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A surface and colloid chemical study of the interaction of proteins with polystyrene latex (PSL) Olal, Andrew Dandy 1990

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A SURFACE AND COLLOID CHEMICAL STUDY OF THE INTERACTION OF PROTEINS WITH POLYSTYRENE LATEX (PSL) By ANDREW DANDY OLAL B . S c , Makerere U n i v e r s i t y , Kampala, Uganda, 1978 M . S c , U n i v e r s i t y of B r i s t o l , B r i s t o l , U . K . , 1981 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES (Chemistry Department) We accept th i s thes i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA May 1990 © Andrew Dandy Q l a l , 1990 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of The University of British Columbia Vancouver, Canada DE-6 (2/88) ABSTRACT I n t h i s t h e s i s v a r i o u s p h y s i c o c h e m i c a l f a c t o r s w h i c h d e t e r m i n e t h e c h a r a c t e r i s t i c s o f l a t e x a g g l u t i n a t i o n immunoassays a r e e x a m i n e d . A model o f a n t i b o d i e s r e a c t i n g w i t h a n t i g e n ( b o v i n e serum a l b u m i n ; BSA) a d s o r b e d t o t h e s u r f a c e o f p o l y s t y r e n e l a t e x (PSL) beads was e x a m i n e d . The a d s o r p t i o n s t u d i e s o f BSA t o PSL showed t h a t t h e mass o f BSA a d s o r b e d a t s a t u r a t i o n depends on t h e t y p e o f p o l y s t y r e n e l a t e x . L a t e x e s w i t h h i g h l y h y d r o p h o b i c s u r f a c e s a d s o r b e d more BSA m o l e c u l e s t h a n t h o s e w i t h l o w e r h y d r p h o b i c i t y . D e s o r p t i o n s t u d i e s showed t h a t l a t e x e s t h a t max im ize a d s o r p t i o n l o s t t h e l o w e s t f r a c t i o n o f t h e i r bound BSA m o l e c u l e s f o l l o w i n g e x t e n s i v e b u f f e r wash. P a r t i a l d e s o r p t i o n o f BSA f r o m PSL was a c h i e v e d b y t h e a d d i t i o n o f d e t e r g e n t , whereas t h e a d d i t i o n o f more BSA m o l e c u l e s o r o t h e r m a c r o m o l e c u l e s such as PEG o r IgG d i d n o t d i s p l a c e t h e a d s o r b e d BSA m o l e c u l e s . E x a m i n a t i o n o f t h e m a t e r i a l removed f r o m t h e s u r f a c e o f t h e l a t e x e s by SDS-PAGE a n a l y s i s showed t h a t t h e c o m p o s i t i o n o f t h e a d s o r b e d l a y e r was e n r i c h e d i n t h e h i g h e r m o l e c u l a r w e i g h t o l i g o m e r s o f BSA, r e l a t i v e t o t h e i r c o n c e n t r a t i o n s i n t h e s t o c k s o l u t i o n . A model i n w h i c h a d s o r b e d p r o t e i n i s assumed t o u n d e r g o a p o l y m e r i z a t i o n r e a c t i o n p r o v i d e s a g e n e r a l e x p l a n a t i o n o f t h e o b s e r v e d r e s u l t s . S t u d i e s o f p o l y c l o n a l a n t i b o d y ( a n t i - B S A IgG) b i n d i n g t o a n t i g e n - c o a t e d PSL showed t h a t t h e s u r f a c e c o n c e n t r a t i o n o f bound a n t i b o d y depends on t h e s u r f a c e c o n c e n t r a t i o n o f a n t i g e n on t h e l a t e x p a r t i c l e s and on t h e a v a i l a b i l i t y o f PSL s u r f a c e a r e a n o t o c c u p i e d by a n t i g e n . A n a l y s i s o f s h e a r i n d u c e d a g g r e g a t i o n r e s u l t s show t h a t f o r low s u r f a c e c o v e r a g e o f l a t e x p a r t i c l e s by p r o t e i n a n t i g e n i n s t a b l e s u s p e n s i o n , r e l a t i v e l y low c o n c e n t r a t i o n s o f s p e c i f i c a n t i b o d i e s a r e r e q u i r e d t o cause a g g l u t i n a t i o n . I n c r e a s i n g s u r f a c e d e n s i t y o f a n t i g e n r e q u i r e s s i g n i f i c a n t l y h i g h e r c o n c e n t r a t i o n s o f s p e c i f i c a n t i b o d i e s t o p r o d u c e a g g l u t i n a t i o n . Fo r a g i v e n s u r f a c e c o v e r a g e o f a n t i g e n , r e s u l t s show t h a t i n c r e a s i n g t h e s h e a r r a t e d e c r e a s e s t h e a n t i b o d y c o n c e n t r a t i o n n e c e s s a r y t o p r o d u c e a g i v e n d e g r e e o f a g g l u t i n a t i o n . A r e m a r k a b l e s t r u c t u r e f o r m a t i o n and l o n g r a n g e o r d e r i n g e x h i b i t e d by f l o e s o f l a t e x c o a g u l a t i n g i n s a l t u n d e r i n t e r m e d i a t e s h e a r r a t e s was o b s e r v e d . T h i s s t r u c t u r e f o r m a t i o n was n o t o b s e r v e d d u r i n g a n t i b o d y - i n d u c e d a g g l u t i n a t i o n u n d e r s h e a r . . i i i Table of Contents Page Abstract i i Table of Contents i i i List of Tables v i i i List of Figures ix Acknowledgement x i Chapter one. General Outline 1.1 Introduction 1 1.2. Polymer Latex P a r t i c l e s 1.2 (a). Description and Classification 3 1.2 (b). Preparation 4 1.2 (c). General Uses 9 1.3. Properties of Polymer latexes 1.3 (a). Surface Functional Groups 12 1.3 (b). Particle Size 17 1.3 (c). Colloidal Stability 19 Electrical Double Layer 22 van der Waals Attractive Forces 24 Total Free Energy of Interaction (DLVO Theory) 25 Steric Forces 28 Agglutination of Antigen-coated PSL 30 Total Free-Energy of Interaction (General Equation) 31 Relative Stability 32 1.3 (d). Fluid Motion and Colloidal Stability 32 Slow Coagulation 36 1.4. In t e r a c t i o n of Proteins with Polymer Latexes 1.4 (a). General Considerations 38 1.4 (b). Theoretical Considerations 47 1.4 (c) Binding of Antibody to Antigen-coated PSL Immunoglobulin G Structure 49 1.5. Research Approach 53 i v Chapter Two. BSA Adsorption Page 2.1. Introduction 55 2.1 (a). Experimental Considerations 55 2.1 (b). Stru c t u r a i Features of Albumin 57 2.1 (c). Albumin Heterogeneity 60 2.2. BSA Adsorption Procedure 2.2 (a). Introduction 63 2.2 (b). Materials 64 2.2 (c). Methods: (i) . Radiolabeling of BSA 67 ( i i ) . Adsorption Experiments 69 ( i i i ) . Wash Analysis 71 2.3. Results and Discussion 2.3 (a). Adsorption Isotherms: (i) . Variation of Surface Area of the PSL. 72 ( i i ) . Variation Total Volume of BSA Solution. 82 2.3 (b). Comparison of the Amount of BSA Adsorbed per unit area at Constant Surface Area. 86 2.3 (c). Wash Analysis of Adsorbed BSA: (i) . Buffer Wash. 88 ( i i ) . Comparison of Buffer Wash with SDS,BSA, IgG and PEG Washes. 91 2.3 (d). Electrophoresis Analysis of BSA Removed from the latex Surface. 94 2.4. Summary of BSA Adsorption Studies 111 Chapter Three. Antibody Binding to Antigen-Coated PSL 3.1. Introduction 113 3.1(a). Interaction of monovalent Antibody and monovalent Antigen in Solution 114 3.1(b). Multiple Equilibria: General Relationships 115 3.1(c). Interaction of Antibody and Particle-bound Antigen 118 V 3.2(a). Preparation of Antigen-Coated Polystyrene Latexes 122 3.2(b). Rabbit anti-BSA Immunoglobulin G Antibody: (i) . Immunisation of Rabbits 122 ( i i ) . Purification of Rabbit anti-BSA Immunoglobulin (G) 123 3.2(c). Antibody Binding Experiments 124 3.3. Results and Discussion 3.3(a). Polyclonal Antibody Binding to Antigen-coated PSL 124 3.3(b). Comparison of Amount of Antibody bound to BSA-coated latex with amount of surface density of of BSA. 128 3.3(c). Binding of Nonspecific IgG Antibody to bare and BSA-coated PSL. 133 3.4 Summary; Antibody Binding to Antigen-coated PSL 139 Chapter Four. Antibody-Induced Aggregation of PSL 4.1. Introduction 141 4.2. Materials and Methods 141 4.2(a) Constant Shear rate Aggregometer 142 4.2(b) Determination of rate constants for Coagulation and Aggregation Kinetics 146 4.3. Results and Discussion 147 4.3(a) Absorbance Measurements of PSL 147 4.3(b) Stability of BSA-coated PS latexes under Shear 153 4.3(c) Agglutination of BSA-coated PSL under shear: (i) The effect of varying anti-BSA IgG concentration 160 ( i i ) The effect of varying shear rate 167 ( i i i ) The effect of varying BSA-coated latex concentration 168 4.3(d) S truc ture formation in PSL Dispersions 171 4.4. Summary of Antibody-Induced Aggregation 176 Chapter Five. Conclusions Page General Conclusion 178 Glossary of Terms 183 Glossary of Symbols and Abbreviations 185 Appendices 188 Appendix 1 188 Procedure for electrophoretic analysis of protein samples. Appendix 2a 191 Outline of procedure used to calculate the amount of BSA adsorbed per unit area of PSL. Appendix 2b 194 Adsorption isotherms for BSA adsorption to sulfate latex: Reproducibility data. Appendix 3 197 4% SDS-Polyacrylamide electrophoretic gels for IgG fractions used] in antibody binding to antigen-coated PSL and agglutination of antigen-coated PSL. Appendix 4 198 Outline of procedure used to calculate the amount of polyclonal rabbit anti-BSA IgG bound per unit area of BSA-coated PSL. Appendix 5 200 Binding isotherms of polyclonal rabbit anti-BSA IgG to BSA-coated PSL. Appendix 6 201 Scatchard plots of the binding isotherms of polyclonal rabbit anti-BSA IgG to BSA-coated PSL. Appendix 7 203 A model of the stoichiometry of specific and nonspecific binding of polyclonal anti-BSA to latex coated with various concentrations of antigen. Appendix 8(a) 207 Absorption spectra of PSL at different volume fractions. Appendix 8(b) 208 Beer-Lambert plots of the absorption spectra of PSL. Appendix 9(a) 209 Plots of optical absorbance vs wavelength at various times for coagulating PSL. Appendix 9(b) 210 Plots of optical absorbance vs time at different wavelengths for coagulating PSL. Appendix 10(a) 211 Optical absorbance vs time plots for agglutination of BSA-coated sulfate latexes with different surface densities of antigen. Appendix 10(b) 213 Plots of optiocal absorbance at various agglutination times as a function of equilibrium IgG concentrations for shear agglutination at 28 s"1. Appendix 10(c) 214 Optical absorbance vs time plots for agglutination of BSA-coated sulfate latex. The effect of varying shear rates. Appendix 10(d) 216 Optical absorbance vs time plots for agglutination of BSA-coated sulfate latex. The effect of varying BSA-coated latex concentration. Appendix 11(a) 217 Optical absorbance vs time plots for agglutination of BSA-coated amidine ( + ) latex (BSA « 0.45 mg m ). The effect of varying shear rates. Appendix 1Kb) 218 Optical absorbance vs time plots for agglutination of BSA-coated amidine( + ) latex (BSA ~ 0.60 mg m ). The effect of varying shear rates. Appendix 11(c) 219 Optical absorbance vs time plots for agglutination of BSA-coated amidine ( + ) latex (BSA ~ 0.75 mg m ). The effect of varying shear rates. Appendix 11(d) 220 Optical absorbance vs time plots for agglutination of BSA-coated amidine ( + ) latex (BSA « 1.80 mg m ). The effect of varying shear rates. Appendix 12 221 Floe formation in agglutinating BSA-coated sulfate latex at different shear rates (3.7 and 21.6 s ). Bibliography 222 List of Tables Table Page I Characteristics of Polystyrene latexes used in adsorption and agglutination studies. 66 II Adsorption maxima of BSA adsorption isotherms in Figure 6 as estimated from the isotherms. 76 III Adsorption maxima of BSA adsorption isotherms in Figure 9, as estimated from the isotherms. 84 IV Comparison of the amount of BSA adsorbed per unit area for four latex types at roughly "constant" surface area. 87 V Amount of BSA retained on the PS latex pellet after extensive wash with equilibrium buffer. 89 VI Summary of Adsorption Data for samples used in SDS-PAGE electrophoresis analysis (a). 96 VII(a) The distribution of BSA oligomers in equilibrium solution and on PSL surfaces as a percentage of BSA added. 100 VII(b) The distribution of BSA oligomers on PSL surfaces as a percentage of BSA adsorbed. 102 VIII(a) Summary of Adsorption data for samples used in SDS-PAGE electrophoresis analysis (a). 102 VIII(b) Summary of Adsorption data for samples used in SDS-PAGE electrophoresis analysis (b). 103 IX Summary of amount of BSA loaded to each gel, the total amount of BSA adsorbed on the latex surface and the total amount in supernatant. 105 X(a) The distribution of BSA oligomers on amidine and sulfate latexes as a percentage of BSA added. 108 X(b) The distribution of BSA oligomers on amidine and sulfate latexes as a percentage of BSA adsorbed. 109 XI Comparison of amount of anti-BSA bound to latex with different amounts of surface bound BSA. 131 XII Mean rate of shear in the gap of the coaxial cylinder aggregometer. 144 XIII Absorption maxima from optical spectra of aqueous suspensions of the four PSL used. 150 XIV C r i t i c a l coagulation concentrations of PSL as estimated from supernatant absorbance readings. 155 i x Table Page !XV I n i t i a l rate of change of absorbance at two e q u i l i b r i u m antibody concentrat ions for d i f f e r e n t BSA surface coverages. 165 X LIST OF FIGURES Figure Page 1. Surface Functional groups of typical latex particles. 13 2. The electrical double layer in the interfacial region close to a charged particle surface and the potentials in the interface region. 15 3. Typical form of the total potential energy of interaction between electrostatically stabilised polystyrene latex particles. 27 4. Typical adsorption isotherms for (a) flexible, highly solvated polymers and (b) globular proteins (compact molecules). 46 5. Schematic representation of Immunoglobulin G (IgG) molecule 50 6. Adsorption isotherms for BSA to latexes indicated at room temperature from 0.05M phosphate buffer, pH 7 .20. Variation of surface area of latex. 73 7. The adsorption data of Figure 5 plotted as a function of the amount of non-adsorbed BSA per unit area in solution, r = (C*V/S). 79 8. The amount of BSA adsorbed at saturation as a function of latex syrface area, conditions as in Figure 5. 81 9. Adsorption isotherms for BSA to latexes idicated at room temperature from 0.05M phosphate buffer, pH 7 .20. Variation of total volume of BSA solution. 83 10. The adsorption data of Figure 8 plotted as a function of the amount of non-adsorbed BSA per unit area in solution, r = (C*V/S). 85 11. Amount of BSa retained on PSL after washing first with equilibrium buffer, followed by repeated wash cycles with buffer, 2% sodium dodecyl sulphate (SDS), equilibrium nonlabeled BSA, anti-BSA IgG, and 27. PEG (6000). 93 12. Optical density profiles of Coomassie Blue stained 4% polyacrylamide gels of BSA from the supernatant (dashed line) and that removed from the pellet (solid line). 98 13. Optical density profiles of Coomassie Blue stained SDS 4% polyacrylamide gels of stock BSA, unexposed to the latex surface. 99 X I Figure Page 14. Optical density profiles of Coomassie Blue stained 4% polyacrylamide gels of BSA from the supernatant (dashed line) and that removed from the pellet (solid line) of the adsorption experiment on amidine latex reported in Figure 5. 104 15. Optical density profiles of Coomassie Blue stained 4% polyacrylamide gels of BSA from the supernatant (dashed line) and that removed from the pellet (solid line) of the adsorption experiment on sulphate latex reported in Figure 5. 106 16. The possible structures involved in the binding of divalent antibodies with particle-bound antigens. 120 17. The binding of polyclonal anti-BSA IgG to BSA-coatld sulfate PSL at room temerature from 0.01M phosphate buffer, pH 7.20. variation of PS1 concentration. 126 18. The binding of rabbit anti-BSA to BSA-coated sulphate latexes from 0.05M phosphate buffer, pH 7.2. Variation of BSA surface coverage. 127 19. A Scatchard graph of the data for binding of anti-BSA IgG by BSA-coated sulphate latex (data from Figure 18). 129 20. A comparison of relative amounts of specific antibodies (anti-BSA IgG) bound to latexes with different amounts of surface antigen (BSA). 132 21. The binding of non-specific IgG to BSA-coated sulphate latexes from 0.05M phosphate buffer, pH 7.2. 134 22. Scatchard plots of data from Figure 21. ^ 135 23. A comparison of relative amounts of specific antibodies (anti-BSA IgG) and non-specific IgG bound to latexes with different amounts of surface antigen (BSA). 137 24. A schematic diagram of a constant shear aggregometer 145 25. Measured absorbance of aqueous suspensions of sulphate, carboxyl, carboxyl modified, and amidine (+) latexes. 148 26. The absorption spectra of sulphate latex at different volume fractions and Beer-Lambert's plots. 151 27. Optical absorbance of supernatant vs concentration of NaCl for sulpahte, carboxyl, carboxyl modified and amidine (+) latexes. 154 28. Absorbance change with time for shear flocculation at 28 s - 1 of BSA-coated sulphate latexes. 156 Figure Page x i i 2 9 . S t a b i l i t y o f B S A - c o a t e d s u l h a t e l a t e x a t i o n i c s t r e n g t h 0 .5M as a f u n c t i o n o f p r o t e i n s u r f a c e c o v e r a g e . 158 3 0 . S t a b i l i t y o f b a r e s u l f a t e and B S A - c o a t e d s u l f a t e l a t e x e s a t i o n i c s t r e n g t h 0.5M as a f u n c t i o n o f s h e a r r a t e . 159 3 1 . Abso rbance v s e q u i l i b r i u m IgG c o n c e n t r a t i o n f o r s h e a r a g g l u t i n a t i o n o f B S A - c o a t e d s u l p h a t e l a t e x a t 28 s . 161 3 2 . P l o t s o f i n i t i a l r a t e c o n s t a n t s v s e q u i l i b r i u m IgG c o n c e n t r a t i o n s f o r v a r i o u s BSA c o v e r a g e o f s u l p h a t e l a t e x e s . 163 3 3 . P l o t s o f a b s o r b a n c e and i n i t i a l r a t e c o n s t a n t s v s e q u i l i b r i u m IgG c o n c e n t r a t i o n f o r s h e a r a g g l u t i n a t i o n a t 14, 2 8 , and 81 s o f s u l p h a t e l a t e x . 166 3 4 . P l o t s o f i n i t i a l r a t e c o n s t a n t s v s e q u i l i b r i u m IgG c o n c e n t r a t i o n f o r d i f f e r e n t c o n c e n t r a t i o n s o f B S A - c o a t e d s u l p h a t e l a t e x . 169 3 5 . P l o t s o f i n i t i a l r a t e c o n s t a n t s v s number o f p a r t i c l e s p e r u n i t vo lume f o r d i f f e r e n t e q u i l i b r i u m IgG c o n c e n t r a t i o n s . 170 3 6 . S t r u c t u r e f o r m a t i o n i n c o a g u l a t i n g s u l p h a t e l a t e x u n d e r s h e a r a t room t e m p e r a t u r e . 173 3 7 . S t r u c t u r e f o r m a t i o n i n a g g l u t i n a t i n g B S A - c o a t e d s u l p h a t e l a t e x u n d e r s h e a r a t room t e m p e r a t u r e . 175 3 8 . P l o t s o f i n i t i a l c o a g u l a t i o n r a t e s (A) and i n i t i a l a g g l u t i n a t i o n r a t e s (B) v s e q u i l i b r i u m e q u i l i b r i u m NaCl and a n t i b o d y c o n c e n t r a t i o n f o r s h e a r a t 28 s and 81 s o f naked s u l f a t e l a t e x and B S A - c o a t e d 12 -2 s u l f a t e l a t e x w i t h c o v e r a g e o f 1.05 x 10 m o l e c u l e s cm . 176 x i i i Acknowledgements I am deeply grateful to Dr. D. E. Brooks for the guidance, continuous support and encouragement that he provided me throughout the course of this work. I would also like to thank J. Sibley for his invaluable assistance in the maintenance of a l l those equipment that went kaput each time I used them, and also for constructing the shear aggregometer that I used for my kinetic experiments. Finally, I would like to thank everybody in the lab for their understanding and assistance. I am especially grateful to C. Ramey for his patience in explaining things to me and for his help with PC communications. xiv To Margaret and Atim 1 CHAPTER ONE  GENERAL INTRODUCTION 1.1 Introduction Dispersions of polystyrene latex (PSL) particles sensitized with antibodies (Ab) or antigens (Ag) are widely used in slide agglutination tests for qualitative as well as semi-quantitative analysis of Ab and Ag from biological fluids [1 -3 ] . In these analysis, latex particles are f i r s t sensitized (i.e. rendered sensitive to the action of specific antibody or antigen) with either Ab or Ag. The sensitization involves immobilization of the reactants (Ab or Ag) on the surface of the latex particles either by physical adsorption or by covalent coupling, making them also antigenic [4]. Addition of a sample containing the homologous Ab or Ag to the dispersions causes Ag-Ab linkages to occur between the surfaces of the particles. Because of the relatively large size of the latex particles (diameter range 0.1 to 1 um), the reaction causes the formation of visible precipitates (or aggregates) of the latex. The most familiar example of latex-based immunoassay technique is the pregnancy slide test [5]. The pregnancy test is a test for the presence of human chorionic gonadotropin (hCG), the hormone produced in normal pregnancy. In this assay, a preparation of latex particles, to which has been attached the antibody to human chorionic gonadotropin (hCG), is mixed with a drop of urine. Using a clean plastic rod, the latex suspension and urine sample are thoroughly mixed until a uniform distribution of the latex particles is achieved. The slide is then gently t i l t e d back and forth, as the reaction proceeds for a given length of time. This "rocking" imparts f l u i d motion to the system which 2 increases the number of c o l l i s i o n s r e s u l t i n g i n a g g l u t i n a t i o n ( i . e . the formation of large and v i s i b l e aggregates as a r e s u l t of i n t e r a c t i o n between Ag-coated p a r t i c l e s with s p e c i f i c Ab) i n about two to ten minutes. In a v a r i a t i o n , the hCG i s l inked to the latex p a r t i c l e s . An a l i q u o t of ur ine i s mixed with the antibody (anti-hCG) reagent, to al low any hCG i n the ur ine to react . Then the ant igen (hCG) i s immediately added. I f there i s no hCG i n the sample, the antibody reacts with the ant igen, and a g g l u t i n a t i o n occurs , i n d i c a t i n g a negative r e s u l t . If there i s small amount of hCG i n the u r i n e , the antibody binds to the hCG and i s unava i lab le to react with the Ag- la tex p a r t i c l e s , so no a g g l u t i n a t i o n occurs . The use of latex p a r t i c l e s i n a n a l y s i s of Ab and Ag i n b i o l o g i c a l f l u i d s has increased r a p i d l y over the l a s t few years [ 6 , 7 ] . However, la tex immunoassays do not as yet provide a d e f i n i t i v e d iagnos i s . Th i s i s probably because most of the latex d iagnos t i c t e s t s , at present , are developed on an e m p i r i c a l bas i s due to the fac t that there are numerous imprec i se ly understood physicochemical f a c t o r s that inf luence the outcome of la tex a g g l u t i n a t i o n tes t s . These inc lude: p r o t e i n adsorbing p r o p e r t i e s to la tex p a r t i c l e s ; the s t a b i l i t y of la tex p a r t i c l e s p r i o r to, dur ing and a f t e r p r o t e i n coat ing procedure; s o l u t i o n condi t ions such as pH, b u f f e r s , e l e c t r o l y t e and p r o t e i n concentrat ions; and the latex p a r t i c l e s i z e , dens i ty and surface c h a r a c t e r i s t i c s . In a d d i t i o n , out of necess i ty , the ant igen and antibody preparat ions used i n these tes t s are often impure and contain a wide v a r i e t y of mater ia l s not involved i n the ant igen-ant ibody r e a c t i o n of i n t e r e s t . A l l these f a c t o r s make i t d i f f i c u l t to f u l l y descr ibe and o u t l i n e the mechanism involved i n such complex mixtures and has meant that r e l a t i v e l y l i t t l e publ i shed research 3 outlining the mechanisms involved in such systems i s available. In this thesis, an attempt has been made, using a model antigen (bovine serum albumin (BSA)) and polyclonal anti-BSA antibody, to provide some basic information regarding the behaviour of protein adsorption to latex particles and the reactions that such systems undergo when antigens and antibodies are present. 1.2 Polymer Latex Particles 1.2 (a) Description and Classification Latex particles are spherical polymer particles, often referred to as microspheres, synthesized from a variety of monomers by emulsion polymerization. They possess different properties depending on the specific monomers used [8]. These particles are dispersed, usually in aqueous media, but also commonly in non-aqueous media to form suspensions. Most latex suspensions are colloidal in nature, meaning that the dimensions of the particles in the dispersion medium range from lnm to lOOOnm. Polymer latexes can be classified as homopolymers or heteropolymers. Homopolymer latexes are formed by the polymerization of a single species of monomer, for example polystyrene latex (PSL) derived from the styrene monomer and polyvinyl toluene (PVT) latex made from vinyl toluene. Heteropolymer latexes are produced by copolymerization of two or more different species of monomer, for example styrene-butadiene copolymer. The polymerization of a mixture of two or more monomers gives a copolymer with properties intermediate between those of the 4 corresponding homopolymers. The properties of copolymers depend not only on the overall composition of the polymer molecules, but also on the compositional distribution of monomer molecules in the polymer chains and the distribution of polymer molecular weights. Copolymerization is often used to produce latex particles with differing physical properties such as density, solubility and optical characteristics [9]. 1 . 2 (b) Preparation The four basic ingredients in an emulsion polymerization process are the monomer (e.g. styrene), a surface active agent such as sodium dodecyl sulfate; a free-radical initiator such as potassium persulphate (K S 0 ) 2 2 8 or hydrogen peroxide > a n c* water [ 1 0 ] . The surface active agents are normally amphiphatic long chain fatty acid salts with a hydrophilic "head" and a hydrophobic " t a i l " . When such surface active agents are placed in high enough concentration in water, they form micelles consisting of 50 to 100 molecules oriented with their hydrophobic t a i l s inwards and their hydrophilic heads in contact with the water, thus creating an interior environment of hydrocarbon. These micelles are formed once the monomeric concentration of the solute molecules reaches a c r i t i c a l value, the c r i t i c a l micelle concentration (CMC); the aggregates exist in equilibrium with free solute molecules in the aqueous phase. Micelles tend to be composed of the same number of surface active molecules and are therefore uniform in diameter. Addition of more surface active molecules simply leads to the formation of more micelles of the same size. 5 When a monomer such as styrene i s added to the m i c e l l e s i n water, some of i t migrates to the c e n t r a l hydrophobic phase of the m i c e l l e s , thereby swe l l ing them, and some remains i n the aqueous phase as d r o p l e t s . The most commonly used i n i t i a t o r i s persulphate , which produces s u l f a t e free r a d i c a l s : K S 0 > 2K + + 2*0S0~ 2 2 8 3 These free r a d i c a l s react with the double bond i n the styrene monomer (M) producing monomeric free r a d i c a l s which react with other styrene monomer s ide chains to form o l igomeric r a d i c a l s : "0S0" + M > "M—0S0~ 3 3 'M—0S0" + nM > "M (M) — 0 S 0 " 3 n 3 Thus, a chain r e a c t i o n i s i n i t i a t e d and l i n e a r po lymer iza t ion occurs . The po lymer izat ion w i l l proceed u n t i l the supply of monomeric styrene i s exhausted or u n t i l the growing o l igomeric r a d i c a l s react with one another to terminate the po lymer izat ion . The l i n e a r chain terminates with s u l f a t e groups at both ends of the chain: 'M (M) — 0 S 0 " + "M (M) — 0 S 0 > 0 SO (M) 0S0 n 3 n 3 3 m + n 3 There are two bas i c hypotheses f o r the mechanism of emulsion po lymer izat ion; the monomer-swollen e m u l s i f i e r mice l l e s hypotheses was postu lated by Harkins [11], and q u a n t i f i e d by Smith and Ewart [12], In 6 this model, which is mainly applicable to monomers which are sparingly soluble in water such as styrene and butadiene, nucleation i s thought to be initiated by free radicals which diffuse through the aqueous phase and penetrate both the monomer-swollen micelles and the droplets. Since the concentration of the micelles far exceeds that of the droplets, polymerization takes place almost exclusively in the micelle interior. The nucleation stage ends when a l l of the micelles have been transformed into polymer particles. The continuous aqueous phase mechanism is the second emulsion polymerization hypothesis, proposed by Priest et al [13] and developed further by Stannett et al [14] and Fitch et al [15]. It i s applicable to monomers such as vinyl acetate and vinyl chloride which are more soluble in water. The mechanism of nucleation in the aqueous phase i s thought to be through the i n i t i a t i o n of a free radical in the aqueous phase, followed by addition of monomer molecules until the oligomeric radical exceeds i t s solubility and precipitates from the solution. The precipitated oligomeric radical either nucleates a particle or flocculates with a particle already nucleated depending on whether i t s surface area exceeds a c r i t i c a l value. The function of the surface active agent here is simply to stabilize the suspensions that are formed. Kotera et al and Goodwin at ei[16], have developed methods for making surfactant-free polystyrene latexes. Surfactant-free latexes offer clear advantages over those made in the presence of surfactants in that the removal of adsorbed surfactant is a lengthy and tedious process; and the presence of any residual surfactants in latex preparation can cause reduction in protein adsorption onto latex surfaces. The principle involved in surfactant-free latex preparation is the same as that of 7 general emulsion polymerization in that the monomer is polymerized in an aqueous phase through i n i t i a t i o n by a free radical. The solubility of styrene in water is low and so the bulk of the monomer in the reaction vessel forms a separate phase. Rapid s t i r r i n g is required to give rapid transfer of monomer to the water in order to maintain a monomer-saturated aqueous phase. Initiation occurs in the aqueous phase, followed immediately by a small amount of propagation until a c r i t i c a l nucleus size i s reached. At this point the rapidly growing hydrocarbon chain collapses into a co i l and precipitates. The nuclei have insufficient electrical charge to make them colloidally stable and so coagulation occurs. During coagulation the solvated sulfate end-groups remain at the polymer-water interface and so the surface charge density rapidly increases until colloidal s t a b i l i t y i s achieved. The coagulation stage is c r i t i c a l both for the control of the degree of monodispersity and the fi n a l particle size. Three types of emulsion polymerization processes are often used in the preparation of polymer latexes [17] ; batch polymerization, semi-continuous and continuous polymerization. For batch polymerization, a l l ingredients are added at the same time at the beginning of the reaction and heated with s t i r r i n g at the polymerization temperature. Decomposition of ini t i a t o r forms the free radicals, which in i t i a t e the polymerization and nucleate the particles. Nucleation i n i t i a l l y proceeds concurrently with particle growth; ultimately only particle growth occurs. Batch polymerization is d i f f i c u l t to control except by cooling and variation of recipe to alter the number of particles. Semi-continuous or semi-batch polymerization occurs when monomer is 8 added to the reactor in increments. Nucleation in semi-continuous polymerization is achieved in two ways: either a small portion of the monomer is charged i n i t i a l l y and polymerized in batch to prepare a seed latex in situ or the monomer is added continuously as the polymerization is started, making nucleation proceed concurrently with particle growth until i t stops and only particle growth occurs. The different modes and rate of monomer addition give different results since they control the rate of polymerization and, i f two monomer types are present, the copolymer composition distribution. Semi-continuous emulsion polymerization is used to make particles with a variation in composition from center to surface, by adding different monomer compositions in sequence. These are known as structured or multi-phase latexes; latexes with a well-defined concentration composition gradient are called core-shell latexes. The use of finely divided magnetite has resulted in the preparation of magnetized polymer latexes (core-shell latexes with magnetite as core) [18]. In continuous polymerization a l l ingredients are added continuously to one part of the reactor system and partially or completely converted latex is removed continuously from another part. The rate of polymerization i s controlled by the rate of monomer addition, but nucleation occurs throughout the reaction so the number of particles varies continuously and the particle size distribution i s more d i f f i c u l t to control. A l l three processes consist of nucleation and particle growth stages which may occur sequentially or concurrently. The nucleation stage is not always reproducible and this causes batch variation in number and particle size of successive polymerizations using the same recipe. The 9 particle growth stage, however, i s reproducible and can be easily-followed. In a l l three processes seeded emulsion polymerization may be used to control the number of particles and the particle size distribution, thus obviating the unreproducible particle nucleation stage. Advances in emulsion polymerization like the modeling of batch, semi-continuous and continuous polymerization and copolymerization processes and the use of functional monomers such as acrylic acid, sodium styrene sulphonate or acrylamide and polymeric emulsifiers tailored to specific applications have enabled the production of latex particles with excellent colloidal s t a b i l i t y and surface characteristics that are more suitable for the many different applications than those made with conventional emulsifiers. 