 461 181.7 2.54 0.50 HD26066 494 181.2 2.73 0.54 aTaken from Pharmacia information l e a f l e t s . Because of the variable water content of dextran and F i c o l l powders, and the d i f f i c u l t y of making up standard solutions of these viscous polymers by volume, the following method was used to make up stock solutions of (ca.) 20% dextran, and 40% F i c o l l . Twenty two grams of dextran, or forty four grams of F i c o l l was mixed to a paste with forty grams of water. Water was added to give a t o t a l weight of one hundred grams. The solutions were then boiled and s t i r r e d u n t i l the polymers completely dissolved. The exact f i n a l concentrations of the dextran and f i c o l l stock solutions were determined by polarimetry (Drs. Steeg and Reuter, Hamburg, FDR, with a 20 cm tube, precision 0.05°) or re f r a c t i v e index (vide i n f r a ) on samples accurately diluted by weight. PEG stock solutions (30 %w/w) could be made up by accurate weighing of the s o l i d PEG, since dissolution of t h i s polymer was -74-rapid and complete, and i t contained less than 0.6% water as determined by exhaustive drying over phosphorus pentoxide at 60° C. The ref r a c t i v e index of standard polymer solutions was measured on a Bausch and Lomb refractometer (precision _+ 0.0005), which was calibrated using sucrose standards (CRC Handbook of Chemistry and Physics, 59th Edn., 1979), and the r e f r a c t i v e index increment of a 1% solution determined (Table 2.2). TABLE 2.2 SELECTED PHYSICAL PROPERTIES OF THE PHASE POLYMERS Polymer Specific Optical Rotation °/(% m) Refractive Index Increment x l O 3 (%-!) P a r t i a l Specific Volume (ml/g) PEG 0.0 F i c o l l 400 5.65a Dextran T500 19.9 a 1.39+0.03 1.53+0.03 1.53+0.04 0.833+0.005 0.650+0.005° 0.611^ aAlbertsson, 1971 bpharmacia F i c o l l Paque Information Booklet cGranath, 1958. The densities of standard polymer solutions 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 additive for concentrations up to at least 10%. The p a r t i a l s p e c i f i c volumes were then calculated (Table 2.2). Refractive index thus provided an alternative method to polarimetry or freeze drying for 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 solution densities calculated 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 (referred to i n t h i s thesis as PEG ester or ester) was obtained from Chem Services Inc., Philadelphia, Pa. The ester was p u r i f i e d and analysed by Jim Van Alstine and Milton Harris, and f u l l d e t a i l s are given by Van Alstine (1984). The ester was p u r i f i e d by ether pr e c i p i t a t i o n from acetone solution, followed by LH-20 exclusion chromatography using methanol/water (5:1 v/v), to remove un-esterified palmitic acid. The purity from free fatty acids was checked by high pressure l i q u i d chromatography (HPLC, see Harris et a l . , 1983) and by TLC, and found to be better than 99.9% on a weight basis. 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 acid ester assay (Van A l s t i n e , 1984); 9.9% of the end groups were e s t e r i f i e d , giving 17.9% mono-ester and 1% di-ester. 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 Harris, using C-palmitic acid (0.22 MBq/mmole, Amersham Radiochemicals), and p u r i f i e d PEG. The ester was synthesized by reaction of the PEG with o x a l y l chloride activated palmitic acid 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 palmitic acid, and hydrophobic a f f i n i t y chromatography on o c t y l sepharose CL-4B to remove unreacted PEG. Purity was checked by TLC, the plate 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 found to be 99.9% on a weight basis, 98.2% ester on a mole basis. -76-i i ) Preparation of Phase Systems Stock solutions of 20% dextran, 30% PEG and 40% F i c o l l , 0.3M sodium phosphate buffer, 0.6M sodium chloride and 0.6M d-sorbitol solutions were made up. These stock solutions were then weighed into a beaker, using a top loading balance to an accuracy of O.Olg, and made up to 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 solutions of other s a l t s or components required i n high concentrations were substituted as appropriate i f other compositions were required. The phase system was then mixed well for 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 (for large volumes) or by careful pipetting using a wide tipped 10 ml glass pipette. The i n t e r f a c i a l region and the lower portion 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 to reach room temperature just before use. Systems were generally used within two weeks, and stocks within two months, to avoid changes due to b i o l o g i c a l or chemical degradation. Whole phase systems could also be frozen at -70° C for several months i f required. For most experiments equal volumes of each phase at room temperature were combined and mixed to allow complete re-equ i l i b r a t i o n . At t h i s stage addition of other components that were only required i n very small amounts, such as PEG ester, was carried out. A stock solution of the component, twenty to one hundred times the f i n a l concentration, was made up i n a buffer 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 series of systems with the same polymer and s a l t compositions but varying amounts of a ligand to be rapidly made up. For brevity and c l a r i t y phase system compositions are subsequently referred to using the following 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 respectively, p, q and r refer to the concentrations of sodium phosphate buffer, sodium chloride and s o r b i t o l respectively, i n millimoles per kilogram of system (approximately equal to molarity, mM, i f the phase densities are close to one), and s i s the concentration of PEG 8000 palmitate ester, i n pmoles/kg of system. I f either z or s i s zero that term i s omitted. Buffer compositions are also referred to using the above convention. Thus PBS i s equivalent to a 10,130,0 buffer. A l l differences i n quantities between the phases are given as top - bottom, where the top phase i s the PEG r i c h phase. Simi 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 additives 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 either of the phases, or the bulk concentration for any other volume r a t i o , unless the additive 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 relationships c = ( r v + D c W r v K + l ) [2.1] -78-c L = (r v+l)Kc/(r vK+l) [2.2] where c \ c 3 , 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 ref 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, for a 20 cm tube length by: where 0 was the o p t i c a l rotation i n degrees. The PEG concentration, c was given by where r i ^ was the r e f r a c t i v e index contribution of the phase buffer, 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 buffer partitioned equally between the phases. This i s a good approximation, and leads to l i t t l e error except for the PEG r i c h phase of systems very far from the c r i t i c a l point, 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 c d = 0/2.98 [2.3] [2.4] -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 to 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 calculated from the differences i n polymer concentrations between the phases, to within 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 rotating drop method (Vonnegut, 1942, Princen et a l . , 1967, Bamberger et a l . , 1984a). The apparatus consisted of a modified minature lathe (model 334 B400, Jensen Tools and Alloys, 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 Optical Co., Buffalo, N.Y.), and a d i a l gauge micrometer. The rate of rotation was controlled by a continuously variable 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 Alto, Ca.). A 7mm dia . 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 to allow the expulsion of a i r bubbles from, and the in j e c t i o n of phase system into the cylinder. The glass tube was bevelled on the inner surfaces at both ends, and was held i n the lathe between two b a l l bearings of a s l i g h t l y larger diameter than the tube. This automatically centred the tube along the horizontal axis of rotation. 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 of the l i g h t e r phase, volume 0.5-10 J J I, was injected into the cylinder with a microsyringe -80-(Hamilton, Reno, Nv.). The tube was immediately mounted on the lathe, and rotated at 500-2500 rpm, depending on the tension and size of the drop. Centrifugal forces cause the drop to migrate to the axis of rotation, and to elongate along the axis. This elongation i s balanced by the surface tension forces which tend to make the drop spherical. The drop size and the rotation rate were adjusted so that the equilibrium drop shape had a length to width r a t i o of two to f i v e , systems with higher tensions requiring larger drops and/or higher rotation speeds. After the drop had come to equilibrium, the length was measured by means of 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 for the lens effect of the glass cylinder by dividing by the r e f r a c t i v e index of the lower phase. The drop volume and tension were calculated from the length, width, rotation rate and density difference between the phases using the tables of Princen et a l . (1967). Precision was generally better than 4%. The advantage of the rotating drop method i s that -5 -1 i t retains i t s accuracy, even for u l t r a low tension systems (10 -10 dynes/cm), and does not involve contact of the interface with a t h i r d phase or surface. Secondary flows due to buoyancy and i n e r t i a l effects can arise (Manning and Scriven, 1977), but can be avoided by using s u f f i c i e n t l y small drops and high rotation rates (Bamberger et a l . , 1984a). v) E l e c t r o s t a t i c Potential Difference The i n t e r f a c i a l potential difference between the phases was measured using reversible 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 acid u n t i l the surfaces had a uniform white 'mosaic' appearance. They were then rinsed with water, connected to the anode of a D.C. voltage supply and immersed i n a plating solution of 0.01 N hydrochloric acid. They were plated at a current of about 2 1 mA/cm for two hours, with constant s t i r r i n g of the plating solution. The electrodes were tapped occasionally 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 microcapillaries with 20-50 pm i . d . t i p s , also f i l l e d with 1 M KC1. The narrow openings of the microcapllaries 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 for one hour. Micr 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 pipette 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 pl a t i n g , or that deplated during use, were re-plated as above, after f i r s t removing the old AgCl with concentrated ammonia. The electrode/salt bridge pairs t y p i c a l l y had a resistance of 1 MS7. Abnormally high resistances indicated that the microcapillaries 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 3A65A, impedence 1 0 1 0 f t ) using soldered connections and grounded coaxial cables, free of ground loops, to reduce noise. The t i p s of the microcapillaries were immersed i n 20 ml of equilibrated, well s e t t l e d phase system, and the whole apparatus except the voltmeter enclosed by a grounded metal cage to sh i e l d i t from stray voltages. One of the electrodes was moved -82-between the phases, and the difference i n voltmeter readings was taken as the e l e c t r o s t a t i c potential difference. Generally at least ten readings were averaged. A bias voltage of more than 5 mV when both electrodes were i n the same phase usually indicated poorly plated or conditioned electrodes, blocked microcapillaries or a non-equilibrated phase system. The precision 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 solution and heated to 60° u n t i l dissolved. The lower half of Pasteur pipettes were then f i l l e d with the agar solution. The agar was allowed to set, and the ends trimmed flush with the pipet t i p to ensure complete drainage of phase system from the t i p s . The electrodes were inserted i n the KC1 f i l l e d upper ends of the pipettes. 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 solute concentration i n each phase after mixing and centrifugation (10 min at 200g). The apparent concentration r a t i o was then multiplied by three correction factors to obtain the true p a r t i t i o n . a) Sampling volume correction. Due to the differences i n v i s c o s i t i e s of -83-the upper and lower phases, the automatic pipettors used to sample the phases delivered different volumes of each phase. The correction factor was obtained by weighing a series of pipetted samples and averaging. For 1ml samples t h i s correction factor was 0.973. b) Polymer volume correction. The polymers occupy di f f e r e n t volumes of solution i n each phase, i e the concentration of water i n each phase i s di f f e r e n t , due to the difference i n polymer concentrations and p a r t i a l s p e c i f i c volumes. This factor was 0.972 for a (5,4) system. c) Assay correction. PEG and dextran can affect the assay used to determine the solute concentrations, often by di 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 correction factor was determined for each assay method as appropriate, using standards made up i n each phase. In some cases the amount of solute was measured before addition to the phase system, and the t o t a l percentage recovered from each phase determined. After applying the appropriate corrections, the difference between these two amounts represented the amount of solute adsorbed at the interface, or adsorbed non-specifically to the tube or a i r water interface. i i ) P a r t i t i o n Coefficients Chloride ion p a r t i t i o n s were measured with a Buchler-Cotlove automatic chloride t i t r a t e r , using 0.1ml samples. No correction for the effects of the -84-phases was necessary. Precision 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 ^S0^~ ( 3 x l 0 5 Ba/ml of phase system, New England Nuclear (NEN), Boston, Mass.): 0.5ml duplicate samples of each phase were taken into 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 s c i n t i l l a t i o n 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 either the top or bottom phase. 14 PEG 8000-palmitate ester p a r t i t i o n s were measured using C r a d i o l a b e l e d ester, f i n a l a c t i v i t y 1.46 Bq/mmole, mixed with unlabelled 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 interface was also measured. Palmitic acid p a r t i t i o n was measured by dissolving a sample of t r i t i a t e d palmitic acid (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 palmitic acid concentration of 10~^ M, well below the c r i t i c a l micelle concentration (cmc) (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 palmitic acid, 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 ester, 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 in t e r n a l standard, which had previously been calibrated using a series of flame sealed quenched standards (Beckman Instruments, Palo Alto, Ca.). -85-i i i ) PEG Ester C r i t i c a l Micelle Concentrations C r i t i c a l micelle concentrations (cmc's) were measured by the method of fluorescence enhancement, whereby the quantum y i e l d of a fluorescent probe i s increased on pa r t i t i o n i n g from the aqueous phase into the hydrophobic i n t e r i o r of a micelle (Tong et a l . , 1965). Solutions of 3 pm 6-propionyl-2-dimethylamino naphthalene (PRODAN) or 7 p i l-anilino-8-naphthalene sulphonic acid (1-8-ANS) (Molecular Probes, Piano, Texas) were made up i n d i s t i l l e d water or either phase of a (5,4)10,130,0 system. PEG ester was added to the probe solution to give an i n i t i a l concentration of 20CjpM. The fluorescence was measured at 385/485nm. The ester solution was then sequentially diluted with the probe solution, the probe concentration thus remaining constant, and the fluorescence intensity measured. The cmc was estimated as the ester concentration at the break i n a , plot of fluorescence intensity against concentration (for a t y p i c a l plot see Fig. 5.1). The method was checked by measuring the cmc of sodium dodecyl sulphate. Both probes gave values i n the range of 0.7 to 1.3 mg/ml, somewhat lower than the l i t e r a t u r e value of 1.4-2.6 mg/ml (Mukerjhee and Mysel, 1971), probably due to the mixed micelle effect of the probe. D. Preparation of Erythrocytes Human blood was obtained by venipuncture of the c u b i t a l vein of the author, or other healthy volunteers. Rabbit blood was obtained from the ear -86-vein. Blood was collected into 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. a) Haematocrit measurements. The c e l l suspension was drawn up ir. fo an uncoated glass c a p i l l a r y , i . d . 0.1 mm, and one end plugged with clay. The tube was spun at 11,000 rpm for 5 min i n a microhaematocrit centrifuge (International 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. Precision was +0.5% (absolute e r r o r ) . Haematocrits could be converted to number of cells/ml using a human erythrocyte volume, i n isotonic media, of 90 j-im"5, or to a weight fraction 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 dia. 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 suspension was diluted to below lxlO* 5 c e l l s / m l , the counts were l i n e a r with c e l l concentration, precision 5%, and agreed with the haematocrit method to within 5%. For the c e l l concentrations usually used for p a r t i t i o n 40 pi of system was diluted into 10 ml of counting buffer. -87-E. Erythrocyte P a r t i t i o n Washed packed erythrocytes were resuspended i n a small volume of upper phase to give a haematocrit of about 50%. Small aliquots 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 c e l l s / m l ) . One or two ml of the upper phase plus c e l l s was added to an equal volume of 2 lower phase i n 1 cm xlO cm glass culture tubes (referred to subsequently as 1+1 or 2+2 ml respectively). The phases were mixed by inverting the tubes twenty times. At t h i s stage additional solutes such as a f f i n i t y ligands were added i f necessary. The tubes were again mixed by inversion, and the phases allowed to s e t t l e for 15 min for the 1 ml volumes, or 30 min for the 2 ml volumes. The top phase was sampled by automatic pipettor from the middle of the phase, taking care not to disturb or aspirate the interface 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 calculated (%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 interface) =%P/(100-%P). P a r t i t i o n s were usually reproducible to within 2-5% (absolute error). In some experiments c e l l s were suspended i n , or sampled from the lower phase. Phase volume ra t i o s were also varied within t h i s general protocol. Isopycnic systems were allowed to separate for one hour, and the inner and outer phases ca 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 of labelled polymer from solution on adding c e l l s (Janzen, 1985). In addition 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 for trapped volume must f i r s t be shown to bind to the c e l l at least an order of magnitude more weakly than the polymer i t s e l f , and are thus not very useful. The following protocol was adapted from Brooks et a l . (1980; see Janzen, 1985 for a more detailed a n a l y s i s ) , to enable trapped and bound material to be distinguished. * 4C labelled PEG 8000 (3X10 1 2 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 la b e l l e d PEG were made up i n buffer or either phase of a (5,A) system as appropriate. Washed erythrocytes were pelleted at 165,000g for 15 min i n a 13 mm xlOO mm polyallomer tube (Beckman Instruments model LS-65 ultracentrifuge, 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 solution by puncturing the bottom of the polyallomer tube and expelling the c e l l s with positive pressure. The c e l l suspensions were mixed gently by inversion for one hour. Each tube was then f i l l e d to wi t h i n 2 mm of the top (to prevent the tube collapsing during ultracentrifugation) with an inert o i l intermediate i n density between the buffer and c e l l s (1:3.5 w/w -89-cottonseed oilrbenzoyl benzoate, density 1.078 g/ml), and centrifuged 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 cleanly separated from the p e l l e t , and also produced a very compact p e l l e t , thus reducing the amount of unbound lab 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 into 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 less 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 follows (adapted from the Beckman |_SC Applications Handbook): T r i p l i c a t e samples of p e l l e t about lOmg were accurately weighed into 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 Protosol tissue 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° for 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 addition of 0.5 ml 0.5 N HC1 to reduce quenching by the basic quaternary amines i n the tissue s o l u b i l i z e r . The f i n a l solution 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 calibrated with flame sealed quenched C standards (Packard Instruments). -90-The rest of the c e l l p e l l e t was accurately weighed into a 15mm xlOOmm polycarbonate tube as before by puncturing the bottom of the centrifuge tube and expelling the p e l l e t with positive pressure. Eight volumes of buffer were added, the c e l l s resuspended by inversion for f i f t e e n minutes and pelleted at 500g for 5 min. Ninety percent of the buffer was removed, counted and replaced with fresh buffer. This washing and analysis 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 la b e l coul'j be distinguished from bound l a b e l , as follows, since i t was rapidly diluted 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 after each wash was calculated 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 subtracting the t o t a l amount of la b e l released into the wash buffers. The decrease i n c e l l p e l l e t a c t i v i t y after each wash could be well f i t t e d by the sum of two decaying exponentials. The extrapolation 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 difference between the two values was assumed to be trapped material, which could then be corrected f o r , to obtain the amount bound. The apparent trapped material varied 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 sizable correction. 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 written i n Fortran, using the damped Newton-Raphason method (Fletcher, 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 solution. One ml volumes of 14 C labelled ester solutions of the required concentrations were made up i n buffer or either 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 buffer or phase, and the haematocrit accurately determined. The c e l l suspension was accurately weighed into the ester solutions to give the required f i n a l c e l l concentration. The c e l l suspension was mixed gently by inversion for 30 min and the c e l l s pelleted at 10,000 rpm for 1 min (1.2 ml volume polypropylene micro tubes i n an Eppendorf 3200 micro centrifuge). 