1.2 (c) General Uses Polymer particles have been extensively used in a wide variety of applications [1-4,19-28]. They have been used as additives to various materials: styrene-butadiene copolymer latexes are used as additives for paper coatings, carpet backing, non-woven fabrics, reinforcement of concrete; polyvinyl acetate and vinyl acetate copolymer latexes are used as additives in adhesives, paints and other coatings; polychloroprene latexes are used as additives for synthetic rubber and generally as Theological modifiers; inverse polyacrylamide latexes (water-soluble polymers) are used as additives for flocculation, sludge treatment and o i l recovery. Small quantities of monodispersed polymer latexes are used as size 10 c a l i b r a t i o n standards for l i g h t s c a t t e r i n g instruments, e l e c t r o n and o p t i c a l microscopes and var ious p a r t i c l e counting devices such cou l t er counters , and for the determination of pore s i z e s . Because of t h e i r perfect s p h e r i c a l shape, extremely uniform s i ze d i s t r i b u t i o n , and w e l l - c h a r a c t e r i z e d surfaces , polymer latexes are widely used as model c o l l o i d s to tes t theories i n c o l l o i d , surface and r h e o l o g i c a l sc iences . Recent ly a s i g n i f i c a n t number of a d d i t i o n a l a p p l i c a t i o n s of polymer latexes i n the biomedical f i e l d have emerged. These a p p l i c a t i o n s e x p l o i t advances i n polymer chemistry and the new developments i n biotechnology. Some of these a p p l i c a t i o n s are f u l l y r e a l i z e d now whereas others are s t i l l at the e a r l y developmental stages. Magnetic monosized polymer latexes with appropriate monoclonal ant ibodies are used to remove T c e l l s from bone marrow that i s to be used f o r t r a n s p l a n t a t i o n across h i s t o c o m p a t i b i l i t y b a r r i e r s [25]. Removal of the T - c e l l s prevents gra f t -versus -hos t d isease , which i s presumably caused by minor d i f f erences i n h i s t o c o m p a t i b i l i t y complexes. The same method can a l so be used to remove tumor c e l l s from human bone marrow c e l l suspensions that are used i n autologous bone marrow t r a n s p l a n t a t i o n . Polymer latex microspheres loaded with chemotherapeutic agents and targeted s e l e c t i v e l y to the tumor s i t e us ing monoclonal ant ibodies are p o t e n t i a l l y an exce l l ent drug d e l i v e r y system s ince targe t ing and c o n t r o l l e d re lease of drug can both be achieved by t h i s method [26,27]. Although a number of polymer latexes have been s tudied ex tens ive ly for a p p l i c a t i o n s to drug d e l i v e r y systems, t h e i r use has been l i m i t e d because of the r i g i d demands on the proper t i e s of the microspheres; i n order to be accepted for use they must be biocompatible , biodegradable , non-toxic 11 and allow the entrapment and release of drugs at controllable rates, and at the same time have appropriate size to penetrate blood capillaries. As mentioned in the introduction, protein-coated polymer latexes have been extensively used in diagnostic immunoassays as solid supports. Latex particles between 0.1pm and 1.5/im in diameter are used mainly as carriers for Ag-Ab reactions in latex agglutination tests [1-4]. The particles are coated with soluble antigens and used as reagents for testing the presence of antibodies or antigens in a given f l u i d sample. Since each antibody molecule has two binding sites when the test sample containing the appropriate antibody is added to the antigen-coated latex particle suspension, a precipitate forms as a result of the interaction between the antigen and the antibody. Dissolved antigen competes with bound Ag for Ab so i f the response to a known Ab concentration is known i t s modification by the presence of soluble Ag can be calibrated to allow estimation of the Ag concentration in the test f l u i d . This process is examined in some detail in this thesis. Particles with sizes from 1.5um to lOOum or larger, are used in immunoassays in which labels such as gamma and beta emitting isotopes, free radicals, enzymes and coenzymes, or fluorescent, bioluminescent, or chemiluminescent molecules are employed [ 3 ] . The label is used only as a tracer and does not usually interfere with the Ag-Ab interaction. Porous and non-porous styrene-divinylbenzene latex particles in the size-range 10-1000/im have been traditionally used in a number of chromatographic systems. The particles can be used as such or modified to give ion exchange resins. More recently, strongly hydrophilic porous particles made from highly hydrophilic vinyl compounds in water and o i l emulsions have found wide use in fast protein liquid chromatography 12 (FPLC) [ 2 8 ] . These p a r t i c l e s are of uniform s i z e with very highly h y d r o p h i l i c surfaces and are produced i n the form of strong cation and anion exchangers with poly-buffer exchanger capacity f o r chromatofocusing. The FPLC systems have found wide a p p l i c a t i o n s i n separation and analysis of b i o l o g i c a l materials and the polymer p a r t i c l e s used with them have proven to be superior to other natural polymers l i k e dextran and agarose. Other a p p l i c a t i o n s of latex p a r t i c l e s i n the biomedical f i e l d include t h e i r use as flow cytometry standards, latex based DNA/RNA hy b r i d i z a t i o n assays, in vivo imaging a p p l i c a t i o n s such as the use of radioidonated microspheres to determine the s i t e of i n t e r n a l bleeding, and phagocytosis research to i d e n t i f y blood c e l l s or to i n s e r t chemicals into c e l l i n t e r i o r s [ 6 ] . 1 . 3 Properties of Polymer Latexes 1 . 3(a) Surface Functiona1 Groups Most polymer latex p a r t i c l e s have an inherent surface f u n c t i o n a l group such as s u l f a t e (-0S03H), carboxyl (-COOH), hydroxyl (-0H), or amide (-C0NH2) which i s introduced during polymerization using an appropriate choice of i n i t i a t o r : s u l f a t e groups can be introduced by using potassium persulphate as i n i t i a t o r , and carboxyl groups by using cyanopentanoic a c i d as i n i t i a t o r . Functional groups can also be added to the p a r t i c l e surface a f t e r polymerization by surface chemical modification.. Several f u n c t i o n a l groups, i n varying proportions, can be 13 added to the latex particle surface giving a latex with carboxyl, sulfate, and hydroxyl surface functional groups. Typical latex surface functional groups are shown in Figure 1. 0) Figure 1. Surface functional groups of typical latex particles. (a) Sulfate latex (b) Carboxyl latex (c) Carboxyl Modified latex (d) Amidine (+) latex 14 The i o n i s a t i o n of these surface f u n c t i o n a l groups i n s o l u t i o n r e s u l t s i n a net charge at the p a r t i c l e surface. The surface charge density ranges from about one charge group per every 100 A 2 of the p a r t i c l e surface down to about one charge group f o r every 3000 A depending on the type of charge group and the conditions used i n the preparation of the latex p a r t i c l e s . Latex p a r t i c l e s with low surface charge density are predominantly hydrophobic i n character and those with high surface charge density are predominantly hydrophilic. Many latex types, however, can have intermediate surface c h a r a c t e r i s t i c s . The surface charge density i s important as an i n d i c a t i o n of the number of the a c t i v e chemical functional groups that might be a v a i l a b l e f o r surface reaction, as an i n d i c a t i o n of the r a t i o of hydrophobic to h y d r o p h i l i c areas of the p a r t i c l e surface, and as a guide to the latex s t a b i l i t y . The s t a b i l i t y of the polymer latex suspensions a r i s e s mainly from the i o n i s a t i o n of the chemical groups at the p a r t i c l e surface or by adsorption of surface active agents from s o l u t i o n [29]. A net charge develops at the p a r t i c l e surface, and t h i s a f f e c t s the d i s t r i b u t i o n of ions i n the surrounding i n t e r f a c e region, r e s u l t i n g i n an increased concentration of counter ions (ions of charge opposite to that on the p a r t i c l e surface) close to the surface and an outer d i f f u s e region away from the surface where' the ions d i s t r i b u t i o n i s determined by a balance of e l e c t r o s t a t i c forces and random thermal motion. This d i s t r i b u t i o n or arrangement of ions around the p a r t i c l e i n such a manner i s known as the e l e c t r i c a l double layer and i s formed around each p a r t i c l e i n the d i s p e r s i o n [30]. This i s schematically represented i n Figure 2. 15 0) O o • t CO o o CL 3 3) © Aqueous Medium © © © © © © © © 0 © O 0 intern (rigid) Layer Slipping Plane Diffuse Layer Distance f r o m Particle Surface Figure 2. . The electrical-doubleTTayer; in the interfacial region close to a chargecT particle surface and the potentials in the interface region. (Adapted from Lyklema, J. [29]). 16 The l a t e x p a r t i c l e s u r f a c e c h a r g e can be d e t e r m i n e d by d i r e c t c o n d u c t i o m e t r i c t i t r a t i o n t o d e t e c t t h e e q u i v a l e n c e p o i n t , i n a s i m i l a r way t o c o n d u c t i o m e t r i c a c i d - b a s e t i t r a t i o n . F o r t h e l a t e x p a r t i c l e s , however , a l l t h e c h a r g e d g r o u p s must be c o n v e r t e d t o t h e a c i d f o r m , and any a d s o r b e d s u r f a c e m a t e r i a l w h i c h i s n o t an i n t e g r a l p a r t o f t h e l a t e x s u r f a c e , must be removed p r i o r t o t i t r a t i o n [ 1 0 ] . T h i s i s u s u a l l y a c c o m p l i s h e d b y one o f t h e f o l l o w i n g methods : d i a l y s i s o f t h e l a t e x p a r t i c l e s i n d i s t i l l e d w a t e r , r e p e a t e d wash b y c e n t r i f u g a t i o n / d e c a n t i n g p r o c e d u r e , o r more e f f i c i e n t l y by t r e a t i n g t h e l a t e x d i s p e r s i o n w i t h a m i x e d - b e d i o n - e x c h a n g e r e s i n . The c o n d u c t i o m e t r i c t i t r a t i o n method d e t e r m i n e s a l l t h e c h a r g e g r o u p s w i t h i n t h e p e r i p h e r a l zone o f t h e l a t e x p a r t i c l e and as s u c h may n o t g i v e an a c c u r a t e i n d i c a t i o n o f t h e number o r d i s t r i b u t i o n o f p e r i p h e r a l s u r f a c e g r o u p s w h i c h d e t e r m i n e t h e l a t e x i n t e r a c t i o n w i t h i t s e n v i r o n m e n t . I t i s t h e r e f o r e o f t e n used i n c o m b i n a t i o n w i t h o t h e r t e c h n i q u e s such as e l e c t r o p h o r e s i s t o p r o v i d e a more c o m p l e t e c h a r a c t e r i z a t i o n o f t h e s u r f a c e c h a r g e o f t h e p a r t i c l e . I n e l e c t r o p h o r e s i s t h e s u r f a c e c h a r g e o f t h e l a t e x i s c a l c u l a t e d f r o m t h e p a r t i c l e v e l o c i t y r e s u l t i n g when an e l e c t r i c f i e l d i s a p p l i e d t o a s u s p e n s i o n o f t h e p a r t i c l e s . The p a r t i c l e s m i g r a t e t o w a r d s t h e e l e c t r o d e o f o p p o s i t e c h a r g e a t c o n s t a n t v e l o c i t y and t h e e l e c t r o p h o r e t i c m o b i l i t y ( p a r t i c l e v e l o c i t y p e r u n i t o f a p p l i e d e l e c t r i c f i e l d ) i s a measure o f t h e s u r f a c e c h a r g e o f t h e p a r t i c l e s . An i n d i v i d u a l p a r t i c l e and i t s most c l o s e l y a s s o c i a t e d i o n s ( S t e r n l a y e r , [ 3 1 ] ) move t h r o u g h t h e s o l u t i o n as a u n i t , and t h e p o t e n t i a l a t t h e b o u n d a r y o f t h i s l a y e r , t h a t i s , a t t h e h y d r o d y n a m i c s u r f a c e o f s h e a r be tween t h e p a r t i c l e and i t s i o n a t m o s p h e r e i s known as t h e z e t a p o t e n t i a l , £ (see F i g u r e 2.). The z e t a p o t e n t i a l i s a c c e p t e d as a measure o f t h e p a r t i c l e s u r f a c e p o t e n t i a l , b u t 17 i t i s l o w e r t h a n t h e p o t e n t i a l g e n e r a t e d a t t h e p a r t i c l e s u r f a c e by t h e c h a r g e d ( i o n i z e d ) f u n c t i o n a l g r o u p s . N e v e r t h e l e s s , i t i s t h e r e l e v a n t e l e c t r i c a l p o t e n t i a l when d i s c u s s i n g p a r t i c l e s t a b i l i t y . I t a l s o d e t e r m i n e s t h e l o c a l i o n i c c o n c e n t r a t i o n c l o s e t o t h e e l e c t r o p h o r e t i c s u r f a c e o f a p a r t i c l e w h i c h w i l l d i f f e r f r o m t h e c o n c e n t r a t i o n o f i o n s i n t h e b u l k s u s p e n d i n g medium. S i n c e t h e H + and OH i o n d i s t r i b u t i o n s a r e a f f e c t e d by t h e l o c a l p o t e n t i a l , t h e pH n e a r t h e s u r f a c e , pH , w i l l s d i f f e r f r o m t h e b u l k v a l u e as measured by a c o n v e n t i o n a l pH m e t e r . Thus , f o r a n e g a t i v e l y c h a r g e d l a t e x p a r t i c l e pH w i l l be l o w e r t h a n t h e b u l k s v a l u e s i n c e t h e h y d r o g e n i o n s c o n c e n t r a t i o n w i l l be h i g h e r n e a r t h e n e g a t i v e l y c h a r g e d s u r f a c e . Fo r a p o s i t i v e l y c h a r g e d l a t e x , t h e s u r f a c e pH w i l l be h i g h e r t h a n t h e b u l k v a l u e . H a r t l e y and Roe [32] showed t h a t t h e r e i s a d i f f e r e n c e o f one u n i t o f pH be tween t h e b u l k medium and t h e l a t e x s u r f a c e f o r e v e r y 59mV o f a z e t a p o t e n t i a l . I n t e r m s o f t h e a d s o r p t i o n o f i o n i c s p e c i e s , t h e z e t a p o t e n t i a l i s a u s e f u l i n d i c a t o r o f t h e ease o f a c c e s s o f t h e i o n i c s p e c i e s t o t h e s u r f a c e o f t h e l a t e x p a r t i c l e s . 1.3 (b) P a r t i c l e Size As i n d i c a t e d e a r l i e r , p o l y m e r l a t e x e s can be p r e p a r e d w i t h s i z e s t h a t c o v e r a w i d e range o f d i a m e t e r s , f r o m a b o u t 0 .02pm t o 100pm, d e p e n d i n g on a v a r i e t y o f f a c t o r s d u r i n g t h e p o l y m e r i z a t i o n p r o c e s s . These i n c l u d e t h e a v a i l a b i l i t y o f monomer and f r e e r a d i c a l i n i t i a t o r s d u r i n g p o l y m e r i z a t i o n , and t h e t e m p e r a t u r e o f t h e r e a c t i o n . 18 The particle sizes of latexes can be determined by a variety of methods including transmission electron microscopy [33], light scattering [34], electrophoresis [35], hydrodynamic chromatography [36], electronic particle size analysis [37], and centrifugation [38]. Transmission electron microscopy is frequently used for particle size determination because the whole of the particle size range can be measured by this method. However, light scattering is also a popular method because of the simplicity of the technique. Usually batch preparations with a coefficient of variation on the diameter of less than 10 per cent are termed "monodisperse" and those with a higher coefficient of variation are considered as "polydisperse". The physicochemical behavior of polymer latexes is dependent on their particle size and state of dispersion. Characteristics such as stability and viscosity of latex suspensions are greatly influenced by their size and monodispersity. In general, latex particles with diameters larger than approximately 0.6um tend to sediment under the action of gravity on prolonged standing. Such latex particles can be redispersed readily by gentle agitation. Surface active agents such as sodium dodecyl sulfate (SDS) are often used at low concentrations (<0.1%) to assist in the redispersion of latexes i f the surfactant can be tolerated later in the use of the particles. Some of the applications of the latex particles mentioned earlier depend primarily on the uniformity and size range of the particles. The use of latex particles as standards to calibrate equipment like particle counters, electron and optical microscopes and the various light scattering instruments depend specifically on the uniform size of the particles and on the ability to measure them accurately. Particles with 19 known diameters are used to check openings i n f i l t e r s , pores and blood vessels [39]. Larger p a r t i c l e s (>3fim) are used i n various chromatographic columns. The importance of uniformity i n p a r t i c l e s i z e here i s to control the pressure drop necessary to get flow through the packed bed. Uniform spheres give packing with more por o s i t y (void space) and larger pore diameter than non-uniform spheres. The use of uniform latex spheres minimizes the pressure drop and leads to better flow. 1.3 (c) Colloidal Stability C o l l o i d a l dispersions are two-phase systems, the dispersed phase i n the present case being a s o l i d (polystyrene latex) and the d i s p e r s i o n medium a l i q u i d , water. If the dispersed phase i s highly compatible with the d i s p e r s i o n medium, the c o l l o i d a l system i s described as h y d r o p h i l i c or l y o p h i l i c . When the two phases are incompatible, the system i s described as hydrophobic or lyophobic. The concept of s t a b i l i t y i n c o l l o i d science i s generally understood to mean k i n e t i c s t a b i l i t y , i . e . , s t a b i l i t y imposed by a p o t e n t i a l energy b a r r i e r larger than the average k i n e t i c energy of the p a r t i c l e s and act i n g to reduce contact between the suspended p a r t i c l e s . The average t r a n s l a t i o n a l energy of c o l l o i d a l p a r t i c l e s undergoing Brownian motion i s of the order of (3/2)kT per p a r t i c l e , where k i s Boltzmann's constant, and T i s the absolute temperature. Thus, provided the p o t e n t i a l energy b a r r i e r i s s u f f i c i e n t l y high, compared with kT, the d i s p e r s i o n i s s a i d to be c o l l o i d a l l y stable. If the r a t i o of the p o t e n t i a l energy b a r r i e r to kT i s reduced to le s s than 2, then c o l l o i d a l i n s t a b i l i t y ensues. 20 P o l y m e r l a t e x p a r t i c l e s d i s p e r s e d i n a c o n t i n u o u s medium a r e i n c o n s t a n t B r o w n i a n m o t i o n . They e x p e r i e n c e i n t e r a c t i o n f o r c e s o f v a r i o u s t y p e s , t h e m a g n i t u d e s o f w h i c h s t r o n g l y depend on t h e i n t e r - p a r t i c l e d i s t a n c e s . F o u r t y p e s o f f o r c e s b e t w e e n c o l l o i d a l p a r t i c l e s have been d i s t i n g u i s h e d : L o n d o n - v a n d e r Waals a t t r a c t i o n , e l e c t r i c a l d o u b l e - l a y e r r e p u l s i o n , s t e r i c e f f e c t s due t o a d s o r b e d o r g r a f t e d p o l y m e r s , and s h o r t - r a n g e s t r u c t u r a l f o r c e s a s s o c i a t e d w i t h s t r u c t u r a l d i f f e r e n c e s b e t w e e n t h e i n t e r f a c i a l r e g i o n o f f l u i d i n t h e v i c i n i t y o f a p a r t i c l e compared w i t h t h e b u l k l i q u i d [ 4 0 ] . The o v e r a l l c o l l o i d a l s t a b i l i t y o f t h e d i s p e r s i o n i s t h e r e f o r e d e t e r m i n e d by t h e c o m b i n a t i o n o f t h e v a r i o u s t y p e o f i n t e r a c t i o n f o r c e s . L o n d o n - v a n d e r Waals f o r c e s o r i g i n a t e f r o m t h e f l u c t u a t i o n s i n t h e c h a r g e d i s t r i b u t i o n i n one m o l e c u l e p o l a r i z i n g a second m o l e c u l e and v i c e v e r s a . The London f r e e e n e r g y o f a t t r a c t i o n b e t w e e n a p a i r o f a toms o r m o l e c u l e s , AG , i s v e r y s h o r t r a n g e , v a r y i n g i n v e r s e l y w i t h t h e s i x t h A power o f t h e s e p a r a t i o n d i s t a n c e [ 4 1 ] : AG = A (3/4)hv a o o H~ 6 (1.1) where a i s t h e a t o m i c p o l a r i s a b i l i t y , h i s P l a n c k ' s c o n s t a n t , v i s t h e o * J o d i s p e r s i o n f r e q u e n c y and H i s t h e d i s t a n c e o f s e p a r a t i o n o f t h e a toms . F o r an a s s e m b l y o f atoms o r m o l e c u l e s London f o r c e s a r e , t o a f i r s t a p p r o x i m a t i o n , a d d i t i v e and t h e t o t a l a t t r a c t i v e e n e r g y b e t w e e n t h e a s s e m b l y o f p a r t i c l e s can be computed by summing t h e a t t r a c t i o n s b e t w e e n a l l i n t e r p a r t i c l e p a i r s . Fo r examp le , a c o l l o i d a l d i s p e r s i o n c o n t a i n i n g 21 say, 10 p a r t i c l e s would have the a t t r a c t i v e i n t e r a c t i o n magnified by a f a c t o r of 5 x 10 5, as a r e s u l t of a d d i t i v i t y [ 4 2 ] . The theory of the s t a b i l i t y of c o l l o i d a l dispersions d i s t i n g u i s h e s between lyophobic dispersions, i n which the dispersed p a r t i c l e s are not s i g n i f i c a n t l y solvated, and l y o p h i l i c dispersions, i n which layers of solvent molecules cover the surface of the p a r t i c l e s and help s t a b i l i z e them against aggregation. The theory of the s t a b i l i t y of l y o p h i l i c dispersions i s s t i l l not well understood. However, i t i s well known that t h i s system can be aggregated by p a r t i a l removal of the solvent layer e i t h e r by a d d i t i o n of r e l a t i v e l y large amounts of ions that hydrate r e a d i l y , or by the a d d i t i o n of a second solvent with high a f f i n i t y f o r the d i s p e r s i o n medium. For hydrophobic dispersions, such as PSL i n water, the i n s i g n i f i c a n c e of the solvent layer means that the s t a b i l i t y of the system i s l a r g e l y determined by the i n t e r a c t i o n between the p a r t i c l e s during the course of t h e i r c o l l i s i o n . When charged latex p a r t i c l e s dispersed i n aqueous medium approach each other, e l e c t r o s t a t i c i n t e r a c t i o n s between the i n d i v i d u a l i o n i c double layers surrounding the p a r t i c l e s lead to mutual repulsion. This repulsive force i s dependent on the charge on the p a r t i c l e (and hence on the e l e c t r i c p o t e n t i a l at i t s surface) and on both the type of e l e c t r o l y t e and i t s concentration i n the medium of dispersion. A balance between the e l e c t r i c a l properties of the p a r t i c l e s and the London-van der Waals a t t r a c t i v e forces determines the suspension s t a b i l i t y . This i s the basis of the t h e o r e t i c a l model of c l a s s i c a l c o l l o i d s t a b i l i t y as put forward by Derjaguin and Landau [43] and independently by Verwey and Overbeek [44] who described the i n t e r a c t i o n i n energetic terms and combined the repulsive p o t e n t i a l 2 2 energy of the particles due to their electrical double layer interactions and the attractive potential energy due to the London-van der Waals forces to give the total potential energy of interaction for a pair of hydrophobic particles. When attraction dominates, the particles adhere and the dispersion aggregates and becomes unstable. When repulsion dominates, the system remains in a stable, dispersed state. This theory is commonly known as the DLVO theory, in recognition of i t s originators. A summary of the principles involved in this theory, with no detailed derivations, is given below. Electrical Double Layer In an aqueous medium, most colloidal particles acquire an electrical charge on the surface which gives rise to a surface electrostatic potential , which is assumed to be at the effective slipping plane between the particle (and associated fluid) and the bulk f l u i d . The total free energy of electrostatic repulsion arising from interaction between individual double layers of two particles, AG near each other, R is best represented as [44]: A ~ - , 2 2 exp {-m(H-Za)) ,, AG = 47TE e \b a ^ ( 1 . 2 ) where e is the dielectric permittivity of the medium; CQ is the permittivity of free space; a is the radius of particle; H is the distance between the centers of the particles; and K is the reciprocal 23 Debye-Hlickel e l e c t r i c a l double layer thickness. If the i o n i c double layer i s thin, i . e . Ka»l, then the a l t e r n a t i v e Derjaguin approximation provides the appropriate free energy of i n t e r a c t i o n f o r p a r t i c l e s with constant 0q [45]: AG = 4rce e t/r2ln {1 + exp (-n(ff-2a))} (1.3) R s 0 0 The Debye-Hiickel e l e c t r i c a l double layer thickness i s given by: - I 1/2 lOOOekT 8Tte 2N I A (1.4) where * k i s Boltzmann's constant; e i s the e l e c t r o n charge; T i s the absolute temperature; N i s Avogadro's number; and I i s the i o n i c A strength of the s o l u t i o n = 1/2 £ z 2 C ; z i s the valency of the i t h i o n i c i species; and i s the molar concentration of the i t h i o n i c species. When the thickness of the double layer 1/K i s large , the f r e e energy of repulsion decreases very slowly with separation distance whereas the opposite i s the case with small double layer thickness. This thickness i n turn i s c o n t r o l l e d by the type and concentration of e l e c t r o l y t e i n the system, i . e . by the i o n i c strength. Thus, at low i o n i c strengths the e l e c t r o s t a t i c repulsion provides a long range term, whereas at high i o n i c strengths the repulsion energy term decays very r a p i d l y with distance. 24 van der Waals Attractive Potential The t o t a l f r e e energy of i n t e r a c t i o n , AG , between two sp h e r i c a l A p a r t i c l e s of equal radius, at small separations (ff-2a), was derived o r i g i n a l l y by Hamaker [46] i n the form: where A i s the composite Hamaker constant f o r p a r t i c l e s i n the medium, given by A = ( A1'2 - A1/2 ) 2 (1.6) 11 22 with A = the Hamaker constant of the p a r t i c l e s and A that of the 11 22 medium. The Hamaker (microscopic) approach to the c a l c u l a t i o n of the a t t r a c t i v e energy between p a r t i c l e s assumes a d d i t i v i t y of interatomic dipole-induced dipole i n t e r a c t i o n s and deals with a d i s p e r s i o n frequency c h a r a c t e r i s t i c of the material f o r c a l c u l a t i n g the i n t e r a c t i o n constant. This approach has been shown to be unsatisfactory [47], as there are contributions to the i n t e r a c t i o n constant from a l l the frequencies, and, i n addition, allowance f o r the presence of a medium i s unsatisfactory. Some of these problems associated with the Hamaker (microscopic) theory 25 are overcome by the continuum theory of L i f s h i t z [48], i n which expressions are derived f o r the i n t e r a c t i o n between two bodies separated by a medium, including contributions from a l l i n t e r a c t i o n frequencies. This r e s u l t s i n a more accurate c a l c u l a t i o n of the van der Waals a t t r a c t i v e forces. However, to apply the L i f s h i t z theory, one has to use experimental data on bulk samples and the necessary data are often not a v a i l a b l e f o r many materials. The electromagnetic waves which are responsible f o r the London a t t r a c t i o n between p a r t i c l e s propagate at the speed of l i g h t between the p a r t i c l e s . Thus, f o r a widely separated p a i r of p a r t i c l e s , a time lag or a phase di f f e r e n c e develops between the v i b r a t i o n s at the two locations. This time lag or retardation increases as the separation becomes comparable to the wavelength of the propagating f i e l d . Consequently the d i s p e r s i o n forces w i l l decrease more r a p i d l y than predicted by the Hamaker equation (1.5). Total Free-Energy of Interaction (DLVO Theory) Usually the zeta p o t e n t i a l (£) of the p a r t i c l e , i . e . , the p o t e n t i a l at the hydrodynamic shear plane of the p a r t i c l e , i s equated with the surface p o t e n t i a l of the p a r t i c l e , \f> . For the s i t u a t i o n i n which only o e l e c t r o s t a t i c and van der Waals in t e r a c t i o n s are predominant, the t o t a l f r e e energy of i n t e r a c t i o n between two p a r t i c l e s , A G t > i s given by the DLVO theory as [41]: A G = A G + A G T A R (1.7) 26 The total free energy curves for AG , AG , and AG between two & J T A R particles are illustrated in Figure 3. The sharp increase of repulsion energy at very close approach is due to repulsion between the electron clouds of atoms of the particles and is referred to as the Born repulsive energy. In general, the energy-distance curve can show three main features: a primary minimum, M , at close contact, a maximum P , and a shallow secondary minimum at long distance of separation, M^. The introduction of a distance of closest approach is important with regard to the shape of the total interaction energy-distance curve. A deep primary minimum is obtained only i f the particles come into contact. But direct contact is unlikely since the distance of closest approach is determined by adsorbed layers of counter ions (in the Stern layer) and/or adsorbed solvent molecules. The higher the value of P , the more kinetically stable the suspension. According to the DLVO theory, an energy barrier of about 15 kT is sufficient to produce a highly dispersed system. In practice, however, there i s a spread of potential energies and coagulation can occur at this energy barrier level, so a value of P in excess of 25kT is taken as a c r i t e r i a for stability. The theory also indicates that the magnitude of the energy barrier depends on the dimensions of the particles and their surface potential. With large particles, the net potential energy may develop a secondary minimum at an appreciable distance of separation. For latex particles, calculations show that the influence of the size of particles on the energy barrier is such that for particles with radii « 200 nm or greater, a secondary minimum of sufficient depth for flocculation is formed. 27 P -M « -M 2 -A V -Electrostatic Repulsion - P r i m a r y M a x i m u m - P r i m a r y M i n i m u m - S e c o n d a r y M i n i m u m - E n e r g y Bar r i e r t o Coagu la t i on rotal Potential Energy 2 'van der Waals Attraction Distance, H Figure 3. Typical form of the. total-interaction free energy between electrostatically stabilized polystyrene latex particles with separation distance H. (Adapted from Everett, [531). 28 Therefore in practice., primary minimum coagulation and secondary minimum coagulation can occur simultaneously under certain conditions. The characteristics of the aggregates formed in the secondary minimum are quite different from those formed in the primary minimum. Primary minimum aggregates are compact and usually extremely difficult to redisperse, whereas the aggregates formed in secondary minimum are weak and can easily be disrupted by hydrodynamic shear forces. Although the DLVO theory forms the basis of classical colloid stability theory, more recently various other interactions between colloidal particles have been identified. These include the steric forces which are long-range repulsion arising from polymers adsorbed and/or anchored to the interacting surfaces; and structural forces, which are strong repulsive forces that arise as a result of changes in the solvent structure in the vicinity of the colloidal particle surface or interface. Steric Forces Additional repulsive interactions can occur when the particles bear adsorbed layers of surfactants or macromolecules. An adsorbed layer thickness, 5, may be defined in terms of the configuration of the adsorbed surfactant or macromolecule in analogy, for instance, to the radius of gyration of a free polymer molecule [140]. When two particles with adsorbed layers approach each other to a separation distance that is less than twice the adsorbed-layer thickness (H<25), interference may occur. Under certain conditions this interference may lead to repulsion for the following possible reasons [49]: 29 (i) The mixing of adsorbed layers may lead to repulsion. This i s because the solvent chemical p o t e n t i a l i n the overlap region i s lower than that i n the bulk s o l u t i o n and as a r e s u l t , d i f f u s i o n of solvent molecules occurs from the bulk s o l u t i o n to the overlap region, leading to repulsion. ( i i ) As the adsorbed layers approach each other, the volume a v a i l a b l e f o r the adsorbed chains becomes r e s t r i c t e d . The loss of c o n f i g u r a t i o n a l entropy of the chains as a r e s u l t of such an approach leads to repulsion. This e f f e c t i s often referred to as the volume-restriction e f f e c t . ( i i i ) The van der Waals a t t r a c t i v e force between the p a r t i c l e s i n disp e r s i o n v a r i e s with distance of separation as a power law ( i . e « r 6 ) . Thus the e f f e c t of increasing adsorbed-layer thickness i s to e f f e c t i v e l y reduce the a t t r a c t i v e van der Waals forces [51]. Various models have been developed f o r s t e r i c i n t e r a c t i o n forces and expressions have been derived f o r the cont r i b u t i o n of s t e r i c i n t e r a c t i o n to the t o t a l repulsive energy of i n t e r a c t i o n between two p a r t i c l e s . For example, Napper, [50] has given the following approximate expression f o r the s t e r i c i n t e r a c t i o n between two spheres with adsorbed polymer layers: 2 TT a k T V 2 T 2 2 2 (i/2 - x ) S + 2 na k T T S m i x 2 e l (1.8) where V i s the solvent molecular l volume, T i s the adsorbed amount 2 F l o r y polymer/solvent i n t e r a c t i o n geometric functions that depend on volume, V 2 i s the polymer molecular of polymer per unit area, x i s the parameter, and S and S are the m i x e l the form of the segment concentration 30 profile p(z), in the adsorbed layer normal to the interface. The need to establish the variation of the concentration profile, p(z) with separation distance of the particle and the many assumptions made in the derivation of the equation limits the applicability of this expression in practical systems. In general, the presence of polymer either on the surface of colloidal particles or free in solution can lead to other types of interactions between the particles. For example, high molecular weight polymers present in low concentration can cause bridging flocculation by attaching to several particles at the same time [52]. An excess of non-adsorbed polymer in a colloidal dispersion can also cause depletion flocculation in which polymer molecules are excluded from the space between particles as they approach each other, reducing the concentration of polymer between the particles below that in the bulk solution. The osmotic pressure difference between the gap and the bulk solution results in an interparticle attraction. Agglutination of Antigen-coated PSL When the mechanism producing particle aggregation arises from specific interparticle bridging by ligands or macromolecules, as in the case of an antigen-antibody interaction, the process of aggregation is termed "agglutination." The forces involved in agglutination reactions include the short range van der Waals attractive forces, repulsive electrostatic force, steric repulsion, and the specific antigen-antibody interactions. The short-range van der Waals attractive forces are, to a f i r s t approximation, independent of pH and ionic strength. The 31 electrostatic repulsive force is controlled by the pH and ionic strength of the system, i t s magnitude being dependent upon the charge of the particle which in turn is dependent upon the charge of the coating protein. The antigen-antibody interaction force can involve electrostatic, hydrogen bonding, hydrophobic, and van der Waals forces but is primarily dependent on the spatial complementary configuration of the reactive binding site on the antibody and the determinants on the antigen molecule. Total Free-Energy of Interaction (General Equation) It is clear from the brief consideration above that the total free interaction energy between two colloidal particles can be influenced to a varying degree by several contributions. Thus, the most general equation for the total free energy difference between particles can be obtained by adding a l l the contributions [41]: AG = AG (van der Waals) + AG (short range) + T A R AG (electrostatic) + AG (steric) + AG (other effects) ...(1.9) R R However, in practice i t is not necessary to consider a l l these contributions simultaneously, except in certain special cases. 32 Relative Stability The measure used to determine the relative s t a b i l i t i e s of different polymer latexes that are stabilized by electrostatic interaction is called the c r i t i c a l coagulation concentration (the c.c.c. value). Coagulation of charge stabilized latexes occurs at a well-defined electrolyte concentration that is strongly dependent on the valence of the added counterion. It has been established that the c r i t i c a l coagulation concentration varies inversely as the sixth power of the counterion valency; this is known as the Schultze-Hardy rule [ 5 3 ] . Similar expressions are used to describe flocculation of colloidal particles induced by the presence of polymer either on the surface of the particles or simply present in solution. For example, the term " c r i t i c a l flocculation concentration" (c.f.c.) i s used to describe the c r i t i c a l particle volume fraction for the onset of flocculation in the presence of polymer, and " c r i t i c a l flocculation temperature" (c.f.T) to describe the observation that for a given particle volume fraction, a c r i t i c a l flocculation temperature is reached, beyond which the onset of weak (reversible) flocculation is observed. 1 .3 (d) Fluid Notion and Colloid Stability Coagulation caused solely by Brownian motion of the particles is usually referred to as "perikinetic coagulation" and that caused solely by a velocity gradient is called "orthokinetic coagulation". Any 33 coagulation caused by external forces is treated as a special case of orthokinetic coagulation, since the movement of particles relative to the liquid also creates velocity gradients. In terms of the attractive and repulsive forces that are operative during coagulation, "rapid coagulation" occurs when there are no surface repulsive forces between the particles, that is when every collision leads to aggregation; and "slow coagulation" occurs when only a fraction of the collisions result in aggregation, that is when there exists a significant surface repulsion force causing a barrier to coagulation. The theoretical analysis of coagulation kinetics was first outlined by Smoluchowski [54], who considered the case where double layer interaction between the particles was absent, so that the rate of coagulation is fully governed by Brownian motion (perikinetic coagulation). For monodispersed colloidal particles, Smoluchowski showed that the rate of diffusion-controlled coagulation is proportional to the collision radius of the particles, the diffusion coefficient, and the square of the concentration of the particles: = 4 T I D R n = k n ( 1 . 1 0 ) dt i i i where = diffusion constant of a spherical particle of radius a^  = kT/6irna (Einstein Equation) TJ is viscosity of the continuous phase, k is Boltzmann's constant, and T is absolute temperature. R = collision radius ( = 2a for homodisperse i i 34 particles), n = number of particles per cm , and k^ = 4T I D R , is the rate constant for diffusion-controlled coagulation. Since coagulation is a continuous process, particles of different radii are involved in the coagulation even i f the original system is homodispersed. That is, the values of diffusion constant, the collision radius, and the rate constant should strictly be: k = 4T I D R , R = a + a , and D = D + D . i j i j i j i j i J i j i j However in theory it is assumed that a^  = a^  to simplify the rate expressions. Equation 1.10 only applies to rapid coagulation that occurs by Brownian diffusion and bulk fluid motion is of no consequence, and where there are no energy barriers present to interfere with the coagulation process. At another extreme, Smoluchowski also considered coagulation caused solely by bulk flow of fluid in a laminar shear field giving a constant velocity gradient (shear-induced or orthokinetic coagulation). In this case Smoluchowski considered a stationary reference particle in a constant velocity gradient and assumed that the uniform shear field is unperturbed by the presence of the particles, and, therefore, the path followed by a particle is rectilinear. He also assumed that only binary collisions occurred, each resulting in a new aggregate composed of two interacting particles. Using similar assumptions and simplification as for the case of Brownian coagulation, i.e. uncharged spherical particles interacting through van der Waals attractions, Smoluchowski obtained the following equation for coagulation under uniform shear field: 3 5 -dn 4G#n (1.11) dt where G is the velocity gradient, and <f> is the volume fraction of particles. Equation 1.11 is strictly applicable for coagulation caused solely by a uniform shear field. However, in practice it is difficult to obtain a uniform shear field as constant velocity gradients are difficult to achieve. A close experimental form of a uniform shear field occurs in the annular gap between coaxial rotating cylinders (couette apparatus). More recently, the effects of interparticle forces on shear-induced aggregation have been treated theoretically. Using improved hydrodynamic results for binary interactions between spheres presented by Batchelor and Green [55], Curtis and Hocking [56], van der Ven and Mason [57], and Zeichner and Schowalter [58] have developed a trajectory analysis approach for the determination of shear stability which incorporates hydrodynamic forces as well as London-van der Waals attractive forces and electrostatic repulsive forces as described by the DLVO theory. These analyses indicate that the presence of fluid between the particles as they approach one another reduces the likelihood of a collision and so reduces the coagulation rate. Van der Ven and Mason have calculated that in the absence of any repulsive forces between particles this hydrodynamic effect caused a reduction in coagulation rate which was proportional to the shear rate to the 0.18 power. When combined with the explicit first order coagulation rate dependence on shear rate, this gives rise to a coagulation rate which is proportional to the 0.82 power of the shear rate. 36 Slow Coagulation The coagulation analyses presented above consider two extreme cases where coagulation occurs rapidly either by Brownian c o l l i s i o n only or by shear c o l l i s i o n only. The frequency with which the reference particle is bombarded by the other particles is given by [ 5 9 ] : J° = 4T T D R n (for Brownian collision) B i j i j 0 3 and J = 4/3 n R G (for shear collision) s i j Coagulation can also occur with slower rates of collisions as when there is an energy barrier in the form of double layer repulsion between the particles, or , put another way, the coagulation occurs in the secondary minimum, the primary maximum being assumed to be so large that i t is insurmountable. In this case, the departure of coagulation rates from the extreme cases (rapid) can be expressed as a s t a b i l i t y ratio: W = J°/ J (1.12) where J° can be a Brownian or a shear-induced c o l l i s i o n frequency limit. This idea was introduced by Fuchs [60] who considered the case of coagulation where particle interactions are important and found that the total c o l l i s i o n rate is lowered by an amount W. He obtained the 37 following expression for W: W - 2a f e x P ( 7 / k T ) dr (1.13) where V is the potential energy of interaction and kT is the thermal energy. W can also be defined simply as the ratio of the rate constant of the fast coagulation to that of the slow coagulation: W = k / k (1.14) f s where k f the rate constant of fast coagulation, where there i s no energy barrier, and k is the rate constant of slow coagulation where s there is an energy barrier due to interparticle repulsive forces. A plot of log W versus log C (C = concentration of electrolyte) can be used in practice to distinguish between slow and fast coagulation [ 6 1 ] . Above a c r i t i c a l coagulation concentration, that is in the region of rapid coagulation, W = 1 and so log W = 0. Below the CCC value, i t is observed that log W increases linearly with decrease in log C. 38 1.4 Interaction of Proteins with Polymer Surfaces 1.4 (a) General Considerations The ongoing interest in (bio)polymer adsorption to particles is largely due to i t s importance in t e c h n i c a l applications such as the control of sta b i l i t y , flocculation and T h e o l o g i c a l properties of colloidal dispersions [23]. The role of polymer adsorption in tertiary o i l recovery and the regulation and control of lubricant properties, where surface treatment by polymer is used to adjust wetting are further examples of technical applications [62]. The adsorption of biopolymers in membranes, c e l l walls and in natural and a r t i f i c i a l blood vessels leads to important phenomena in biology, pharmacology and medicine [63]. In different types of chromatography, biopolymer adsorption is a key factor in controlling the fractionation of uncharged and charged macromolecules by gel permeation, af f i n i t y , and hydrophobic chromatography. Polymer and biopolymer adsorption studies are also of special interest from a purely theoretical and experimental viewpoint in that they give insight into structural, thermodynamic and dynamic properties of macromolecules in solution and at interfaces. This in turn contributes to our understanding of biochemical processes such as blood coagulation and c e l l adhesion to a r t i f i c i a l surfaces. Understanding of the properties of colloidal systems dispersed in solutions containing molecular species such as proteins must be based on a thorough knowledge of the interaction between the colloidal particles 39 and the protein molecules in solution and of the structure of the resulting interface between the colloidal particle and the protein molecule. The protein molecule adsorbs onto the particle surface due to forces such as the London-van der Waals interaction force, hydrophobic interactions, hydrogen bonding , and ionic interactions. Many authors, using a wide variety of different techniques, have reported on the adsorption of proteins at the solid/liquid interface [64-75]. Hence, many of the general aspects of protein adsorption to a solid surface are well documented: the amount of adsorbed protein is known as a function of protein concentration in solution, and as a function of adsorption conditions for solids surfaces with different characteristics [76-79]. Other parameters such as the competitive adsorption behavior of proteins, the conformation of the protein at the solid surface as a function of total surface area available for adsorption, the adsorbed layer thickness and structure, and the consequence of such conformational changes and layer thickness on the interaction forces between the surfaces are less well documented [66]. This is partly because of the many variables which affect the adsorption of proteins onto solid surfaces. Protein adsorption can be affected by the nature of the protein including its size, charge, structure, purity, and concentration; the nature of the solid surface such as hydrophobic/hydrophilic ratio, uniformity and surface energetics, and by experimental conditions such as the buffer, pH, ionic strength, and equilibration (flow or static) conditions [66]. Consequently, different results have been observed for protein adsorption at seemingly similar conditions and, likewise, various interpretations have been proposed to explain similar trends in protein 40 adsorption. For example, plateau values are often found; to be not far from those of the close-packed monolayer of native molecules in a side-on or end-on orientation [70]. On the other hand, multilayer adsorption has also been noted [80-85]. The increase in adsorption towards the isoelectric point of the protein is explained by Norde et al [86] as being due to structural changes of the albumin molecule. They conclude that the adsorption behavior of albumin is determined mainly by the structural changes of the albumin molecule. Roe, [86], on the other hand, explains similar increase in adsorption of BSA onto polyoxymethylene surface as arising mostly from reduced electric charge on BSA molecule and not from any change in i t s shape. He concludes that the predominant factor governing the adsorption of BSA on the polyoxymethylene surface is the electrostatic repulsion between the adsorbing BSA molecules. With regard to protein adsorption to polymer latexes, the factors that control the interaction seem to be the hydrophobic/hydrophilic balance on the surface of the latex, electrostatic interactions, and solution conditions [87]. For most proteins, hydrophobic interactions between the hydrophobic amino acid side chains of the protein and the uncharged regions of the polymer latexes seem to be responsible for adsorption. Several authors have noted that the a f f i n i t y between a given protein and an adsorbent increases with the hydrophobicity of the surfaces [88-100]. Hence, for a given protein, adsorption increases with the hydrophobicity of the polymer latex surface [100]. The hydrophobic/hydrophilic ratio is determined by the number of functional groups on the latex surface, since the bulk polymer is hydrophobic. Too many functional groups on the latex surface can interfere with physical or chemical binding of proteins. 41 Since latexes have various hydrophobic to hydrophilic ratios, adsorption of proteins onto the surface of latex particles dif f e r from one particle to another. For latex particles that are highly hydrophobic (<5 charges per 1000A of surface), protein adsorption shows characteristics that are often independent of the sign of the net charge on both the protein and the polymer latex as, for instance, the pH changes. For ideal adsorption, latex particles should have sufficient hydrophobic surface area for protein adsorption. Hydrophobic interactions lead to protein molecules being strongly adsorbed to the latex surface; proteins desorb more easily from hydrophilic surfaces [101]. Electrostatic interactions may also strongly influence the patterns of protein adsorption onto polymer latex surfaces [76,88,90-93]. The electrostatic effects, however, seem to be only superimposed upon the stronger hydrophobic effects. This i s indicated by the fact that a l l proteins studied to date adsorb strongly to polymer latexes, regardless of the sign of charge on the latex and by the fact that positively charged polymer latexes show enhanced adsorption of negatively charged proteins, presumably through electrostatic attraction [71]. It is not clear, however, i f the electrostatic interaction simply acts to increase the local concentration of the protein near the latex particle surface or i f i t i s directly involved in ionic bonding. At high surface coverage, electrostatic repulsion between the polymer latex and protein bearing the same charge signs may hinder further adsorption. Solution conditions such as the pH and ionic strength strongly affect saturation adsorption of proteins to polymer latexes. For example, i t has been shown that protein adsorption is a strong function of pH, with a maximum in the amount adsorbed at pH values near the isoelectric point of 42 the p r o t e i n [102]. Th i s i s explained i n terms of the e f f ec t which the charge of the p r o t e i n molecule has on i t s c o n f i g u r a t i o n and i n terms of the r e p u l s i o n between the adsorbed p r o t e i n molecules. The lower amount adsorbed at pH values away from the i s o e l e c t r i c point of the p r o t e i n i s a t t r i b u t e d mainly to s t r u c t u r a l rearrangements of the p r o t e i n molecules. In many cases p r o t e i n adsorpt ion to polymer latexes i s found to increase with i o n i c s trength of the e q u i l i b r i u m buf fer . Th i s i s thought to be due to the reduct ion i n the p r o t e i n - s u r f a c e e l e c t r o s t a t i c i n t e r a c t i o n s , p r o t e i n - p r o t e i n r e p u l s i o n and p r o t e i n conformational changes. On the other hand, other r e s u l t s show much less dependence of p r o t e i n adsorpt ion on pH and i o n i c s trength [80], and, with regard to s o l u t i o n cond i t ions , no general r u l e s seem a p p l i c a b l e . There are many other f a c t o r s that are involved i n the i n t e r a c t i o n between p r o t e i n molecules and the polymer latexes , but most of them are e i t h e r not yet wel l documented enough to c l a r i f y the nature of the i n t e r a c t i o n , or are d i f f i c u l t to determine by most a v a i l a b l e experimental techniques. For example, considerable e f f o r t i s now being devoted to the understanding of the s t r u c t u r a l and conformational d e t a i l s of adsorbed prote ins at the s o l i d / l i q u i d i n t e r f a c e s . Information from such s tudies w i l l be use fu l with regards to the o r i e n t a t i o n or conformation and b i o l o g i c a l a c t i v i t y (e .g. enzyme a c t i v i t y ) of the adsorbed p r o t e i n s . Surface energet ic proper t i e s of the adsorbing surfaces i s another f a c t o r that perhaps deserves more cons iderat ion i n p r o t e i n adsorpt ion s tudies [103-105]. Baszkin [100] concluded that the r a t i o of the po lar and d i s p e r s i o n components of the work of adhesion (Wp/Wd) determines the A A degree of a f f i n i t y of the p r o t e i n f or the adsorbent and that maximum a f f i n i t y occurs when (Wp/Wd) approaches u n i t y . Andrade [101] and 43 Ruckenstein et ai [102] concluded that neither the total surface free energy of the solid nor the fractional contributions of the solid's component surface free energy should be considered indicators of i t s a b i l i t y to adsorb protein. Rather, the interfacial energy between the solid and water is a more natural parameter which should be related to protein adsorption. The larger the latter the greater the adsorption. On this basis a surface energetic criterion for biocompatibility of surfaces was suggested [102]. Another aspect of protein adsorption to polymer surfaces that is incompletely understood is the competitive adsorption behaviour of proteins [106]. Much of the work done in this area has been focused on: (a) the understanding of the behaviour protein adsorption, as i t occurs from relatively complex solutions of protein mixtures, to implanted biomaterials [107]; (b) a desire to understand the sequence of events leading to clot and thrombus formation on solid surfaces in contact with blood [108]; and (c) protein chromatography [109-111]. Horbett and Brash [106] l i s t some of the important properties of proteins that influence competitive adsorption as follows: molecular size and el e c t r i c a l charge of the protein, hydrophobicity-hydrophilicity and chemical functional groups on the surface of the protein, conformational sta b i l i t y , interlayer (i.e. protein-protein) interactions in the adsorbed layers; and the surface characteristics of the adsorbent. An important result that i s reported in a number of competitive protein adsorption studies is that i n i t i a l l y , the effect of concentration on diffusion dominates and so the protein with the highest bulk concentration is adsorbed f i r s t . Later, as the concentration of higher a f f i n i t y trace proteins near the surface increases they are adsorbed and the f i r s t adsorbed protein is 44 displaced. This mechanism is the basis of sequential adsorption in multi-protein systems [112]. The effect of f l u i d shear on the adsorption of proteins has been studied by a number of authors [113-116]. Brash et al [108] u t i l i z e d polyethylene and glass surfaces in the form of tubing segments and found that as much as 75% of adsorption is complete within a few minutes and equilibrium is attained within about one hour. Their results show that exchange of proteins between surface and solution occurs and that this exchange varies with the nature of the surface (i.e greater for hydrophilic than for hydrophobic), and depends upon such factors as protein concentration and flow rates. Rudee et al [114] designed a flow c e l l to which a thin film of test material (e.g. polystyrene) could be mounted on i t s surface. In the flow c e l l , the test material is exposed to flowing protein solutions under well characterized conditions. Following exposure of the test surface in the flow c e l l , the surfaces were examined in an electron microscope. Their results show differences in the morphology of the adsorbed individual protein molecules and protein films formed, on the type of surface to which the proteins are adsorbed, and the flow conditions under which the protein solutions contact the materials. However, the mechanism leading to the formation of the network of adsorbed proteins is not understood. Robertson et al [115] studied the i n i t i a l adsorption, desorption, and exchange kinetics of BSA on six polymer surfaces with widely varying surface properties and functionalities using total internal reflection fluorescence and found that the i n i t i a l adsorption of BSA on surfaces such as polydimethylsiloxane (PDMS) is diffusion limited up to wall shear rates of 4000 s 1, whereas adsorption of BSA on polystyrene sulphonate 45 (PSS) is diffusion limited at shear rates below approximately 70 s~ but becomes kinetically controlled at higher shear rates. They also found that BSA adsorption on polymethyl methacrylate (PMMA) is kinetically controlled, and polyethylene oxide (PEO) surfaces show no adsorption of BSA under the conditions studied. Nakamura et al [116] examined BSA adsorption onto porous polymer resins by a pulse injection method and showed that the amount of BSA bound irreversibly to the resins is independent of the protein concentration and the flow rate studied. Usually the adsorbed mass per unit area, T, is determined as a function of the equilibrium protein concentration in solution, C , and an p adsorption isotherm (T vs. C ) is constructed. For flexible, highly p solvated polymers, high-affinity isotherms are almost always obtained. A typical high-affinity isotherm is given in Figure 4a. At low polymer concentration, virt u a l l y a l l the polymer is adsorbed until the surface is f u l l y covered; the i n i t i a l part of the isotherm merges with the ordinate axis. With higher polymer concentration, a continuously increasing value of T is usually found. This is explained by structural rearrangements in the adsorbed molecules, involving a decreasing number 2 of attached segments per molecule. Near saturation T reaches a few mg/m of the adsorbent surface [71]. Pure, single globular proteins (compact molecules), in many cases develop well-defined plateau values with a f i n i t e i n i t i a l slope as shown in Figure 4b [71]. The plateau values are often reached at dilute or semi-dilute protein concentrations in solution, depending somewhat on the conditions (adsorbent surface charge (o* ), pH, temperature, and salt o concentration) and correspond to a close-packed monolayer of native 46 p r o t e i n s i n a s i d e - o n o r e n d - o n o r i e n t a t i o n s . -Equilibrium Polymer Concentration Equilibrium Protein Concentration Figure 4. T y p i c a l a d s o r p t i o n i s o t h e r m s f o r (a ) f l e x i b l e , h i g h l y s o l v a t e d p o l y m e r s and (b ) g l o b u l a r p r o t e i n s (compact m o l e c u l e s ) . ( A d a p t e d f r o m N o r d e , W. [ 7 1 ] ) . 