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 solution a c t i v i t y , after correcting for 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 for experiments where the effects of c e l l concentration were being studied, the f i n a l haematocrit was adjusted to between 2.5 and h%, since t h i s resulted i n approximately equal amounts of ester being bound and free, thus minimizing the effects 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 analysis. The second method diffe 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 centrifugation was analysed d i r e c t l y , after 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 for trapped and remaining buffer by using the difference 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 (in phase binding). This method, although more d i f f i c u l t and less accurate, was developed so that the ester binding could be measured from both phases simultaneously, under the conditions used for 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 for c e l l p a r t i t i o n (section E above), using duplicate sets of tubes. The phases were mixed by inversion and allowed to s e t t l e for 30 min. For one set of duplicates, 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 pelleted at 11,000 rpm for 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 less 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 buffer, divided into 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 calculated. The other set of duplicate tubes was centrifuged l i g h t l y (200 g for 5 min) to p e l l e t a l l the c e l l s into 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 for f i f t e e n minutes, to allow the binding to re-equilibrate, 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 transferred to Eppendorf microtubes and the binding determined as for 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 for p a r t i t i o n (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 aspirating a l o t of the c e l l s when removing the supernatant before digestion. i i i ) Desorption of PEG and PEG-palmitate Desorption of the ester from the c e l l surface was analysed by means of sequential washes. After the binding was measured, between 80 and 90% of the buffer was removed and i t s a c t i v i t y determined. The same weight of fresh buffer or phase was added, the c e l l s resuspended by gentle mixing for ten minutes, and the c e l l s re-pelleted by centrifugation (10,000 rpm for 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 buffer, pH 8). In these experiments controls were washed with buffer of the same io n i c strength made isotonic with s o r b i t o l . -94-G. Contact Angle Measurements  i ) Apparatus Contact angles formed between the two phase interface and the c e l l surface were measured using the micro-pipette aspiration and micromanipulation apparatus of Evans (1980). A diagram of the measurement chamber i s given i n Fig. 2.1. An inverted microscope (Leitz 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 for vibration 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 directed to a high resolution black and white monitor (RCA, Lancaster, Pa). The time was also 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 also recorded on a video cassette recorder (Sony VO-5600 VCR) for o f f - l i n e analysis. A stainless s t e e l frame mounted on the specimen stage held two pairs of glass cover s l i p s 2mm apart (Fig. 2.1a). The cover s l i p s were held to the frame and sealed by vacuum grease. The spaces between the coverslips 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 action. Two f l u i d f i l l e d chambers were thus formed, open at both sides, and separated by a 3mm a i r gap, into which micropipettes could be inserted. Two custom made a i r piston driven micromanipulators could be used to position and control two micropipettes to a resolution of less than one micron. The pressure within the pipettes could be controlled by mouth suction or by a micrometer driven hydrostatic pressure head. Figure 2.1 Measurement of Contact Angles, a) Apparatus, b) Analysis of image. Symbols defined i n the text. -96-i i ) Preparation of Pipettes Pipettes were drawn on a v e r t i c a l pipette p u l l e r from 0.4 mm i . d . sodium glass tubing. The pipette opening was trimmed to the required inside diameter using an e l e c t r i c a l l y heated loop of nichrome wire mounted on a three dimensional micromanipulator, viewed with a stereomicroscope. Each experiment required one small pipette, 1-1.5 ym i . d . for c e l l aspiration, and one large pipette, 20-50 pm i . d . for c e l l transfer. The small pipette was f i l l e d with 150 mOsm buffer (10 mM phosphate buffer, 60 mM NaCl) by bo i l i n g i t i n the buffer under reduced pressure for 30 min. The larger pipette was p a r t i a l l y f i l l e d , to within ca. 20 jjm of the t i p , with an in e r t o i l by c a p i l l a r y action, so as to eliminate any f l u i d flow within i t during the experiments. i i i ) Experimental Procedure A l l experiments were done with phase systems and buffers of 150m0sm, approximately half i s o t o n i c , to swell the erythrocytes. This did not affect the p a r t i t i o n c o e f f i c i e n t of the c e l l s . Thus when a c e l l was aspirated into the small pipette, as large an area as possible of the c e l l was l e f t exposed for contact with the phase system drops, making the contact angle measurements easier. About I JJ I of blood from a fingerprick was diluted i n 5ml of buffer. This buffer, (but not the phase systems) contained 0.1 % human serum albumin, to prevent adherence of the c e l l s to the small pipette. The extremely low concentration of c e l l s (about 10^ cells/ml or 10~ 5% -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 into the small pipette u n t i l a r i g i d spherical surface was produced (Fig. 2.2). The t i p of the pipette was inserted about forty microns into the buffer f i l l e d mouth of the large pipette. The c e l l was then transferred to the chamber containing the phase system by translating the stage holding the chambers, r e l a t i v e to the pipettes. The small pipette holding the c e l l was then withdrawn from the mouth of the large pipette. The c e l l was manoeuvered into contact with a droplet of the lower phase so that i t wetted the c e l l surface and formed a contact angle (Fig 2.2). The c e l l and drop were oriented so that the i r outlines were simultaneously i n focus, thus ensuring that t h e i r centres lay i n the same o p t i c a l plane, perpendicular to the o p t i c a l axis. An additional check on the alignment was to ensure that the contact c i r c l e (Figs. 2.1b and 2.2) appeared as a straight 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 axis. The image was then videotaped for subsequent analysis. In some experiments the c e l l s were incubated i n buffer then the lower phase before making the measurements. iv) 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 electronic video c a l i p e r (Model 305, Vis t a Electronic, La Mesa, Ca.). The video ca l i p e r s were calibrated i n the x and y directions from microscope images of a stage mounted micrometer. Measurements of several diameters of both c e l l s and drops confirmed that they were indeed - 9 8 -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 into a pipette at l e f t , and i s wetted by a drop of 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 of the contact c i r c l e , which appears as a straight l i n e i n t h i s orientation. -99-spherical, as expected. The contact angle could thus be obtained trigonometrically from the two diameters, 2a p and 2a d, and the diameter of the c i r c l e of three phase contact, 2a c, (Fig. 2.1b) using: 0 = s i n _ 1 ( a c / a p ) + s i n _ 1 ( a c / a d ) [2.5] In p r i n c i p l e any diameters of the c e l l and drop images could be used. However with regard to o p t i c a l errors there are two p a r t i c u l a r l y useful diameters- those p a r a l l e l to the contact c i r c l e , for 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 . Calculation of the angle was found to be more objective and precise than di r e c t angle measurements with a protractor. As a check on the measurements the height of 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: ld = ( a d - a c ) 1 / 2 + a d ^ Only when the calculated and measured values of t h i s length agreed to within 5% were the results used. The average angle was taken from measurements on at least f i v e c e l l s , using three different drops per c e l l . Angles greater than 20° could be measured to within 2-3°. H. Treatment of Results and Determination of Experimental Uncertainties Measurement uncertainties were determined from the precision of the -100-relevant instruments. A l l measurements within experiments were carried out at least i n duplicate. Most experiments were repeated at least once. Standard deviations i n f i n a l quantities were determined either from variations between experiments i f possible, from variations between replicates within an experiment, or from regression analysis as appropriate. Where linea r regression was used, estimates of the standard deviation i n the slope, a g , and intercept, o\, were calculated from the following formulae (Mendenhall and Schaeffer, 1973): cr 2 = SSE/(n-l)V v [2.7] [2.8] where SSE i s the sum of the squared errors, n i s the number of data, and V x i s the variance of the independent variables, x^. Error bars on figures and error l i m i t s i n tables are t y p i c a l for that data set unless otherwise indicated. -101-Chapter Three. Theoretical Results Empiricism may serve to accumulate facts, but i t w i l l never build science. The experimenter who does not know what he i s looking for w i l l not understand what he finds- Claude Bernard A. Potential Difference i n Single Salt Systems The difference i n inner or Galvani potentials between two phases i s not di r e c t l y measurable, as was discussed i n Chapter One. General thermodynamic considerations (Adamson, 1976, Ch. 8) suggest that the potential difference that i s measured, A tym, i s the potential difference between the phases, ^ tb' D'''US a ^ e r m a r * s * n q ^ r o m *-ne chemical work performed on moving the test charge(s) between the phases A|i^. Thus: In the experimental set up described i n t h i s work the test ions could be K , CI (and Na +, S0~, HPO^ or H2P0~, depending on the buffer). The phase system at equilibrium can provide no work, so the measured potential must arise from the difference i n (phase) junction potentials, ^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 calculated by integrating the equation for the dif f u s i o n potential across the junction zones (Kortlim, 1965, pp 291-2): [3.1] [3.2] -102-where a^, n^, are the a c t i v i t y , transport number and valence of the i t h ion. Determining n and a, which vary with position, would be extremely d i f f i c u l t . However changes i n the potential difference 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 equilibrium the chemical potential of every species i s the same i n both phases. Thus for the K + ion (subscript k) i n a system containing for example only KC1 (subcript c) we have: H 0 t + kTln c f c ^ + e vli* = H o b + kTln c b f 5 + ei|J b \ c K,c k,c c V V Kc Y c [3.3] Where the superscripts t and b refer 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 . Rearranging: - Ap° = kTln K k c + kTln r k c + e Aty Q [3.4] Where K=c t/c b i s the p a r t i t i o n c o e f f i c i e n t , T=f^/f^ i s the 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 , Ai|>= i|#t- i p b , and Ap= \£- u.b. S i m i l a r l y for the K + ion i n a system containing only IC^ SO^  (subscript s ) : -Au,0 = kTln K. + kTln r. + eAdj [3.5] KS K i b K » b b Each phase i s e l e c t r i c a l l y neutral, hence for single 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 respective counterion, K or K respectively. Hence K. C j C S j S KyC = K = K , and K. = K = K . Subtracting [3.4] and [3.5] C j C C K jS S j S S -103-(eg. Davis and Rideal, 1961) gives: AI}J S - AV)Jc = k j i n (K c/K s) + kTln ( r c / r s ) [3.6] e e + (Au° k > c - A ^ ) S ) / e Now the l a s t term on the ri g h t hand side i s not measurable. However for two systems having very s i m i l a r upper and lower phase compositions, and hence very similar t i e l i n e lengths i t can be assumed that: K,s - K,c [ 3 - 7 1 leaving only measurable quantities. B. Potential Difference i n Mixed Salt Systems The approach and notation used for single s a l t systems can be generalized to 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 zK ++S 2~, (subscript m), where z i s the net charge of the second anion. An expression i s required r e l a t i n g the potential i n the mixed system to those i n the two single s a l t systems, as a function of i t s s a l t composition. For the two systems containing only KC1 and K 2S, [3.4] and [3.5] apply. For the mixed system we have: " A V k T l n + k T l n r M + [ 3 - 8 ] -104-•Aii° = kTln K + kTln r m - eAiJJ [3.9] cm c,m c,m Tm Ai? = kTln K + kTln r m - zeAiiJ [3.10] sjn s,m s,m Tm and for the anions i n the single s a l t systems, the complementary equations to [3.4] and [3.5] are .A£ = kTln K + kTln r - zeAib [3.11] S S i>, i> o, s b • Au° = kTln K „ + kTln r n - eAtb [3.12] rc.c c,c c,c Y c Electroneutrality gives: Kk,m = c^ m= zCs,m + cc,m = zKs,mcs,m + Kc,mcc,m [3.13] n Vf Vr V» V ck W ) z cs,m + cc,m 2 Cs,m + cc,m The bulk concentration of an ion i can be written: ci,m = ci,m ( Ki,m rv + ^ / ( r v + 1 } ^3.14] where r sv^/v*3 i s the r a t i o of upper to lower phase volumes, and a parameter r s , the r a t i o of bulk concentrations of the two s a l t s i n an equal volume system can be defined as: = c s,m = c c,m s.m (Kc • mrv .m^Cjm^^v 1) [3.15] For r = 1, the appropriate value of r can be obtained using -105-[3.14-5]. Equation 3.13 can then be written: Kk,m = z K s , n A s + Kc.m [3.16] *s m + 1 K n m + l • zrr£ 1 Ks,m+1 Kc,m+1 Again i t i s assumed that the phase compositions of the three systems are very s i m i l a r . Hence Vk,c = Vk,s = A&,m [3.17] ^ s , s = Vs.m A £ , 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 eliminating Au. from [3.10] 4 using [3.12] and A u ^ f r o m [3.9] using [3.11] gives s,m kTln K s - zeA^ = kTln K g m - ze A ^ m [3.20] kTln K - eAlk = kTln k B - e A i | ) [3.21] c t c,m m o Au. can be eliminated from [3.08] using [3.05] (or [3.04]), to give: kTln K s + eA^s = kTln + eA+m [3.22] At t h i s point i t i s convenient to introduce a dimensionless function of the potential, AV)J. with respect to some reference p o t e n t i a l , Avp Q. Let v i = exp(e(A^ -b%)/kl) [3.23] -106-Choosing A4<0 as A ^ gives Vc= 1. This function serves two purposes. I t enables [3.20-22] to be expressed i n product form, f a c i l i t a t i n g algebraic manipulation. Also a l l potentials appear as differences, which are the only quantities that can be measured (Section A above). Using [3.6] equations [3.20-22] become Ks,m / Ks = <VV C3'2A]  Kc,m / Kc = Vm C 3 ' 2 5 ]  Kk,mVm = K s V s = K c C 3 - 2 6 ] These equations are es s e n t i a l l y the same as those derived by Kortum (1965, pp 407-10) which also relate the p a r t i t i o n c o e f f i c i e n t s and potential differences i n mixed s a l t systems. Equation [3.16] can also be written as; z rs ( Kk,m - Ksfm> + (Kk,m ~ Kc,m ) = ° 3 ' 2 7 ] Kc m + 1 m + 1 s,m c,m Eliminating 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 gA + B = 0 [3.28] where -107-A = ( l - ( V m / V s ) Z + 1 ) / ( l + ( V m / V s ) Z ' K c / V s ) [3.29] B = ( l - V ^ ) / ( l + K c V m ) [3.30] where [3.28] i s a polynomial i n V , the reauired Quantity. Now O^r^OO, which may be inconvenient to deal with, so r g may be rewritten 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 varies between one and zero: f = c /(c m + c m ) = r / ( r + 1) [3.31] s s,m s,m c,m s s In the l i m i t s of f = 0 and 1 (r = 0, 00 ), [3.28] gives the single s a l t potentials Ai|>m = and A ^ s respectively: I f f g= 0 then then [3.28] gives B = 0. Using [3.30] t h i s implies that Vm= 1, or that AS|J= A<K I f f = 1, [3.30] gives A= 0, and [3.29] implies that V m = V s or that Alp = Alp. m c Equation [3.28] can be generalized to systems containing a single cation, and n anions, each with valence z^, and present at a mole r a t i o of r ^ : J V i ^ V V ' 1 ^ = o [ 3- 3 2 ] 1 = 1 ( l + ^ / V . ^ O ^ / V . ) 2 ! ) 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] either the p a r t i t i o n c o e f f i c i e n t or the potential i s required from each single s a l t system. -108-Similar expressions to [3.32] can be obtained for systems with a common anion. The effects of non-ideality can be incorporated by replacing 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 of a c t i v i t i e s . Some charac t e r i s t i c s of [3.28] are i l l u s t r a t e d i n Fig. 3.1, for various values of K g/K c and z. A l l the curves of potential pass through Ai|>s and at f = 1,0 respectively, for 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 of 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 potentials are additive, for pa r t i c u l a r values of 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 unlike the anions are, i n either p a r t i t i o n or valence, the more curved the plots become. C. Polyelectrolyte P a r t i t i o n A further generalization of the treatment of e l e c t r o s t a t i c effects i n phase systems can be made for the case where a multivalent ion, or a polyelectrolyte such as a protein, i s present with a s a l t . Previous treatments of the effect of s a l t on protein p a r t i t i o n were summarized i n the introduction, Chapter One, section C . i i i . The l i m i t a t i o n s of these treatments were discussed, and the approach of deLigny and Gelsema (1982) mentioned. A general expression i s now derived, using the formalism of - 1 0 9 -Figure 3.1 Potential and Salt Composition. Theoretical Curves of potential as a function of the mole f r a c t i o n of one of the s a l t s i n a mixed s a l t system, calculated from Eqn.3.32- Ks/Kc=o.75, z=3 (A), K s/K c=l, z=3 (B), Ks/Kc=2, z=l (C), K s/K c=l, z=l and Ks/Kc=1.12, z=0.5 (D), K s/K c=l, z=0.5 (E), Ks/Kc=0.3, z=l (F). A^s=2mV, =0 for a l l curves. -110-section A, and related to t h e i r expression. I t i s convenient to st a r t with [1.16], v a l i d for any concentration r a t i o of s a l t to (anionic) protein: In K M = -AfjJ/kT - In r m + z ^ / k l [3.33] An i d e n t i c a l equation can be written down (using primed symbols) for a system containing the protein and another uni-univalent s a l t with with the same cation and pH: In Km = -Au*/kT - In r \ z meAi|j/kT [3.34] subtracting [3.33] and [3.34], and assuming that z m = z m gives: In HL/K = (Au* - AU-'VkT - In r ' / r [3.35] T n m r m m m m + zme(Aij/-A4!>/kT An expression for the difference i n potentials between two systems with a common cation (subscript +) has already been derived i n section A ([3.6]), and can be substituted i n to y i e l d : i n ( K M / K M ) = (Au; - Au m)/kT - i n ( r > m > [3.36] + v l n ( K + / K ; } + v l n (r+/r;} + zm(AH° - A!4+')/kT Now i f the two systems have i d e n t i c a l phase compositions, i e . the two sa l t s have a negligible effect on the phase separation, or the same ef f e c t , - I l l -then the difference i n standard state chemical potentials of both the protein and the cation w i l l be the same i n both phases. With these assumptions, [ 3 . 3 6 ] becomes: In ( K ' / K ) = - In ( r ' / r j + z m . l n ( K , ' ) [ 3 . 3 7 ] m m m m m +/K + + z . l n (r ') m +/r + A simi l a r expression can be obtained for systems with a common anion. I f the s a l t s i n the two systems do not have a common ion, then the difference i n potentials i n [ 3 . 3 5 ] can be expressed as Ai|/ - Aip = ( Ail / - A<JJ") - ( A i p - Ai|>") [ 3 . 3 8 ] it where AIJJ i s the potential difference i n a system containing a common cation with the f i r s t (unprimed) system, and a common anion (subscript -) with the second (primed) system, or vice versa. Two substitutions of the form of [ 3 . 6 ] can be made, and with the same assumption that the difference i n standard state chemical potential for any species common to two systems i s equal, we obtain: In ( K M / K ) = - In (r / r ) + z . l n ( K K / K K ) [ 3 . 3 9 ] m m m m m + - + -+ z .In (r* r' / r r') m + - + -I f the s a l t i s i n excess, then K + = K =K for 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 . 3 9 ] becomes -112-l n (K ' / K ) = z ..In ( K " 2 / K . K ) [3.40] m m m 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 unlikely to be v a l i d simultaneously. This, combined with the neglect of a c t i v i t y c o e f f i c i e n t s may be s u f f i c i e n t to account for t h e i r incorrect prediction of protein p a r t i t i o n c o e f f i c i e n t s at the i s o e l e c t r i c point. The treatment of section B also applies to a polyelectrolyte, where the charge z on the ion S i s large. Equations [3.24-26] correspond to [3.36] i n the l i m i t i n g case where one of the systems contains only the protein and i t s counterion. This can be seen by eliminating V m/V g from [3.24] using [3.26]. Equation [3.24] then becomes K = K ( K / K . ) Z C 3 ' 4 1 ] s,m s s k,m which i s i d e n t i c a l to [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 s s' w n e r e ^ n e primed system i s equivalent to the s a l t plus protein system (subscript m) and the unprimed system contains only the protein (subscript s) -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 effect of an a f f i n i t y ligand on the surface free energy difference, Ay , may be obtained by integrating the Gibbs equation^": [3.42] where r \ i s the surface excess of the i t h conponent, and 6\l^ i s the change i n chemical potential of the i t h component. I t may be noted that the change i n the chemical potential of any component at a surface w i l l equal the change i n chemical potential of that component i n the solution, since at equilibrium the chemical potential 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 written as: dAy = £ T b d n b - £ d | i * [3.43] where the superscripts t and b refer to the upper and lower phases respectively. To find the t o t a l change i n Ay on adding a ligand to the phase system, [3.43] must be integrated from zero to the required ligand concentration. 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 for suggesting t h i s approach. -114-surface concentration of any fixed surface components. Secondly, that the only component that makes a s i g n i f i c a n t contribution to the i n t e g r a l of [3.43] i s the ligand. This w i l l be a good approximation for low concentrations of ligand, since the change i n the chemical potentials of the other components i n solution w i l l be small. Also at low surface coverage by the ligand, the surface excesses of the other components w i l l not change much with ligand concentration. Thus under these conditions the contributions of the other T^.d u.^  terms to the i n t e g r a l w i l l be small compared to that of the ligand. With these approximations, [3.43] may be wri tten as: dAv = T b d u b - ^ d ^ [3.44] 1 1 I I where the subscript 1 refers to the ligand. The chemical potential of the ligand i n the upper phase i s ^ = u 0 1 1 + 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 \il = kT dcVc* [3.46] The surface excess of the ligand i n the upper phase i s the amount of ligand bound per unit area. This i s some function of the solution chemical potential of the ligand 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 ligand binding s i t e s per unit area. The term ide a l refers to the fact that the binding s i t e s are independent (no cooperative effects) 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 state for the bound ligand obeys a two dimensional form of the gas law TT = n V r [3.47] where n 1 i s the number of ligands bound per unit 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 written n f c = n c V l k 1 + c-) [3.48] where i s the dissociation constant for the binding. The integral of the second term i n [3.44] i s nkT.dgt <t + ct) [3.49] Performing the integration gives y f _ yt = n k T l n ( k t + ct> Ic* [3.501 I 0 0 Evaluating the l i m i t s , - 116 -- Y f c = nkT.ln (k* + c 1 ) / [3.51] Integrating the corresponding equation for the lower phase gives Y b - Y b = nkT.ln ( k b + c b ) / k b [3.52] t o Subtracting [3.51] from [3.52] gives A Y i - A Y 0 = n k T l n f k j? + fo-k* [3.53] (kt + cl).kP From the form of the Langmuir isotherm, (k b + c b) = n.c b/n b [3.54] Substituting t h i s and the corresponding expression for the upper phase into [3 .53] , and noting that c V c b = K-^ , the ligand p a r t i t i o n c o e f f i c i e n t , we obtain: AY 2 - AY 0 = nkT In n L k t [3.55] rPj<P. Ki Since AG° = -kT.ln K±, and A G 0 1 = kT.ln k 1, [3.55] can be written AYX - A Y 0 = n( A G o t - A G o b + AG° + kT . ln nVn b ) [3.56] which i s i d e n t i c a l to the free energy of transfer of a solute of unit area between the phases, [1 .39] , Chapter One. -117-Several l i m i t i n g cases of [3.56] are of in t e r e s t , and there are pa r a l l e l s with the case of interacting solutes i n phase systems, discussed by Albertsson (1983). °t «b t b a) A covalently bound ligand. Let AG , AG-*oo , thus n = n.= n giving AV X - A Y Q = n AG° [3.57] b) A ligand that i s completely hidden from the phase system on binding. From Fig. 3.2, using the fact that the free energy i s a state function, A G ^ - A G ^ - A G ^ =AG* b , the free energy of tranferring the bound o ligand between the phases, while bound. I f the ligand i s hidden AG^= 0 *b <t o and thus AG - AG = AG^. Also from the form of the Langmuir isotherm, [3.48], n^ = n b must hold, since c V c 3 = = k^/k^. This yields A Y 1 - AY 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 ligand. AG l b = AG^ and thus AG = AG , giving AY 2 . AYQ s n ( A G^ + kT.ln n t / n b ) [ 3 . 5 9 ] -118-Top Bottom phase phase 1 ^ 1 B A G T I A G 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 : Effect of complex surface on the effect of a ligand on the p a r t i c l e surface free energy difference. A l l symbols are defined i n the text. 119-In practice the ligand could never be completely exposed to the phase system, since at least some small portion must be involved i n the binding inte r a c t i o n , such as the palmitate t a i l of the PEG-ester. Eauation [3.59] gives the dependence of the surface free energy difference on ligand concentration i m p l i c i t l y . Using the equations for the Langmuir isotherms ([3.48]) to eliminate n*" and n b, and expressing everything i n terms of c b gives AYX - A Y 0 = n( A G o t - A G 0 D + AGi + kT.ln (k b + c^) [3.60] ( r k + c D) where r ^ k v K } . Some chara c t e r i s t i c s of [3.60] are i l l u s t r a t e d i n Fig. 3.3 for various values of n, k\ k b, and K^. A l l the curves have the same general form: the surface free energy difference increases i n a sigmoidal fashion with ligand concentration, and f i n a l l y the curve reaches a plateau at a value determined by ( k V k bK^) n when the binding i n both phases saturates. This i s s i m i l a r to a cooperative binding curve (Mustacic and Weber, 1978). Considering Fig. 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 1 i s increased, the curves 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 of k^/kbK^, the curves r i s e more steeply as the dissociation constants are decreased (D,F). Referring to Fi g . 3.3b, decreasing n decreases the effect of the ligand, but does not a l t e r the concentration dependence (A,C,E). The effect of changing also decreases with n (A,B and E,F). -120-u \ CO C D CH LU •>—' 00 9 8 7 6 5 4 3 2 1 0 - 1 a _ A • ...-L. 1 _l l i i i n - 1 L_ l l i i n — 1 1 1 1 I.I.XJ-I i i i i 1 1 I I 0.1 10 100 1000 1 10 100 LIGAND CONCENTRATION ( PM) 1000 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) Effect of ligand 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 b = i , Kj=l (A), kVk b= if Ki=1.02 (B), kVk b=1.5, K 1 =1.53 (C), k t , k b= 3, K 1 =1.03 (D), k*= 3, kb=2, K 1 =1.545 (E), kt= 1, k b= 0.33, K 1 =3.09 (F). n = 7 x l O 1 2 molecules/cm 2 for a l l curves, b) Effect of number of binding s i t e s and phase volume r a t i o . kfyk b=3 for a l l curves, n = 7 x i o l l molecules/cm 2, (A,B), n = 3.5 x l O 1 2 , (C,D), n = 7 xlO* 2 (E,F). K]=3.06 (A,C,E), Kl=3.09 (B,D,F). -121-Chapter Four. E l e c t r o s t a t i c Effects 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 - Alfred North Whitehead A. Introduction The importance of e l e c t r o s t a t i c effects 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 of p a r t i t i o n (Albertsson, 1971; Walter, 1977; Fisher, 1981). In addition 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 attributed to differences i n c e l l surface charge density (eg. Walter et a l . , 1980). The effects of charge on the p a r t i t i o n have been assumed to resu l t from the potential difference between the phases. Another reason for studying such e l e c t r o s t a t i c effects i s that they are experimentally accessible 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 possible to manipulate the potential independently of other phase system properties. Prompted by the theoretical treatment of Chapter Three, another question considered i s under what conditions can such potentials be measured, and do such measurements agree with the theory? This forms the necessary background for a study of the effect of potential on the c e l l surface free energy difference, and c e l l p a r t i t i o n . The effect on the former i s of par t i c u l a r interest since t h i s quantity can be measured at thermodynamic equilibrium v i a contact angle measurements. -122-B. Effects of Buffer Composition on Phase System Properties i ) Effect of Phosphate on the Binodial In phase systems that do not contain charged polymers, the potential i s controlled by the buffer composition, often by a l t e r i n g the r a t i o of phosphate to chloride. The buffers used i n t h i s study contained s o r b i t o l , sodium chloride and sodium phosphate buffer, pH 7.16. The binodial 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 sensitive systems), and a chloride r i c h buffer 10,130,0 (charge insensitive) were determined by polarimetry and refractometry. The lower sections of the two binodials are shown i n Fig. 4.1. Except at high polymer concentrations the three points representing the compositions of each phase and the bulk composition of each system are colinear within the error of the measurements, ind 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 error i n these determinations. Increasing the phosphate/chloride 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 binodial towards lower concentrations. Thus systems just below the binodial that w i l l not phase separate with sodium chloride r i c h buffer w i l l form two phases with 110 mM phosphate. The effect of phosphate on the composition decreases i n systems further from the p l a i t point, since the two binodials converge at higher concentrations. Altering the sodium chl 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 fect on the phase composition (data not shown). -123-0L 1 ' J ' 1 0 2 4 6 8 10 % DEXTRAN Figure 4.1 Effect of Salts on the Phase Diagram. Lower parts of the binodials are drawn together to show the effect of increasing the phosphate concentration from 10mM ( s o l i d l i n e ) to llOmMM (dotted l i n e ) while decreasing the chloride concentration from 130 to 0 mM. -124-i i ) Effect of Buffer on I n t e r f a c i a l Tension The effects 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 chloride to phosphate, the phosphate concentration and polymer concentration are summarized i n Table 4.1. The tensions were measured by the rotating 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 chloride and s o r b i t o l have l i t t l e effect on the tension, the largest change being about 10% when 130 mM sodium chloride 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 for the contact angle measurements, has l i t t l e effect on the tension. Increasing the phosphate concentration from 10 to 110 mM at constant polymer concentration has a large effect on the tension, increasing i t by 30 to 50%, the effect being greater for systems closer 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 for the buffer compositions 110,0,0 and 10,0,100. -125-TABLE 4.1 EFFECT OF PHASE COMPOSITION ON INTERFACIAL TENSION System Tie Line Length TensionxHp (%) erg/cm2 (5,4)10,130,0 11.85+0.2 5.73+0.2 (5,4)5,60,0 12.3 6.37 (5,4)10,16,68 12.0 6.45 (5,4)10,0,100 12.2 6.31 (6,4)10,0,100 14.0 10.3 (7,4.4)10,0,100 16.8 21.3 (5,4)110,0,0 12.7 9.11 (6,4)110,0,0 14.3 13.9 (7,4.4)110,0,0 17.0+0.4 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 Ytb= a + b.ln 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 buffers 10,0,100 and 110,0,0 respectively i i i ) Discussion The effects of phosphate on the binodial (Fig. 4.1) are si m i l a r to those found for dextran T40/PEG 8000 systems (Bamberger et a l . , 1984a). In the published study the effects were shown to be due to the unequal p a r t i t i o n of phosphate between the phases. The phosphate partitioned more into the dextran r i c h phase, t h i s tendency increasing with the t i e l i n e length. Unequal p a r t i t i o n of a s a l t can be due either to exclusion of the s a l t by one of the polymers, an association with the other polymer, or a combination of both. In addition both polymers may exclude or associate with both the co- and counter-ions, but to diff e r e n t extents, giving the same re s u l t . For -126-the case of phosphate, Bamberger et a l . showed by equilibrium d i a l y s i s that the effect was due almost e n t i r e l y to phosphate exclusion by the PEG, the phosphate p a r t i t i o n depending only on the difference i n PEG concentrations, irrespective 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 for the effects i n Dx 500/PEG 8000 systems as well. Sodium chloride 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. Sorbitol also 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 effect of these solutes on the phase compositions. In systems closer to the c r i t i c a l point the s a l t s have more effect 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 binodial 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 position of the binodial r e s u l t i n larger changes i n the t i e l i n e length. In addition the s a l t forms a larger fraction 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 altered, affecting p a r t i t i o n and other measurements. Important effects 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 res u l t s indicate that provided the concentrations of phosphate, s o r b i t o l and chloride do not exceed 10, 100, and 130 mM respectively, 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 -127-variation i n the po 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 raised or lowered for systems farther from,or closer to,the c r i t i c a l point. Since i n most systems used by other workers for c e l l separation work the s a l t i s always a small fraction of the t o t a l polymer weight, composition changes have often been overlooked. In particular the phosphate concentration (and the chloride concentration) i s usually altered to change the po 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 for q u a l i t a t i v e separation work, i t can invalidate the interpretation of more quantitative studies, such as those of Reithermen et a l . (1973), and Zaslavsky et a l . (1982). C. Potential and Salt P a r t i t i o n i ) Salt Bridge Effects In Chapter Three i t was pointed out that no work could be obtained from a phase system at equilibrium, and that the measured potential must resu l t from the difference i n potentials at the electrode/salt bridge phase junctions. To give meaningful information about the phase system, the measured potentials should not depend on the nature of the electrode/salt bridge. To investigate 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 effect on the measured potential ( 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 -128-Zaslavsky et a l . 1982) commonly contain 2% agar to reduce leakage of KC1. Comparison of the potentials obtained i n potassium sulphate containing systems using s a l t bridges with and without 2% agar gel show that as the s a l t concentration of the phase system i s increased, the potentials measured with the agar bridges drop by 1.3mV, and are 0.6 to 1.8mV less than the potentials obtained using bridges without agar. Measurements obtained using bridges without agar did not change with sulphate concentration. With sodium phosphate containing systems, the potentials 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 Salt Salt bridge Potential (mV) concentration bridge type: (M) agar microcapillary (7,A.4) 110,0,0 0.5 nd a 2.5A+0.0A it II 1.0 nd 2.A3+0.0A II II 2.0 nd 2.57+0.07 (5,4) 1 mM K 2S0 4 1.0 1.79+0.1 2.35+0.1 II 10 mM " 1.0 1.11+0.06 2.32+0.2 ti 100 mM " 1.0 0.55+0.05 2.26+0.05 II 200 mM " 1.0 0.51+0.05 2.19+0.06 II 300 mM " 1.0 0.50+0.05 2.30+0.03 (5,4) 110,0,0 1.0 2.40+0.16 1.80+0.1 (5,4) 96,50,0 1.0 1.67+0.1 1.35+0.1 and: not determined. i i ) Single Salt Systems -129-In Chapter 3A i t was suggested that the difference i n potentials between two systems, A I ^ - A I J J., could be measured under conditions where the common ion standard state chemical potential terms, Au, f were the same for both systems. Therefore a test was made of the expression r e l a t i n g the difference i n potentials to the s a l t p a r t i t i o n s for two systems containing a common ion, [3.6]. Ai|>s _ Ai}>c = k j l n (K c/K s) + kTln ( r c / r s ) [3.6] e e + (Au° k > c - Au° k > s)/e The difference i n the standard state chemical potential 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 state chemical potential depends only on the polymer and water composition of each phase at 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 sit u a t i o n was approximated experimentally by comparing systems with the same t i e l i n e length. In collaboration with Stephan Bamberger of the Oregon Health Sciences Center, Portland, a test of t h i s equation was made. The potentials, 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 either potassium chloride or potassium sulphate. Although these s a l t s are not generally used for c e l l buffers, they were chosen for the i r good s o l u b i l i t y , and to avoid complications due to buffer equilibrium. The potassium ion 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 calculated from the Debye Huckel expression (Robinson and Stokes, 1959): -130-log f = -AI A /V(l+BaI- L /' £) [4.2] where A=0.5115 (1/mole) , B=0.3291 r ' V ( m o l e A), I i s the ionic strength, calculated from the s a l t concentration i n the phase. The parameter a, the effective hydrated ion diameter, was chosen so as to give the best f i t of [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 for the sulphate and chloride systems respectively. The data are summarized i n Tables 4.3 and 4.4, and the predicted and measured potentials for the sulphate systems plotted against the t i e l i n e length i n Fig. 4.2. TABLE 4.3 SALT PARTITION AND POTENTIAL IN SINGLE SALT SYSTEMS. I. POTASSIUM CHLORIDE CONTAINING SYSTEMS3 Salt Tie Line P a r t i t i o n A c t i v i t y Coeff- Measured Cone. (mM) Length (%) Coefficient i c i e n t Ratio Potential (mV) 1 nd b 0.952+0.01 nd 0.51+0.1 3 nd nd nd 0.20 10 10.5+0.1 0.973 1.001 0.11 30 10.45 0.956 1.002 nd 100 10.25 0.964 1.004 0.08 200 10.0 0.950 1.006 0.07 300 10.1 0.961 1.006 0.05 400 9.95 0.955 1.007 nd a A l l systems contained potassium chloride and had a bulk polymer composition of (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 for these systems were t y p i c a l for a l l data i n Tables 4.3-4.5. Dnd: not determined -131-TABLE A. A SALT PARTITION AND POTENTIAL IN SINGLE SALT SYSTEMS. I I . THE EFFECT OF SULPHATE3 Salt Tie Line P a r t i t i o n A c t i v i t y Coefficient Potential 0(mV) Cone. (mM) Length (%) Coefficient Ratio Measured Calculated 1 nd 0.888 1.003 2.27 2.39 3 nd 0.883 1.007 2.25 2.15 10 nd 0.880 1.010 2.25 2.A8 30 10. A 0.879 1.015 2.25 1.95 100 11.1 0.8A1 1.025 2.30 3.05 200 11.25 0.815 1.031 2.39 3.36 300 11.5 0.790 1.037 2.52 A.30 AOO 12.0 0.760 1.0A5 2.92 5.03 aSystems 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. DCalculated potentials i n Tables A.A-A.5 were obtained using [3.6] and the potassium chloride system with the most sim 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 LENGTH3 System Tie Line P a r t i t i o n A c t i v i t y Coeff. Potential (mV) Composition Length (%) Coefficient Ratio Measured Calculated (5,4)30 10.7 0.870 1.015 2.17 2.21+0.3 (4.85,3.88)100 10.5 0.856 1.029 1.82 2.29 (4.63,3.7)200 10.0 0.881 1.020 1.42 1.79 (4.27,3.42)300 9.25 0.910 1.014 1.14 1.08 (4.44,3.52)400 9.85 0.880 1.020 1.47 1.80 aSystems i n t h i s table 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 similar t i e l i n e lengths to those i n Table 4.3. The chloride concentration has l i t t l e effect 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 potential (Table 4.4). However as the sulphate concentration i s increased, the t i e l i n e length and the potential 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 for phosphate i n section B, i e . exclusion of sulphate by PEG, since PEG/I^SO^ mixtures can also 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 solutions, so as to keep the s a l t concentrations the same, while decreasing the polymer concentrations. The phase compositions were thereby kept close to those of the chloride systems, thus s a t i s f y i n g the assumptions used i n deriving [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 Theoretical and Experimental Pote n t i a l s , a) Single s a l t systems containing 0.001 to O.AM potassium sulphate (Tables A.3-5). Effect of t i e l i n e changes on measured (o) and predicted (*) potentials from [3.6]. b) Mixed s a l t systems, composition (5,A), containing sodium phosphate buffer and sodium chloride. Measured (o). Predicted (*), using [3.28] with z=1.735, Kc=0.938, AiVs=2.65mV,A4ic=0.0AmV. Data from Reitherman et a l . , 1973 (0), Ba l l a r d et a l . , 1979 (+). -134-to those i n the chloride systems, there i s good agreement between the predicted and measured potentials at a l l sulphate concentrations. i i i ) Phosphate Concentration Effects The results of section i i indicate that the s a l t concentration can affect the potential 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 to 400 mM. The effect on the potential of a l t e r i n g the phosphate buffer concentration i s shown i n Table 4.6 for a system close to the c r i t i c a l point (5,3.8), which i s expected to be sensitive to changes i n s a l t concentration, and for two systems further away, (5,4) and (7,4.4). In each case the potential i s approximately constant, with perhaps a small decrease of 0.2 to 0.3 mV below 20 mM. TABLE 4.6 EFFECT OF PHOSPHATE CONCENTRATION ON POTENTIAL3 System Phosphate Concentration (mM) Potential (mV) (5,3.8) 10 1.84+0 II 40 2.06 it 110 1.99 (5,4) 5 2.42 ti 10 2.65 ti 30 2.72 II 110 2.60 (7,4.4) 10 2.97 II 20 3.34 it 30 3.30 ti 110 3.35 asystem buffers contained only phosphate buffer, pH 7.16 i v ) Mixed Salt Systems -135-Phase systems used for 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 additional s a l t s . I t i s therefore of p r a c t i c a l use to extend the theory of potentials to deal with such mixed s a l t systems, p a r t i c u l a r l y to aid the interpretation of the experiments i n section D below. In t h i s work the potential i s controlled by the concentration r a t i o of phosphate to chloride. The common ion i n th i s case i s sodium, and the anions present are chloride, HPO^ and H2 P I " V T b e aPP r°P ri- at e equation to test would therefore be [3.32] with n = 3. The i n i t i a l bulk concentration r a t i o of mono and divalent phosphate i s 2.8, which gives a pH of 7.16. However the analysis i s complicated by the fact that the concentration of these two ions i n each phase i s not fixed, 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 al t e r n a t i v e l y the two phosphate ions have different 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 ion 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 potential (as given by, for 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 ion r a t i o i n the buffer stock used to make up the systems, but they vary with potential i n some manner, subject to the condition that the t o t a l phosphate concentration i s fixed. This amounts to the fact that the s a l t composition of the phase system depends on the potential. Fortunately, i n dealing with t h i s problem, some simplifying approximations can be made, without knowing the precise manner i n which r ? -136-and r ^ vary. These can be j u s t i f i e d by showing that for the conditions used i n t h i s work the potential i s f a i r l y i nsensitive to the change i n the r a t i o r 2 / r 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 small. Except for t h e i r effect on the equilibrium between mono- and di-basic phosphate ions, t h e i r contribution to the potential w i l l therefore be small. Only the mono- and di-basic phosphate ions need to be considered. Secondly i t i s assumed that the effects of phosphate on the potential i n these systems can be described by the behaviour of a hypothetical 'average phosphate ion', 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 H2P0^, and whose concentration i s equal to the t o t a l phosphate concentration. This i s achieved by using equation [3.28] with an ion of non in 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 ion i n a 2.8:1 mixture of dibasic and monobasic phosphate. To calculate V g, the potential i n a system with 10,0,100 buffer, pH 7.16, (2.65 mV) was used, which of course i s already an 'average' determined by both ions. The potential 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 chloride system are 0.04 mV, and 0.938. Using these data the predicted potentials were calculated using [3.28], where r g was the r a t i o of t o t a l phosphate to chloride ions. F i n a l l y , the maximum probable error 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 potentials i n system -137-containing 10 mM of either the mono or d i basic phosphate (pH 4.5 and 9 respectively) were measured as 1.5 and 2.9 mV. These data were put into [3.32] for a three s a l t system. 