47 1.4 (b) Theoretical Considerations Analyses of polymer adsorpt ion have ranged from very simple a p p l i c a t i o n s of models der ived for small molecules, to d e t a i l e d s t a t i s t i c a l mechanical treatments of the conformational changes that u s u a l l y accompany polymer adsorpt ion [117-125]. Biopolymers such as g lobu lar pro te ins do not have the f l e x i b i l i t y nor the s i m p l i c i t y of synthe t i c polymers. They d i s p l a y a complex 3-dimensional s t r u c t u r e with a m u l t i p l i c i t y of intramolecular i n t e r a c t i o n s , surface f u n c t i o n a l groups, and conformational dynamics [126]. In p r i n c i p l e the synthe t i c polymer s t a t i s t i c a l method could be extended to the adsorpt ion of p r o t e i n s , but there are ser ious l i m i t a t i o n s that have not been reso lved to date. A major l i m i t a t i o n i s the use of the mean-f ie ld approximation to compute the l a t e r a l i n t e r a c t i o n between segments, which does l i t t l e j u s t i c e to the c h a r a c t e r i s t i c a l l y high s p e c i f i c i t y of p r o t e i n s . On the other hand, re levant advances are being made and the extension of the theory to p o l y e l e c t r o l y t e s (polypeptides) has accounted, at l east s e m i - q u a n t i t a t i v e l y , f or the e f f ec t s of pH and i o n i c s trength on adsorpt ion of these types of polymer [127]. One other aspect of polymer and p r o t e i n adsorpt ion that has not been widely considered i n both t h e o r e t i c a l treatments and experimental a n a l y s i s of adsorpt ion isotherms i s the p o l y d i s p e r s i t y e f f e c t . Many (bio)polymers used i n experimental s tudies are e i t h e r po lyd i sperse , by nature of t h e i r synthes i s , or form oligomers i n s o l u t i o n [128]. U s u a l l y adsorpt ion isotherms are in terpre ted assuming the adsorbed species i s a s i n g l e (monomeric) (bio)polymer so lute . There i s an increas ing amount of 48 experimental and theoretical evidence [129,130] that shows that larger polymeric molecules, in a mixture, adsorb preferentially over smaller ones. Other studies show the existence of weakly and tightly bound proteins [131]. The physical reason for preferential adsorption of larger polymeric molecules is based on the idea that protein adsorption occurs via multiple contact points with the solid surface; and that higher a f f i n i t y molecules bind preferentially. Thus, more bonds per molecule are formed for larger molecules than for smaller molecules. Indeed, the model proposed by Cohen Stuart et al [130], in which the polydispersity of the polymer is taken into account, shows that many discrepancies between polymer adsorption theory and experiment (e.g. the rounded shape of isotherms, the dependence of the adsorbance on adsorbent concentration, and the lack of desorption upon dilution) can be attributed to polydispersity effects. The simple theory developed in Cohen Stuart et al [130] predicts that the dependence of the amount adsorbed on the surface area to solution volume ratio, which is due to polydispersity, can be eliminated i f adsorption is plotted as a function of polymer concentration, (C ), times the ratio of solution volume to p adsorbent area (V/S). That i s , for the adsorption of polydispersed polymers the relevant independent variable is not the equilibrium solution concentration, (C ), but the non-adsorbed amount per unit area : p T = C/ (S/V). The prediction of this theory [130] is that the p dependence on (S/V) due to polydispersity ought to collapse to a single curve i f plotted as described above. 49 1.4(c) Immunoglobulin G Structure P r o t e i n molecules present i n blood serum or body f l u i d s of an animal that combine with s p e c i f i c antigens are c a l l e d antibodies. Proteins with antibody a c t i v i t y are r e f e r r e d to as immunoglobulins (Ig). Most immunoglobulins are Y-shaped. Each such immunoglobulin molecule consists of four polypeptide chains, co n s i s t i n g of two l i g h t , L (M 22000 to 24000 r and two heavy, H, carbohydrate-containing chains (W 50000 to 73000), as r shown i n Figure 5 [132]. There are f i v e known classes of immunoglobul ins, IgA, IgD, IgE, IgG and IgM, based on the primary structures of t h e i r respective heavy chains. The heavy chains are linked to each other by one or more d i s u l f i d e bonds (two shown here f o r IgG); and the l i g h t s chains are linked to the heavy chains by d i s u l f i d e bonds. Each chain i s made up of a s e r i e s of homology u n i t s of approximately 110 amino acids held together i n a loop, or domain. The o v e r a l l structure i s also s t a b i l i z e d by strong non-covalent bonds. Studies show that the two H chains are composed of v a r i a b l e V , C 1, C 2 and C 3 domains and the two l i g h t L chains of V H H H H 6 L and C^ domains. Cleavage of the IgG molecules at the hinge generates two i d e n t i c a l Fab fragments, each containing one i n t a c t l i g h t chain disulphide-bonded to a fragment of the heavy chain containing the V and H C 1 domains [133]. Each Fab fragment contains one antigen-combining s i t e . The remaining portion of the IgG molecule consists of a dimer of C 2 and C 3, c a l l e d the Fc portion. The Fc portion i s homogeneous and H H contains no antigen-binding a c t i v i t y . The v a r i a b l e regions of the H- and L-chains are located at the tf-terminal of the amino acid sequence of the homology un i t s . 50 Figure 5. Schematic representation'•of Immunoglobulin G (IgG) molecule. The two heavy chains are composed of V , C 1, and C 2 and C 3 H • H H - H • and the two light chains of V l and domains. (Adapted from [132]). 51 The sequence within the variable regions are extremely variable at some locations, called the hypervariable regions, but conserved at other locations. The V and the V domains fold in such a way that the H L hypervariable regions are brought together to form an antigen-combining site. 1.4(d) Binding of Antibody to Antigen-Coated Polystyrene Latex (PSL) The binding of a specific antibody to an antigen-coated latex suspension can cause the antigen-coated particles to adhere and form clumps. This process, commonly known as agglutination is similar to precipitation, but the latex particles used in agglutination are larger and are in suspension rather than in solution. The formation of clumps results from cross-linking of antigen-coated particles by antibodies from solution. Thus multivalent antibodies (e.g. IgG with a valency 2 or IgM with a valency of 10) can induce agglutination, whereas monovalent antibodies (e.g. Fab fragment) with only a single binding site cannot cause cross-linking of antigen-coated particles by this mechanism. The process of agglutination can be conceptually divided into two steps. In the f i r s t step, the binding of free antibody in solution to the antigen-coated particles leads to a partition of antibody molecules into those that are free in solution, not bound to any antigenic molecules, and those that are bound to one or more antigens on the particles. The second step is the formation of cross-links (bridges) between antigen-coated particles. This second step is somewhat similar to a polymerization reaction in which the antigen-coated particles constitute the monomeric units and the linking of one antigen-coated 52 particle with another by specific antibodies leads to the formation of a network of particles connected by antibodies. It i s to be expected that antibody binding to the antigen-coated latex particles would be affected by such factors as the surface area of the latex particle and i t s total concentration, the antibody binding constant (or affinity) and i t s concentration in solution, and the total antigen concentration which is determined by the density of antigen coverage on the surface of a particle and the total particle concentration. However, there has been very l i t t l e work done on the details of such reactions, with respect to antigen-coated latex particles. Considerable work, which is relevant to latex immunoreactions in vitro, has been done on (a) the binding of antibodies to antigens on c e l l surfaces [134-141]; (b) the mechanism of receptor-carrier liposome based immunoassays [142]; and (c) studies involving multiple reactive site polymers based on distribution functions describing the probability of polymers having a certain number of sites unreacted [143,144]. These theoretical studies have included kinetic as well as equilibrium analyses of monovalent, bivalent, and multivalent ligands interacting with monovalent or bivalent receptors. The binding of ligands to receptors that are cell-bound or otherwise fixed, as on a latex bead, is more d i f f i c u l t to understand theoretically. The results of these theoretical analyses indicate that when receptors are clustered in space, as when they are confined to c e l l surfaces, their rates and equilibrium constants can be quite different from those observed when they are uniformly distributed in solution. This is because their binding and rate constants are dependent on many physical properties of the system such as the binding site density on the c e l l surface; diffusion coefficient 53 differences; concentration, size and shape of the reactants; and orientational requirements for reaction. 1.5 Research Approach The background outlined above gives a brief description of polymer latexes, some of their applications and uses; their physicochemical properties with emphasis on their colloidal properties and surface chemistry, and a summary of the major qualitative features of their interactions with proteins. The aim of this project is to carry out a systematic study of the interaction of Ag and Ab with well-characterized polystyrene latexes in an attempt to rationalize the surface and colloid chemistry involved in the interactions. The general approach taken is f i r s t to examine the adsorption of a protein Ag (bovine serum albumin) onto polystyrene latexes with different surface characteristics and establish the dominance of such adsorption in determining the colloidal s t a b i l i t y of the resultant protein-coated polystyrene latexes. Purified antibodies to the adsorbed protein are prepared and the equilibrium binding of the purified antibody to the antigen-coated polystyrene latex i s studied in order to obtain an estimate of the average number of antibodies bound per antigen-coated particle and the variation of this average number with concentration of antigen on the latex surface. To study the kinetics of flocculation (agglutination) of these colloidal dispersions (protein-coated polystyrene latexes) under various shear rate conditions, a couette 54 shearing device is used in which suspension turbidity can be continuously monitored as a measure of aggregation. The results provide a contribution to the understanding of the mechanism of interactions of proteins with polystyrene latexes and the determinants and kinetics of reversible and irreversible flocculation of Ags and Ag/Ab coated latexes.. For this work surfactant-free polystyrene latex beads with different surface functional groups were chosen (Interfacial Dynamics Inc. , Portland, OR). Bovine serum albumin (BSA) Fraction V (Miles Lab.) was used as the antigen, and purified polyclonal rabbit anti-BSA, prepared in this laboratory by immunizing rabbits with BSA Fraction V were used. The antigen (BSA) was adsorbed onto the various polystyrene latex beads, and the degree of surface coverage assayed by measurement of the adsorption isotherms with radioidonated BSA. BSA desorption from the polystyrene surfaces was examined by washing the latex beads with buffer of the same composition and pH as the adsorbing solution. In order to examine to some degree the composition of the adsorbed layers, the latex was washed in a solution of surface active buffer (sodium dodecyl sulfate, SDS-buffer) and the released protein run on SDS electrophoresis gels The colloidal s t a b i l i t y of the various polystyrene latexes coated with BSA at different surface coverage was determined by measuring their rate of flocculation as a function of NaCl concentration using a concentric cylinder constant shear couette device that was designed and built in our laboratory in such a way that i t f i t the c e l l compartment of an HP 8450 UV/VIS Spectrophotometer. Using this apparatus, the agglutination of BSA-coated latex particles by rabbit anti-BSA antibody was studied under different shear rates. 55 CHAPTER TWO  BSA ADSORPTION TO POLYSTYRENE LATEXES 2.1 Introduction 2.1 (a) Experimental Considerations One usually requires measurements of the adsorbed amount, the bound fraction and the layer thickness to characterize an adsorbed polymer fu l l y . This information could be obtained from the concentration profile through the adsorbed layer i f i t were available but unfortunately the number of experimental systems where this profile can be measured is at present somewhat limited. The most commonly used method to study polymer adsorption is to measure the amount adsorbed per unit area of adsorbent, for which there are two basic approaches: one can detect either the depletion of polymer from the solution or the accumulation of adsorbate on the substrate. The f i r s t of these methods is usually preferred and a wide range of analytical techniques is available for the measurement of the concentration of free polymer in solution. Given the surface area of the substrate, the adsorbed amount per unit area may be calculated. Assuming » constant molecular volume i t is possible to make generalizations regarding the thickness of the adsorbed layer based on amount adsorbed per unit area at saturation. However, arguments based on such measurements can often be ambiguous as there is no a priori information on the conformational state of the polymer in the adsorbed layer, and because the specific surface area "seen" by the polymer is not always precisely known. 56 The f r a c t i o n o f a d s o r b e d p o l y m e r segmen ts , p, can be measured by i n f r a r e d ( I R ) , n u c l e a r m a g n e t i c r e s o n a n c e (NMR), e l e c t r o n s p i n r e s o n a n c e (ESR) s p e c t r o m e t r y and by m i c r o c a l o r i m e t r y [ 1 4 5 - 1 4 9 ] . U s i n g i n f r a r e d , t h e I R - b a n d s ( v i b r a t i o n o r t o r s i o n ) o f f u n c t i o n a l g r o u p s o f p o l y m e r s l i k e c a r b o n y l - , p h e n y l - , and p y r i d i n e can be measured q u a n t i t a t i v e l y i n c a r b o n t e t r a c h l o r i d e ( c c l 4 ) o r c h l o r o f o r m (CHC1 3). Upon a d s o r p t i o n , t h e I R - b a n d s o f t h e a d s o r b e d segments a r e s h i f t e d t o l o w e r wave numbers . The NMR t e c h n i q u e r e l i e s on t h e d i f f e r e n c e i n m o b i l i t y o f t h e segments i n t h e l a y e r d i r e c t l y a d j a c e n t t o t h e s u b s t r a t e , compared t o t h e m o b i l i t y o f f r e e l o o p s and t a i l s i n s o l u t i o n . Fo r ESR, a s u i t a b l e s p i n l a b e l t h a t can be i n c o r p o r a t e d i n t h e p o l y m e r c h a i n i s r e q u i r e d . The l a b e l s a t t a c h e d t o l o o p s and t a i l s a r e e x p e c t e d t o be more m o b i l e t h a n t h o s e on t h e a d s o r b e d p a r t o f t h e p o l y m e r , r e s u l t i n g i n d i f f e r e n c e s i n s p e c t r a l l i n e w i d t h o f t h e l a b e l s . The t h i c k n e s s o f an a d s o r b e d p o l y m e r l a y e r can be o b t a i n e d by a v a r i e t y o f t e c h n i q u e s i n c l u d i n g e l l i p s o m e t r y , c a p i l l a r y f l o w , p h o t o n c o r r e l a t i o n s p e c t r o s c o p y (PCS) and s m a l l - a n g l e n e u t r o n s c a t t e r i n g (SANS). I n e l l i p s o m e t r i c measurements [ 1 5 0 ] , t h e change i n t h e s t a t e o f p o l a r i z a t i o n o f l i g h t upon r e f l e c t i o n f r o m a s u r f a c e i s measured . From t h e phase s h i f t and a m p l i t u d e o f t h e r e f l e c t e d beam w i t h r e s p e c t t o t h e i n c i d e n t beam, t h e t h i c k n e s s and r e f r a c t i v e i n d e x o f t h e a d s o r b a t e can be c a l c u l a t e d . The e l l i p s o m e t r i c s y s t e m r e q u i r e s a f l a t o p t i c a l l y r e f l e c t i n g s u r f a c e . I n b o t h t h e c a p i l l a r y f l o w and PCS [ 1 5 1 ] methods a h y d r o d y n a m i c model i s r e q u i r e d t o i n t e r p r e t t h e r e s u l t s . I n c a p i l l a r y measurements , t h e h y d r o d y n a m i c t h i c k n e s s i s deduced f r o m t h e r e d u c t i o n i n f l o w r a t e o f t h e f l u i d i n a c a p i l l a r y t u b e when t h e r e i s p o l y m e r a d s o r b e d . The r e d u c t i o n i n f l o w r a t e i s due t o a d e c r e a s e i n t h e r a d i u s o f t h e c a p i l l a r y t u b e . SANS [ 1 5 2 ] , g i v e s a d i r e c t e s t i m a t e o f t h e second 57 moment of the volume fraction profile, which is independent of a model for the adsorbed layer. Most of 1 these experimental methods have only been introduced recently and are in developmental stages. In most cases, they are restricted to specified conditions and are not universally applicable. In addition, the spectroscopic techniques used in protein adsorption studies may give information only on localized areas of the protein which i s then assumed to apply to the whole protein molecule. 2.1 ( b ) Structural Features of Albumin The protein antigen used in this work, bovine serum albumin (BSA), is a single polypeptide chain of approximately 580 amino acids; the exact number of amino acids depends on the type of albumin. Earlier models based on physicochemical properties of the protein suggest two general structures for the molecule [153,154]. Both models assume that at neutral pH levels the molecule forms a compact globule. Foster at el [153] suggest that the globule is made of four compact sub-units connected by short lengths of polypeptide chain and on lowering the pH the sub-units move away from one another but s t i l l retain their local structure. Franglen et al [154] suggest that the globule consists of a highly organized core covered by a less organized coating of polypeptide chain and on lowering the pH the molecule expands through unwinding of this coating but the core s t i l l retains a high degree of organization. Later models based on amino acid sequencing [155] suggest that the albumin molecule is composed of nine double loops linked together by short chains of amino acids [156]. The folding of the nine double loops into the three dimensional structure is dependent on non-covalent bonds. 58 Based on observable differences in the physicochemical and structural properties of the molecule under various conditions, the number of "subunits" has been reduced to three [157 ,158] and these have been designated as structural and functional domains [ 1 5 9 ] . This has been confirmed recently by crystallographic investigation of the three-dimensional structure of human serum albumin [ 1 6 0 ] , in which the electron density maps reveal the structure of albumin as a predominantly a-helical globular protein, which agrees with a variety of other studies [161] that depict albumin to be an oblate ellipsoid with semi-axes of 140 A by 40 A. The entire structure is maintained by 17 disulfide bonds. Each domain, consisting of approximately 190 amino acid residues, is an independent folding unit with a large double loop, a short connecting segment, a small double loop, a long connecting segment (hinge), another large double loop, and a connecting segment to the next domain. Although considerable homology in general structure can be seen between domains, the amino acid sequence and function of each domain are considerably different. The majority of the similarity between a l l three domains centers on the disulfide bonds [ 1 6 2 ] . The albumin molecule has i t s most stable state at pH 6-7 and temperatures just below 5°C. The bonds which maintain the domains in their three-dimensional structure can be disrupted reversibly by lowering the pH to 3.4 -3 .6 [ 1 6 2 - 1 6 4 ] . The albumin molecule undergoes reversible expansion under these condition as indicated by changes in i t s physicochemical properties: the sedimentation constant and the diffusion constant decrease, and the intrinsic viscosity and number of interchangeable hydrogen atoms increases [ 1 6 2 - 1 6 4 ] . Foster [163] proposed that in this reversible pH-induced transformation, the molecule 59 isomerises first from a normal form (N), to an F form (for faster migration) which is somewhat expanded. Later [163], it was established that in this N-F transformation, the molecule loses about 10 percent of the native three-dimensional structure, as measured by its content of a-helix determined by the optical rotation technique. Elevating the pH range from neutrality to about 9 unfolds the protein molecule to a more open structure; this loss in structure is also reversible and is called the N-B transformation. The N-B transition is accompanied by a reduction in the measured a-helix content of as l i t t l e as 3 percent [166]. The albumin molecule also undergoes temperature-dependent reversible transitions between molecular states which are not well-defined. With respect to temperature, the molecule has its most stable structure at a temperature just below 5° C . and undergoes transitions above this temperature. At 37° C and pH 7.5, there is 20 percent less helical structure than at 5° C [164]. Above 50° C albumin starts to denature irreversibly, before the entire three-dimensional structure is lost. The pH- and temperature-dependent reversible transitions are independent of each other, which indicates that different parts (loops or domains) of the albumin molecule are involved in the unfolding [164]. When the albumin molecule unfolds from the N to the B state the molecule is more easily irreversibly denatured than in the N-state. The heat-induced loosening (unfolding) of the albumin structure also renders the molecule less rigid against irreversible transformations. It is observed that a specific type of denaturation, due to intramolecular SS-interchange, runs slowly at pH 7 but increases to a maximum value at around pH 8.5 [167]; it is also observed that the rate of irreversible heat denaturation and denaturation due to storage change from a minimal to a maximal level in the same pH interval [165,168]. 60 2.1 (c) Albumin Heterogeneity Isolated BSA, especially samples that have been lyophilised, heat-treated, or stored in solution, almost always contain oligomerrs. The formation of the oligomers is thought to occur during preparation and storage of the protein. The proportion of the oligomer depends on a number of parameters such as the nature of the starting plasma, fractionation procedure, addition of stabilizers, concentration of the solution, storage conditions and length of storage [169-174]. Freshly isolated serum albumin monomer consists of approximately 70 percent mercaptalbumin (containing one sulphydryl group per mole of albumin) and 30 percent non-mercaptalbumin (where the sulphydryl group is blocked through mixed disulfide formation with cystine and, to a lesser extent, glutathione [175]). The sulphydryl groups are the most reactive of any amino acid side chain and ionize at slightly alkaline pH, giving the reactive anion (-S ). Disulfide exchange reaction between the anion (-S ) of one BSA molecule and a disulfide bond (-S-S-) of another molecule leads to the formation of a dimer molecule with four disulfide bonds [143]: -S—S—| - S — s - s + - s — s -- s — s -- s — s -S—S—I -S—S-s—I -S-S - s The dimer can then react further to form higher polymeric BSA molecules. This is the basis of the formation of dimers and higher polymeric species of BSA during prolonged storage of the protein. Whether this occurs or not depends on the accessibility of the disulfide 61 bonds and the free sulphydryl group of the BSA molecule. Protein disulfides are generally stabilized by the protein conformation, so that favorable unfolding of the BSA molecule would have to occur in order for i t s disulfide bonds to be exposed. Similarly, the free sulphydryl group of the BSA molecule is thought to be attached to the relatively compact N-terminal portion of the BSA molecule that is apparently folded inward to gain protection from oxidation. However, disulfide interchange has been encountered unexpectedly by many workers [143]. That the albumin molecule is able to unfold in several more or less independent steps is not surprising since the net energy which keeps a protein in i t s three dimensional structure i s quite small, at least according to the few cases in which i t has been experimentally determined [176]. For example, the free energy accompanying the unfolding of ribonuclease and lysozyme from their native structure to a restricted random c o i l (without breaking any S-S bridges) amounts to only 3 and 4 J g"1 [176]. For albumin, the unfolding takes place in several more or less independent steps, and for this reason i t has not been possible to determine the free energy of complete denaturation. Hydrogen exchange studies, done at 25°C and pH 6.5, [164] give a rough indication of the free energy which holds the albumin molecule together; i t is found that less than 25 kJ mol 1 is sufficient to open the molecular structure enough to let the surrounding water molecules enter and come into contact with about 60 percent of the peptide bonds of the molecule. Increasing the pH from 6.5 to 7.6 makes the albumin molecule become more unstable, and 70 percent of the peptide bonds are in contact with water. The nature of the dimer and polymer that usually occur in serum albumin samples is not clear. Hartley et al [177] found that about half 62 the dimers in albumin could be s p l i t into monomer on treatment with mercaptoethanol. The other half of the dimers that are not s p l i t by mercaptoethanol seemed to be relatively stable. What holds them together is not known. Treatment of these dimers with detergent solutions and their s t a b i l i t y in mercaptoethanol solutions at low and high pH show that hydrophobic and electrostatic bonding are probably of limited importance for keeping the dimers together. It is suggested that both kinds of dimer (reducible and non-reducible) are kept together by disulfide bonds but that in one of them the disulfide bond is situated in the interior of the molecule and not accessible for reaction with mercaptoethanol in the native state of the molecule [ 1 7 8 ] . In this work passive adsorption measurements of iodine-125 labeled BSA to polystyrene latexes bearing different surface functional groups were made with the aim of using these BSA-coated latexes as a model in fundamental studies of reactivity of polymer-borne biological molecules. Our approach to protein adsorption studies was,three-fold: (i) . To determine, as accurately as possible, the amount of protein adsorbed by the various types of latexes under different solution conditions using radiolabeled protein. ( i i ) . To determine how much protein i s retained on the latex particle surfaces after extensive rinsing with equilibrium buffer; i.e. the reversibility of the adsorption. ( i i i ) . To determine the molecular weight distribution of the adsorbed protein. 