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 potential changed by about 0.2 mV. This was calculated for a phosphate/chloride r a t i o of one, where the effects would be largest (based on Figure 3.1). This indicates that the error introduced by averaging the effects of the two phosphate ions i s c e r t a i n l y not much larger than the precision of the measurements. Since [3.28] and [3.32] also neglect the effects 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 equilibrium 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 theoretical value, applies only to these system, i n the limited range of s a l t compositions used here. Additional confirmation that t h i s approximation i s reasonable comes from the fact 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 difference between the phases of 4.3 %, and the plot of phosphate p a r t i t i o n against PEG concentration difference given i n Bamberger et a l . (1984a). Systems containing 10 mM phosphate buffer with increasing amounts of chloride 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 results of section B indicated 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 results of section i i , i t was assumed that the ion standard state chemical potential differences were thus unchanged. The potentials i n these systems were measured with microcapillary electrodes. The theoretical and experimental -138-curves of potential against percentage phosphate are plotted i n Fig. 4.2b, showing good agreement. The data of Reitherman et a l . (1973), measured with agar s a l t bridges, and Ballard et a l . (1979) are shown for comparison. v) Discussion From fundamental considerations, the inner or Galvani potential difference between two phases i s not measurable (Section 3A): the potential that i s i n fact measured, A i p m , i s the sum of the Galvani potential difference, Alp (=ip- iy ) and the difference i n standard state chemical potentials of the potential determining ion(s). The effect of changing the chloride concentration shows that there i s no junction potential due to the s a l t i n the bridges. In Fig. 4.2a, the agreement between theoretical potentials and those measured with microcapillary electrodes without agar i s confirmed. However the different potentials obtained with and without agar (Table 4.2) indicate that i f there i s agar present there i s a polymer induced junction potential which depends on the s a l t concentration i n the phase system. At 0.1M s a l t the potentials obtained using the two bridge types d i f f e r by 1.7mV for the sulphate system, but only by 0.4mV for 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 results imply that measurements made by other workers (Zaslavsky et a l . , 1981; Reitherman et a l . , 1973) are too low, and show too strong a dependence on the phase system s a l t concentration. In testing 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 to 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 -139-give r i s e to an increasing discrepancy between the predicted and measured potentials (Table 4.4), as the difference between the t i e l i n e lengths of the sulphate and chloride systems increases. This effect i s l i k e l y to be due to changes i n the standard state chemical potential 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 si 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 ion standard state chemical potential differences, given the size of the potentials usually encountered and the precision to which they can be measured. The effect of phosphate concentration on potential i s of interest both t h e o r e t i c a l l y , and for studies i n which the io n i c strength of the system i s varied (section D below). The small decrease i n potential 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. Ballard et a l . (1979) also found a si m i l a r decrease for (5,5) systems. Both Ballard et a l . and Zaslavsky et a l . (1982) found a decrease i n potential with increasing phosphate concentration, although t h i s could be due to the effects of using agar f i l l e d s a l t bridges. The effect of phosphate on the t i e l i n e length was not considered i n either of these studies. I t seems f a i r to conclude that i n the absence of t i e l i n e length changes the potential i s independent of s a l t concentration, at least up to 400 mM. The approach to predicting potentials from s a l t p a r t i t i o n s used i n section 3A was generalized to deal with mixtures of 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 results of -140-Fig. 4.2b show good agreement between the theory and experiment, despite the device used to account for 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 invalidate the assumptions used i n i t s derivation. The result of such effects i s indicated 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. T i l s curve does not have the same general shape as the theoretical curve, while the data of Ballard et a l . (1979), where the phosphate concentrations were kept below 10 mM, does show the correct theoretical shape. The fact that the theoretical curve i s not straight also i l l u s t r a t e s the fact that the potentials are not additive. This was also demonstrated experimentally for mono and di-basic phosphate containing systems by Zaslavsky et a l . (1982). As well as v e r i f y i n g that the measured potentials i n the mixed s a l t systems were correct, another important Quantity could be obtained from the equations i n section 3B: the difference 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 potential using the ion p a r t i t i o n c o e f f i c i e n t s calculated 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 effect 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 p a r t i t i o n . However they did not consider the fact that i t i s only -In-differences i n io n i c strength between the phases that contribute to A y . An expression for the t o t a l e l e c t r o s t a t i c contribution to the c e l l surface free energy difference, A \ , i s ea s i l y obtained from equations 13 and 23 of Verwey and Overbeek (1948) (see Brooks et a l . , 1985): A y e l = 2 T T 0 - 2 ( l / x t - 1/XD)/E + A i p a [4.3] where cr i s the surface charge density, e i s the d i e l e c t r i c constant of the phase system (assumed to be the same i n both phases), Atp i s the potential difference, and H ^ ' K d are the Debye-Huckel parameters i n the upper and lower phases respectively, which are proportional to the square roots of the ionic strengths. Now for phosphate/chloride systems, both s a l t s p a r t i t i o n into the lower phase, so the f i r s t term i s positive. 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. I f i t i s assumed that the s a l t p a r t i t i o n s and the potential 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 written: A y e l = B a2r1/2(K~1/2 - 1) + Aipcr [4.4] where B i s a constant, I i s the lower phase ionic strength, and K g i s the net s a l t p a r t i t i o n (ie 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 variation of A Y e ^ with the bulk i o n i c strength at constant potenti a l . -142-Although the potential 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 potentials, are being considerably altered, the absolute sizes of the potentials cannot be compared with each other. This d i f f i c u l t y applies to any interpretation of the observations of Johansson (1978), who found that the measured potential i n potassium chloride systems depended l i n e a r l y on t i e l i n e length. The results of sections B and C show that for these systems the potential can be varied independently, and that changes i n the measured potential agree with the predictions of theory, providing the t i e l i n e length of the system i s not altered by more than about 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 Salt Composition Chapter Six deals more f u l l y with the question of what determines c e l l p a r t i t i o n . However, anticipating the connection between the c e l l surface free energy difference and p a r t i t i o n , some effects 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 section. These results show that the changes i n potential described i n section C above do affect c e l l p a r t i t i o n , and they also aid i n the interpretation of i o n i c strength effects on the c e l l surface free energy difference. The effect of s a l t composition i n phosphate- and chloride-containing systems i s shown i n Fig. 4.3a. The c e l l p a r t i t i o n increases rapidly with increasing phosphate, the rate of -143-increase being greater at high and low p a r t i t i o n s . Fig. 4.3b shows the p a r t i t i o n as a function of po 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 rapidly when the potential i s above 2 mV. Changing the phosphate concentration from 30 to 10 mM has l i t t l e effect on either the potential (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 Fig. 4.3b since the potential also decreases (Table 4.6, section C i i i ) . The effect of 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 STRENGTH3 Buffer Ionic Strength Potential P a r t i t i o n (mM) (mV) (%) 5,0,114 10,0,100 20,0,73 30,0,45 12.4 24.7 49.4 74.1 2.42+0.05 46+3 2.65 82 2.72 85 2.60 87.5 aPolymer composition of a l l systems was (5,4) -144-LU >—i C_J g0. 01 0. It 0 0. 5 MOLE FRACTION OF PHOSPHATE 1. 0 0 1 2 POTENTIAL (mV) Figure 4.3 Effect of Salt 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 of mole fr a c t i o n of phosphate, b) P a r t i t i o n as a function of po t e n t i a l . Buffer: 5,0,114 ( + ), 10,0,100 (*), 20,0,73 (o), 30,0,45 (<». -145-I t can be seen that a s i x f o l d change i n i o n i c strength has no effect on the p a r t i t i o n other than that expected from the concomitant change i n potent i a l . i i ) C e l l Surface Free Energy Difference and Potential The c e l l surface/interface contact angle was measured i n a series of systems with different r e l a t i v e amounts of phosphate and chloride ions. Fig. 2.2 i s a photo taken from the video monitor during an experiment, showing the spherical c e l l , drop, and the contact l i n e . The c e l l surface tree energy difference was calculated from Young's eauation, [1.23], and the energy of c e l l / i n t e r f a c e interaction was calculated from equation [1.28], using the tensions measured i n Table 4.1: The c e l l p a r t i t i o n was also measured i n these system, and these quantities are tabulated i n Table 4.8 (actually the intensive quantity A E U = 2 ^ E t i / ' T T a p * s 9^ v e n * n t°* s table). Data for the potentials were obtained from Fig. 4.2. 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, chloride and phosphate ions were calculated from the potential 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 ionic strength and Debye-Huckel parameter i n each phase were calculated. These data were used to calculate A (column seven of Table 4.8), the parameter characterizing the ionic strength contribution to Ay , ([4.3]): y t _ y D = A y = - [1.23] A E t i = T T a p Y t b ( 1 - C 0 S 9 ) 2 [1.28] -146-A = 2 TTU/X* - l/V. b)/e [4.5] When measuring contact angles, the c e l l s were usually 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 did not change s i g n i f i c a n t l y (t t e s t , p>30%). Advancing and receding contact angles were also the same. This indicated that the equilibrium contact angle was being measured. The drop diameter was varied from 5 to 50 pm, and there was no correlation of contact angle with drop size (chi squared t e s t , p>10%)^ As the phosphate percentage i s increased, the potential and c e l l p a r t i t i o n increase, while the c e l l surface free energy difference, the contact angle and c e l l / i n t e r f a c e interaction energy decrease. The c e l l surface free energy difference i s plotted against the potential i n Fig. 4.4. This plot was found to be l i n e a r (r=0.982) with a slope of -553+100 2 esu/cm . The ionic strength parameter, A, decreases with increasing i o n i c strength, and increasing chloride percentage. The surface charge density ( l a s t two columns) was calculated from the positive and negative roots of [4.1]. A l l the values given by the positive root f a l l within 10% of t h e i r mean, while the variation i n the values given by the negative root i s much 1 The variation of contact angle with drop size i s described by cos 9 = AY/ Ytb + T^ac w n e r e t i s the l i n e tension, and a c 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 - 3 dynes/cm, and a precision of 2-3° in measuring the angles, t h i s puts an upper l i m i t of around 10" 6 dynes for the l i n e tension i n t h i s system. TABLE 4.8 ERYTHROCYTE PARTITION AND CONTACT ANGLE. THE EFFECT OF POTENTIAL AND IONIC STRENGTH Contact AY A E t i A a x l O 1 0 Charge Potential Angle («) x-1 P a r t i t i o n (erg cm2 Density 0 Buffer (mV) (ergs/cm^) x H r (%) esu~2) (esu/cm2 ) x - l 10,0,110 2.65+0.1 46.5+3 44.5+2 6+2 79.5+4 13.9+1 552+60 5803+500 10,4,92 2.3 52 40 9 25 12.4 582 5550 10,8,84 2.0 58 34.5 14 16 11.1 576 5400 10,12,76 1.7 63.5 29 20 13.5 10.0 582 4950 10,16,68 1.6 67.5 25 25 10 9.2 519 5169 5,0,114 2.4 53 38 10 46 19.6 543 3573 10,0,100 2.75 45 44 5.5 82 13.9 521 6074 10,130,0 5,0,94° 0.1 90.5 -1 65.5+7 2+1 2,9 - -2.3 69 33 39 12 26.3 536 2330 10,0,85c 2.5 60 47 23 30 18.6 640 3888 aCalculated from eauation [4.5]. °Values obtained from the positive and negative roots of [4.3] respectively c(5.5,4) systems. -148-Figure 4.4 Effect of Potential on the C e l l Surface Free Energy Difference. Buffer: 10,x,y (*), 5,x,y (o), x and y given i n Table 4.8. -149-larger, some of the values d i f f e r i n g by a factor of two. Values obtained with 5 mM instead of 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 increasing the phosphate to chloride r a t i o has been well 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 tvs been shown to depend on the c e l l surface charge (Brooks et a l . , 1971). This interpretation i s supported by the fact that the e l e c t r o s t a t i c potential increases with phosphate percentage (Section C), and that the p a r t i t i o n correlates well with the potential (Fig. 4.3). The c e l l surface free energy difference i s proportional to the potential (Fig. 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 calculated from t h i s plot (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 acid derived from chemical or enzymic assays of -10,600 esu/cm (Cook, 1976). This twentyfold discrepancy i s puzzling, and several possible explanations were considered: a) The change i n c e l l surface free energy i s not due to the change i n potential, but due to some other concomitant change i n the phase system properties, such as ion binding. This i s believed to be un l i k e l y , since i f the effect i s due to a s p e c i f i c interaction with the phosphate (eg. an exclusion of phosphate from the c e l l surface, resulting i n increased -150-p a r t i t i o n into the upper, phosphate poor phase), then the addition of a small amount of chloride, which on i t s own has no effect 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 difference to the extent i t does. Also changing the phosphate concentration has no effect on the dependence of either 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 difference i n i o n i c strengths between the phases might be important. This difference decreases as the percentage phosphate decreases, since chloride 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 small, even though a i s large. 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 ioni c strength at constant poten t i a l . This i s not supported by the data in 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 potential change (Fig. 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 larger root represents the case where the i o n i c strength term i s large and comparable to the potential term. The smaller root arises 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 s i t u a t i o n . c) The t h i r d explanation considered i s that the potential as measured by -151-the s i l v e r electrodes i s not the actual potential between the phases, as 'seen' by the c e l l . However the good agreement between the theoretical and measured potentials described i n section AC does not support t h i s p o s s i b i l i t y . d) The actual net charge on the c e l l surface may be considerably smaller than that calculated from the amount of s i a l i c acid, due to the presence of other charged groups, p a r t i c u l a r l y on the proteins. No r e l i a b l e estimates are available 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 cert a i n l y have both.positively charged amine groups and negatively charged carboxylic acid groups. Thus while the net charge may well be less 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 effect could not completely account for 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 into contact with, and cross, the interface 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 descriptions of t h i s effect i n electrophoresis 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 distributed through t h i s layer over some depth normal to the surface. I f neither of the -152-phases f u l l y penetrates the glycocalyx, then only the charge that experiences the ionic milieu of both phases w i l l contribute to the c e l l surface free energy difference. This hypothesis i s consistent with the results of t h i s work, and the nature of the c e l l surface, although there i s no direct evidence that the phases are excluded from t h i s glycocalyx. That other molecules can be excluded i s indicated by the c r y p t i c i t y of certain erythrocyte g l y c o l i p i d s to antibodies raised against the p u r i f i e d antigen (Hakamori, 1981), increased proteolytic digestion of membrane proteins after removal of the s i a l i c acid (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 after enzymatic removal of some of 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 also be attributed to exclusion. To test 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 les, could be used for s i m i l a r contact angle measurements. Ionic strength effects would also be expected to be s i g n i f i c a n t for smooth p a r t i c l e s with charge densities comparable to 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 Ay as the s i a l i c acid i s removed by enzymic treatment. I f the other charges were n e g l i g i b l e , Ay would be l i n e a r l y related to the amount of s i a l i c acid l e f t on the surface. Other studies i n the l i t e r a t u r e on the role 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 -153-manner. However i f t h i s i s the case, then the observed p a r t i t i o n differences i n charge sensitive systems (Brooks et a l . , 1971) may r e f l e c t changes i n only a small fraction 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 less charge to the phase system, while the amount of t o t a l charge remains unchanged. In conclusion, the results of t h i s chapter show that the potential difference between the phases can be controlled independently, providing the concentrations of the ions are s u f f i c i e n t l y low. This w i l l depend on the phase systems and s a l t s used, but for (5,A) systems, conditions where the t i e l i n e changes by less than 0.5% are s u f f i c i e n t . Under the same conditions, differences i n potential 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 single and mixed s a l t systems. The p a r t i t i o n of c e l l s into the upper phase increases as t h i s phase i s made more positive with respect to the lower phase. The c e l l surface free energy difference i s l i n e a r l y related to the potential. However the effect of the potential i s smaller than predicted based on the surface charge density estimated from the amount of s i a l i c acid on the c e l l . This i s attributed primarily 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 talent for absorbing p o s i t i v e knowledge- Albert Einstein 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 ligand. This can r e s u l t i n more s p e c i f i c and higher resolution separations. Specific a f f i n i t y ligands have been used to separate proteins, nucleic acids and membrane recptors, but are only just being developed for 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 of the admittedly few tests that have been made do not confirm t h i s theory. In Chapter Three a theory was developed to describe the effect of an a f f i n i t y ligand on the c e l l surface free energy difference. This chapter i s concerned with studying the effect of PEG-palmitate ester (ester) a f f i n i t y ligand, and determining the a p p l i c a b i l i t y of the theory. This ligand 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, Van A l s t i n e , 1984), and i s e f f e c t i v e at low concentrations. 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 effects of changing the ester concentration on several phase system properties are f i r s t examined. The behaviour of the ester i t s e l f i n the phase system i s then studied. F i n a l l y the effect of ester on the c e l l -155-surface free energy difference and i t s interaction with the c e l l surface are measured. These are then related by the theory of Section 3D. B. Effect of PEG-palmitate on the Phase System i ) Compositional and E l e c t r o s t a t i c Effects Because of i t s PEG head group, the ester i s expected to p a r t i t i o n predominantly into the PEG r i c h phase, and t h i s unequal p a r t i t i o n could appreciably affect the phase separation i n a manner analogous to phosphate (Chapter Four). The effects on the phase system are summarized i n Table 5.1. TABLE 5.1 EFFECT OF ESTER ON PHASE COMPOSITIONS3 Additive Phase Compositions (%) Tie l i n e Length Top Bottom (%) Potential (mV) 0.1 ml water 125 JJM 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 (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 nd° 0.24+0.10 nd 0.18 1.82 1.80 3system was (5,3.8)10,130,0 °not determined csystem was (5,3.8)10,0,220 Within the error of measurement, the ester has no more effect on the phase composition than that due to either the same amount of unesterified PEG, or the c a r r i e r buffer added with the ester, even at concentrations of 20 J JM, four times the maximum amount generally used. The potential between - 1 5 6 -the phases i s also unchanged. i i ) Effect of 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 sensitive measure of changes i n the phase composition, as well as being very important for 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 results from experimental uncertainty. TABLE 5 . 2 EFFECT OF PHASE COMPOSITION ON INTERFACIAL TENSION System Tie Line Length (%) TensionxlO 3 erg/cm2 ( 5 , 4 ) 1 0 , 1 3 0 , 0 1 1 . 8 5 + 0 . 2 nd a 5 . 7 3 + 0 . 2 ( 5 , 4 ) 1 0 , 1 3 0 , 0 + 0 . 3 ( 5 , 4 ) 1 0 , 1 3 0 , 0 + 1 . 2 ( 5 , 4 ) 1 0 , 1 3 0 , 0 + 3 . 0 ( 5 , 4 ) 1 0 , 1 3 0 , 0 + 6 . 0 nd nd nd 5 . 4 5 5 . 6 9 5 . 9 2 6 . 1 4 and: not determined -157-i i i ) Discussion The addition of the ester has l i t t l e effect on the phase composition, even though i t p a r t i t i o n s predominantly into the PEG r i c h phase, probably as a re s u l t of the low concentrations used. Since the potential i s also unaffected, presumably the ion d i s t r i b u t i o n s are also unchanged by the ester. This ligand also has l i t t l e effect on the tension. I t i s therefore assumed that providing the ester concentration i s kept below 6 J J M, i t has no s i g n i f i c a n t effects on the phase system properties. This makes i t a convenient model ligand for detailed study. C. Behaviour of PEG-palmitate i n the phase system i ) P a r t i t i o n The percent p a r t i t i o n of PEG-palmitate into the upper phase of a (5,4)10,130,0 system as a function of ester concentration i s shown i n Fig . 5.1a. The results 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 partition/binding 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 set, measured simultaneously with c e l l p a r t i t i o n , show si 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 interface, and that t h i s -158-100 0. 01 160 0 . 1 1 .0 10 ESTER CONCENTRATION CuM) 200 E S T E R C O N C E N T R A T I O N (>JM> Figure 5.1 Behaviour of 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 of concentration (o). Measured simultaneously with ester binding to erythrocytes (*). Apparent percentage of ester at the interface, xlO (+). b) Example of fluorescence plot for determining the cmc. Data for the ester i n water containing PRODAN, cmc i s given by the break i n the plot at approximately 35 J J M . -159-amount has no meaningful dependence on concentration (Fig. 5.1a). Experiments where the area of tube crossection, and hence the i n t e r f a c i a l area, was varied by a factor of four gave ess e n t i a l l y the same re s u l t s . Loss of ester by adsorption to the sampling pipettes was found to be less than 0.5% by assaying an aliquot of radio-labelled ester before and after ten sequential samplings with fresh pipettes. This could not therefore account for the observed re s u l t s . Volume r a t i o changes were also ruled out by direct measurements before and after the experiment. i i ) PEG-Palmitate C r i t i c a l Micelle Concentrations Both the ester p a r t i t i o n r e s u l t s of section i above, and the interpretation of the ester binding to erythrocytes and i t s effect on thei r p a r t i t i o n (Section D), required that the c r i t i c a l micelle concentration (cmc) of the ester i n each phase be measured. A variety 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 conductivity measurements (Mukerjhee and Mysels, 1971), but almost a l l of these are inapplicable 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 less affected by these problems, and so was used to measure the ester cmc's. A t y p i c a l plot of fluorescence against ester concentration i s shown i n Fig. 5.1b, and the results are summarized i n Table 5.3. -160-TABLE 5.3 PEG ESTER CRITICAL MICELLE CONCENTRATIONS Solvent Probe cmc (uM) Water PRODAN 37+5 Water ANS 42+5 (5,4)10,130,0 Top (5,4)10,130,0,Bottom ANS 20+5 ANS 10+5 13% PEG i n water ANS 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 micelle effect of the probes, which themselves are hydrophobic, tends to lower the apparent cmc (see discussion below). The cmc i n both phases appears to be well above the range of concentrations where the p a r t i t i o n increase i s seen i n Fig. 5.1a, and the t y p i c a l concentrations used for 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 to the dextran r i c h phase, showing the large effect of 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 puzzling (Fig. 4.4a). The p a r t i t i o n increases from 65 to 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 to 4.26, a very s i g n i f i c a n t change. I t i s also surprising that the ester p a r t i t i o n i s less 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 theore 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 palmitic acid 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, section D), i e about A.3. Various control experiments eliminated possible systematic errors associated with sampling, incomplete s e t t l i n g of the phases, phase volume changes and adsorption at the interface. The ester has l i t t l e effect on the tension, which also indicates that l i t t l e adsorption i s occurring at the interface, although t h i s might be expected because of the ester's amphiphilic and detergent properties. This i s probably because both the palmitic acid t a i l , and the PEG head group separately p a r t i t i o n into the PEG r i c h phase (K = 1.16 and 3.9 respectively). Therefore there would be no free energy decrease for an ester molecule adsorbed at the interface. 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 section 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 rapidly at low ester concentration, where the ester has l i t t l e effect on the tension, and increases less rapidly at higher concentration, where i t would be expected to have the most ef f e c t , so t h i s seems unlikely to be the explanation. Another explanation for t h i s effect could be that the free energy of ester transfer between the phases, given by the difference i n standard state chemical potentials, 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 micelle formation. The formation of micelles i s expected i n the l i g h t of the commercial application of t h i s type of ester as detergents (Rosen, 1978). The cmc's of a number of PEG fatty acid esters, and the analogous PEG fatty acid ethers, with smaller head groups have previously been measured (Elsworthy and MacFarlane, 1962). For the palmitate series the cmc (expressed as moles/litre) was found to be related to the number of ethylene units i n the head group, n, by cmc = -5.93 + 0.0245n [5.1] for n = 6-21. Extrapolation of t h i s equation to a head group molecular weight of 6650 g/mole (n = 120) gives a cmc i n the millimolar range, well above the concentration range i n Fig. 5.1a. However such a figure cannot be used u n c r i t i c a l l y since i t i s based on a considerable extrapolation, and i t also takes no acount of the system polymers. The results i n Table 5.3 indicate 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 in t e r e s t . These data must be considered as semi-ouantitative i n view of the uncertainties i n defining and measuring the cmc, especially for polydisperse. material. The lower values are not surprising since the effect of each additional ethylene head group i n increasing the cmc would be expected to decrease as the head group becomes larger, and conforms more to the random c o i l configuration. The phases decrease the apparent cmc. This effect appears to be due mainly to the dextran, since the effect i s greater i n the lower phase, and -163-13% PEG alone increases the cmc. Such an effect i s understandable i f micelle formation i s viewed as a form of phase separation (Tanford, 1976), the effect of the polymers on micelle formation being the same as their effect on p a r t i t i o n i n g the ester between the phases. The onset of micelle formation would be expected to increase the net ester p a r t i t i o n since a micelle would be expected to have a larger p a r t i t i o n c o e f f i c i e n t into the PEG r i c h phase than an ester monomer (This can be seen from [1.38], i f the micelle 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) also found an increase i n ester p a r t i t i o n at higher concentrations (0.1-1 mM) which they attributed to micelle formation. The p a r t i t i o n was close to that of the PEG i t s e l f below 1 mM, and increased, as expected i f micelles were forming, to forty times the PEG p a r t i t i o n . I f the phase separation model of micelle formation i s used then the chemical potential of the ester i n the free and micelle form are equal, leading to (Tanford, 1976): H°e " H = k T l n ^ e " k T / n l n ( X T / n ) [ 5 ' 2 ] o w oh where u.g, u.g are the standard state chemical potentials of the ester i n aqueous and hydrocarbon solvent ( i e . the micelle i n t e r i o r ) , X^, X ™ are the mole fractions of ester i n monomeric and micellar form, and n i s the number of ester molecules per micelle (assumed constant). The l e f t hand side i s constant, and [5.2] can be re-written as -164-X g / ( X g ) 1 / n = const. [5.3] w For reasonably large m i t can be seen that X ? changes very slowly as the w m t o t a l amount of ester, X e + X e » increases. Such behaviour i s behind the concept of a cmc. A possible a r t i f a c t of cmc measurements made by means of hydrophobic probes, the so ca l l e d mixed micelle e f f e c t , results from the fact 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 into the hydrophobic micelle i n t e r i o r , thus driving micelle formation. From [5.2] i t can be shown that the cmc w i l l be lowered by a factor 1 - X , where P Xp i s the mole fraction concentration of probe i n the micelle. Thus the actual 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 for 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 drive for micelle 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 of the amphiphiles i n the micelle i n t e r i o r . Such an exclusion of water presupposes a certain 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 of gyration of about 25 A (Cabanes, 1982) i s much larger than the palmitic acid t a i l (with a crossectional 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 micelle. Bearing i n mind the implications of [5.3], the significance of the apparent cmc's measured with the fluorescent probes i s not clear. -165-I t i s possible that the apparent cmc's measured here are an a r t i f a c t due to the presence of the probe i t s e l f , which allows larger micelles to form, and that the p a r t i t i o n effects are due to small aggregates or 'proto-micelies' which occur at lower concentrations, and which cannot be detected by the fluorescent probe. Micelles of SDS have been shown to adsorb to PEG molecules i n aqueous solution (Cabanes, 1982). A similar type of association between PEG and the ester 'micelles' could provide an explanation for the complex behaviour seen here. Whatever the reason, these res u l t s e f f e c t i v e l y l i m i t the experimentally accessible range of ester concentrations, and make precise determination of the free energy of ester transfer between the phases d i f f i c u l t . D. PEG-palmitate/Erythrocyte interactions i ) C e l l P a r t i t i o n Before studying the effect of ester on the c e l l surface free energy difference, the range of concentrations over which the ester affected the c e l l p a r t i t i o n was determined (Fig. 5.2a). The ester increases the c e l l p a r t i t i o n dramatically, even i n the micro-molar concentration range. The plot of log 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 unlabelled ester used for the work i n t h i s thesis have polydisperse PEG head groups. They also d i f f e r i n t h e i r purity, the commercial ester containing 84% unesterified PEG, the r a d i o l a b e l e d ester containing less than 1%. However ester from both sources has the same -166-0. 01 0 0 . 5 1 .0 1 . 5 100 80 Q 60 2 40 ct: « < Q_ b * o / J ... i i _ i 0 1 2 3 4 E S T E R C O N C E N T R A T I O N (>JM) Figure 5.2 Erythrocyte P a r t i t i o n and Ester Concentration, a) C e l l s partitioned i n a (5,4)10,130,0 system. Ester expressed as bulk concentration for an equivolume system, b) Comparison of commercial (*) and ^ C la b e l l e d (o) ester. -167-effect on c e l l p a r t i t i o n on a mole basis (Fig. 5.2b), which i s a sensitive indication that there i s no s i g n i f i c a n t difference between them. i i ) Binding Studies The interaction of the ester with the c e l l s was investigated 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 control, and also 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 Fig. 5.3, and can be seen to be es s e n t i a l l y l i n e a r up to 6% PEG, for binding from the upper phase. Binding i n buffer 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 point, and given the weakness of the binding and the consequent large errors, 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 effect 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 points. b) PEG-palmitate Adsorption The ester binding isotherms for binding from both phases of a (5,4)10,130,0 system are shown i n Fig. 5.4a. Ester concentrations indicated -168-Figure 5.3 Adsorption of PEG 8000 to Erythrocytes. Incubation medium: PBS (*), 110,0,0 buffer (+), 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 10 ESTER CONCENTRATION (pM) Figure 5.4 Ester Binding to Erythrocytes. The Effect of the Phases and C e l l Concentration, a) Effect of incubation medium. Top (o) and bottom (*) of a (5,4)10,130,0 system, at 3% haematocrit. b) Effect of c e l l concentration. 3% haematocrit (o), other haematocrits given on the figure (*). -170-are equilibrium concentrations. Both isotherms appear to be lin e a r at low concentration, and saturate at higher concentration. The binding i s stronger from the lower phase. Several control experiments were done for the ester binding, to check the results shown i n Fig. 5.4a. Most of the studies were o done at a haematocrit of around 3%, equivalent to 3x10 c e l l s / m l . Increasing the haematocrit from 2 to 40% lowers the equilibrium ester concentration, but does not affect the isotherm (Fig. 5.4b). Binding was measured either by disappearance of la b e l from solution 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 results within experimental error, indicating that a l l the radiolabel could be accounted for (data not shown). Studies on the time course of ester binding and desorption indicated that the binding reaches equilibrium within three minutes (the shortest feasible sampling time), and does not change for up to two hours (results not shown). The binding of PEG, dextran and ester i s compared i n Fig. 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 indicated on t h i s figure. c) Desorption Studies Many studies have shown that when the polymer concentration i n a medium in equilibrium with a surface i s lowered, desorption of polymer from the surface reaches equilibrium very slowly (eg. see Adamson, 1976). This has been shown for dextran and fibrinogen adsorption to erythrocytes -171-POLYMER CONCENTRATION <%> Figure 5.5 Comparison of PEG 8000, Dextran T500 and Ester Binding. Incubation medium: PBS for PEG ($) and Dextran (o), top (5,4)10,130,0 for PEG-palmitate (*). Dextran data from Joe Charalambous, personal communication. Dotted l i n e s indicated estimated amounts of 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 of 50%. -172-(Brooks et a l ^ , 1980). Since PEG, dextran and ester are unequally distributed i n the phase system, slow desorption effects could i n p r i n c i p l e be important when the c e l l i s transferred from one phase to the other. The desorption of PEG and ester were investigated by wash of f studies. The results of 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 Fig. 5.6a. The semi-log plots of the fraction of PEG l e f t a f t e r each wash are nonlinear i n a l l three cases, proportionally less material again being removed with each wash." Washing with the upper phase removes more bound PEG, by a factor of 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 (Fig. 5.6b). A l l of the semi-log plots are non-linear, with the exception of that for the upper phase, proportionally less material being removed with each wash. The amount of material removed per wash increases i n the order: lower phase, PBS (high i o n i c strength buffer), phosphate buffer (low ionic 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 ly s i n g the c e l l p e l l e t with hypotonic buffer. When the c e l l s are lysed after three washes, the amount of ester released i s equal to that for the control buffer of the same io n i c strength. When the c e l l s are lysed on the f i r s t wash, the amount of ester released i s less than with the control. In fact about twice as much ester i s associated with the membrane after l y s i n g . This i s interpreted as material released from the outer surface by the l y s i n g buffer, which was being re-bound on the previously unexposed inner membrane surface. I t i s therefore assumed that PEG can not cross the membrane. -173-100* -J < on UJ o o_ ZD O CD Figure 5.6 Desorption of PEG and Ester from Erythocytes. a) Desorption of PEG. b) Desorption of ester. 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 buffer, pH 8, and the c e l l membranes pelleted at 15,000g for 15min. -174-For the experiments where the c e l l s were washed with the phases, the amount of ester bound after each wash was plotted against the equilibrium ester concentration i n the wash, and compared with the binding isotherms (Fig. 5.7). For the top phase, the points for the wash off l i e i n a f a i r l y straight 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 off 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 Fig. 5.4 are replotted on a Scatchard plot i n Fig. 5.8a. The binding from both phases give l i n e a r plots (r=0.966, 0.886, for the upper and lower phases respectively), with very si m i l a r intercepts on the abscissa. The data from the lower phase has a slope just over three times as large. The binding from each phase measured i n the complete phase system i s analysed by Scatchard plots i n Fig. 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 plots, with very s i m i l a r intercepts. 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 analysis of the Scatchard p l o t s , i s summarized i n Table 5.4. Good correlation c o e f f i c i e n t s are obtained for a l l plots. 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 for the complete -175-1. 0 0. 1 0. 2 0. 3 0. 4 E S T E R C O N C E N T R A T I O N (>JM) Figure 5.7 Comparison of Ester Adsorption and Desorption. C e l l s incubated and washed with top (•) or bottom (*) phase of a (5,4)10,130,0 system. Numbers refer to the wash number, zero being the o r i g i n a l amount bound. So l i d l i n e s indicate isotherms from Fig 5.4 -176-0 l 0 - 4 8 10 BOUND ESTER (10 g/g CELLS) Figure 5.8 Scatchard Plots 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 for 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 for both methods. TABLE 5. A SUMMARY OF ESTER BINDING DATA FROM SCATCHARD PLOTS Dissociation Binding Phase Binding Sites Constant Energy Regression 1 0 6 / c e l l JJM kT/molecule Coefficient Top 8.A8+0.3 3.3+0.3 -16.6+0.2 0.966 Bottom 8.68+0.6 0.85+0.2 -18.0+0.4 0.886 Top 3 10.9+1 2.82+0.3 -16.8+0.A 0.887 Bottoms 10.3+1.5 0.90+0.3 -17.9+0.A 0.950 ameasured i n a complete system. i i i ) PEG-palmitate and the C e l l Surface Free Energy Difference A series of (5,A)10,130,0 systems containing increasing amounts of 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 difference and c e l l / i n t e r f a c e attachment energy were calculated 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. These data are l i s t e d i n Table 5.5 (as before, the intensive variable AE f c i i s actually tabulated). The amount of ester bound per unit surface area of the c e l l i n each phase was calculated 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 (Fig. 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 table, although the data from the lower phase were very s i m i l a r , the values being about 10% smaller. The contact angle decreases as the ester concentration increases. 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 interaction energy. The c e l l surface free energy difference i s essen t i a l l y zero i n the absence of ester, 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 ESTER3 E s t e r 0 Contact Cone. (JJM) Angle (°) Ay _ AEti (erg/cm 2)xl0 5 P a r t i t i o n (%) Bound Ester/10 1 2 molecules/cm 2) c 0 92+3 2+3 68+6 0.5+1 0 0 90 -0.3 63 3.5 0 0.2 86 -A.5 55 10.5 0.7 0.3 80 -11 A3.5 13 1.1 O.A 78.5 -13 A l 16.5 1.3 0.5 76 -15.5 37 19 1.5 0.6 6A.5 -27 21 2A.5 1.75 0.7 62 -30 18 29 2.0 0.8 60.2 -31.7 16.1 3A.5 2.2 1.0 A7.5+3 -A3+2 6.5+: 1.5 51.5+3 2.5+0.3 1.2 AA.5 -A5.5 5 70 2.8 3System composition: (5,A)10,130,0 °bulk concentration cMeasured i n the upper phase. -179-The dependence of c e l l surface free energy difference, Ay , on the ester concentration i s shown i n Fig. 5.9, along with some theoretical curves calculated 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 varied within the l i m i t s of the data i n Fig. 5.1a for the 'in 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 to 3.28 as the ester concentration was increased from 0 to 1.2 (bulk concentration for equal volumes of each phase). iv) Discussion Studies of the effect 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 effect 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 dramatically from 2% to 100% over a concentration range of 0 to 2 J JM. Therefore the ester must exert i t s effect on c e l l p a r t i t i o n primarily by i t s interaction with the c e l l surface. This made i t suitable for a detailed study of the the effect of an a f f i n i t y ligand on the c e l l surface free energy difference. To study the interaction of the ligand with the c e l l surface, several types of binding studies were carried out. The binding i s more than three times as strong from the lower phase as from the upper phase (Fig 5.4a), which i s consistent with the general rule that binding i s increased from a poorer solvent (Adamson, 1976). For t h i s type of effect to occur, the bound -180-B U L K E S T E R C O N C E N T R A T I O N (JJM) Figure 5.9 Effect of Ester on C e l l Surface Free Energy. Comparison with Theory. Experimental (*), th e o r e t i c a l ( ) calculated from [3.60] with n=10.9xl0 6 molecules per c e l l , kt=2.82 uM, kD=0;898 JJM. given on the figure. Ester i s expressed as bulk concentration for an equivolume system. -18 im-material must be at least p a r t i a l l y removed from contact with the solvent, otherwise there i s no driving force for such an e f f e c t . The implications of t h i s w i l l be clearer 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 ester was studied by removing the ester from the c e l l s by a series of washes. Figure 5.6b summarizes several experiments. The amount of material removed per wash varies with the wash medium. More i s removed by the top phase than the bottom phase since the former i s a better solvent for the ester. The lower phase excludes PEG and the ester, so tends to remove l i t t l e . The top phase removes ester better than the buffer. This i s probably due to the high PEG concentration. At any point on the isotherm, at equilibrium i n the presence of the polymer i n solution, the rates of binding and desorption must just balance each other. However polymer desorption often reaches equilibrium extremely slowly when the free polymer concentration i s lowered, due to the fact that i t attaches to the surface at several points (Silberberg, 1962). This multi-point 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 solution which competes for the attachment s i t e s . Such non-equilibrium desorption behaviour i s indicated by the non-linear semi-log wash o f f curves for both PEG and the ester i n the absence of the top phase. The implication 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 multiple attachments, and that the high concentration of PEG i n the upper phase competes for these attachment s i t e s . Similar slow desorption behaviour was also seen for dextran and fibrinogen 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 puzzling, since the binding i s not ioni c i n nature. This may be due to alterations 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 ester. Desorption of ester i n the upper phase seems to reach the same equilibrium as the binding, as indicated by the s i m i l a r i t y of the two isotherms i n Fig. 5.7. This i s not the case for the lower phase. The binding of dextran T500, PEG 8000 and the ester are compared i n Fig. 5.5. I t can be seen that the ester binding i s three to four orders of magnitude stronger than the binding of either of the phase polymers. However the amount of material bound at, 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 figure also 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 for PEG. In addition the nature, and perhaps the location, of the ester and PEG 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 binding appears not to.saturate, or at least does so at a much higher surface concentration than does the ester. This indicates 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), indicating 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 larger fraction of PEG i s removed per wash (Fig. 5.6), again indicating a -183-greater a c c e s s i b i l i t y to the phase system. The ligand binding i n both phases showed the c l a s s i c Langmuir isotherm shape (Fig. 5.4a). The ester binding data were therefore analysed by Scatchard plots (Fig. 5.8). Plots for both the phases are quite l i n e a r , although there i s more scatter for 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 interpretation 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 gyration for PEG 6000 of 25 A (Cabane, 1985). The binding energies were estimated from these plots as -16.6+0.3 and -17.9+0.3 kT/molecule i n the upper and lower phases respectively. The free energy of transfer of palmitic 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 carboxylic acid head group (Tanford, 1976). These figures are comparable, and support the proposed mechanism of PEG-palmitate action (Eriksson and Albertsson, 1978, Van A l s t i n e , 1984), whereby the palmitate t a i l intercalates into the l i p i d b i l a y e r - a hydrophobic interaction. The low ligand 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 ligand (about one t h i r d of the saturation value at 100% p a r t i t i o n , estimated from Fig. 5.2b and the data i n Table 5.5), suggest that the theory developed i n Chapter 3D can be applied to t h i s data. Another estimate of the binding energy can be obtained without using -184-Scatchard plots 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 solution and the l i p i d b i l a y e r , which i s treated as having the cha r a c t e r i s t i c s of a two dimensional hydrocarbon solvent. Then we have (Tanford, 1976): AG 0 = kT In X1/"Xb [5.4] where X^, X^ are the mole fraction concentrations of ligand i n solution and i n the bilayer respectively. 