63 2.2 BSA Adsorption Procedure 2.2 (a) Introduction Of the several methods a v a i l a b l e to assay p r o t e i n concentration and perform p r o t e i n adsorption studies, we chose to use r a d i o l a b e l i n g . This was f o r two main reasons: i t i s an accurate method f o r determining pr o t e i n concentration over a wide range, and i t has the s e n s i t i v i t y to be used to determine the amount of adsorbed p r o t e i n e i t h e r d i r e c t l y or by measuring depletion from s o l u t i o n a f t e r e q u i l i b r a t i o n with p a r t i c u l a t e s . In the depletion method, the disappearance of the p r o t e i n from s o l u t i o n i s equated with the amount adsorbed by the substrate, provided that the substrate does not absorb the protein and corrections are made fo r the i n e v i t a b l e adsorption onto the surface of the tube or vessel containing the adsorption mixture. Usually t h i s method works best when the uptake corresponds to at least a 10 percent change i n the pro t e i n s o l u t i o n concentration; enough surface area i s required f o r such a change to occur. The other method, of d i r e c t l y counting the labeled protein associated with the substrate surface, involves d i s t i n g u i s h i n g between the adsorbed labeled protein and the l a b e l l e d p r o t e i n i n s o l u t i o n i n the i n t e r s t i t i a l f l u i d surrounding the substrate p e l l e t . It i s also important to ensure that the bond between the l a b e l and the p r o t e i n molecule i s stable under adsorption conditions and that the la b e l i n g method or the label i t s e l f does not change the adsorption properties of the protein. The labeled p r o t e i n i s characterized by ei t h e r chromatographic or electrophoretic methods to a s c e r t a i n that i t s 125 behaviour resembles that of the nonlabeled protein. I was chosen as the r a d i o l a b e l and the la b e l i n g procedure i s described i n d e t a i l below. 64 2.2 ( b ) Materials Iodinat ion Ion-exchange r e s i n (Dowex SBR 8% cross-linked, 20-50 mesh) was obtained from Sigma. Iodo-beads (immobilized chloramine T molecules on non-porous polystyrene beads (1/8 inch diameter)) were from Pierce Chemical Company. 125 Na I i n d i l u t e sodium hydroxide solu t i o n , with t y p i c a l s p e c i f i c a c t i v i t y of 12-15 mCi per gram, was purchased from Amersham. Bovine Serum Albumin (BSA), F r a c t i o n V, Lot # 388 was from Miles Labs. T r i c h l o r o a c e t i c a c i d (TCA), Lot # E5X was from Eastman Kodak Company. An LKB 1282 Compugamma Universal Gamma Counter was used. Sodium azide was from Fisher S c i e n t i f i c Company and sodium chloride was from BDH Chemicals. Mono and d i b a s i c sodium phosphate were from Sigma. Phosphate buffer (0.01M, pH = 7.20), was prepared by adding a s o l u t i o n of 0.2M NaH PO (72ml) to 0.2M Na HPO (28ml) and d i l u t i n g with d i s t i l l e d water to 2 4 2 4 2 l i t e r s . Polystyrene Polystyrene latexes synthesized without surfactants, with d i f f e r e n t surface f u n c t i o n a l groups, were monodisperse samples obtained from I n t e r f a c i a l Dynamics Corporation (IDC), Portland, OR. Some of the properties of the polystyrene latexes that were used i n the adsorption studies are summarized i n Table I. The r e c i p r o c a l of the surface charge 65 density represents the average area surrounding each titratable charge group. Comparison of this area per charge group with theoretical area 2 2 per charge group (e.g. 20-25 A /S04 or 20 A /C00H) gives a rough guide of the percentage of the particle surfaces that are occupied with ionic groups and that which is available for adsorption of molecules like proteins. This is included in Table I and i t can be seen that the sulfate latex has about 9% of i t s surface occupied by the SO" groups, while the carboxyl, carboxyl modified and amidine (+) have 6%, 40-50%, and 177. respectively. Thus, 91% of the sulfate latex and 94%, 50-60% and 84% of the carboxyl, carboxyl modified and amidine (+) latex surfaces are available for the adsorption of protein molecules assuming only the hydrophobic area is active. Particles with lower surface charge densities, for example the sulfate latex with surface charge density of -2 -2 6.70 fiC cm , and the carboxyl latex with 2.88 fiC cm , have more area on their surfaces for adsorption of other molecules than do latex particles with higher surface charge densities. The carboxyl modified latex beads have hydrophilic groups on their surface which add s t a b i l i t y to the particle and additionally contain a significant amount of surface attached water-soluble polymer. The concentrations of latex suspensions used in adsorption studies were determined by diluting the stock suspensions received from the suppliers gravimetrically and drying in an oven at 60-80°C for 24 hours. The stock latex suspensions for adsorption experiments were prepared by centrifuging a weighed amount of the supplier's suspension with 0.01M phosphate buffer, pH 7.2, (4000 x g for 30-60 min, depending on latex type), and resuspending in the same buffer. 66 Electrophoresis SDS(Sodium dodecyl sulfate), Acrylamide, BIS(Af, Af-methlene-bis-acrylamide, TEMED (Af, N, AT , AT-tetramethylethylnediamine) and ammonium persulphate, were Electrophoresis Purity Reagents from Bio-Rad. Coomassie Blue G-250, was from Kodak, Lot #B9H and Pyronin Y was from Baker Chemical Co., Lot # 923344. Tris-HCl was from Sigma. Methanol, glacial acetic acid and perchloric acid were from BDH. A l l chemicals were of analytical grade. The electrophoresis procedure followed is given in detail in Appendix 1. Table I Characteristics of Polystyrene latexes used in adsorption and agglutination studies Latex type: Sulfate Carboxyl CML Amidine Diameter: (nm) 1073±5.04% 984±5.1% 865±5.3% 489±6.90/ Specific Surface area: (cm g )xlO 53.0 57.8 65.8 116.3 Surface Charge density -2 (uC cm ) 6.70 2.88 30.7 12.2 Area per charge group (A /group) 239 557 52 131 % of Surface occupied with ionic groups 9 6 40-50 17 % of surface that is hydrophobic 91 94 50-60 83 67 2.2 (c) Methods 2.2 (c) (i) Radiolabeling of BSA The iodination procedure followed was that developed by Markwell [179,180], Prior to iodination , Dowex SBR anion exchange resin, 8% cross-linked was soaked in water for 10 minutes. A large batch (240 ml) was suspended in 6M NaCl, and washed in a Buchner funnel with decreasing concentrations of sodium chloride. The f i n a l suspension was washed and suspended in a 0.15M NaCl containing 0.02% NaN^ and stored at 4°C. When required, 6-8ml of the ion-exchange resin was placed in a disposable column, washed thoroughly with phosphate buffer (0.01M, pH 7.20) followed by a 0.1% (w/w) solution of BSA. The ion-exchange resin suspension was then washed thoroughly with phosphate buffer again to remove excess protein. On the day of iodination, two or three Iodo-beads were washed twice in phosphate buffer (0.01M, pH 7.20) using approximately lml/bead in a small beaker, then blotted dry on f i l t e r paper. One hundred micrograms of protein in 0.5ml of phosphate buffer was added to an incubation tube 125 along with 5 to lOul of I solution (l-2uCi). The iodination reaction was initiated by the addition of two to three Iodo-beads and allowed to proceed in the capped tube and stirred for 15 minutes at room temperature in an iodinating fume-hood. The iodinated protein was then transferred to the ion-exchange column with a Pasteure pipette, leaving the Iodo-beads in the reaction tube. For maximal recovery the beads were washed twice with 1.0ml of phosphate buffer and the wash added to the ion-exchange column. Appropriate fractions (10, 15 or 20 drops) containing the iodinated 68 protein were then collected from the ion-exchange column, eluting with an equal bed-volume amount using phosphate buffer. Aliquots (5ul) of each fraction were collected, transferred into a counting tube and made up to counting volume (2ml) with ice-cold phosphate buffer, containing a 127 0.2mg/ml albumin and 0.5mol carrier iodide (Na I), for measurement of the total radioactivity present in the sample. After this count, an equal volume (2ml) of 20% (w/v) of TCA was added to the counting tube and mixed well. This is partly to ensure the presence of enough protein for the formation of sedimentable aggregates on precipitation and partly to reduce adsorptive losses of radioactivity on the tube surface. The suspension was then centrifuged for 10 minutes at 1500 X g while s t i l l cold. Two m i l l i l i t e r s of the supernatant were transferred to a second tube and both samples were counted for gamma activity. The fraction of radiolabel bound to protein was estimated from the sample act i v i t i e s as: % label bound = (P-S)/P x 100, and % label free = 100-% bound, where P i s the total i n i t i a l count in solution and S is the supernatant count. It was found that after the separation of radio-labeled protein from the free label through the ion-exchange column, 5-10% of the label was s t i l l present free in the labeled protein samples. Further removal of the free label was necessary; this was done using a Centriprep-10 concentrator device made by Amicon. The device is a disposible u l t r a f i l t r a t i o n tube with a f i l t r a t e collector and a membrane cutoff of 10,000 MW. The iodinated-protein samples were collected into the Amicon device and washed through the f i l t e r three or four times with buffer, using a centrifuge (3000 x g for 15min). The f i n a l f i l t r a t e was diluted with fresh phosphate buffer to the desired activity. 2.2 (c) ( i i ) 69 Adsorpt ion The stock latex suspensions for adsorption experiments were prepared by washing a weighed amount of the supplier's suspension with the phosphate buffer. A maximum of four concentrations of latex solution were then determined gravimetrically by drying in an oven at 60-80°C for 24 hours. The stock protein preparation for adsorption studies was made by mixing 1-5 percent radioactive protein with a solution of nonradioactive protein prepared by dissolving a weighed amount of crystalline BSA in the appropriate phosphate buffer. The concentration of the stock protein mixture was determined from i t s absorbance and extinction coefficient of BSA at 278nm (i.e., Absorbance Unit of 0.667 for BSA at 278nm = 1 mg/ml). The specific activity of the stock protein concentration was determined by measuring the radioactivity counts of a weighed sample. A Mettler balance with an uncertainty of ±0.0001g was used for a l l weights. Adsorption isotherms were determined in three different ways. First, the protein concentration and the surface area of the latexes were varied at constant total volume in order to measure the binding isotherms at different surface areas of the latex. Second, the total protein solution volume in each set of samples was varied while the total surface area of the latex was kept constant. Finally the total surface area of the latex was varied, but the amount of protein and the total volume in each sample was kept constant. A typical adsorption experiment was carried out as follows: the appropriate amount of stock latex, BSA, and buffer were weighed into a polystyrene tube (Evergreen, 4.5ml). The weighed suspensions were mixed gently and allowed to equilibrate under gentle horizontal shaking, using 70 a Khan shaker (Eberbach) , for six to eight hours at room temperature. After incubation of the latex particles with the protein, the samples were centrifuged for 60-90 minutes at 12000 X g using a Sorval centrifuge in order to separate the adsorbed protein on the latex surface from the equilibrium protein in solution. Three aliquots ( = 200ul) of the clear supernatant were removed from each sample tube, weighed and gamma counted. Adsorption isotherms were calculated from the difference in the supernatant and the i n i t i a l concentration of BSA according to the following expression: r = c x v (2 .D a x m s -2 where V = amount adsorbed per unit area (mg cm ) C = C - C i e C = i n i t i a l concentration of BSA (mg/g ) i s oln. C = equilibrium concentration of BSA (mg/g ) e soln. V = amount of f l u i d in suspension (g) 2 a = specific surface area of latex (cm /g) s m = mass of latex added (g) The i n i t i a l concentration of BSA in each sample was determined from the amount of BSA solution added and the specific radioactivity of stock BSA. The equilibrium concentration of BSA was determined from the average of the activity of three samples removed from the supernatant and the specific activity of the stock BSA. The mass of latex in each sample was determined from the average of mass fractions of the stock latex suspension obtained gravimetrically. The specific surface area of the latex was calculated from the expression: 71 6 x 104 (2.2) a dp s - 3 where d is the particle diameter in cm, and p is the density in g cm . An example of these calculations i s given in Appendix 2a. In order to determine the molecular weight distribution of the adsorbed protein by electrophoresis analysis and to determine the reve r s i b i l i t y of the adsorption of BSA onto the various latex surfaces under different solution conditions, a wash analysis was performed. The samples used in electrophoresis analyses were i n i t i a l l y washed with 2ml of 0.01M phosphate buffer, pH 7.2 three or four times using a centrifuge, followed by three 200fil portions of Fairbanks electrophoresis sample reagent containing 2% sodium dodecyl sulfate (SDS). The samples used in reve r s i b i l i t y studies were i n i t i a l l y washed with 4ml 0.01M phosphate buffer, pH 7.2 under the same conditions as the adsorption measurements, equilibrating each wash for 6-8 hr. The successive wash cycles with pure buffer, nonlabeled BSA, anti-BSA IgG, 2% polyethylene glycol (PEG) solution, and 2% SDS were performed in the same manner, each for 6-8 hr. 2.2 (c) ( i i i ) Wash Analysis 72 2.3. Results and Discussion 2.3 (a). Adsorption Isotherms for BSA to the Four Latex Types: The adsorption isotherms reported below are the results of single isotherm measurements in which three aliquots (« 200fil) of the clear supernatant solution were removed from each sample tube. Estimates of the uncertainty in the measured concentration of BSA in each of the three supernatant aliquots, the i n i t i a l concentration of BSA and the total surface area of latex used in each experiment, formed the basis of the error analysis as outlined in Appendix 2a and given in tabulated results. A separate set of experiments in which the adsorption of BSA to sulfate latex was repeated in order to give an indication of the reproducibility of the adsorption data is given in Appendix 2b. ( i ) . Variation of Surface Area of the PSL Figure 6 shows the adsorption isotherms for BSA adsorbing from 0.01M phosphate buffer, pH 7.2 at room temperature to the four latexes described in Table I. In each case three different surface areas of latex were used. Generally, a l l the isotherms show the typical "Langmuir" shape reported in many previous studies [64-72]. With the exception of the CML isotherms, there is an i n i t i a l steep rise in the amount adsorbed with increasing BSA concentration to a semi-plateau value that is dependent on the total surface area of the PS latex available for adsorption. 73 Equilibrium Baa Coneantnrtlon (mg/ml) Equilibrium Bio Concantnrtlon (mg/ml) 5.0 CML (0.865/ im) .(202 cm!) 3*7(541 crrr) 0.0 0.2 0.4 0.6 0.8 Equilibrium Baa Concentration (mg/ml) ^J74 cm*) Amidine ( + ) latex (0.489/im) „ (395 cm*) • 0 n em*) 360 cm1) 0.0 0.2 0.4 0.6 0?8 Equilibrium Baa Concentration (mg/ml) Figure 6 . Adsorption isotherms, for .BSA to the latexes indicated at room temperature, from 0.01M phosphate buffer, pH 7.20; The total surface areas of latex used in each experiment are as indicated. 74 Norde and Lyklema [76] carried out extensive studies on the adsorption of human serum albumin (HSA) to various polystyrene latexes. Since the composition of HSA and that of BSA are very similar [181], a comparison, with respect to general trends in adsorption isotherms, is made here with their results. Their studies show that the adsorption of HSA on polystyrene latexes develops plateau values at sufficiently high equilibrium concentrations. They considered that different parts of the isotherm reflect interactions that may lead to different modes of adsorption. For example, they suggest that at low coverage of the PSL surface, the shape of the isotherm is i n i t i a l l y determined by protein-polystyrene interactions. At high coverage, lateral interactions between adsorbed protein molecules may also play a role in the adsorption process. Although the adsorption isotherms appear to be Langmurian in nature, the fundamental postulates of the Langmuir isotherms are not f u l f i l l e d in most cases in protein adsorption studies [70,71,76,91,92,99]. Protein adsorption on solid surfaces i s , generally, found to be virtua l l y irreversible to dilution over times of many hours [69,71,101,113]. This is thought to occur because proteins interact with the PSL surface at many points of the protein molecule, a l l of which must be released simultaneously for spontaneous desorption to occur. Surface-induced conformation changes may take place upon adsorption and lateral interaction may also occur at high concentrations of adsorbed proteins. Thus, protein adsorption isotherms on solid surfaces cannot be evaluated according to the Langmuir method to extract equilibrium thermodynamic binding constants. Norde and Lyklema also find inflection points or kinks in their adsorption isotherms for HSA at intermediate coverage and suggest that 75 reorientation or conformational alteration of the adsorbed HSA molecules is accountable for this. They rule out the possi b i l i t y of multilayer adsorption on the basis that the adsorption is completely irreversible towards dilution. The present results do not indicate the existence of any inflection points. The isotherms show a rounded shape up to equilibrium concentrations of about 1 mg/ml, for a l l the latexes. Saturation values or plateau values were estimated from the adsorption data and their values are listed in Table II. With the exception of the carboxyl modified latex (CML), a l l the plateau values _2 are within the range of 1 to 5 mg m observed by several other investigators using BSA and polystyrene latex [64-72,76]. Taking the BSA molecule to be a oblate ellipsoid with major and minor semi-axes a and b respectively, the side-on cross-sectional area of the molecule is given by wab. Monolayer adsorption for a side-on packing arrangement can be estimated using the cross-sectional area and the relative molar mass of BSA, to a good approximation by, M r =- r rcabN where N = Avogadro's number, M = relative molar mass of BSA (66000) r and for BSA 2a = 140 A and 2b = 40 A [161]. This leads to a value of _2 2-2.5 mg m depending on the value of the dimension and molecular weight of the BSA molecule used. Thus, there seems to be no evidence of multilayer adsorption in our experimental results, based on the estimated monolayer plateau values. 76 Table II Adsorption maxima of BSA adsorption isotherms in Figure 6, as estimated from the isotherms. Variation of Surface area: Sulfate (mg m 2) 1.81±0.12 1.3710.08 1.03±0.07 Carboxyl CML (mg m ) (mg m ) 2.7710.07 2.4210.12 1.4010.18 0.4410.01 0.34+0.01 0.2910.02 Amidine (mg m ) 1.8610.04 1.4210.12 1.1710.12 NB: 1 , 2 , & 3 correspond to the surface areas of the latexes given in Figure 6 from lowest to highest. 77 A l l o u r a d s o r p t i o n s t u d i e s were p e r f o r m e d a t pH 7.2, w h i c h i s w e l l above t h e i s o e l e c t r i c p o i n t o f BSA, a p p r o x i m a t e l y pH 5.2. The s u l f a t e , c a r b o x y l and c a r b o x y l - m o d i f i e d l a t e x e s a r e a l l n e g a t i v e l y c h a r g e d and t h e BSA m o l e c u l e i s a l s o n e g a t i v e l y c h a r g e d a t t h i s pH. I f p r o t e i n - s u r f a c e e l e c t r o s t a t i c i n t e r a c t i o n s were d o m i n a n t , a d s o r p t i o n t o t h e s e n e g a t i v e l y c h a r g e d l a t e x e s w o u l d be e x p e c t e d t o be m i n i m a l because o f r e p u l s i o n . I f , on t h e o t h e r h a n d , p r o t e i n - s u r f a c e e l e c t r o s t a t i c i n t e r a c t i o n s a r e a b s e n t o r m i n i m a l , t h e n t h e a d s o r p t i o n o f n e g a t i v e l y c h a r g e d BSA t o t h e n e g a t i v e l y c h a r g e d l a t e x e s w o u l d p r o b a b l y be c o n t r o l l e d by h y d r o p h o b i c i n t e r a c t i o n s . F o r t h e p o s i t i v e l y c h a r g e d a m i d i n e l a t e x , b o t h p r o t e i n - s u r f a c e e l e c t r o s t a t i c and h y d r o p h o b i c i n t e r a c t i o n s may i n f l u e n c e t h e a d s o r p t i o n o f t h e n e g a t i v e l y c h a r g e d BSA. Norde and L y k l e m a o b s e r v e d an i n c r e a s e i n p l a t e a u a d s o r p t i o n v a l u e (T ) o f HSA w i t h i n c r e a s i n g n e g a t i v e c h a r g e o f t h e PSL s u r f a c e a t pH m a x . v a l u e s g r e a t e r t h a n t h e i s o e l e c t r i c p o i n t o f HSA. They a t t r i b u t e t h i s t o t h e uneven d i s t r i b u t i o n o f c h a r g e i n t h e p r o t e i n m o l e c u l e s , c a u s i n g d i f f e r e n t d e g r e e s o f t i l t i n g o f t h e m o l e c u l e a t s u r f a c e s h a v i n g d i f f e r e n t c h a r g e d e n s i t i e s . However , t h e y a l s o i n d i c a t e t h a t t h e d i f f e r e n c e i n t h e h y d r o p h o b i c i t y o f t h e l a t e x e s may e q u a l l y w e l l be r e s p o n s i b l e f o r t h i s o b s e r v a t i o n [ 7 6 ] . I t can be seen f r o m F i g u r e 6 t h a t t h e r e i s a dependence o f t h e amount o f BSA a d s o r b e d p e r u n i t a r e a on t h e l a t e x s u r f a c e a r e a i n a l l c a s e s . As t h e e q u i l i b r i u m BSA c o n c e n t r a t i o n i n c r e a s e s , t h e dependence on l a t e x s u r f a c e a r e a becomes o b v i o u s f o r a l l t h e l a t e x e s e x c e p t t h e CML w h i c h shows o n l y a modera te dependence o f s u r f a c e c o n c e n t r a t i o n on s u r f a c e a r e a . The a d s o r b e d amount d e c r e a s e s , a t c o n s t a n t e q u i l i b r i u m BSA c o n c e n t r a t i o n , when ( a t c o n s t a n t BSA s o l u t i o n v o l u m e ) t h e t o t a l PSL s u r f a c e a r e a a v a i l a b l e f o r a d s o r p t i o n i n c r e a s e s . T h i s u n e x p e c t e d r e s u l t 78 was observed, to a varying degree, in a l l of our experimental studies of the adsorption of BSA to PS latexes. As discussed earlier, BSA can form oligomers in solution. The preferential adsorption of these dimeric and/or oligomeric species may have a great influence on the total amount of protein adsorbed. As w i l l be seen, i t seems likely that the latex area dependence is due to the presence of BSA oligomers in solution which adsorb more strongly than monomeric BSA, based on our analysis of the adsorbed BSA molecules (see Electrophoresis Analysis section below) and the fact that this effect has been observed previously in both synthetic polymer adsorption and BSA adsorption in other systems. Vander Linden and van Leemput [182], using gel permeation chromatography reported experimental evidence for the preferential adsorption of high molecular weight polystyrene to s i l i c a surfaces. Zsom [183] studied the adsorption of several BSA samples containing different amounts of dimeric and/or polymeric species onto polystyrene latexes by high-performance liquid chromatography (HPLC), and demonstrated that BSA dimers and/or polymers adsorb preferentially to BSA monomer. Lensen, H.G.W. et al, [184] used high-performance liquid chromatography to follow the adsorption of HSA onto polystyrene and observed a strong preferential adsorption of HSA dimer over monomer. Cohen Stuart et. al. [130] give a quantitative analysis of these effects and show that for a mixture of two components with different molecular weights, f u l l preference in adsorption is attained i f the molecular weights differ by more than a factor of two. It seems likely the above behaviour is responsible for the area dependence observed. Higher molecular weight fractions show a higher a f f i n i t y for the surface since there are more groups per molecule 79 available to interact with the surface. A consequence of this preferential adsorption is that the distribution of the molecular weights between the adsorbent surface and the solution is dependent on the total adsorbent surface area and the solution volume of the system. For example, when a low total surface area is available predominantly the fraction of the polymer with very high molecular weights and therefore high a f f i n i t y w i l l bind to the surface, resulting in large adsorption values. On the other hand, i f a larger area is available, smaller, lower a f f i n i t y species w i l l occur on the surface, and the amount per unit area and the average molecular weight of the adsorbate w i l l be smaller. Accordingly, we have used the analysis of Cohen Stuart et al [ 1 3 0 ] for the data shown in Figure 6. If their treatment applies, i t is predicted that i f the data is plotted as T , the amount adsorbed per unit * area, versus T = C/(S/V), the nonadsorbed amount per unit area, the area dependence should collapse onto a single curve. The plots are shown in Figure 7. Generally most of the data f a l l on the same curve, implying that Y * is a function of T only and not just C, the equilibrium BSA concentration. The prediction is borne out sufficiently well to give some confidence in the explanation given above. Figure 8 further illustrates this dependence of the surface concentration of BSA on latex surface area in a l l cases. In these experiments, the amounts of BSA adsorbed per unit area were determined at an i n i t i a l concentration of 0.50 mg/ml BSA for different surface areas of each latex, keeping the total volume in each sample constant. A correction for the mass of latex in suspension was made in the calculation of the amount of BSA adsorbed per unit area. 80 Sulphate latex (1.07/um) 0.0 o. 000 0.002 0.004 0.006 0.008 0.010 0.012 O V / S (mg/m 1) 6.0 | 4 . 0 13.0 -3 • $ 2.0 1.0 Carboxyl latex (0.984/im) o.o -f 1 1 1 1 1 1 • 1 0.000 0.010 0.020 0.030 0.040 O V / S (mg/m*) 5.0 CML (0.865/xm) .£1 0.000 0.0K) 0.020 0.030 O040 C»V/S (mg/m*) E ^4.0 J_ -o V € 3.0 n 2 2.0 Amidine latex (0.489/im) Y 0-0 i 1 1 1 1 r 0.000 0.002 0.004 0.006 0.008 0.010 0.012 O V / S (mg/m*) Figure 7. The adsorption data of Figure 6 plotted as a function of the amount of non-adsorbed BSA per unit area in solution, T = (CxV/S) , where C is the equilibrium BSA concentration, V is the volume of supernatant in equilibrium with the latex and S is the total surface area of latex in equilibrium with BSA solution. 81 CML lotex (0.865/xm) i i i—i i—i—i—i—i—i 460 8<M 1200 1600 2000 Surfac* Ana (cm*) 5.0 E 4.0 | 3.0 o n 3 O l i . o 0.0 Amidine latex (0.489/irn) 6 4A0 ' e6o 1200 ' 1600 ' 2000 Surfaca Ana (enV) Figure 8. Amount of BSA adsorbed as a function of latex surface area"~at room temperature from 0.01M phosphate buffer, pH 7.20. I n i t i a l [BSA] = 0.50 mg/ml. 82 The d e c r e a s e i n t h e amount o f BSA a d s o r b e d p e r u n i t a r e a i s n o t due t o d e p l e t i o n o f t h e p r o t e i n as a r e s u l t o f l a t e x s u r f a c e a r e a i n c r e a s e ; r a t h e r t h e a r e a dependence shown i n t h e s e f i g u r e i s due t o t h e r a n g e o f a f f i n i t i e s o f t h e BSA components i n s o l u t i o n and on t h e i r c o n c e n t r a t i o n s . The r i s e i n t h e amount o f BSA a d s o r b e d p e r u n i t a r e a a t low s u r f a c e a r e a s o f t h e l a t e x e s , i s c o n s i s t e n t w i t h t h e r e s u l t s i n F i g u r e 6 . I f o n l y a s i n g l e p r o t e i n s p e c i e s were p r e s e n t one w o u l d e x p e c t , f o r a p a r t i c u l a r l a t e x t y p e , t o g e t t h e same amount o f BSA a d s o r b e d p e r u n i t a r e a a t a l l l a t e x c o n c e n t r a t i o n s . ( i i ) . Variation of Total Volume of BSA solution at constant Surface Area of PSL. I n t h e s e e x p e r i m e n t s , t h e t o t a l p r o t e i n s o l u t i o n vo lume i n each s e t o f samp les was v a r i e d w h i l e t h e t o t a l s u r f a c e a r e a o f t h e l a t e x was k e p t c o n s t a n t . I n t h i s case t h e i n f l u e n c e o f t h e t o t a l aqueous phase vo lume a t i d e n t i c a l e q u i l i b r i u m BSA c o n c e n t r a t i o n on t h e d i s t r i b u t i o n o f t h e p r o t e i n b e t w e e n s u r f a c e and s o l u t i o n i s s o u g h t . These e x p e r i m e n t s were done f o r each o f t h e f o u r l a t e x t y p e , and t h e r e s u l t s a r e g i v e n i n F i g u r e 9. As can be seen f r o m t h e i s o t h e r m s and t h e p l a t e a u v a l u e s o f t h e i s o t h e r m s g i v e n i n T a b l e I I I , t h e o b s e r v e d dependence o f t h e s u r f a c e c o n c e n t r a t i o n on t h e r a t i o o f s u r f a c e a r e a t o t h e t o t a l vo lume o f t h e aqueous phase i s a l s o seen h e r e . A t c o n s t a n t e q u i l i b r i u m c o n c e n t r a t i o n , C, a v a r i a t i o n i n t h e s u r f a c e a r e a t o vo lume * ( S / V ) r a t i o amounts t o a change i n T (= C x V / S ) , t h e n o n a d s o r b e d amount w h i c h , i n t u r n , a l t e r s t h e amount a d s o r b e d p e r u n i t a r e a . Thus i t i s seen t h a t t h e amount a d s o r b e d i n c r e a s e s as t h e t o t a l vo lume o f t h e 83 aqueous phase increases. Figure 9. Adsorption isotherms for BSA to the latexes indicated at room temperature from 0.01M phosphate buffer, pH 7.20. The total volume of BSA solution used in each experiment are indicated. The total surface area of the latex used in each isotherm were as follows: Sulfate (361.4), Carboxyl (160.1), CML (247.9) & Amidine (+) (403.6) cm2. 