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 Gier, 1974) as g 5 xlO molecules per c e l l . The r a t i o of mole fractions 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 giving an estimate of the binding energy as -12.5 kT/molecule, which i s somewhat smaller than that obtained from the Scatchard plots. However the difference 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, for either method of analysis, providing the number of binding s i t e s i s the same in 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 difference, to be made. Binding experiments were also done i n complete phase systems i n order to more closely duplicate 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 close i n each phase, indicating the i n t e r n a l consistency of the measurements (Fig 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 additional complication i s that at low ester concentrations the c e l l s a l l accumulate-at the interface. The binding energy i n the lower phase i s the same i n the two experiments, indicating that there i s no difference i n binding when the c e l l s are either added to the lower phase d i r e c t l y , or added f i r s t to the upper phase then transferred 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 results to those measured i n separate experiments (Fig 5.1a). The dependence of the c e l l surface energy difference on the number of ester molecules bound was obtained by contact angle measurements i n the presence of various ester concentrations (Table 5.5). The c e l l surface free energy difference, Ay decreases by -0.06 kT/molecule bound, which i s extremely small compared with the ester binding energies or the energy of ester transfer between the phases. A test of [3.60] was made by substituting i n the values of n, k^, k D obtained from the 'in phase' binding experiments and determining Ay as a function of concentration. The rate of increase of Ay given by [3.60] was very sensitive to 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 (Fig. 5.9), since t h i s equation was derived from [3.56] which contains the differences i n three large, s i m i l a r l y sized terms. I t was not possible to f i t the data exactly with one value, which probably r e f l e c t s the fact 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 to give the best f i t , by increasing i t s l i g h t l y from 3.145 to 3.16 over the range 0 to 2 JJM. These values lay within the range -186-determined experimentally i n Fig. 5.1. I f the binding data from the separated phases were used instead, 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 quantitative agreement with the theory of the effect of an a f f i n i t y ligand on the c e l l surface free energy difference 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 effects of the ester and PEG. Because the ester binding energy i s high, i t has an appreciable effect on the c e l l surface free energy, even though the ester may only contribute a fraction of the t o t a l PEG bound to the c e l l surface (Fig. 5.5). The model also explains the small increase i n c e l l surface free energy per bound ester molecule. The physical basis for t h i s i s that the ligand i s p a r t i a l l y hidden from the phase system, an interpretation consistent with the difference i n binding energies i n each phase. This can be seen more c l e a r l y with reference to Fig. 3.2, and the l i m i t i n g cases discussed i n Chapter Three. In the extreme case a ligand not exposed to the phase system at a l l would have no e f f e c t , and the difference i n binding energies would be just equal to the energy of ligand transfer between the phases, which varies from -0.69 to -1.21 kT i n the range 0 to 1 jjm (Curve A, Fig. 3.4b). By contrast, a bound ligand that i s completely exposed to the phases would have the same binding energy i n both phases. The actual data for the ester shows that the type of binding i s closer to the f i r s t case. The idea of a hidden ligand again invokes the concept of exclusion of the phase polymers which was encountered i n section 4D. Additional support for t h i s effect comes from the difference i n PEG and ester binding behavior. The model of ester binding by insertion -187-of the palmitate t a i l group into the l i p i d bilayer 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 well be p a r t i a l l y inaccessible i f the glycocalyx were 70 A thick (Levine et a l . , 1983). At the same time the binding energy argument and differences i n wash off 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 large as PEG, i t would also be expected to bind to the outer regions. Of course the analysis of the model of a f f i n i t y ligand effects assumes that the ligand binding i s at equilibrium i n both phases, and of the Langmuir type. The binding energy estimates from the Scatchard plots also use t h i s assumption. While these plots 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 equilibrium under a l l conditions. This could affect 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 effects into t h i s theory. The effect of ester on Ay has some implications for measuring c r i t i c a l tensions i n phase systems. Extrapolating to higher ester concentration (Fig. 5.9) i t can be seen that Ay would become numerically equal to the 3 12 tension, Y T B (6.3 xlO dynes/cm) at around 2 JJM (3.5 xlO 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 saturation value of 6 xlO 2 t molecules/cm , so either 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 l a t t e r s i t u a t i o n implies that Y B i s not equal to 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 state of Neumann et a l . (1974) do not appear to be applicable to these two phase systems. To summarize, a number of interesting conclusions can be drawn from the results i n t h i s chapter. At low concentrations, the ester has l i t t l e effect on the phase system, but increases c e l l p a r t i t i o n dramatically. 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 difference i s decreased by the bound ester, but the effect per molecule i s quite small. This i s attributed to exclusion of the phases from the glycocalyx, which e f f e c t i v e l y hides the bound ester. This hypothesis i s consistent with the fact that the difference i n binding energies i n each phase i s s i m i l a r to the energy of ester transfer between the phases. Desorption studies showed that bound PEG i s more accessible to the upper phase than i s the ester, which again i s consistent with the exclusion hypothesis. The ester did not appear to reach desorption equilibrium 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 equilibrium during p a r t i t i o n , since the amount of ester bound i n both phases at equilibrium i s s i m i l a r . The amount the c e l l surface free energy difference 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 ester. The theory predicts that the binding energy of the ligand i s important, and thus that small changes -189-in the amounts of PEG and dextran bound to the surface would have comparatively l i t t l e effect since these polymers bind very weakly. However a more extensive test of the theory with t h i s ligand i s not possible for 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 micelles form at concentrations greater than 10 J J M . Therefore i t i s not possible to get a good estimate of the energy of ester transfer between the phases, a quantity required to test the theory. This also means that the high ester concentration range i s experimentally inaccessible. As a consequence i t i s not possible to test the prediction that the effect of ester should reach a maximum and then decrease to a plateau,value (Fig. 3.3). However i t i s possible that t h i s maximum (plus the effects of micelle formation) i s responsible for the plateau i n c e l l p a r t i t i o n at less than 100% seen by Van Alstine (1984) i n many systems containing various PEG-alkyl esters. -190-Chapter Six. Factors Determining C e l l P a r t i t i o n True science however, cannot exist without an aesthetic appreciation of the objects examined- Mikhail 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 relationship between the phase system properties, the c e l l surface properties and the r e l a t i v e a f f i n i t y of the c e l l for either phase? These effects are expressed thermodynamically i n a single quantity, the c e l l surface free energy difference, Ay . This quantity can be determined at equilibrium 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 effect of the other thermodynamic quantity involved i n measuring Ay , namely the i n t e r f a c i a l tension between the phases, i s studied. Then the relationship of tension and Ay to p a r t i t i o n i s investigated. 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 section 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 of 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 effects 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 either 10,0,110 or 110,0,0 buffer with increasing polymer concentrations were made up. The tensions of several systems were measured (Table 4.1), and the rest calculated from t h e i r t i e l i n e lengths using the relations given i n the Table. Increasing the tension reduces the c e l l p a r t i t i o n dramatically (Fig. 6.1). Log K decreases l i n e a r l y with increasing tension down to about K = 0.2, and then decreases less rapidly. Systems with 10 and 110 mM phosphate give essentially'the same re 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 also 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 to incomplete s e t t l i n g of cell/droplet aggregates from the upper phase. This was checked by par t i t i o n i n g c e l l s i n two systems containing 10,130,0 buffer, which have simi l a r tensions and v i s c o s i t i e s , but less positive potentials. These control systems give much lower p a r t i t i o n s , indicating 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 s e t t l i n g . Data for the microorganism Acholeplasma l a i d l a w i , of around 1 jjm diameter, taken from Van Alstine (198A), are shown for comparison. i i ) Polymer Composition and Contact Angle The effect of polymer concentration on the c e l l surface free energy difference was also examined by making contact angle measurements on c e l l s i n the 10,0,110 buffer systems of section i ) . The resu 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 partitioned 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 interaction energy, k E ^ / i r a ^ increases at a proportionally greater rate than the tension. The c e l l surface free energy difference, A y , does not have a simple dependence on the tension, but appears to show two small maxima over t h i s range. TABLE 6.1 ERYTHROCYTE PARTITION AND CONTACT ANGLE. EFFECT OF TENSION3 System Contact Tension AE^i P a r t i t i o n V t h ~ 1 / 2 Angle (°) — (erg/cm 2)x!0 A — (%) (cm/erg 1/ 2) (5,3.8) 37+3 42 -33.5+2 1.7+0.5 89.5+5 15.4+0.2 (5,4) . 52+4 63+2 -39 9.2 73 12.6 (6,4) 69 102 -37 42.0 16.5 9.9 (7,4) 70 145 -49.5 63 8.5 8.3 (7,4.4) 78 213+5 -43 135+15 3+1 6.9+0.2 3A11 systems contained 10,0,110 buffer Schurch et 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 to estimate surface free energies (Zisman, 1964, G i r i f a l c o and Good, 1957), could be used i n a sim i l a r fashion i n phase systems. A plot of cos 6 against the reciprocal square root of the tension (A Good-Girifalco plot) was li n e a r (r=0.990) (Fig. 6.2). An extrapolation of t h i s plot to cos 6= 1 gives an estimate of -3 2 3.0+0.4 xlO ergs/cm for the c r i t i c a l spreading tension, and hence for the cell/lower phase interface free energy. The data of Schurch et a l . (1981) for very s i m i l a r systems are also plotted on Fig. 6.2 for comparison, and have slopes of the opposite sign, giving an estimate for the cell/upper  phase free energy, with a value four times smaller. -194-Figure 6.2 Good-Girifalco Plots for 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 Cell/Interface Interactions The theory of 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, relates 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 interface into the top phase, A E ^ A E t i = a p T T t b ( 1 " c o s e ) 2 In K = - AE t i/kT [1.22] 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 for the normalized attachment energies were taken from Tables 4.8, 5.5 and 6.1, and a radius of 3.5 pm used for the c e l l . The p a r t i t i o n i n these three sets of curves was manipulated by varying either the pot e n t i a l , the tension, or the ligand concentration. In a l l cases the ordinate intercepts are around 10 to 15. The i n i t i a l slopes are si m i l a r and give, using [1.22], values of around 2x10^ kT/cell for the ch a r a c t e r i s t i c energy (E c) of p a r t i t i o n . The slopes decrease i n a l l three 4 5 curves, to give around 4x10 and 2x10 kT/cell respectively for E c > Because of the experimental scatter, the plot for the a f f i n i t y ligand could perhaps be interpreted as being l i n e a r (r=0.960). The data from Fig. 6.3 were also expressed as percent p a r t i t i o n as a function of the minimum force required to remove a c e l l from a plane interface, estimated from [A4] of Appendix A, and t h i s i s shown i n Fig. 6.16. In a l l three cases the plots resemble step functions, the one for the tension showing a more gradual -196-0. 01 0 A E t | x l 0 9 (ERGS) Figure 6.3 Dependence of Erythrocyte P a r t i t i o n Coefficient on the Cell/Interface Interaction Energy. Data taken from Tables 4.8, 5.5 and 6.1, where the potential (+), the phase composition (tension) (G), or ester concentration (*) were varied. -197-0 5 10 15 DETACHMENT FORCE (10" 6 DYNES) Figure 6.4 Dependence of Percent Erythrocyte P a r t i t i o n on the Detachment Force. The minimum force necessary to detach a c e l l from a plane interface was calculated from the data i n Tables 4.8, 5.5 and 6.1 using [A4]. Tension (o), potential (*), or ester concentration (+) was varied. -198-decrease i n p a r t i t i o n as the force i s increased. i v ) Discussion Since the p a r t i t i o n decreases with increasing tension (Fig 6.1), the prediction of the Br^nsted equation (in the form on [1.31]) of the role 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 predicts 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). Of course when the polymer compositions are altered, v i r t u a l l y every other property of the phase system i s also altered, indicating here that other factors are involved i n p a r t i t i o n . In addition t h i s equation predicts that p a r t i t i o n to the interface should increase exponentially with area, and that the dependence of p a r t i t i o n on the tension should increase rapidly with area. Figure 6.1 shows that these predictions 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 carried out on solutes over an enormous size range, where i t i s expected that the size of the Ay terms would not vary by more than an order of magnitude. These observations indicate that the p a r t i t i o n i s actually 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 parttion 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 Br^nsted equation for describing c e l l p a r t i t i o n (vide i n f r a ) . -199-There i s a s t r i k i n g difference i n the Good-Girifalco plots seen i n Fig. 6.2 for 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 directions i n the chloride 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 s o r b i t o l , the results of Chapter Four, section D indicate that the potential contributes s i g n i f i c a n t l y to AY . Since the potential increases with t i e l i n e length (and therefore with tension), then the weak dependence of AY on t ^ must be due to an increasingly positive contribution to AY from other terms, such as polymer interactions. This emphasises the point made i n the Introduction that AY i s a resultant 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 results i n Fig. 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 difference i n estimates for the c e l l surface free energy, Y*3 obtained from the c r i t i c a l spreading tension obtained i n the different systems show that t h i s quantity i s a r e l a t i v e one, which applies only to the surface i n the phase that wets i t at that c r i t i c a l tension. Thus the l i n e a r i t y of such Good-Girifalco plots need indicate only that yt and Y b vary i n an orderly fashion with Y t b, rather than i n d i c a t i n g that Y t = 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 for phase systems, and i s i n fact inconsistent with the effects 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 quantities, 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 interface, f . Either 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 distributed. The relationships between the c e l l p a r t i t i o n and the c e l l interface attachment energy, A E ^ , and the detachment force, f are shown i n Figs. 6.3 and 6.A respectively. Now i n the Br0nsted theory the p a r t i t i o n i s determined solely by ^ E t i ' w n * c n * s 1 i n e a I ' l y related to the log 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 relationship between p a r t i t i o n and the attachment energy i s not s t r i c t l y confirmed for erythrocytes. The work of Gerson (Gerson, 1980, Gerson and A k i t , 1980) was not a satisfactory test of the Brc/>nsted r e l a t i o n for reasons given i n the Introduction. The slopes of the plots i n Fig. 6.3, however, are four to f i v e orders of magnitude smaller than predicted from [1.22], giving 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 k T / c e l l . I t i s clear that c e l l p a r t i t i o n i s not a thermodynamic equilibrium 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 interface. 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, re f e r r i n g to the time dependence of p a r t i t i o n (eg. Raymond and Fisher, 1981; Fisher and Walter, 1984; see section l C . i v ) . 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 for c e l l p a r t i t i o n extended from about twenty to f i f t y minutes after mixing the phases, so the p a r t i t i o n was ess 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 i n d e f i n i t e l y . The curvature of the plots i n Fig. 6.3 could be interpreted as changes i n the chara c t e r i s t i c energy of p a r t i t i o n , as the appropriate parameter of the system, such as the tension or potential i s varied. Certainly as the tension of the system i s increased by increasing the polymer concentrations, almost every other property of the system i s being altered, so the non-linearity of t h i s plot i s not surprising. Alternatively 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 of even the exponential form of the p a r t i t i o n equations. The exponential form ari s e s , however, from quite general considerations of the stochastic 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 par 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 plausible alternative. P a r t i t i o n may also be viewed as a mechanical, force driven process: c e l l s are attached to 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 res u l t i n continually varying drag forces on the c e l l s . These forces can pot e n t i a l l y remove c e l l s from the interface, 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 a ) i s thus important i n determining -202-whether c e l l s can be removed from the interface, i e . whether the p a r t i t i o n i s greater than zero. The minimum force necessary to detach a spherical p a r t i c l e from a plane interface, f , can be estimated from the contact angle and equation [A3]. The partition/force curves i n Fig. 6.4 have the same general form, a type of step function, the p a r t i t i o n decreasing r e l a t i v e l y quickly as f i s increased. However assignment of a physical interpretation to a cha r a c t e r i s t i c force obtained from the curves i n the th 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 to the same size 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 Fig. 6.4 would be perfectly sharp step functions. There would be a c r i t i c a l retaining 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 th 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 of as representing the ' d i s p e r s i t y 1 , or randomness of the p a r t i t i o n process. The curve where the tension i s varied has the greatest d i s p e r s i t y , since not only i s the necessary detachment force (f ) being altered, but the separation of the phases, and consequently the forces applied to the c e l l s are also being altered as the polymer concentrations are increased. -203-The force view also may make i t easier to explain the weak dependence of p a r t i c l e p a r t i t i o n on area. Such behaviour could be explained by the plausible assumption that the forces experienced by the p a r t i c l e s which tend to remove them from the interface decrease as t h e i r area decreases, u n t i l ultimately they could be distributed by d i f f u s i o n alone. To conclude t h i s section, the results show that erythrocyte p a r t i t i o n i s not a thermodynamic equilibrium process. However, for a system of given polymer composition, under i d e n t i c a l conditions for 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 c e l l / i n t e r f a c e attachment energy, a thermodynamic quantity related to the tension and the r e l a t i v e a f f i n i t y of the c e l l for each phase. As t h i s quantity (or a related quantity, the minimum force of detachment) i s decreased, by a l t e r i n g the potential or adding an a f f i n i t y ligand for example, the p a r t i t i o n into 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 differences i n the cell/phase system interaction. In cases where the system parameters are held constant, differences i n p a r t i t i o n therefore r e f l e c t differences i n c e l l surface properties. P a r t i t i o n has a weak dependence on the c e l l area, shape (hypertonic swelling 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 results of the previous section indicate that c e l l s are not distributed by thermal motion, i n the manner of solutes, and that the p a r t i t i o n i s not completely characterised by Y t b and AY. Other properties of the system are thus important. The effects of two of these, volume r a t i o and phase density difference, were examined. a) Phase Volume Ratio The effect of changing the phase volume r a t i o i s shown i n Fig. 6.5a. Four (5,4)10,130,0 systems were made up with varying amounts of ester, so as to give a range of c e l l p a r t i t i o n s from 20 to 90%. P a r t i t i o n experiments were performed with either the top or t o t a l volumes held constant, with es 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 effect 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 difference between the phases, and the t h i r d system has a more dense dextran r i c h phase. The effect -205-of ester 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 Fig. 6.5b. In the absence of ester, the c e l l s p a r t i t i o n mostly to the interface, but the p a r t i t i o n into the F i c o l l r i c h phase increases with ester 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 less sensitive to ester concentration than i n PEG/dextran systems. c) Visual Description of P a r t i t i o n Other workers (Albertsson, 1971, ppl34-6; Van Al 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 early on i n the separation of the phases after 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 of possible 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 visual and stereomicroscopic examination of phase systems during p a r t i t i o n . Figures 6.6 and 6.7 show the appearance of c e l l p a r t i t i o n i n isopycnic Dx/PEG/Fi systems. The appearance of c e l l p a r t i t i o n i n Dx/PEG systems was si m i l a r , but because of the rapid flow of the phases due to the density difference, they could not e a s i l y be photographed. The rate of phase separation by coalescence i s f a i r l y rapid, the phases being completely separated after 15 min (Fig. 6.6d). At one minute the. difference between high and low p a r t i t i o n i s already evident, the interface 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 of c e l l s there, compared to the right hand one (%P = 100). This i s more apparent i n the magnified view (Fig. 6.7). Comparing photos a) (%P = 0) and b) (%P = 100) the difference between the high and low -206-2 0 0 . 