84 Table III Adsorption maxima of BSA adsorption isotherms in Figure 9, as estimated from the isotherms. Variation of Total Volume Sulfate Carboxyl CML Amidine 1ml 0.98±0.05 1.24±0.04 0.54±0. ,07 1.35±0.17 2ml. 1.29±0.04 1.42±0.03 0.86±0. ,01 1.95±0.07 4ml. 1.4710.04 2.16±0.06 1.00±0. , 18 2.1510.05 Figure 10 presents the replot of data of Figure 9 as surface concentration against the non-adsorbed amount of BSA per unit area, instead of the equilibrium solution concentration, as suggested by Cohen Stuart et al [130]. Again i t illustrates the general prediction of their polydispersity theory. 85 S.0 •5 3.0 o m 3 $2.0 H Sulphate latex (1.07/im) 0.0 o.ooo 1 1 1 1 T 0.004 0.008 0.012 O V / S (mg/m*) 5.0 t o E, 1 , 0 \ o 3 8 2-0 3 ' ° Carboxyl latex (0.984/im) ."» . o.o t 0.000 0.010 0.020 0.030 0.040 O V / S (mg/m*) 5.0 -t 5.0 -> | 3.0-I m 3 ^2.0 -0.0 CML (0.865/im) •I .t. 0.000 0.010 0.020 0.030 O V / S (mg/m 1) 0.040 IT E "£4.0 E, •o £ 3 . 0 O fi 3 22.0 2 1-° 0.0 0. Amidine latex (0.489^ m) T—i—i—i—i—i—i—i—i—• 000 0.004 0.008 . O V / S (ma/cm 1) • i i • 0.012 Figure 10. The adsorption data of Figure 9 plotted as a function of the amount of non-adsorbed BSA per unit area in the solution,"T*. = (CxV/S), where C is the equilibrium BSA concentration, V is the volume of" supernatant in equilibrium with latex and S is the total surface area of latex in equilibrium with BSA solution". 86 2.3. ( b ) . Comparison of Amount of BSA Adsorbed per Unit Area for the Four Latex Types at Constant Surface Area of Latex The difference in the amount adsorbed per unit area for the different latex types can be deduced from the isotherms in Figure 8, in which the amount of BSA adsorbed per unit area is plotted as a function of surface area of latex. The amounts of BSA adsorbed per unit area as the surface area tends to zero is probably a good estimate of the maximum amount of BSA (saturation values) adsorbed by the latex particles. These values are estimated to be 2.98 mg m of BSA for the amidine (+) latex, -2 -2 2.30 mg m for the carboxyl latex, 2.20 mg m for the sulfate latex, -2 and 1.15 mg m for the carboxyl-modified latex. Thus the estimated values from Figure 8 indicate that the greatest adsorption of BSA is for the amidine (+) latex followed by carboxyl, sulfate and carboxyl modified latex (CML). Further support of this trend is illustrated by the summary of adsorption data (Table IV) obtained for similar surface areas of the different polystyrene latexes. Two different equilibrium concentrations of BSA were used in these experiments which were performed at relatively high surface areas of the latexes. The results indicate a similar trend as the estimated values from Figure 8. Since the adsorption experiments were a l l performed above the isoelectric point of BSA, a c r i t i c a l factor in this trend of amount adsorbed per unit area seems to be the area of hydrophobic sites available on the surface of the latex particle. As an indication of the ratio of hydrophobic to hydrophilic areas of the particle surface, the cross-sectional area of a typical charged group, e.g. -0S03 , is compared with the surface charge density of the charge groups on the latex particle. 87 Table IV Comparison of the amount of BSA adsorbed per unit area for four PS latex types at roughly "constant" surface area. Latex type Added in Solution Adsorbed from Solution PS BSA 7. Total 2 . - l -2 cm mg mi mg m Average Average 0. 698 0. 696 30.6 0.32310. 006 Sulfate 1,967 2. 070 2. 069 18.5 0.59110. 071 0. 691 0. 690 30.5 0.34210. 006 Carboxyl 1,850 2. 042 2. 061 18.4 0.625+0. 038 0. 690 0. 702 15.4 0.17510. ,002 CML 1,834 2. 056 2. 057 11.3 0.38510. ,020 0. 685 0. 694 35.5 0.42310. ,011 Amidine (+) 1,756 2. 033 2. 050 24.3 0.86810. ,061 88 Assuming the cross-sectional area of a charged group to be about 2 2 0.20-0.25nm (20-25A ) [4], the percentage of the latex particle surface that is hydrophobic and available for physical adsorption is approximately 91% for the sulfate latex, 94% for the carboxyl latex , 50-60% for CML, and 83% for the amidine (+) latex (see Table I). For the three negatively charged latexes (sulfate, carboxyl, and CML), the amount of BSA adsorbed per unit area at the same equilibrium BSA concentrations is related to the area per unit charge group of each latex, i.e., the adsorption increases in the same order as the hydrophobicity. Thus the CML with the lowest hydrophobic to hydrophilic ratio adsorbs the least amount of BSA and the carboxyl the highest. The sulfate latex with hydrophobicity close to that of carboxyl latex, adsorbs similar quantities of BSA. The strong binding of BSA to the positively charged amidine latex, even though the latex has an intermediate hydrophobicity in comparison with the three negative latexes is probably due to the additional effects of electrostatic interactions, expected between the negative BSA molecules and the positively charged amidine latex surface. Thus, although hydrophobicity seems to be a major factor in physical adsorption of proteins to polystyrene latexes, other effects such as electrostatic interactions are often superimposed upon hydrophobic effects. 2.3 (c) Wash Analysis of BSA Adsorbed onto PS Latexes: (i) Buffer Wash In order to further examine the characteristics of the adsorption of BSA on the latexes and obtain an estimate of how much BSA is retained on the latex surface following exposure to phosphate buffer, a wash analysis 89 of the adsorbed BSA was done on selected samples from the adsorption experiments. After spinning down the latex and removing aliquots for counting, the rest of the supernatant was decanted and kept for SDS-PAGE gel electrophoresis analysis. The remaining compact latex pellet was resuspended in pure buffer up to the starting volume and centrifuged again. This centrifugation and washing procedure was repeated until a negligible change in the total count of the latex pellet was obtained. The f i n a l count was taken as an estimate of the amount of protein retained on the latex surface after extensive wash. Table V gives the desorption data for the BSA adsorption described in Table IV. Table V Amount of BSA retained on the PS latex pellet (experiment reported in Table IV) after extensive wash with equilibrium buffer. Amount bound Amount bound Latex type (before wash) (after wash) Difference (mg m 2) (mg m"2) (mg m ) °/o Sulfate 0.323 0.269 0. 054 16. .7 0.591 0.435 0. 156 26. 4 Carboxyl 0.342 0.287 0. .055 16. , 1 0.625 0.472 0. , 153 24, ,5 CML 0. 175 0.119 0. .056 32. ,0 0.385 0.202 0. , 183 47. ,5 Amidine (+) 0.423 0.380 0. ,043 10. ,2 0.868 0.680 0. , 188 21. .7 As can be seen from Table V, for adsorption at low equilibrium BSA concentration there is a difference of between 10 and 17 percent in the amount of BSA adsorbed per unit area before and after wash with equilibrium buffer for the low surface charge latexes, i.e. carboxyl, 90 sulfate, and amidine; a larger difference of 22 to 26 percent is observed for adsorption at high equilibrium BSA concentration for these latexes. For the high surface charge CML the difference at low equilibrium BSA concentration is about 32 percent, and much higher, 47.5 percent, at high equilibrium BSA concentration. For the negatively charged latexes, the trend in desorption also seems to be related to the area per charge group of the latexes. It can be seen that the desorption decreases as the hydrophobicity of the latexes increases. Carboxyl latex with the highest hydrophobicity loses the lowest fraction of bound BSA following extensive buffer wash and the CML, with the least hydrophobicity loses the largest fraction of i t s adsorbed layer upon adsorption. This difference in the amount of BSA that is removed by washing from the low surface charge latexes (carboxyl and sulfate) and the high surface charge latex (CML) is probably due to the nature of the interaction between the surfaces and the BSA molecules. The high surface charge latex has a polyectrolyte-type surface and is therefore more hydrophilic; polar interactions between this type of latex and the protein molecule probably have a large influence on the adsorption process. It might be expected that water could compete with these interactions and that repulsive electrostatic interactions would i f anything enhance protein release. The removal of the protein from the hydrophilic surface by extensive rinsing is therefore easier than removal from a hydrophobic surface. When electrostatic attraction is superimposed upon the hydrophobic interactions of BSA molecules with the latex surface as in the case of the positively charged amidine latex, the amount of BSA desorbed following extensive buffer wash is. minimal. It can be seen from Table V 91 that the latex with the highest BSA surface concentration (amidine latex) at equilibrium loses the lowest fraction of i t s bound protein compared to a l l the other latexes, although i t has an intermediate hydrophobicity in comparison with the negatively charged latexes (carboxyl and sulfate latexes). Conversely, the system with the highest hydrophilicity and negative charge (CML) and the lowest amount of bound BSA at equilibrium releases the largest fraction of i t s adsorbed layer upon extensive buffer wash. The low desorption from the amidine surface seems also to suggest that the electrostatic interaction between the negatively charged protein and the positively charged latex may involve ionic bonds, since i f the electrostatic interactions enhanced adsorption were due simply to increasing the local concentration of the protein molecules near the latex surface, one might expect a greater amount of desorption to occur following extensive buffer wash. ( i i ) . Comparison of Buffer Wash with SDS, BSA, PEG and IgG Washes It is well known that an adsorbed layer of polymer on a solid surface, when placed in a solution with a f i n i t e bulk polymer concentration, can exchange some molecules with the solution. For example, the displacement of a polymer species in the adsorbed state may be achieved by another polymeric species of larger size [185]. For polydisperse samples of synthetic polymers, preferential adsorption of large molecules over small ones occurs, however, extreme preferential adsorption is usually not observed [129,186]. Brash et al [113] found that when proteins of identical mass are adsorbed to various solids, adsorption appears to be irreversible with respect to dilution. 92 The literature on the reversibility and exchange of adsorbed protein was reviewed in Chapter One Section 1.4 (a). An indication of whether BSA molecules in the adsorbed layer were removable by dilution or exchanged with molecules in solution was obtained by experiments in which radioactively labeled BSA was adsorbed onto the PSL surfaces at saturation values and the amounts of radioactively labeled BSA retained on the PSL after extensive wash cycles with solutions of sodium dodecyl sulfate (27. SDS), unlabeled BSA, rabbit anti-BSA IgG, and 27. polyethylene glycol (6000) were measured. Figure 11 gives the relative amount of BSA retained on the PSL after successive wash cycles, each step being for between 6 and 8 hours. It can be seen that for a l l the latexes there is very l i t t l e desorption of BSA when pure buffer, nonlabeled BSA, anti-BSA IgG or 2% PEG solution is used for washing. There appears to be very l i t t l e or no exchange between adsorbed BSA molecules and the bulk solution molecules under these conditions, even for the higher molecular weight IgG molecules. The wash analysis measurements were performed under the same conditions as the adsorption experiments, in which the equilibrium state was assumed to be established after = 6-8 hours. No kinetic studies were performed, the aim being to use time courses applicable to latex agglutination systems. Since desorption even in the presence of polymeric molecules in solution is a slow process [185] and is not diffusion controlled, we cannot draw any conclusions about reversibility and/or i r r e v e r s i b i l i t y of adsorbed proteins at the solid/liquid interface over longer time periods. However, on a time of hours to a few days l i t t l e exchange or desorption occurs. 93 o>1.00 E CO 0.80 a. c o V c '5 "v 0.40 CC 55 mo.20 -co.oo g 0.60 CUL Buffv. BSA IsC, PEC 2.00 "lOO 4J$0 Number of wash cycles Amidlnt (+) Latu 0 1 1 5 I Number of wash cycles Figure 11. Amount of BSA retained on PSL after washing first with equilibrium buffer, followed by repeated wash cycles with.0.01M phosphate, buffer pH 7.20, 2% SDS, nonlabeled BSA (at the concentration with which the surfaces were equilibrated, 1.87 mg/ml), anti-BSA IgG 0.094 mg/ml, and 27. PEG (6000) in 0.01M phosphate buffer, pH 7.2. 94 Solutions of SDS, however, solubilise and displace adsorbed BSA from the various latex surfaces to a much greater extent. This is clearly indicated by the amount of BSA retained on a l l the PSL surfaces in Figure 10, after the SDS washes. The f i r s t and/or second wash with a SDS solution seems to remove most of the adsorbed BSA from a l l the latexes. The subsequent washes have a relatively small effect. This probably indicates the existence of a range of weakly and tightly bound BSA molecules on a l l the latexes studied. 2.3 (d) SDS Gel Electrophoresis of BSA Removed from the Latex Surface Many proteins, including albumin, form polymeric species in solution and these can be readily detected by sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE) [187,188]. In SDS electrophoresis, proteins are separated on the basis of size alone. The SDS binds to the protein molecules, converting their compact 3-dimensional shape into denatured random coils. Since the SDS molecules often bind to polypeptides with a constant ratio of SDS to polypeptide mass, the charge per unit weight is constant. Thus, the protein's native charge is totally masked with the negative charge of the SDS. When subjected to polyacrylamide gel electrophoresis, the proteins, which are now equal in charge density, are separated purely according to size by the molecular sieving effects of the gel matrix. SDS-PAGE is widely used to estimate the molecular weights of unknown proteins by comparing their relative electrophoretic mobility (R ) to standard proteins of known 95 molecular weights. In order to examine the composition of the adsorbed BSA layer on the latex surface, the latex was washed i n i t i a l l y with equilibrium phosphate buffer followed by SDS-PAGE buffer containing 2% SDS, and electrophoresis gels of the removed material run. An attempt to make quantitative comparisons between polymeric contents of the removed (radio iodinated) adsorbed protein exposed to different latex surface areas and the concentration of oligomers present in the original unexposed solution of BSA was made on the basis of SDS-PAGE gel scans since the protein specific activity was too low to produce reliable data by s l i c i n g the gels and counting. The bands on gels were recorded by scanning them on a Beckman Model 25 Spectrophotometer with a rod gel scanning adaptor at 590nm. The gel scans were then digitized to a scale approximating the actual length of the gels (10 cm) using a Digi-Pad graphic digitizer Model DP5A-1117A. The area under each peak was obtained by integrating the gel profile over several subintervals using the familiar trapezoid rule: area of a trapezoid is given by i t s average height times the base. The integrated peak areas from the gel scans represent the amount of each oligomer type present in the electrophoresis sample load. These values were then used to calculate the total amount of each oligomer in the equilibrium BSA solution and that on the surface of the latexes. The results of SDS-PAGE electrophoresis analysis presented here are those for the proteins removed from the latexes used in : (a) the experiment performed at constant surface areas for the four latexes, as reported in Tables IV and V; and (b) the sulfate (1.073p.m) and amidine (0.489pm) latexes of the adsorption experiments whose isotherms are given in Figure 6. For case (b) only the samples with the highest equilibrium concentrations and adsorbed amount per unit area for each case of the 96 three different surface areas (see Figure 6. ) of the two latexes were analyzed. Table VI summarizes the adsorption data for the samples analyzed by SDS-PAGE electrophoresis. Table VI Summary of Adsorption Data for samples subsequently washed with 2% SDS and amount of BSA used in SDS-PAGE electrophoresis analysis (a): Surface Amount bound Amount bound Latex type Area (before buffer wash) (after buffer wash) (cm2) (mg m ) (mg m 2) Sulfate 1,967 0.323 0.269 Carboxyl 1,850 0.342 0.287 CML 1,834 0.175 0.119 Amidine (+) 1,756 0.423 0.380 Electrophoresis: Supernatant(ng) Pellet(ng) Sulfate: (electrophoresis load) 15 26 (estimated Total BSA) 1420 530 Carboxyl: (electrophoresis load) 18 50 (estimated Total BSA) 1420 530 CML: (electrophoresis (estimated Total load) BSA) 18 1710 31 220 (electrophoresis Amidine (+): (estimated Total load) BSA) 12 1300 72 660 97 The concentration profiles from SDS-PAGE gels of the BSA remaining in the supernatant at equilibrium with the saturated surfaces and of the BSA removed by SDS from the surfaces of the latexes are shown in Figure 12. In these gels the lowest molecular weight species appears farthest to the right. The molecular weights of the BSA monomer and oligomers were confirmed by comparison of the relative mobility of the BSA removed from the latex surface with that of high molecular weight calibration kit (Pharmacia). Only 44% of adsorbed BSA was removed from the surface of the sulfate latex, 75% from the carboxyl latex, 94% from the carboxyl modified (CML) latex and 76% from the amidine latex under the conditions used here. The concentration profiles given in Figure 12 represent only the above percentages of the total BSA adsorbed to the latexes. It is evident, from the concentration profiles, that there is an enrichment in the higher molecular weight oligomers of BSA removed from the latexes relative to the amounts of these higher molecular weight oligomers in the supernatant or in the original stock BSA solution before exposure to the latexes (see Figure 13.). The percentage values of the concentration profiles of BSA SDS-PAGE gels quoted above and those given below have a considerable amount of uncertainty (15-20%) associated with them due to the d i f f i c u l t y in determining the concentration of BSA used in electrophoresis. However, in an experiment in which BSA was subjected to SDS-PAGE at protein loads ranging from 1 to 50 fig, a plot of the monomer, dimer and total protein peaks versus protein load was linear up to protein load of about 30 ug. 98 Gel Length (cm) Figure 12. Optical density profile of Coomassie Blue stained SDS 4% polyacrylamide gels of BSA from the supernatant (dashed line) and'pellet (solid line)of the adsorption experiment reported in Table IV. The latex pellets were extracted with 2% SDS and the extracts run on SDS-PAGE gels. I 99 Figure 13. Optical density, profiles of Coomassie Blue stained SDS 4% polyacrylamide gel of stock BSA used in the adsorption experiment reported in Table IV. .The profile represents the composition of the original BSA that has not been"exposed to the latexes. BSA experimental concentration, 0.69 mg/ml; 33 pg protein loaded.^ 100 The BSA sample used in these adsorption studies contained approximately 44% monomer, 31% dimer and 15% trimer as determined from the concentration profiles of the SDS-PAGE electrophoresis analysis. Table VII (a) gives the percentage of the polymeric species of the original BSA solution before exposure to the latexes, and the percentages of the polymeric species of BSA in the equilibrium supernatant and that removed from the surface of the latexes which had been equilibrated with BSA solution. Table VII(a) The distribution of BSA oligomers in equilibrium solution and on PSL surfaces as a percentage of total BSA in experiment. The adsorption data is summarized in Table VI. Original BSA Monomer Dimer Trimer (%) (%) (%) 44 31 15 BSA in Equilibrium Solution  Monomer Dimer Trimer (%) (%) (%) BSA Adsorbed on PSL and removed with SDS Monomer Dimer Trimer Tetramer (%) (%) (%) (%) Sulfate Carboxyl CML Amidine 52 41 59 44 18 7 11 2 23 10 12 5 4.7 2.3 1.1 0.6 4.4 4.0 2.4 1.4 3.1 1.7 0.7 0.2 3.2 2.9 2.2 1.9 NB: The percentages given in Table VII (a) are those of the total BSA i n i t i a l l y added to the latex suspension. 101 It can be seen from Table VII(a) that the amount of each polymeric species removed from the surface of the latexes is much less than the corresponding amount in the equilibrium solution, due to the relatively small surface area present. The concentration of monomeric species in the equilibrium solutions is comparable to that in the original unexposed BSA solution, while the concentrations of the dimeric and trimeric species in the equilibrium solutions are considerably reduced. On the other hand, the relative concentrations of oligomers are increased in the material originating from the latex surface. The increase in the concentration of these higher polymeric BSA oligomers on the surface of the latexes does not correspond to the decrease in their concentrations from the original BSA solution, however. Instead, i t can be seen from the concentration profiles, particularly from the amidine latex, that higher polymeric species (tetramer, pentamer, etc) were present on the latex surfaces whereas their presence in the original BSA solution and in the equilibrium solution is not observed (Figure 12 and 13). This is further illustrated in Table VII(b) below in which the concentration of each polymeric species derived from the surfaces of the latexes is now given as a percentage of the total amount of BSA adsorbed at equilibrium. Again i t is clear that the monomer:dimer:trimer ratios vary considerably for the different latexes and dif f e r from the BSA stock. The higher polymeric species contribute considerably to the total amount of BSA adsorbed. 102 Table VII(b) The distribution of BSA oligomers removed from PSL surfaces as a percentage of BSA adsorbed. The adsorption data is summarized in Table VII. BSA Adsorbed on PSL and removed with SDS Monomer Dimer Trimer Tetramer Pentamer (%) (%) (7.) (%) (7.) Sulfate 43.5 22 11 5.4 3.9 Carboxyl 29.5 27 15.8 9.7 7.0 CML 43.5 24 10.5 3.0 2.6 Amidine 12.9 12 8.9 7.8 6.8 Table VIII (a) and (b) summarizes the adsorption data of the second set of samples analyzed by SDS polyacrylamide gels (Figure 6). Table VIII(a) Summary of Adsorption Data for samples used in SDS-PAGE electrophoresis analysis (b): Sulfate Latex (1.073pm) Sample Total Surface Area of Latex (cm ) I n i t i a l [BSA] (mg/ml) Amount Adsorbed _2 (mg m ) (mg) A 242.7 0.793 1.93 0.468 B 696.3 0.796 1.46 1.018 C 1160.3 0.798 1.10 1.273 103 Table VIII (b) Summary of Adsorption Data for samples used in SDS-PAGE electrophoresis analysis (b): Amidine Latex (0.489/im) 395.4 0.796 1.81 0.715 B 988.6 0.795 1.57 1.547 1368.9 0.798 1.32 1.807 The concentration profiles from SDS-PAGE gels of the BSA remaining in the supernatant and of the BSA removed from the surfaces of the two latexes (amidine and sulfate), different areas of which had been equilibrated with BSA, are given in Figures 14 and 15, respectively. It can be seen from the concentration profiles that there is a great enrichment relative to the equilibrium supernatant of the higher molecular weight oligomers of BSA removed from the latex surfaces which becomes more evident as the total surface area of the latexes exposed to the BSA solution increases and larger quantities of protein are recovered. The percentages of the polymeric species of BSA in the supernatant solution and that adsorbed onto the latex surfaces are given in Table IX (a) and (b). 1.00 0.60 -T I I [2 0.60 o ° 0.40 O CL o 0.20 0.00 IL00 4.00 6.00 8.00 JLOO 4.6O 6.00 8.60 Gel Length (cm) I T " / i ' i 0.00 10.00 10.00 I F 4.0 I F 8.0 10.0 F igure 1 4 . O p t i c a l d e n s i t y p r o f i l e s o f Coomassie Blue s t a i n e d SDS 454 po lyacry lamide ge ls o f BSA from the supernatant and p e l l e t o f the adsorp t ion experiment on s u l f a t e l a t e x repor ted i n F igure 6 . A, B, & C correspond to th ree d i f f e r e n t su r face area of the l a t e x as I n d i c a t e d l n F igure 6 and Table V I I I ( a ) . The amount o f BSA loaded on each g e l and the t o t a l amount adsorbed on the l a t e x sur face are g i v e n l n Table IX. 105 Table IX Summary o f amount o f BSA l o a d e d t o each g e l , t h e t o t a l amount o f BSA a d s o r b e d on t h e l a t e x s u r f a c e and t h e t o t a l amount i n s u p e r n a t a n t s o l u t i o n : S u l f a t e l a t e x Supernatant(ug) P e l l e t ( f j g ) A Loaded T o t a l 10 2740 19 373 B Loaded T o t a l 8 2180 39 780 C Loaded T o t a l 7 1940 46 918 A m i d i n e ( + ) S u p e r n a t a n t ( u g ) P e l l e t (jig) A Loaded T o t a l 9 2520 32 642 B Loaded T o t a l 6 1640 67 1340 C Loaded T o t a l 5 . 3 1430 78 1550 10.00 Gel Length (cm) F i g u r e 15. O p t i c a l d e n s i t y p r o f i l e s o ( C o o m a s s i e B l u e s t a i n e d SDS 4% p o l y a c r y l a m i d e g e l s o f BSA f r o m t h e s u p e r n a t a n t a n d p e l l e t o f t h e a d s o r p t i o n e x p e r i m e n t o n a m i d i n e ( + ) l a t e x r e p o r t e d i n F i g u r e 6 . A , B , & C c o r r e s p o n d t o t h r e e d i f f e r e n t s u r f a c e a r e a o f t h e l a t e x a s I n d i c a t e d l n F i g u r e 6 a n d T a b l e V I I I ( b ) . T h e a m o u n t o r BSA l o a d e d o n e a c h g e l a n d t h e t o t a l a m o u n t a d s o r b e d o n t h e l a t e x s u r f a c e a r e g i v e n l n T a b l e I X . 107 S i m i l a r trends are observed i n the d i s t r i b u t i o n of BSA oligomers i n the supernatant and i n that recovered from the surface of the latexes as seen i n the analyses of samples from the adsorption experiments performed at constant surface area. The gel analysis of the samples from adsorption at three d i f f e r e n t surface areas (Table X (a)) show that, f o r both the amidine and s u l f a t e latexes, the c o n t r i b u t i o n by the higher polymeric species to the t o t a l amount of adsorbed BSA released by SDS increases gradually as the surface area of the latex increases. The decrease i n the dimer concentration from the supernatant s o l u t i o n i s , again, not r e f l e c t e d by the amount of dimer removed from the latex surfaces. It can be seen from Table X (b) that as the surface area of the latex increases, the percentages of the t o t a l BSA adsorbed decreases f o r the monomeric species, and increases f o r the higher polymeric species. It i s c l e a r from the above r e s u l t s that the surface area dependence of adsorption i s accompanied by a depletion i n BSA oligomers from s o l u t i o n and an increase i n t h e i r concentration i n the adsorbed layer, r e l a t i v e to the BSA stock solution. The r e l a t i v e depletion of the oligomer i s greater the stronger the adsorption, amidine showing the largest e f f e c t and CML the smallest i n t h i s regard. These observations suggest that the t h e o r e t i c a l model proposed by Cohen Stuart et al [130] based on the idea that higher molecular weight material adsorbs more strongly and hence w i l l dominate at low surface areas, might explain the data. The good f i t s to the data reduction scheme proposed i n [130] (Figure 7) are consistent with t h i s approach. However, the oligomer d i s t r i b u t i o n data given i n Table X(b) does not support t h i s i n t e r p r e t a t i o n since i t does not show a greater r e l a t i v e depletion of the oligomers at low surface area, as predicted. The uncertainty i n the 108 numerical values may mask the depletion d i f f e r e n c e at low areas but there i s no suggestion i n the depletion data of a trend i n the an t i c i p a t e d d i r e c t i o n . Table X (a) The d i s t r i b u t i o n of BSA oligomers removed from PSL surfaces as a percentage of BSA added. The adsorption data i s summarized i n Table VIII (a) and (b). Amidine latex BSA i n Equilibrium Solution BSA Adsorbed on removed by SDS . PSL and Sample Monomer (7.) Dimer Trimer (%) (%) Monomer (7.) Dimer (7.) Trimer (7.) Tetramer (7.) A 65.7 19.8 — 0.9 0.5 0.2 0.1 B 62.7 17 — 2.0 1.0 0.7 0.4 C 59.4 16 — 3.2 2.2 1.1 0.8 Sulfate latex A 62.2 19.4 — 1.7 0.6 0.4 — B 61.4 17.6 — 2.3 1.3 0.7 0.4 C 56 15.5 — 2.7 1.8 0.9 0.5 109 Table X (b) The distribution of BSA oligomers removed from PSL surfaces as a percentage of BSA adsorbed. The adsorption data is summarized in Table VIII (a) and (b). Amidine latex  BSA Adsorbed on PSL and removed by SDS Sample Monomer Dimer Trimer Tetramer Pentamer tt)tt)tt)tt)tt) A 41.8 21.9 9.6 5.2 — B 31.1 16.4 10.6 5.9 5.2 C 23.8 16.3 8.1 6.3 4.0 Sulfate latex A 43.3 14 9.3 — — B 40.5 23.4 11.8 7.7 5.1 C 34.1 23 11.5 6.4 4.4 110 The oligomer distribution of the adsorbed protein removed by SDS is even less supportive of the above model. This is most evident in the molecular weight distribution of Figure 15 C. The high molecular weight species to the l e f t of the profile were never seen in the BSA stock solutions nor in the equilibrium supernatants. The quantities involved are such that they readily would have been detected in these solutions i f they were present; their levels are too high to just represent concentration of pre-formed oligomers on the latex surface. Given that the depletion data indicates preferential adsorption of oligomers (in agreement with Zsom [183]) the above indicates that the material removed by detergent represents both adsorbed, pre-formed oligomers and species formed by polymerization reactions on the latex surface. The kinetics and chemical determinants of the surface-catalyzed polymerization are not known at present; i t was beyond the scope of this project to characterize i t further. It seems lik e l y that the protein l e f t on the latex surface following SDS washing, representing over 20% of the adsorbed BSA, could have a molecular weight distribution shifted to higher oligomers than the released material and that this would contribute to the i r r e v e r s i b i l i t y of i t s binding. The reaction complicates interpretation of the area dependence of adsorption however, since i t is enhanced at high surface areas, at least for amidine. A model which, qualitatively, could explain the observed behavior is as follows. At a given i n i t i a l protein concentration the amount adsorbed to different surface areas of latex is determined by the molecular weight distribution of the stock, with higher surface concentrations present at low areas due to stronger oligomer adsorption. Higher surface area suspensions would have more monomer adsorbed per unit area, therefore. It is known that monomeric albumin can undergo I l l conformational changes during adsorption [76,189-191]. These changes might be sufficient to open the structure enough to allow for disulfide exchange or other, unknown, polymerization reactions with neighboring molecules on the surface. If the oligomers formed are linear there would be two sites per oligomer, at either end, available for further reaction. Since this would apply to the monomer as well, there would be more potential reaction sites per unit area in the high area latex suspensions than in the low, even though the total mass adsorbed was somewhat higher (30-40%) in the latter case. The higher concentration of reactable ends could produce higher molecular weight oligomers leading, at equilibrium, to the observed results. 2.4 Summary of BSA Adsorption Studies 1. The mass of BSA adsorbed at saturation depends on the type of polystyrene latex. Latexes with highly hydrophobic surfaces tend to adsorb more BSA molecules than those with with lower hydrophobicity. Electrostatic effects, e.g. electrostatic attraction between (-ve) protein and (+ve) polystyrene latex surface or vice versa, may be superimposed upon the hydrophobic interactions between the hydrophobic amino acids of the protein and the uncharged regions of the latex surface. 112 2. The desorption of BSA molecules from PSL surfaces is, to a limited extent, dependent on the type of latex. Latexes that maximize adsorption lose the lowest fraction of their bound BSA molecules following extensive pure buffer wash. Partial desorption of BSA from PSL can be achieved by the addition of detergents such as SDS, whereas the addition of more BSA molecules or other macromolecules such as PEG or IgG does not seem to displace the adsorbed BSA molecules from the surface of the latexes over the time courses used in this work. 3. The adsorption of protein containing oligomers to PSL surfaces depends on the concentration of both protein and latex, higher amounts per unit area adsorbing in suspensions containing lower total surface areas. The adsorbed layer is enriched in the higher molecular weight oligomers, relative to their concentrations in the stock solution. This enrichment may be due to preferential adsorption of higher polymeric species or to the formation of these higher polymeric species on the particle surfaces. At equilibrium, higher molecular weight oligomers are prevalent on the surface when higher total areas of the latex are present. This observation is consistent with a model in which adsorbed protein undergoes a conformational change that allows a polymerization reaction to occur from each end of the monomer or oligomer. The higher monomer concentration predicted to be adsorbed initially in suspensions of high total surface area provides a higher surface concentration of reaction sites for polymerization of adsorbed protein, leading to the observed results. 113 CHAPTER THREE ANTIBODY BINDING TO ANTIGEN-COATED PSL 3.1 Introduction Antigens and their corresponding antibodies interact through non-covalent binding in solution to form antigen-antibody complexes which may or may not be soluble. At an optimal antibody-antigen ratio, an insoluble antibody-antigen complex may aggregate by cross linking and/or hydrophobic interactions to form a precipitate. In the region of excess antibody or excess antigen, the aggregates formed become progressively smaller or less easily precipitable [192]. The specificity of the antigen-antibody interaction cannot be explained on the basis of a single type of attractive force or chemical reaction. Nonspecific short range forces, such as van der Waals and Coulombic forces are thought to be important in many antigen-antibody interactions. Other interaction forces such as hydrogen bonding and hydrophobic bonding are also known to play a significant role. Antigen-antibody interactions depend mainly on a structural complementarity between a determinant on the antigen molecule and a binding site on the antibody. As such, they belong to a large group of noncovalent biological reactions such as the binding of substrate to i t s enzyme, the binding of a hormone to i t s receptor, and the binding of ligands to proteins. The antigen-antibody interactions are, however, complicated by the diverse nature of antigens and antibodies. An antigen may have from one to several thousand antigenic determinants, which may differ from each other, while the biological synthesis of antibodies against an individual antigen determinant usually leads to the formation 114 of a heterogeneous polyclonal antibody population. Many factors affect the interaction between an antigen and its corresponding antibody [193]. The affinity of the antibody for the antigen usually correlates inversely with the reversibility of the interaction; the higher the antibody affinity, the less reversible the reaction. Ionic strength, pH, temperature of the medium and the concentrations of antigenic determinants, and antibody combining sites also influence the outcome of the antigen-antibody interactions. 3.1(a) Interaction of Monovalent Antibody and Monovalent Antigen in Solution The interaction of soluble antigen and its corresponding antibody in solution is theoretically considered as a bimolecular reaction [120]: k [Ag] + [Ab] f [AgAb] (3.1) k r where [Ab] is the concentration of unreacted antibody, [Ag] that of the unbound antigen, [AbAg] the concentration of antigen-antibody complex, and Jcf and Jc are the forward and reverse reaction rates, respectively. Equilibrium is reached when the rate of formation of the complex [AbAg] is equal to the spontaneous dissociation of the same complex, implying that the reaction is fully reversible. The equilibrium constant (binding constant), K is a function of the relative concentrations of the reactants and complex, and is given by the mass action expression: 115 K = -A- = [AbAg] [Ab] [Ag] r As e x p r e s s e d above , t h e e q u i l i b r i u m c o n s t a n t i s g i v e n as an a s s o c i a t i o n c o n s t a n t , w i t h a d i m e n s i o n o f l i t r e s p e r mole ( M * ) . A h i g h n u m e r i c a l v a l u e o f K c o r r e s p o n d s t o a h i g h a n t i b o d y a f f i n i t y . I n p r a c t i c e , i t i s u s u a l l y n o t p o s s i b l e t o e s t i m a t e t h e e q u i l i b r i u m c o n c e n t r a t i o n s o f a l l t h r e e s p e c i e s : t h e a n t i b o d y , t h e a n t i g e n , and t h e a n t i g e n - a n t i b o d y comp lex . T h e r e f o r e , E q u a t i o n 3 . 2 i s u s u a l l y e x p r e s s e d i n t e r m s o f t h e e x p e r i m e n t a l l y a c c e s s i b l e p a r a m e t e r , v, d e f i n e d as t h e a v e r a g e number o f bound a n t i b o d y m o l e c u l e s p e r a n t i g e n m o l e c u l e . I n t h i s c a s e , t h e number o f mo les o f bound a n t i b o d y p e r u n i t vo lume i s e q u a l t o [ A g A b ] , and t h e t o t a l number o f mo les o f t h e a n t i g e n m o l e c u l e p e r u n i t vo lume i s g i v e n by t h e sum ( [ A g ] + [ A g A b ] ) : [AgAb] v = ( 3 . 3 ) [Ag] + [AgAb] and s i n c e [AgAb] = K [ A g ] [ A b ] , K [ A b ] v = ( 3 . 4 ) 1 + K [ A b ] E q u a t i o n 3 . 4 g i v e s a t y p i c a l r e c t a n g u l a r h y p e r b o l a t h a t i s f u n c t i o n a l l y o f t h e same f o r m as t h e M i c h a e l i s - M e n t e n e q u a t i o n o f enzyme k i n e t i c s and as t h e L a n g m i u r a d s o r p t i o n i s o t h e r m [194,195]. S e v e r a l l i n e a r t r a n s f o r m s o f t h i s e q u a t i o n have been d e s c r i b e d [196], t h e most common f o r m b e i n g t h e S c a t c h a r d e q u a t i o n , w h i c h i s o b t a i n e d by r e a r r a n g i n g E q u a t i o n 3 . 4 t o g i v e : 116 v = K - K t i (3.5) [Ab] A Scatchard plot of u/[Ab] versus v w i l l be linear i f the above model pertains, and is particularly useful in determining the stoichiometry of binding when more than one antibody is bound per antigenic molecule. The analysis given above describes the equilibrium reaction between monovalent antibody (Fab fragment) and monovalent antigen. The reaction between divalent antibody and monovalent antigen in solution i s more complicated since the geometry of either partner can interfere with binding to the second combining site. Treatments including such effects have been given [140] but are d i f f i c u l t to apply and are not useful for the binding of polyclonal antibodies to proteins bearing diverse antigenic sites which is of interest here. 3.1(b) Multiple Equilibria: General Relationships Multiple equilibria between an antibody and a macromolecular antigen with more than one binding site may be formulated in terms of a stoichiometric analysis or on the basis of individual binding sites on the macromolecule [197]. The equilibrium expressions for such a system can be written as: Ag + Ab AgAbi ; K l [Ag] [Ab] AgAb2 ; K [AgAb ] 2 2 [AgAbJ [Ab] 117 or in general: [AgAb ] AgAb + Ab = AgAb ; K = - (3.6) i _ 1 1 1 [AgAb^] [Ab] where K , K^, and are macroscopic association constants which may be related to the intrinsic association constant in special cases [193,197]. For instance, for monovalent Ab binding to bivalent Ag, the above macroscopic constants are related to K, the intrinsic (microscopic) constant defined in Equation 3.2, by Kj = 2K and = 1/2K. The binding parameter, v, the ratio of the total moles of antibody bound to the total moles of antigen, for multiple equilibria may be expressed as follows: v = K [Ab] + 2K K [Ab] + . 1 1 2 1 + K [Ab] + K K [Ab] 2 +. 1 1 2 (3.7) The site approach focuses on the individual classes of binding sites on the macromolecular antigen. In the simplest case, where the individual classes of sites are assumed to have fixed (although different) a f f i n i t i e s which do not change with the extent of occupancy by antibodies, the ratio of the moles of antibodies bound per mole of the total antigen is given as [197]: 118 (3.8) v = + + 1 + Kx[Ab] 1 + K [Ab] where K and K are the intrinsic association constants for the binding I II to each class of antibody binding site. If the antigen molecule is monovalent and the antibody is also monovalent, Equation 3.8 reduces to Equation 3.4 with Kj = K, the association constant for the binding of monovalent antibody to monovalent antigen. 3.1(c) Interaction of Antibody and Particle-bound Antigen If the antibody and antigen are monovalent, then there i s no difference between their interaction in solution and their interaction when one of the species is particle-bound. This situation is comparable to the binding of small ions or molecules to a protein with multiple, monovalent sites [143,198,199]. Because of symmetry one can treat the interaction between monovalent antibody and "s" antigenic sites of a particle-bound monovalent antigen in terms of the relation: sK[Ab] (3.9) v = 1 + K[Ab] 119 As expressed above, Equation 3.9 is simply an extension of Equation 3.4, for the interaction of monovalent antibody and monovalent antigen in solution, to cover "s" antigenic sites on a particle. For multiple equilibria involving the interaction of antibodies with particle-bound antigens, the complexity of the equilibrium analysis increases, as does the possibility for diverse types of mechanism of interactions (see Figure 16). This includes the fact that multivalent antibodies can, after the i n i t i a l binding via one of their binding sites, crosslink to antigenic sites (or antigen molecules) via their secondary binding sites. For IgG with a valency of two, the crosslinking is limited to an antibody-antigen complex consisting of two antigenic sites (or antigen molecules) and one antibody molecule. If the divalent IgG molecule binds to the antigen layer on one particle in a configuration that leaves one of i t s antigen binding sites free to bind to an antigen molecule on a second particle, then bridging and aggregation of the particles occur due to this specific interaction between antibody in solution and particle-bound antigen. This type of interaction is referred to as particle agglutination. Because of the crosslinking phenomenon, the lateral antigen density on the particle w i l l have a profound effect on the binding of multivalent antibodies to particle-bound antigens (Figure 16). For example, at high particle surface coverage of antigen and low antibody concentrations, the average number of bound antibody molecules per particles would be small, and the probability that the IgG molecule w i l l bind with both of i t s binding sites occupied on the same particle surface w i l l be high provided the antigenic sites are sufficiently close together to allow binding by the same IgG molecule. 120 (*) do - 0 0 fl>) (<) Y 1 o o -kgglullnallon J ^•Ofc' latex particle • antigen Y antibody Figure 16. The possible structures involved in the binding of divalent antibodies with particle-bound antigens. Binding can occur monovalently, divalently , on "naked"-particle surface or between particles; depending on surface density of antigen, antibody and particle concentrations. 121 On the other hand, at high antibody molecule concentrations, the bound antibody w i l l tend to favor configurations in which one binding site i s free since there w i l l be more competition for antigenic sites at higher antibody concentrations. Geometric factors and restriction of motion of both surface antigen and bound antibodies means that the effective concentrations of both the surface antigen and bound antibody diff e r from those in a bulk solution. This leads to further complication in the thermodynamic consideration of such systems. The straightforward relationships obtained in section 3.1(b) for monovalent antibody binding to bivalent antigen (both in solution) are the mathematical result of a known s t a t i s t i c a l relationship between YL^ and K^ , the macroscopic association constants (equilibrium constants) for such systems. Such a relationship between the sequential equilibrium constants for the binding of ligands to receptors that are otherwise fixed to a particle or c e l l surface is not predictable from f i r s t principles [199], due to orientation factors and restriction of motion of both particle bound receptors and bound ligand (see Chapter One Section 1.4 (d)). Under certain limiting conditions, simplifying assumptions can be made which allow for thermodynamic expressions to be derived for the interpretation of equilibrium data for such systems [199]. However, the present studies u t i l i z e a polyclonal IgG fraction which contains antibodies with a variety of association constants. There is no way to interpret the binding of such material in terms of true microscopic association constants. 122 3.2. Materials and Methods 3.2(a) Preparation of Antigen-Coated Polystyrene Latexes Bovine Serum Albumin, Fraction V, Lot # 388 from Miles Labs., was used as antigen. The polystyrene latexes with different surface functional groups from Interfacial Dynamics Corporation (IDC), Portland, OR. described earlier were used as carrier particles. A large quantity of each latex (6ml of stock suspension) was washed with 0.05M phosphate buffer, pH 7.2 and equilibrated for six to eight hours with unlabeled BSA solutions at four different concentrations, after which the latex suspensions were washed repeatedly in 0.01M phosphate buffer, pH 7.2 and the f i n a l suspensions were dispersed in the same buffer solution and stored at 4°C until required for agglutination experiments. Duplicate experiments were performed under the same conditions with radiolabeled BSA solution as described in Chapter One to determine the amount of BSA retained on the latex surface. 3.2(b) Rabbit anti-BSA Immunoglobulin G Antibody: (i) Immunisation of Rabbits Three New Zealand White rabbits were injected subcutaneously with lOOug of antigen (BSA) emulsified in 1.5ml Complete Freund's Adjuvant (1:3 water-in o i l emulsion [200]). Subsequent boosts at intervals of 3-4 weeks were given in Incomplete Freund's Adjuvant (1:3 water-in-oil emulsion). A week after each boost, approximately 40 ml of blood was drawn from an ear vein of the rabbit. This was repeated to maintain a source of anti-BSA antibodies. 123 3.2(b) ( i i ) Purification of Rabbit anti-BSA Immunoglobulins Serum from the rabbit blood was obtained by leaving the blood to clot at room temperature for about one hour, and then at 4°C overnight. The serum was recovered by centrifugation (lOOOg for 10 min) and carefully decanted from the clot. Cold saturated (NH ) SO was then 4 2 4 added dropwise, while stirring, to the serum to give approximately 40 percent saturation. At this saturation, most of the immunoglobulins were precipitated. The suspension was centrifuged at 10,000g for 10 minutes and the precipitate washed with a solution of cold, 1.75 M (NH ) SO 4 2 4 until it was white. The final white precipitate was dissolved in lOmM sodium phosphate, pH 7.0 and dialysed overnight against water. The precipitated lipoprotein was removed by centrifugation at 10,000g for 10 minutes. The supernatant was dialysed overnight against 0.02M phosphate buffer, pH 8.0 then loaded onto a column of DEAE Affi-gel Blue (4.5ml per ml of rabbit serum) previously equilibrated with the same buffer. The immunoglobulin G (IgG) fraction was eluted with two bed volumes of 0.02M phosphate buffer, pH 8.0 and the fractions collected were dialysed against water and freeze-dried using a Maxi-Dry freeze dryer (Model FD-4.5-6.0) from FTS Systems, Inc., Stone Ridge, NY. The purity of the IgG fraction collected was checked by SDS-PAGE electrophoresis. This is reported in Appendix 3. The IgG was stored at -70°C and dissolved in a buffer of choice for immunochemical work. Since the purified rabbit anti-BSA IgG immunoglobulin was used without affinity purification, specific anti-BSA antibodies in the purified fractions represent at most, 20-307. [201] of the total immunoglobulin in the binding and agglutination studies. 124 3.2(c) Binding Experiments Iodinated antibody was prepared as previously described in Chapter Two, [179]. A fixed amount (0.5, 1.0, and 2.0ml) of 1% labeled antibody solution in 0.01 M phosphate buffer, pH 7.20 was incubated with increasing concentrations of BSA-coated latex particles. This was to determine an optimal range of concentrations of reactants, required for determining the maximum amount of labeled antibody able to bind to the BSA-coated latex particles. A suitable amount of BSA-coated latex suspension was mixed with the labeled antibody in a f i n a l volume of 2 ml. The reaction was performed in 4ml (Evergreen) polystyrene tubes to allow free mixing during equilibration, with gentle shaking, for approximately six hours at room temperature (s 21°). The amount of IgG bound per unit area to BSA-coated latex and the estimate of probable error in the measurement were calculated as shown in Appendix 4. 3.3 Results and Discussion 3.3(a) Polyclonal IgG Antibody Binding to BSA-coated PSL. Figure 17 shows the results of binding radioiodinated polyclonal rabbit anti-BSA IgG to sulfate latex bearing the surface concentrations of BSA indicated. In this experiment, the equilibrium IgG concentration _3 was between 6 and 7.00 x 10 mg/ml for a l l latex concentrations indicated. The total antigen (BSA) concentration was increased by increasing the number of particles carrying each of the four BSA surface concentrations. 125 It can be seen that the total amount of antibody bound decreases rapidly with increasing particle concentration, i.e. there is a strong increase in antibody binding as the latex concentration and hence the surface area per unit volume is reduced. The effect is greatest for latex with the lowest surface concentration of BSA. This latex concentration effect was demonstrated earlier for BSA adsorption to bare latex surfaces (see Figure 8, Chapter Two). In the case of BSA adsorption, the stronger adsorption at low surface area per unit volume was attributed to preferential adsorption of higher molecular weight BSA oligomers present in the sample. For IgG binding to PSL bearing different concentrations of antigen (BSA), there are possibly two effects superimposed upon one another: the effect of the range of affinities present in the polyclonal antibody mixture and the surface area dependence of nonspecific adsorption of the antibody mixture to the remaining area of the latex surface unoccupied by antigen. At low surface density of antigen, the nonspecific adsorption of antibody must dominate since there are many more molecules of IgG present per unit area than BSA; this probably accounts for the stronger increase in the amount of antibody bound. The stronger area dependence observed again implies a wide range of affinities for the bare latex is present in the IgG preparation. Presumably this is due to the inherent variation in structure within the IgG class due. to its polyclonal origin, as there was no significant contamination in the IgG preparation by higher molecular weight material (see Appendix 3). On the other hand, at high surface concentration of antigen, nonspecific adsorption of antibody is probably much lower than the antigen-specific reaction since, as will be discussed, the apparent affinity -constant is higher. The increase in 126 binding as the concentration of latex i s reduced, at this BSA coverage, therefore, is lik e l y to be due to the range of Ab a f f i n i t i e s present in the polyclonal antibody mixture. 10-X £ o 8-6-3 CO _0J> o O 43 O < 2^ in m I o 9 • I •2 BSA (moleculea/cro*) o—--2.72 x i o ; b • 8.11 X 10. — 3.64 X 10, • 1.05 X 10 ix 0.0 i I i i i i i i i i i l i i i i i 0.5 J . O i i i Particle Concentration ( c m / m l ) X 10 -3 1.5 Figure 17. The binding of polyclonal anti-BSA IgG to BSA-coated sulfate PSL at room temperature from 0.01M phosphate buffer, pH 7.20. The PSL concentration was varied to produce the values of surface area per unit volume indicated. 127 Figure 18 shows the binding isotherms of the polyclonal rabbit anti-BSA IgG fraction to the sulfate latex pre-equilibrated with BSA to give the four different surface concentrations as in Figure 17. Similar data for the carboxyl, carboxyl modified and amidine (+) latexes are shown in Appendix 5. 6.4E+011 4.8E+011 -(0 "13.2E+011 & . • E . iPl.6E+011 0.0E+000 l ' ' ' « i i ' i i i i i i i i i i i i i i i i i i i i i i 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0 .0H Equilibrium Concentrat ion of IgG ( m g / m l ) Figure 18. The binding of rabbit anti-BSA IgG to BSA-coated sulfate latexes from 0.01M phosphate buffer, pH 7.20. BSA surface concentrations: (a) 2.72 x 1010, (b) 8.11 x 10 , (c) 3.64 x 1011, (d) 1.05 x 10 molecules cm ; PSL surface area = 134 cm ml . 128 In a l l cases except for the CML, the adsorpt ion and/or b inding of antibody at r e l a t i v e l y h igh e q u i l i b r i u m concentrat ions of antibody increases as the p a r t i c l e surface dens i ty of ant igen decreases but the t o t a l surface area of the la tex i s he ld constant. That i s , the t o t a l amount of IgG bound i s greater the smal ler the f r a c t i o n of the PSL surface occupied by BSA and the l arger the bare surface area of la tex a v a i l a b l e . Therefore , more n o n - s p e c i f i c adsorpt ion of antibody to bare PSL occurs than s p e c i f i c b inding to ant igen ( at low BSA coverage; see l a t e r d i s c u s s i o n ) . For the CML, the amount of IgG bound genera l l y increases with the surface dens i ty of ant igen. It appears that f o r t h i s la tex , adsorpt ion of IgG to the bare surface of the latex i s weaker and one observes the e f f ec t of s p e c i f i c b inding of IgG to the surface-bound ant igen at a l l BSA coverages. This i s i n a l l l i k e l i h o o d due to the low hydrophobic i ty of the CML. It i s a l so cons is tent with the nature of adsorpt ion of IgG molecules which i s be l i eved to occur mainly with the more hydrophobic Fc t a i l i n contact with the la tex surface [202]. 3 . 3 ( b ) Comparison of Amount of Polyclonal IgG Antibody Bound to BSA-coated PSL with Surface Density of BSA. In order to compare the amount of p o l y c l o n a l antibody bound to BSA-coated PSL with the surface dens i ty of BSA, the b ind ing isotherms f o r the s u l f a t e la tex shown i n Figure 18 were transformed and p l o t t e d as Scatchard p l o t s , according to Equation 3 .5 . F igure 19 shows the Scatchard p l o t s for the s u l f a t e latex i n which the r a t i o of the number of moles of IgG bound per gram of s u l f a t e la tex to the molar IgG concentrat ion i s p l o t t e d against the number of moles of IgG bound per 129 gram of latex. Similar data for antibody binding to the carboxyl, carboxyl modified, and amidine (+) latexes are shown in Appendix 6. 1.20E+006 -a 1.00E+006 -i 8.00E+005 \ 6.00E+005 \ Q \ 1 6. 2.00E+005 ~. O.OOE+000 O.OE+000 BSA-Coated SuFphate Latex j . N ° * , p 6 . 0 0 E + 0 0 5 : \ ^ S N ? 4.00E+005 T \ \ lm \ u v s \ \ N ^ \ \ S N v \ N N ^ \ S S \ N V N i » i i i i t i i t i 1 i ) i i i i i l v i i i i i i* i i i I 4.0E-008 8.0E-008 V 1.2E-007 Figure 19. Scatchard graphs of the data for binding of anti-BSA IgG by BSA-coated sulfate latex (data and symbols from Figure 18). v is moles of IgG bound per gram of latex and [Ab] is moles of IgG/litre of solution. 130 The intercept on the abscissa indicates the amount of IgG bound at saturation, i.e. the total number of binding sites. The extrapolation to estimate the binding site values assumes that the data obeys simple Langmuir-type behavior over the whole concentration range (described by equations 3.4 and 3.9). A l l the Scatchard plots indicate that the total amount of IgG bound obey the Langmuir type equations reasonably well over the concentration range studied. At higher concentrations non-linearities might well appear, representing lower a f f i n i t y constant binding, but this range was not examined. The value of the intercepts on the abscissa decreases as the surface density of BSA increases, i.e. the total number of sites to which IgG binds decreases with increasing BSA coverage on the PSL surface. Thus, even at saturation values, more binding of polyclonal IgG is predicted to occur to bare PSL than to the BSA-coated latex surface, except for the CML. The slopes of the Scatchard plots give the apparent binding a f f i n i t y of the antibodies: more negative slopes mean greater binding af f i n i t y . As can be seen from Figure 19 and Appendix 6, except for the CML the slopes increase as the surface concentration of BSA increases. This indicates that high a f f i n i t y antibody binding increases as the bare latex surface is reduced and BSA coverage oh the PSL increased. However, the experimental data on which this conclusion is based was taken over a limited concentration range. Table XI gives the number of IgG molecules bound at saturation to the various latexes at different BSA surface concentrations, as. determined by extrapolation from the Scatchard plots. This data is further illustrated in Figure 20 where the amount of IgG bound at saturation i s plotted against the BSA surface coverage. 131 Table XI Comparison of amount of anti-BSA IgG bound to latex with different amount of surface bound BSA. BSA-Coated latex Amount Bound of BSA Amount of IgG Bound anti-•BSA 2 (molecules/cm ) 2 (molecules/cm ) Sulfate (134 cm2/ml) (a) 2. 72 ± 0. 15 x i o 1 0 1.20 ± 0. ,06 X i o 1 2 (b) 8. 11 ± 0. 23 X i o 1 0 9.32 ± 0. 83 X i o 1 1 (c) 3. 64 ± 0. 17 X i o 1 1 5.57 ± 0. 32 X i o 1 1 (d) 1. 05 ± 0. 14 X i o 1 2 4.55 ± 0 .23 X i o 1 1 Carboxyl (121 cm2/ml) (a) 2. 15 ± 0. 11 X i o 1 0 2.42 ± 0. 09 X i o 1 2 (b) 7. 29 ± 0. 20 x i o 1 0 2.11 ± 0. 05 X i o 1 2 (c) 3. 56 ± 0. 23 x i o 1 1 1.48 ± 0. 06 X i o 1 2 (d) 9. 95 ± 0. 18 X i o 1 1 1.31 ± 0. 04 X i o 1 2 CML (106 cm2/ml) (a) 3. .16 ± 0. 17 x i o 9 4.21 ± 0. 14 X i o 1 1 (b) 4. ,53 ± 0. 29 X i o 9 4.95 ± 0. , 18 X 10" (c) 2. ,75 ± 0. 16 X i o 1 0 6.32 ± 0. ,24 X i o 1 1 (d) 2. ,35 ± 0. 17 X i o 1 1 5.68 ± 0. , 15 X i o 1 1 Amidine (+) (160 cm2/ml) (a) 2. .08 ± 0. 10 X i o 1 0 4.61 ± 0. . 10 X i o 1 2 (b) 6. ,56 ± 0. 15 X i o 1 0 4.25 ± 0. .07 X i o 1 2 (c) 4. .48 ± 0. 18 X i o 1 1 2.95 ± 0, ,09 X i o 1 2 (d) 1. .24 ± 0. 09 X i o 1 2 2.59 ± 0, . 11 X i o 1 2 132 5.00 - i Figure 2 0 . A comparison of r e l a t i v e amounts of r a b b i t ant i -BSA IgG f r a c t i o n bound to latexes with d i f f e r e n t amounts of surface bound ant igen (BSA) at IgG s a t u r a t i o n . 133 In general, the trend in binding of polyclonal IgG antibody to the various latexes, under the conditions studied, is similar to that of BSA adsorption to the bare surface of the latexes. That i s , the amidine (+) latex binds the greatest amount of IgG (at a l l levels of surface antigen concentrations) followed by carboxyl, sulfate, and carboxyl modified latex. This trend presumably indicates the relative strength in nonspecific adsorption of the IgG molecules to the various surfaces. As the BSA surface coverage increases, IgG binding to amidine, carboxyl and sulfate latexes generally decreases, consistent with a reduction in the area available for nonspecific binding and in the increasing effect of specific binding to antigen by antibody. The difference in the amount of IgG bound between the latexes at high BSA coverage presumably represents the difference in strength of binding of IgG to the remaining exposed surface of the latexes. The BSA-coated carboxyl modified latex shows a slight increase in the amount of IgG bound with increasing BSA surface density, indicating that nonspecific adsorption of antibody to CML is much lower in this case. 3.3(c) Binding of Nonspecific IgG Antibody to Bare and BSA-coated PSL In order to estimate the extent of adsorption of IgG to the latex surface unoccupied by the antigen, adsorption isotherms for nonspecific IgG (i.e IgG not specific for BSA) were determined for the sulfate PSL at the same surface concentrations of BSA as in Figure 18. The binding isotherms are given in Figure 21 and the corresponding Scatchard plots in Figure 22. It can be seen that there are considerable differences in the amount of nonspecific IgG bound to the latex with different BSA surface coverage. Non-specific binding to bare or "naked" latex is much greater 134 than non-specific binding to an antigen-covered surface. 