2 0 . 4 0 . 6 0 . 8 1 r FRACTIONAL TOP PHASE VOLUME < CL LU ESTER CONCENTRATION (juM) Figure 6.5 Effect of Phase Volume Ratio and Density Difference on Erythrocyte P a r t i t i o n , a) Effect 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 ester. Total volume 2ml (o), top phase volume 1ml (*), top phase volume 2ml (+). b) Effect of density difference. (7,0,12), with more dense F i c o l l phase,^ = 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 partitioned into the F i c o l l r i c h phase. A l l systems contained 10,130,0 buffer. -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 Fig. 6.5b, with from l e f t to right: 0,2,3,8 JJM ester. Systems were mixed by inversion 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 in (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) after mixing. Magnification x50. -209-p a r t i t i o n i n g systems i s apparent only 45 sec after mixing, and i s s t r i k i n g after 3 min of 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 refr a c t i v e index difference between the phases and the density of the emulsion, but are apparent from the mottled appearance. i i ) Discussion and Proposal of a Mechanism for 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 di s t r i b u t e large (=>1 pm dia.) c e l l s between the interface and the phases, the question arises as to what process does p a r t i t i o n the c e l l s . 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 section B i i i above. Before considering t h i s question further, i t w i l l be helpful 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 stochastic process with a cha r a c t e r i s t i c energy (E c) ranging from 2 to 20 xlO k T / c e l l . P a r t i t i o n of erythrocytes i s independent of c e l l concentration at least i n the range 10 6-10 8 cells/ml (Van Al 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 insensitive to the density difference 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 of the c e l l for the upper phase i s increased, and as i t s a f f i n i t y for the interface i s decreased C e l l p a r t i t i o n i s increased as the height of 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 early on i n phase separation (within a minute) Studying the mechanism of 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 of 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 possible to propose several d i s t i n c t p a r t i t i o n mechanisms, not necessarily mutually exclusive. By a consideration of qu a l i t a t i v e and semi-quantitative arguments (Appendix B), the a b i l i t y of these mechanisms to account for the observed features of c e l l p a r t i t i o n can be discussed. Three types of arguments can be considered: energy arguments, force arguments and qu a l i t a t i v e explanations of the features l i s t e d above. In addition 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 section 1A). Some of the results obtained i n the theory of 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 applicable to 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 of parameters such as density difference, 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 for C e l l P a r t i t i o n The p r i n c i p a l model of 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 fine emulsion -211-i s formed, consisting of a large number of small drops of 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 larger, the area decreasing u n t i l i t i s f i n a l l y equal to the tube crossectional area. This decrease i n area results i n a dissipation of the energy associated with the interface. In t h i s model the relevant forces arise 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 transitory, being quickly 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 large compared to the gra v i t a t i o n a l forces i s evident from the small Eotvos number (Table 6.2). This table also indicates that for small drops viscous and i n e r t i a l forces are also small. For larger 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 DROPLETS3 Dimensionless Number Ratio of Forces Formula Drop dia., 1 (pm) 10 100 1000 Eotvos (Eo) Reynolds (Re) Weber (We) Cap i l l a r y (Ca) gravity/tension i n e r t i a l / v i s c o u s i n e r t i a l / t e n s i o n viscous/tension l 2 Apg/y 1 Apu/ri 1 Apt^/Y Tiu/Y 6 x l 0 " 3 1x10-6 6 x l 0 " 9 6 x l 0 " 3 0.65 65 1x10-2 l x l O " 2 6 x l 0 - 6 6 x l 0 ~ 3 6 x l 0 " 2 0.6 3Data for a lower phase drop i n the upper phase of a (5,4) system: g = 980.9cm/s2, TI=4 cpoise, Y =6xl0 _ 3 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 velo c i t y of one drop diameter per second was used. -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 7 T a 2(2-2 2 / 3) = 5.18a2 [6.2] The energy released on the coalescence of two drops, 0.01 and 0.1 mm dia. 5 7 i s 2x10 and 2x10 kT respectively, which i s considerably larger than the corresponding energies available from sedimentation (Appendix B), and larger than E c for 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 . I t i s also more l i k e l y to dominate the p a r t i t i o n process early on i n the separation, where coalescence i s rapid, 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 state flows, but s t a r t suddenly, and are quickly damped, so i n e r t i a l effects may also be important. Probably the strongest direct evidence for the importance of coalescence i s the independence of p a r t i t i o n from the density difference. In the isopycnic system coalescence phenomena must be responsible for p a r t i t i o n , since no s e t t l i n g occurs. By inference, i t i s also 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 different tensions, v i s c o s i t i e s and densities, such as the Dx/PEG systems. However t h i s would require the ad hoc introduction of a second mechanism. In addition 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 discussion 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 of the phases was ruled out because of the rep 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 for 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 also ruled out because the i n i t i a l drop separation distance i s of the same order as the c e l l s i z e . Sedimentation driven processes were considered unimportant except as a possible secondary effect 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 available, and the small forces generated. In par t i c u l a r the capping process was ruled out because of the independence of 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 partly on energy arguments, but mainly on the fact that c e l l p a r t i t i o n was essenti a l l y unchanged by the presence or absence of s e t t l i n g . c) Consistency of 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 helpful to consider a more detailed q u a l i t a t i v e description 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 description: the measured p a r t i t i o n i s the percentage of c e l l s i n the upper phase, as determined by counting a sample drawn at a certain time from the upper bulk phase (which may contain s i g n i f i c a n t amounts of lower phase, depending on the time of sampling). The true p a r t i t i o n i s defined as the percentage of c e l l s not attached to the interface i n any form ( i e . the bulk interface or drops). The plateau p a r t i t i o n i s the percentage of c e l l s i n the upper bulk phase after a time long enough for a plane interface between the bulk phases to form. When the phase system i s shaken up a very fine emulsion of 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 size would t y p i c a l l y be less than the c e l l diameter, ie. less than 5 JM. For a one to one volume r a t i o , the average distance between drops would be of the order of 0.3 or less of the drop radius, forming an extremely close packed emulsion. The c e l l s would a l l be i n contact with the interface. Because of the close packing, Brownian motion and residual motion from the mixing cause c o l l i s i o n s and rapid coalescence of the drops. L i t t l e s e t t l i n g occurs at th i s stage because of the small size of the drops. Coalescence results i n a dissipation of energy, which has two effects. The c e l l s are distributed between one of the phases and the interface. In addition the f l u i d motions due to drop fusion, combined with the random arrangement of 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 diffuse ( 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 primarily by the size of the c e l l / i n t e r f a c e attachment energy, A E ^ o r attachment -215-force, f . Because of the random d i s t r i b u t i o n of c e l l s and drops, s t a t i s t i c a l l y 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 interface, 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 force, 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 difference 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 interface give the drops more visua l d e f i n i t i o n (See Fig. 6.7). As the drops increase i n size 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 rate as different size drops s e t t l e at different rates. 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 transporting them to the bulk interface. As separation continues, s e t t l i n g of the larger drops can also shear c e l l s o f f the interface, thus increasing the true p a r t i t i o n somewhat. The low tensions and large drop sizes (E , C 0 ^ l ) re s u l t i n the formation of millimeter long o a streams of each phase, flowing past each other at v e l o c i t i e s of 0.001 to 0.1 mm/s. Eventually most of the phases have s e t t l e d . Numerous smaller drops remain i n both phases, especially 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 resultant 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 es 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 in 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 non-specific manner. The measured p a r t i t i o n at t h i s time, however, w i l l more closely 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 acti v e l y being distributed, 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 interface, and clear the upper phase of c e l l s . 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 interface i n the e a r l i e r stages by coalescence, and were therefore not carried to the interface 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 closely 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 rate 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 close to one however, coalescence continues at a surprisingly rapid rate u n t i l the bulk phase that better wets the container completely surrounds the other phase (Fig. 6.6). Coalescence continues even as the drops become large since they remain close packed ( o i 0 . 3 r a d i i apart) irrespective of the change i n scale. At the same time both the energy dissipation per fusion, ([6.2]) and the energy expended to move a drop a distance of one radius at constant veloc 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 scale invariant. 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 Fisher, 1980), i s probably a result 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 further 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 stochastic process. In addition the independence of p a r t i t i o n on c e l l concentration and area i s ea s i l y rationalized 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 rate by aggregating them (Raymond, 1981). This would decrease the p a r t i t i o n . The capacity of the interface could also 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 interface as coalescence decreases the available surface area, increasing the p a r t i t i o n . The effects 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 attributed to changes i n the r e l a t i v e rates 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 quickly i n the early rapid coalescing stage of separation, leaving less droplets to s e t t l e slowly and clear the upper phase of c e l l s . The p a r t i t i o n i s thus higher. Altering the volume r a t i o has two effects. The i n i t i a l coalescence rate drops sharply as the r a t i o i s made smaller or -218-larger than one (Van Alstine 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 altered. As expected the f i r s t effect decreases the p a r t i t i o n , since the chance of a c e l l being transported to the bulk interface by a drop before encountering s u f f i c i e n t coalescence-generated force to remove i t increases as the coalescence rate decreases. This effect occurs irrespective of whether the height of the upper phase i s altered on not, the p a r t i t i o n being maximum at r v= 1 for both constant top phase and t o t a l phase volumes (Fig. 6.b). d) Tests of the Model One test of the coalescence model has already been made by eliminating s e t t l i n g effects using an isopycnic system. However other c r i t i c a l tests are needed. Essentially these would involve an investigation of the correlation of p a r t i t i o n with the rate and energy dissipation 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 ( C a r r o l l , 1976): "...and i t i s s t i l l very true to say that the problem remains one of the betes noires of c o l l o i d chemistry. This quandary arises i n part from the d i f f i c u l t y of studying any of the various factors to the exclusion of the others i n r e a l systems..." Nevertheless i t i s clear that coalescence depends on the drop size d i s t r i b u t i o n , the drop concentration, the density difference, the i n t e r f a c i a l tension, the v i s c o s i t y of both phases, and any interdrop forces -219-that may e x i s t . The experiment i n which the volume r a t i o was altered was a preliminary investigation of the effect of drop concentration, the results of which were consistent with t h i s hypothesis, i e . that coalescence, and hence p a r t i t i o n , decreases with drop concentration. Continuous flow apparatus (eg. Sutherland and Ito, 1980) may permit steady state conditions to be investigated where the dispersity and concentration of drops could ce controlled better. Direct examination of coalescing systems to see whether fusing drops can remove c e l l s from the interface 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 well enough i n the early stages of separation, and i n demonstrating that t h i s mechanism i s not only possible, 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 difference i s e f f e c t i v e l y zero only at a number of defined compositions. However zero gravity experiments (Brooks et a l . , 1984; Van Alstine et a l . , 1984) are currently underway i n which these two parameters can be varied independently i n the absence of s e t t l i n g e f f e c t s . A prediction of t h i s hypothesis i s that for constant c e l l interface 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 dissipation on coalescence would be greater. -220-Chapter Seven. General Discussion and Summary Connect, always connect- Albert Einstein A. Overview This thesis i s an attempt to apply a physical chemical approach to a complex c e l l separation method i n order to better understand the factors involved. The problem naturally divides into two parts, equilibrium 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 relationship to the c e l l and system properties. Here several well established thermodynamic principles can be applied to the analysis. The power of thermodynamic methods i s that they deal with the relationship between general quantities, such as free energy and i n t e r f a c i a l tension, etc. without requiring knowledge of what pa r t i c u l a r factors and mechanism give r i s e to these quantities. This i s valuable when studying a complex process such as p a r t i t i o n . At equilibrium the free energy of the system must be at a minimum, and the chemical potential of each component must be the same i n both phases. Using the equality of chemical potentials, 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 potential difference 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 quantities, the conditions under which these potentials can be measured i s also derived from theoretical considerations, and examined experimentally i n -221-section AB-C. I t i s shown that only differences or changes i n the potential 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 potentials i n two phase systems. The effects of phase composition changes can be looked at from another view point: with respect to the s a l t ions, the 'solvent' i s the water plus both polymers, since these determine the ion standard state chemical potentials. Hence the 'solvents', which are the two phases, are not fixed, 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 potential 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 effect on the c e l l s , depend only on the composition, not the concentration, of the buffer. In section 3D the concept of a thermodynamic state function i s used to derive a theory for the effect of an a f f i n i t y ligand on the surface free energy difference 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 solutes, which d i s t r i b u t e between the two phases. These theories also assumed that p a r t i t i o n i s at thermodynamic equilibrium. Neither of these conditions apply to erythrocyte p a r t i t i o n , so a new theory had to be developed. This theory also applies only at constant phase compositions, l i k e that for the potentials. Composition changes not only change the 'solvents' as noted above, but have a large effect 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 interface, t h e i r p a r t i t i o n i s sensitive to the tension, as i s shown i n section 6B. The results of section 5B demonstrate that suitable conditions for the analysis of a f f i n i t y ligand effects on AY can be obtained i n the concentration range where the ligand affects 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 ligand chosen for study, PEG-palmitate, i s effe c t i v e at very low concentrations. Young's equation, which i s a statement of thermodynamic equilibrium at a three phase boundary, i s used to determine the c e l l surface free energy difference by means of contact angle measurements i n sections 4D and 5D. The effect of potential and a f f i n i t y ligand can thus be studied under equilibrium conditions. The variation of the c e l l surface free energy difference with changes i n these two parameters i s surprisingly 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 interpretation i s supported by an argument based on the difference i n ligand binding energies i n the two phases, again using the concept of a thermodynamic state function. This appears to be the f i r s t evidence that exclusion of 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 results indicating exclusion of the phases from the glycocalyx. Phase exclusion complicates the interpretation 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 implies that p a r t i t i o n i n these phase systems may only be sensitive to a small part of the c e l l surface. The depth to which the phases penetrate may also 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 for keeping the phase compositions constant i n physical studies of t h i s type. Changes i n the extent of phase exclusion with composition may also play a role i n the weak dependence of c e l l surface free energy on tension (section 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 bilayer at which the e f f e c t i v e outer surface occurred. They also 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 interface also 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 state to these systems, which i s shown by the results of Boyce (1984) and the results of section 5D, i s not surprising, since i t was developed for 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, also does not apply to these complex systems (section 6B). Again t h i s i s not surprising, 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 successfully since i t deals with the relationship between general thermodynamic quantities, but the equation of state, and c r i t i c a l wetting, -224-which involve 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 difference. 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 started by G i r i f a l c o and Good (1957), and Fowkes (1963), who considered two component systems where dispersive interactions dominated. The work of Chapters Four and Five represents a f i r s t attempt to relate the contact angle i n a complex system to p a r t i c u l a r surface interactions. 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 properties of the phase system are a l l related to some extent, which has to be taken into account when one i s trying 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 solute behaviour often occurs. In single s a l t systems, ion a c t i v i t y c o e f f i c i e n t s were considered when calculating the potential (section 4C). In the mixed s a l t potential 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 indicates 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 close to one. However i n the a f f i n i t y ligand 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 attributed to changes i n the a c t i v i t y c o e f f i c i e n t . The ester also appears to form micelles above 10-20 JJM. Both these factors r e s t r i c t the test of the ligand theory. -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 effect 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 be s i m p l i f i e d by neglecting some of the components. For example i n the study of potentials i n mixed s a l t systems several components are involved i n the buffer equilibrium. 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 . A second example i s i n the ligand study. Binding experiments show that both the phase polymers, as well as the a f f i n i t y ligand, adsorb to the c e l l surface. However the a f f i n i t y ligand theory developed here suggests one s i m p l i f i c a t i o n , since i t predicts that the effect 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 ligand, the i r contribution to changes i n c e l l surface free energy can be neglected, compared to that of the ligand. The results of section 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 equilibrium process- the equilibrium position for a l l c e l l s i s either at the interface or the bottom of the tube. Non-equilibrium effects thus lead to the second question: what determines the c e l l p a r t i t i o n , and how i s i t related to the c e l l ' s r e l a t i v e a f f i n i t y for the two phases? 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 , (lO^-lQ 5 k T / c e l l , section 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 equilibrium thermodynamic effects discussed above are not important. I f the other non thermodynamic factors are held constant, then p a r t i t i o n w i l l be determined -226-by the surface properties of the c e l l , via t h e i r interaction with the system as expressed through the c e l l surface free energy difference. The statement that p a r t i t i o n i s exponentially related to the c e l l surface properties, 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 fact that p a r t i t i o n i s sensitive to the c e l l surface properties. The non-thermodynamic effects i n p a r t i t i o n are a consequence of the large size of the 'solute', which naturally leads to a more mechanical, hydrodynamic view of p a r t i t i o n . In section 6C attention i s focussed on other physico-chemical processes, such as s e t t l i n g and coalescence. The contribution of thermodynamics i n t h i s view i s brought i n through either the energy or the force needed to detach the c e l l from the interface, which i s determined by the contact angle and tension. P a r t i t i o n requires an input of energy, since the c e l l s are not at thermodynamic equilibrium, and t h i s i s achieved by mixing the systems. Energy can now be dissipated broadly i n two ways, by s e t t l i n g , which dissipates gravitational potential energy, and by coalescence, which dissipates i n t e r f a c i a l free energy. By studying isopycnic systems, the f i r s t mode of dissipation i s eliminated, with l i t t l e e ffect on c e l l p a r t i t i o n . This result and a number of other arguments led 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 distributes larger c e l l s such as erythrocytes. However as the p a r t i c l e size 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 dif f u s i o n dominated process p a r t i t i o n would also be at equilibrium. -227-F i n a l l y , i n order to show the relationship between the important physical and chemical aspects of p a r t i t i o n covered i n t h i s thesis, I have viewed c e l l p a r t i t i o n as a network of related properties and processes, which are presented i n the form of a flow chart i n Fig. 7.1. B. Statement of New Results and Suggestions for 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 physical chemical point of view that was used here. Thus much of the work i n t h i s area i s preliminary. Three types of new results were obtained i n t h i s thesis: theoretical r e s u l t s , experimental r e s u l t s , and conclusions based on these with regard to 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 follows: A new theory r e l a t i n g the potential 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 applicable and can be experimentally tested were suggested. Potential 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. Part of t h i s work has been published previously (Brooks et a l . , 1984). A new theory for the effect of an a f f i n i t y ligand on the surface free energy difference 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 difference i n ligand binding energy i n the two phases. The c e l l surface free energy difference as a function of potential and -228-1. Physico-chemical properties of the polymers and other phase system components 2. Surface properties of the c e l l or p a r t i c l e such as charge density 3. Density difference 4. Viscosity 5. Tension 6. Potential difference 7. Interaction of polymers and other components with the c e l l surface Droplet formation, coalescence and s e t t l i n g behaviour Surface free energy relationships 10. Wettability of the c e l l surface-Contact angle formation. 11. Extent and rate of cell/droplet interactions, such as s e t t l i n g , attachment, detachment and droplet fusion 12. Dist 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 interface, 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 ligand concentration was obtained by means of contact angle measurements on single c e l l s . These two parameters had a small effect on t h i s free energy difference which, combined with the results 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 direct experimental evidence of such an effect. This exclusion also suggests a way i n which conformational changes at the c e l l surface could affect 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 equilibrium process, with a c h a r a c t e r i s t i c energy several thousand f o l d times that of thermal energies. A new mechanism by which large p a r t i c l e s are partitioned, by means of the energy dissipated by coalescence of the emulsion droplets formed on mixing the phase systems, was outlined. Some of the p r i n c i p a l directions suggested by t h i s work are outlined here b r i e f l y . Further tests of the theory of potentials, 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 single 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 for b i o l o g i c a l material 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 also be required. An extensive test of the ligand theory could be made using PEG-alkyl esters, since these are available with a variety of head group sizes, and fatty acid t a i l s , and i n addition t h e i r p a r t i t i o n effects have also been studied by other workers (Eriksson and Albertsson, 1978, Van A l s t i n e , 1984). A test with a ligand that had a constant p a r t i t i o n , and that did not form micelles, i n order to investigate the high concentration range would also be valuable. The prediction that a ligand binding to the outer part of the glycocalyx would have a larger effect than one binding to the inner regions could perhaps be tested using PEG modified sugar binding proteins ( i e . l e c t i n s ) . Tests of the effect of both potential 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 important i n v e r i f y i n g the exclusion hypothesis. These studies could be extended by incorporating g l y c o l i p i d s and glycoproteins into the vesicles, i n order to produce model erythrocyte surfaces with more defined properties. 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 difference i n t h e i r binding to the c e l l surface i n each phase could be useful. This may provide a method of probing the a b i l i t y of such molecules to penetrate into the glycocalyx, and provide useful information about the conformation of the glycocalyx. -231-Studies to investigate the role of coalescence i n p a r t i t i o n , by varying the tension, drop concentration, gravity, phase v i s c o s i t i e s , have already been mentioned i n section 6C. C. Summary The p r i n c i p a l result of t h i s thesis i s that i t indicates that physical chemical methods can be used successfully 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 factors are important. I t i s expected that the results 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 material. This thesis dealt with two aspects of c e l l p a r t i t i o n . The f i r s t was the role of e l e c t r o s t a t i c and a f f i n i t y ligand effects i n determining the r e l a t i v e a f f i n i t y of a c e l l for each phase. The relationship between s a l t p a r t i t i o n and potential was investigated. Phosphate and sulphate s a l t s produce potential differences between the phases which are several m i l l i v o l t s more positive than chloride s a l t s . These potentials arise due to the unequal a f f i n i t y of the cation and anion for each phase, as Albertsson (1971) f i r s t suggested. A thermodynamic treatment was derived to relate the potentials and s a l t p a r t i t i o n s . This agreed well with experimental data for single and mixed s a l t systems. Theoretical considerations showed that only differences i n potentials between two systems can be measured, subject to the condition that the difference i n -232-standard state chemical potential between the phases i n both systems i s the same for any ion. In practice t h i s means comparing systems with the same phase compositions, or at least with the same t i e l i n e length. I t i s also suggested that t h i s should be a general condition s a t i s f i e d i n any si m i l a r physico-chemical study of two phase systems. The potential theory was extended to deal with the behaviour of polyelectrolytes i n the presence of s a l t . The resu 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 of using pairs of systems with the same polymer compositions. The effect of the potential on the c e l l surface free energy was then studied by means of contact angle measurements on single erythrocytes. The free energy difference increases l i n e a r l y with the pot e n t i a l , but i s twenty fold smaller than expected based on the best estimates for the c e l l surface charge density. The hypothesis presented to account for t h i s i s that the phase system i s excluded from most of the charged region of the glycocalyx. The effect of an a f f i n i t y ligand on c e l l p a r t i t i o n and i t s interaction with the c e l l surface were studied from a theoretical and experimental point of view. A thermodynamic theory for the effects of an a f f i n i t y ligand on the c e l l surface free energy difference was derived. In t h i s theory the change i n t h i s parameter depends on the number of ligands bound and the binding energy i n each phase, as well as the ligand p a r t i t i o n c o e f f i c i e n t . Experimental studies were carried out using PEG-palmitate, a hydrophobic -233-a f f i n i t y ligand. This ligand has l i t t l e effect on the phase compositions, i n t e r f a c i a l tension and potential 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 interaction of t h i s ligand with the membrane l i p i d b i layer. 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 for t h i s effect i s unclear, since the ester does not form micelles i n t h i s concentration range, although the formation of small aggregates i s not ruled out. The interaction 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 dissociation constants i n the micromolar range, consistent with a hydrophobic interaction. 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 effect of the ester on the c e l l surface free energy difference, again determined by means of contact angle measurements, was found to be very small per molecule bound. The ligand theory agrees Quantitatively with the experimental results for the erythrocyte/ester system. In t h i s theory, the small effect of the ligand i s also due to exclusion of the phases from the region where the ligand i s bound. PEG and the ester appear to be bound to 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 of binding s i t e s , the effect of the phases on the -234-binding strength, and the desorption behaviour. These results suggest that the ester i s bound more deeply within 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 relationship 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 for the two phases. The role of other factors 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 difference, was also 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 ch 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 indicates that erythrocyte p a r t i t i o n i s not a thermodynamic equilibrium process i . e . the c e l l s are not distributed by d i f f u s i o n . However i f non-thermodynamic factors 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 difference. Although p a r t i t i o n i s sensitive to the c e l l surface properties, 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 affected by the density difference 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 calculations of the energies and forces involved i n c e l l p a r t i t i o n led to the proposal of a mechanism for p a r t i t i o n . 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 large p a r t i c l e s (>l-um dia.) such as c e l l s are distributed between the interface and the two phases. -235-Glossary of Symbols and Abbreviations A l l superscripts t and b refer to Quantities i n the upper and lower phases respectively. I f not e x p l i c i t l y mentioned, the subscripts i , j refer to the i t h species i n the j t h system respectively. A l l differences i n , or r a t i o s of auantities i n , the two phases are expressed as top-bottom or top/bottom respectively. a c radius of three phase contact l i n e ap.a^ , 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 electron charge, A.lxlO""'"^ esu. E c 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 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 ^ force, drag force f ,f detachment force, applied force during p a r t i t i o n ID 3 f mole fraction of s a l t i n a phase system F i F i c o l l g acceleration due to gravity 980.5 dynes/g h height of spherical cap I ionic strength -236-k Boltzmann's constant, 1.36xl0~* 6 ergs/molecule.°K k 1 association constant for ligand binding K,K^ 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 , c^/c3 Mn,Mw number, weight average molecular weight n number of binding s i t e s per molecule or per unit area, transport number n 1 number of molecules bound per unit area or per macromolecule Cn\ the binomial c o e f f i c i e n t , n ! / ( ( n - i ) I . i ! ) J n^ number of drops 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 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 r , r . mole r a t i o of bulk s a l t concentrations s' 1 r v phase volume r a t i o r, r a t i o of association constants k r i 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 volume, phase volume V dimensionless exponential function of potential z+ , z _ valence of cation, anion zm,Zi valence of macromolecule or protein, 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^/ua^, normalised free energy of attachment free energy of p a r t i c l e transfer between phases binding energy/molecule free energy of ligand transfer between phases per molecule free energy of mixing enthalpy of mixing entropy of mixing surface free energy difference between the phases surface free energy difference between phases i n the presence, absence of a ligand. difference i n standard state chemical potentials between the phases 2 d i e l e c t r i c constant of water, 78 esu /cm.erg visco s i t y eauilibrium, complementary, displaced contact angle o p t i c a l rotation of polymer solution angle subtended at centre of p a r t i c l e , drop maximum cap size on a spherical drop Debye-Huckel parameter -standard state, chemical, electrochemical potential density, density difference between the phases surface charge density -238-<t> volume fraction X mole fraction i}j,Aip Galvani, or inner p o t e n t i a l , potential difference 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 buffer, consisting of p mM sodium phosphate buffer, q mM NaCl, r mM s o r b i t o l and s J JM PEG-palmitate. -239-Appendices A. Estimation of the minimum force necessary to p u l l a spherical p a r t i c l e  o f f a l i q u i d interface A detailed analysis of the interaction of a p a r t i c l e with the interface i s given by Schulze (1984), which includes effects due to gravity and pressure variations. However since these effects 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 analysis given here i s s u f f i c i e n t to estimate the necessary force. Consider a spherical p a r t i c l e , radius ap, attached to a plane interface with tension Y t b and restrained at i t s outer edge. Let the equilibrium contact angle be 0 . Now l e t a force f be applied to the p a r t i c l e , displacing 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 (Fig. 1.2b). The interface i s now curved, re s u l t i n g i n a horizontal component of tension that balances the applied force. This component i s given by the product of the horizontal component of the tension and the circumference of c i r c l e B: f = 2 Tra s i n 0 " . Y P tb .sin ( 0 - 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-fm = 2 T T a p V t b s i n 2 ( 9 / 2 ) = * a p Y t b ( 1 " c o s 6 } [A3] For a p a r t i c l e attached to a drop of radius a d, the maximum force w i l l be smaller, since the three phase contact l i n e B i s shorter. The analysis i s complicated by the fact that the drop does not remain spherical, 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 where 6 p i s less than the eauilibrium contact angle, being the angle subtended at the p a r t i c l e centre by the eauilibrium contact l i n e (eg. Fig 2.1), where and a d i s the eauilibrium drop radius. 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 Six. I t l i s t s several 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 Qualitative and semi-auantitative arguments. f = 2 Tra V 4 - K s i n 2 ( 6 /2) m p 'tb p [A4] tan 0 = sin 0 /(cos 0 + a /a .) [A5] -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 agitation 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 into 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 distributed very early i n the p a r t i t i o n process. The chief argument against t h i s mechanism i s the rep 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 inversion, or more vigorously by vortexing the solutions. This model incor r e c t l y predicts that the p a r t i t i o n i n systems with high tensions, which i s usually low, could be increased, ultimately 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 interface. 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 interface at some early 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 explain how small c e l l surface differences could result i n different 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 interface 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 scale of the c e l l radius. The re-attachment i s therefore controlled by the c o l l i s i o n rate between c e l l s and the interface of drops, which would be independent of both the c e l l surface properties, and phase system properties such as potential and ligand concentration, and which would instead depend only on the gross -242-properties of the system such as the density difference and phase v i s c o s i t i e s . 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 fact that microscopic observation shows that the drops produced on shaking are at least 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 interface 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 interface, t h e i r thermodynamic equilibrium position (except for the special 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 interface into the upper phase. Consider the t o t a l energy dissipated by a drop with one c e l l attached, as i t set 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 dissipated for a drop at constant velocity i s the product of the distance and the grav i t a t i o n a l force: 4 TT/3. Ap a 3a pg [Bl] For a (5,4) system the density difference i s 0.04 g/ml, and a p for an erythrocyte i s about 3.5x10"^ cm. For two representative drop sizes of -12 -9 0.01 and 0.1 mm dia. , t h i s gives 7.2 xlO and 7.2x10 ergs, or 180 to 1.8xl0 5 kT. The larger figure i s comparable to the ch a r a c t e r i s t i c energies -243-derived from Fig 6.15. However these estimates are upper l i m i t s , since not a l l of the energy would be available to remove the c e l l , a l o t being dissipated i n f l u i d flow i n and around the drop. Although the energy depends on the cube of the radius, the fraction expended on the c e l l would decrease the larger the drop size i s r e l a t i v e to the c e l l , so the dependence of available energy on the radius would be less rapid. From t h i s one concludes that t h i s process would only occur for large drops ( >0.1 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 early 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 rate and the drops are small. Another type of argument useful i n discussing 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 taking a (5,4) system, containing 0.8 uM ester, at 34% p a r t i t i o n , 6 = 60°, 2 Y^b= 0.0063 ergs/cm (Table 5.5). The minimum force to remove the c e l l , from [A3], i s about 3.5xl0~ 6 dynes, for a plane interface, somewhat less o for a drop. Using [A5] we have for 0.01 and 0.1 mm dia. drops, 6^= 35.8 o _g and 56.6 respectively. Using [A4], f i s about 1.3, 3.1 xlO dynes/cell, respectively. 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): f g = 2 7TApga2ad [B2] —8 This equation gives estimates for the net force on the c e l l as 1.5 10~ and 1.5 x l O - 7 dynes respectively for the two drop sizes. These forces are -244-considerably smaller than those required to remove the c e l l . Using the estimate of f for a plane interface and solving [A3] for a^ gives a diameter of 0.12 cm as the minimum drop size where t h i s p a r t i t i o n mechanism could operate. Of course t h i s analysis i s only v a l i d for an isolated drop, not for 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 analysis also assumed that the f l u i d flow around the drop was essent 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 for the geometry of Fig. 2.1b for a p a r t i c l e attached to a bubble. Their conclusion was that the magnitude of the force was si m i l a r to that i n the above analysis, but that i t was directed 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 pulled into the upper phase from the interface 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 for 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). In t h i s model a cap of c e l l s subtending an angle form on the rear of a sedimenting drop. Tangential stress on t h i s cap results from f l u i d flow past the drop, which i s maximum at the cap centre. I f the res 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 of f the drop as the cap buckles. Thus there i s a l i m i t to the size of cap that a given size drop can sustain. Since the capping mechanism i s driven by s e t t l i n g , the same -245-"available energy" counter-arguments used with the previous model apply, but with even more force, 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 tangential stress can be integrated across the cap to obtain an expression for the maximum cap s i z e , © m (Clarke and Wilson 1983): e m = 3 A E t . / ( T r a W ) [B3] Taking the same c e l l and system parameters as before, for 0.01 and 0.1 mm dia. drops we obtain G = 1.21 xKfVa 2,, which gives 0 > TT m d' 3 m 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 into the upper phase could thus occur under these conditions unless the c e l l concentration i s high enough to completely coat the available interface. For t h i s system 0 becomes less than TT for m drops greater than 0.2 mm dia. Again t h i s mechanism would appear to be too weak at the early stages of separation, but could become more important l a t e r as the drops increase i n si z e . For small angles, the cap angle i s 2 proportional to 1/a^, but the cap area for a given angle i s 2 proportional to a^, so the number of 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 interface would thus be proportional 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 of c e l l s into the top phase occurs because at some point the t o t a l cap capacity i s exceeded. This implies 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 fixed number of c e l l s would stay at the interface. I f the c e l l concentration were further lowered u n t i l the interface capacity was not exceeded, the p a r t i t i o n would always be zero. 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