6.00 -i ,1c) ^ m—t£s n • _ XL _ m i i \ i i i i | i i i i | r i i i | i i i i | i i " i i \ i i i i | 0.000 0.010 0.020 0.030 0.040 0.050 0.060 0.070 E q u i l i b r i u m C o n c e n t r a t i o n o f IgG ( m g / m l ) Figure 21. The binding of nonspecific IgG to BSA-coated sulfate latexes from 0.01M phosphate buffer, pH 7.20. BSA surface concentrations: • m in 11 (a) "naked " latex , (b) 2.72 x 10 , (c) 8.11 x 10 , (d)_3.64 x 10 , (e) 1.05 x 10 molecules cm ; PSL surface area = 134 cm ml 135 2.00E+007 - i 1.50E+007 H 1.00E+007 H 5.00E+006 H \ A \ \ %\ 2 3 \ O.OOE+000 . O.OE+000 ;^_s * ^ • f W r r i i i i i | i i I ' W i i i i | i i i i i l i i i 1 +0  4.0E-008 8.0E-008 1.2E-007 V Figure 22. Scatchard plots of data from Figure 21. nonspecific IgG bound per gram of sulfate latex; [Ab] concentration. v = moles = molar IgG 136 At high surface antigen concentrations, non-specific binding is extremely low, but nevertheless a f i n i t e amount is bound. This suggests that under the conditions of this experiment, saturation of the latex surface by antigen (BSA), even for the highest surface concentration of antigen, was not achieved, consistent with the results shown in Figure 20. The estimated amount of non-specific IgG together with the amount of anti-BSA bound at saturation to the sulfate PSL with various surface concentrations of BSA is illustrated in Figure 23. It can be seen the nonspecific binding of IgG to the latex surface i s strongly reduced by pre-adsorbed BSA whether or not specific antibody to BSA is present in the polyclonal mixture. The data in Figure 23 are saturation values of IgG binding at each equilibrium point. When there is no BSA on the surface of the latex, the IgG adsorbed at saturation to the bare latex 0 12 surface, T , is estimated to be approximately 1.27 x 10 IgG ns 2 molecules/cm whether or not specific antibody is present in the polyclonal mixture. As the coverage of antigen (BSA) on the latex surface increases, both the surface concentration of non-specific IgG, T , and specific anti-BSA IgG, T , decrease linearly, i.e. ns sp pre-adsorption of BSA replaces the non-specifically adsorbed IgG from the latex surface. However, the rate of decrease of non-specifically adsorbed IgG (represented by the i n i t i a l slopes of the two curves in Figure 23) is dependent on whether or not the IgG fraction contains antibodies specific for BSA. When there i s no specific antibody to BSA present in the polyclonal mixture, approximately 8 molecules of nonspecifically adsorbed IgG are displaced by one molecule of BSA. A model for the stoichiometry of specific and nonspecific binding of polyclonal anti-BSA to latex coated with various surface concentrations 137 of antigen is given in Appendix 7. 2.00 -i CM b 1-50 H 0.00 BSA-Coated Sulphate Latex an t i -BSA IgG nonspecif ic IgG 0 .40 0 .80 1.20 BSA m o l e c u l e s / c m X10 -12 1.60 Figure 23. A comparison of relative amounts of specific antibodies (anti-BSA IgG) and nonspecific IgG bound at saturation to sulfate latexes with different amounts of surface bound antigen (BSA). 138 On the other hand, i f the IgG fraction contains antibodies specific for BSA as well, then pre-adsorption of BSA w i l l both displace nonspecifically adsorbed IgG and bind anti-BSA IgG molecules specifically to epitopes on the antigen. The net effect is that approximately 5 molecules of nonspecifically adsorbed IgG are "effectively" displaced by one molecule of BSA. At higher BSA coverage reduction in nonspecific IgG adsorption saturates above some surface BSA concentration, T , due to overlap of BSA * the regions from which BSA excludes IgG molecules. For T >T , the BSA BSA surface concentration of IgG containing no Ab against BSA, T , remains ns constant as more BSA molecules occupy the surface within the regions from which IgG is excluded (see Appendix 7). Since the BSA packing on the surface of the latex is not regular, nonspecific adsorption of IgG does not go to zero even at very high surface antigen concentration. Thus, there is a small amount of nonspecific adsorption remaining at high T , BSA T . When specific Ab binding is present as well as replacement of Ab, ns, s a similar analysis can be applied. At high T , IgG binding again BSA saturates, in this case at a higher value, T , associated with the sp,s specific binding of Ab added to the remnant nonspecifically adsorbed IgG molecules. The Scatchard plots presented in Figures 19 and 22, and Appendix 6 show deviations from the expected linearity (Equation 3.5). These deviations may be due to antibody heterogeneity (polyclonal antibody population with many binding constants), or complex formation (i.e. due to multivalency of the antigen) [203]. Since only a limited range of antigen concentration was covered experimentally, the intercepts determined were points with very low accuracy. 139 3.4 Summary: Antibody Binding to Antigen-coated PSL (1) Polyclonal antibody binding to antigen-coated PSL is complicated due to the presence of a mixture of antibody species with differing a f f i n i t i e s for bound antigen. (2) The surface concentration of bound antibody depends on the surface concentration of antigen on the latex particles and on the ava i l a b i l i t y of PSL surface area not occupied by antigen to non-specifically adsorb antibody. (3) In most cases, the adsorption of IgG increases as the surface concentration of antigen is decreased. That i s , the total amount of IgG bound is greater the smaller the fraction of PSL surface occupied by antigen and the larger the bare surface area, implying that non-specific binding of antibody to bare PSL surface i s more significant than specific binding to antigen at low surface concentration of antigen. As the surface concentration of antigen increases, IgG binding decreases, consistent with the reduction in the area available for non-specific binding and the increasing effect of specific binding of antibody to antigen. While the apparent a f f i n i t y constant for IgG binding to BSA is higher than for binding to the latex surface, the number of antigenic sites available per unit area is evidently much lower on adsorbed BSA than is the density achievable by nonspecific binding, by a factor of about three. The model in Appendix 7 suggests that approximately 7 molecules of IgG are displaced by one molecules of BSA and that about 3 molecules of anti-BSA IgG bind specifically per molecule of BSA. 140 (4) If non-specific adsorption to non-antigen occupied surface is weak (e.g CML), then specific binding to antigen becomes a significant fraction of the total and the amount of IgG bound tends to increase with increasing surface coverage of antigen. (5) The extensive binding of polyclonal IgG to latex surface unoccupied by antigen at low surface concentrations of BSA, results in latex concentration effects as demonstrated for BSA adsorption to bare latex surface in Chapter Two. Such effects decrease as antigen coverage is increased. Latex concentration effects on protein adsorption, therefore, appear to be quite general. 141 CHAPTER FOUR ANTIBODY-INDUCED AGGREGATION OF PSL 4.1. Introduction In practice, a wide variety of techniques is used to assess the degree of aggregation of dispersed particles including light scattering, particle-number counting, sedimentation rate or volume and rheology [204]. However, the two most commonly used methods are direct particle-number counting and light scattering because they yield absolute rate constants which provide the best fundamental basis for comparing the effects of different additives, and additive concentrations. Particle counting allows the individual concentration of each particular aggregate size to be determined as a function of time. Electrical or optical particle counting instruments such as the Coulter Counter can be used for particle-number counting, provided that the aggregate size is within the resolution limit of the instrument. Particle counting instruments usually require very large dilution of the sample in order to avoid coincidence effects, and also the presence of electrolytes to increase the electrical conductivity. Both these factors are a source of major problems with this method because they affect the state of dispersions in themselves. Another factor i s the possible disruption of aggregates on passing through the counter o r i f i c e . Optical methods have the advantage that they do not disturb the system being studied. In general, two types of light-scattering techniques may be used: angular light scattering in which the intensity of the scattered light is measured as a function of the scattering angle, and turbidity x or optical-density determination, where the intensity of 142 the transmitted beam is measured. The procedure most widely used is simply to measure the turbidity of an aggregating system at some chosen time interval. One of the problems with turbidity measurements is the d i f f i c u l t y of interpreting unambiguously the change in turbidity in terms of aggregate size distribution, except under very special conditions. Also, partial sedimentation of aggregates out of the light beam may occur. For many situations however, determination of a detailed aggregate size distribution is not necessary. A simple index, related to the state of aggregation of the particles can be used as an empirical indication of aggregation. More quantitative information can be obtained by monitoring turbidity over the i n i t i a l stages of aggregation at an appropriate wavelength where only scattering occurs [205, 206]. 4.2 Materials and Method Polystyrene latexes, with different surface functional groups from Interfacial Dynamics Corporation, Portland, OR. , described earlier were used in the kinetic studies of antibody-induced aggregation. The antigen-coated polystyrene latex samples and the polyclonal antibody preparations used in the study of antibody binding to BSA-coated PSL reported in Chapter Three were used in the kinetic studies at concentration ratios that match the ratios of antigen-coated PSL and antibody concentrations used in. the equilibrium studies reported in Chapter Three. 143 4.2 (a) Constant Shear rate Aggregometer A constant shear rate aggregometer consisting of two transparent cylinders, made of poly(methyl methacrylate), with a gap of 0.149 cm, and an inner rotating 4.128 cm diameter cylinder was constructed. The inner bob is connected to a constant speed motor as shown in Figure 24. Different shear rates were obtained by changing the constant speed motor. The shear rate G was determined by the rate of the rotation of the inner bob and the radial diameters of the cylinders. The rate of shear is given by the relationship for couette flow as [207]: G = dv dr (-2n/r 2)(R 2x R2) c b (R2 -R 2) c b (4.15) where; R = radius of bob (inner cylinder) b R = radius of cup (outer cylinder) c Q = angular velocity = Zno), u is rev per sec The average shear rates calculated from Equation 4.15 are given in Table XII below, as a function of rotation speed. The device was designed in such a way that it f i t into the light path of an HP 8450 UV/VIS spectrophotometer. At the start of an experiment, a sample of latex dispersion and distilled water was weighed to a total weight of approximately 4 grams and introduced into the annular gap (8 ml) of the apparatus. The salt or IgG solution was then weighed to approximately 4 g and introduced into the apparatus through a long syringe needle. The mixing ratio of the latex dispersion with the salt or IgG solution was therefore 1:1 by weight. 144 Table XII Mean rate of shear in the gap of the coaxial cylinder aggregometer calculated according to Equation 4.15. Motor Speed dv/dr (at bob) dv/dr (at cup) dv/dr (mean) 10 (rpm) 15 sec. - 1 13 sec."1 14 sec. - 1 20 (rpm) 30 sec. - 1 26 sec. - 1 28 sec. - 1 60 (rpm) 87 sec. 1 75 sec. 1 81 sec. 1 After mixing the latex dispersion and the salt solution (or the IgG solution) by plunging the inner bob about three times, the motor was started and the optical absorbance of the dispersion measured. The optical absorbance of the latex sample depends on the latex concentration, particle and/or aggregate size [208], and so an output of absorbance versus time provides a continuous measure of the degree of coagulation or aggregation. 145 OPTICAL AXIS f UCHT BEAU l aont or runs UCHT SENSOR CONSTANT SHEAR AGGREGOMETER Figure 24. A schematic diagram of the constant shear aggregometer which provides a continuous output of the optical absorbance of a suspension subjected to a steady shear as a function of time. 146 4.2 (b) Determination of Rate Constants for Coagulation and Agglutination Kinetics In order to relate the absorbance change of coagulating or flocculating latex particles to the kinetics, Oster [209] has derived the following expression for the turbidity, T, of an aggregating system, in which particles are considered to be Rayleigh scatterers, as a function of time, t T = T (1 + 2p k t) (4.17) 0 0 e f f where T is the i n i t i a l turbidity (t = 0) of the stable dispersion and p o o is the i n i t i a l particle number density (p Q = <p/V, where V is the volume of a singlet particle), and k is the effective rate constant. v e f f Turbidity and absorbance (O.D.) are simply related through the expression A = xi/2.303 (4. 18) where 1 is the optical path length through the aggregometer, (J = 0.298cm). Combining Equations (4.17) and (4.18) leads to: d(A/A )/dt = 2p k = k x constant o 'o e f f e f f (4.19) 147 Thus experimental determination of d(A/A )/dt enables k , the y 0 e f f effective rate constant to be obtained. Both the theory of light scattering and the theory of coagulation are best satisfied by making measurements at the early stages of coagulation. Therefore, (dA/dt) values were used in determining the experimental rate constants in our studies of coagulation and agglutination kinetics. For cases where there is an i n i t i a l increase in absorbance followed by a decrease (cf. Appendix 11), the (dA/dt) values were determined from the maximum values of the absorbance and used as the i n i t i a l rate of change in absorbance with time. 4.3 Results and Discussion 4 .3 (a) Absorbance Measurements of PSL Measured optical absorption spectra for aqueous suspensions of the four polystyrene latexes used in our studies are shown in Figure 25. These curves were obtained by measuring the absorbance of latex suspensions in a 1 cm quartz cuvette using an HP 8450 diode array spectrophotometer, a general purpose microprocessor-controlled parallel-detection instrument providing measurements over i t s f u l l 200nm to 800nm wavelength range with a reproducibility of 0.4% for a one second measurement and a 0.15% for a 10 second measurement over an absorbance range of 0.1 to 1.0. 148 Figure 25. Measured absorbance for aqueous suspensions of sulfate (1.073um) carboxyl (0.984um), carboxyl modified (0.865um), and amidine (0.489um) latexes. 149 In practice, the incident light may be absorbed, as well as scattered, by the latex particles. Thus, the measured absorbance, shown in Figure 25 and Appendix 7, is the combined effect of absorption and scattering in a l l directions by the particle. It i s s t r i c t l y a measure of light lost from the incident beam due to i t s interaction with the particles in the cuvette. It depends on the chemical composition of the particles, their size, shape, orientation, the surrounding medium, the number of particles, and frequency of the incident beam. The relationship between absorption and particle size as a function of wavelength is very complex [210]. The major features found in the measured optical absorbance curves of the polystyrene latexes are the rising absorbance toward shorter wavelengths, which is a general characteristic of nonabsorbing particles small compared with the wavelength, and interference peaks, the f i r s t of which shifts to longer wavelengths with increasing size of the particles [211]. The interference peaks arise from interference between the undeviated incident light and forward-scattered light. The optical spectra of a l l the latexes shown appears to be dominated by scattering since a l l the particles diameters are about the same or longer than the wavelength. The absorption maximum (major peak) occurs at a specific wavelength, depending on the size of the latex particle (Table XIII). The biggest change in signal (absorbance) w i l l occur at these major peaks (wavelengths) corresponding to each latex. However, the choice of wavelength for experimental measurement in the sheared system is limited by the fact that the measuring " c e l l " is made of poly (methyl methacrylate) which absorbs strongly below 400 nm. Thus, a l l absorbance measurements were made at 450 nm, irrespective of latex size. 150 T a b l e X I I I Absorption maxima from o p t i c a l spectra of aqueous suspensions of the four PSL used. Latex Type Size (um) Absorption maximum (A-nm) Sulfate 1.073 428 Carboxyl 0.984 400 CML 0.865 336 Amidine 0.489 290 For a given latex suspension, the absorbance depends on the concentration and l i g h t s c a t t e r i n g properties of the suspended p a r t i c l e s . If the suspension contains only i d e n t i c a l p a r t i c l e s , then the absorbance i s given by: A = log (1/7/) = K'Ci (4.16) where T = transmittance, K' = l i g h t e x t i n c t i o n cross-section, C i s the number of p a r t i c l e s per unit volume, and 1 i s the o p t i c a l path length. Equation 4.16 i s known as the Beer-Lambert law [212]. Figure 26 (a) and (b) show the absorption spectra of the s u l f a t e (1.073 pm) at d i f f e r e n t volume f r a c t i o n s and the corresponding p l o t of absorbance versus volume f r a c t i o n at the wavelengths indicated. It can be seen that the absorbance of the s u l f a t e latex suspension obeys the Beer-Lambert law up to a latex volume f r a c t i o n of approximately 1.05 x 10"3. 151 4.00 0.0E+000 4 . 0 E - 0 0 4 8 . 0 E - 0 0 4 1.2E-003 Figure 26. The absorption spectra of sulfate latex at different volume fractions (a), and the corresponding Beer-Lambert's plot of absorbance versus volume fraction at various wavelengths (b). 152 At higher particle concentrations, the linear dependence of absorbance on particle concentration i s no longer observed because of the multiple scattering effect. The results for the other latexes used in our studies are given in Appendix 8; they a l l show a similar behaviour to that of the sulfate latex. Changes in the nature of the latex particle suspension, such as aggregation, alter the apparent absorption spectrum of the latex considerably. The effect of particle aggregation on absorbance cannot be predicted easily from light scattering theory [210]. For particles smaller than the light wavelength, the absorbance increases with particle size, and the increase in absorbance of an aggregating suspension can be used as a measure of coagulation or flocculation rate [213]. However, for particles of size comparable to the wavelength or greater, specific absorbance usually decreases with increasing particle size (hence with aggregation). For such systems, i t is usually not possible to obtain quantitative information on the aggregate formation from absorbance measurements. However, when there is significant change (decrease) in absorbance as particles aggregate, i t can be used as an empirical indication of aggregation rate. This can be seen in Appendix 8 (a), where the absorbance spectra of coagulating latexes, in a 1 cm x 1 cm cross-section quartz cuvette, at various times after i n i t i a t i o n of aggregation are given together with a plot of the absorbance of coagulating latexes as a function of time at different wavelengths (Appendix 8 (b)). For a given particle the degree of linearity of absorbance with time varies for different wavelengths. The change in absorbance as particles aggregate also varies with wavelength for a given particle. 153 4.3 (b) Stability of BSA-coated PS latexes under shear Figure 27 shows the stability of unsheared PS latex suspensions in the absence of added protein at various concentrations of sodium chloride. The results were obtained by a centrifugal/optical absorbance method in which equal volumes (1.0 ml) of latex dispersion (mass fraction = 0.1%) and electrolyte solutions (NaCl), of varying concentration, were pipetted into each of a series of tubes. The dispersions were shaken and allowed to stand for 2 hours, after which they were centrifuged for 10 minutes at 3000 x g [214]. This centrifugation caused any coagulated material to sediment, considerably reducing the concentration of the latex in the supernatant dispersion. At the end of the centrifugation the absorbance of the supernatant was determined with a spectrophotometer (HP 8450 UV/VIS) using a 1 cm x 1 cm quartz spectrophotometer cell. The critical coagulation concentration (CCC) values for the latexes were identified as the break points in the plots of supernatant absorbance against sodium chloride concentration and are given in Table XIV. The critical coagulation concentration values for the sulfate, carboxyl, and amidine latexes are typical for coagulation of charge stabilized latexes [215]. The modified latex is substantially more stable (CCC = 0.68 mole/1) than the other latexes. This is due to the high density of carboxyl groups chemically bound to the surface of the particles. 154 3.00 Figure 27. Optical absorbance of supernatant vs concentration of NaCl for the sulfate (O)» carboxyl, 0l0, carboxyl modified (•) and amidine ( + ) (•) latexes. 155 Table XIV C r i t i c a l coagulation concentration of the latexes as estimated from supernatant absorbance readings: Latex Type Surface density Charge (uC cm ) CCC (moles/litre) Sulfate (1.073 um) 6.70 0. 15 Carboxyl (0.984 um) 2.88 0.30 CML (0.865 um) 30.7 0.68 Amidine (+) (0.489um) 12.2 0.12 The c r i t i c a l coagulation value for the sulfate latex with surface _2 charge density of 6.70 uC cm , is found to be lower than that of carboxyl latex with a surface charge density of 2.88 uC cm . This difference i s presumably due to the difference in specific adsorption of Na+ ions. As the interaction of Na+ ion with SO^  groups is lik e l y :to differ from i t s interaction with —COO groups, differences in the specific adsorption of Na+ between the two latexes, implying differences in effective surface charge, would be expected. The results of s t a b i l i t y measurements on sulfate latex coated with in in 11 BSA at (a) 2.72 x 10 , (b) 8.11 x 10 , (c) 3.64 x 10 , and (d) 1.05 12 -2 x 10 molecules cm are illustrated at a fixed ionic strength of 0.5 M NaCl in Figure 28. It is seen that the s t a b i l i t y of BSA-coated latex increases with surface coverage, the saturated latex suspension being completely stable at a l l shear rates. At low coverage, (results not shown) latex dispersions are unstable at a l l ionic strengths. At intermediate coverage, the latex dispersions are stable at low ionic strengths but unstable at high ionic strengths. At high surface coverage, latex dispersions are stable at a l l ionic strengths. 156 4.0 Figure 28. Absorbance change with time for shear flocculation in 0.5M NaCl at 14, 28 & 81 s - 1 of BSA-coated sulfate latex with surface in in 11 coverages: (a) 2.72 x 10 , (b) 8.11 x 10 , (c) 3.64 x 10 , and (d) 12 —2 1.05 x 10 molecules cm . The unlabeled lines refer to bare latex. 157 The instability at low surface coverage is probably due to a combination of electrostatic and macromolecular factors. At low coverage, the adsorbed protein is thought to reduce the particle surface potential to an extent that the basic DLVO mechanism probably s t i l l operates, but with some perturbation of the electrostatic environment near the surface of the particle due to the presence of the adsorbed protein [216]. Macromolecular bridging due to protein molecules on one particle adsorbing to a bare patch on another particle in close proximity is also considered a possible explanation for latex destabilisation at low salt and protein concentrations [217]. At the opposite extreme of high protein coverage (saturation) the coated latex particle becomes hydrophilic, and i t s s t a b i l i t y is no longer governed by the DLVO mechanism alone. Both steric factors and electrostatic repulsion between the adsorbed protein layers on the particles l i k e l y contribute to the high s t a b i l i t y exhibited at higher surface coverage of PSL. Under shear, the experimental rate constants for coated latexes are always lower than that for the bare particles (Figure 29 & 30). The rate constants decrease with increasing surface coverage of BSA, since the effective collisions between the particles are progressively reduced with surface coverage of BSA. At high protein coverage (saturation coverage) there is virtua l l y no flocculation observed, and the experimental flocculation rate constant slightly decreases with increasing shear rate. This i s illustrated in Figure 30, in which the experimental flocculation rate constants are plotted against shear rates for the bare sulfate latex and the various sulfate latexes coated with BSA at concentrations as given in Figure 27. 158 4.0E-003 Figure 29. Stability of BSA-coated sulfate latex at ionic strength 0.5M as a function of protein concentration at different shear rates. The experimental rate constants (-dA/dt)tQ is plotted against protein concentration per unit area of particle surface: (O) 14 s - 1, (sfO 28 s - 1, and (0) 81 s"1. 159 Figure 30 . Stability of bare sulfate latex and BSA-coated sulfate latexes at ionic strength 0.5M as a function of shear rate. The experimental rate constants (-dA/dt)to are plotted against shear rates for: (O) bare latex; and for, BSA-coated sulfate latex with surface coverages^ P|Q 2.72 x 1010 , (•) 8.11 x 1010 , (D) 3.64 x 1011 , and (1) 1.05 x 10 molecules cm . 160 This is the reverse of the trend for flocculation rate constants at surface coverages that are intermediate and/or below saturation, in which the rate constants increase with increasing shear rate. Presumably this is due to a complete transition of the coated particle from a hydrophobic to a hydrophilic one, and may represent shear-induced breakdown of the weak floes formed. 4.3 (c) Agglutination of BSA-coated PSL under Shear: The results presented in this section are those for the BSA-coated sulfate latex only. The data for agglutination experiments for the other latexes are included in Appendix 11. 4.3 (c) (i) The Effect of varying Anti-BSA IgG Concentration Figure 31 shows the effect of varying BSA-coverage and anti-BSA antibody concentration on the rate of agglutination in a sulfate PSL suspension in 0.01M phosphate buffer, pH 7.2. The sulfate latex suspension was f i r s t equilibrated with different amounts of BSA to give different degrees of coverage after extensive buffer washes. A polyclonal rabbit anti-BSA IgG preparation was then introduced into the aggregometer and the optical absorbance as a function of time after mixing the BSA-coated sulfate latex suspension and the antibody was measured. 161 4 .00 3.00 H O c o Figure 31. Absorbance (at 900 seconds) as a function of equilibrium IgG concentration for shear agglutination at 28 s for BSA coated sulfate latex with surface coverages: (O) 2.72 x 10*° , (*) 8.11 x 1010 , (<|) 3.64 x 1011 , and (Q) 1.05 x 10 molecules cm 2. 162 The optical absorbance vs time plots are given in Appendix 10 (a), from which the absorbance at 900 seconds after mixing the antibody and latex suspension is plotted as a function of equilibrium antibody concentration in Figure 31. This time point was chosen as i t represents a practical limit to the time over which agglutination assays are performed. Similar plots for earlier times are given in Appendix 10 (b). A l l the BSA-coated samples used in these studies were stable in the absence of anti-BSA antibody, i.e., the absorbance was constant with time. Addition of non-specific antibody to the system did not produce any nonspecific agglutination response, in spite of the adsorption shown earlier to occur. It can be seen from Figure 31 that for the lowest surface coverage 10 —2 of BSA (2.72 x 10 molecules cm ) a very small amount of anti-BSA antibody (<0.6 ug/ml) is sufficient to induce agglutination, and a maximum rate of agglutination (-(dA/dt) = 3.8 x 10 ) is attained at an antibody concentration of approximately 1.0 ug/ml (as determined from the inflection points of the curves in Figure 31 above). Comparison with Figure 18 shows that agglutination is caused by very 10 2 low numbers of bound antibodies of the order of 6 x 10 molecules/cm , 11 2 and that the rate saturates when about 1 x 10 molecules/cm are present. That i s , a very small fraction (~5% of saturation) of antibody can cause agglutination, implying that few Ab bridges are required to hold the aggregates involved together. The proportion of the bound Ab molecules involved in bridge formation cannot be estimated from this data, hoewver. As the BSA surface coverage of the latex increases, significantly higher concentrations of anti-BSA antibody are required to produce agglutination. 163 Figure 32. Plots of initial rate of change of absorbance at 28 s vs equilibrium antibody concentrations for various BSA coverage as given in Figure 31. 164 The IgG concentrations at which the maximum rates of agglutination occur at increasing surface coverage also increases, to 2.4, 3.0, and 3.2 ug/ml as the BSA coverage increases. This i s consistent with the view that at low surface concentrations of BSA, a significant fraction of antibody binds in a configuration that leaves one of i t s binding sites free to bridge and bind to another BSA molecule on a second latex particle, thus enabling agglutination to occur at relatively low antibody concentration. Higher BSA coverage requires more antibody molecules to effect agglutination, presumably because at low concentrations the antibody molecules would likely bind with both sites occupied on the same surface, reducing the probability of a bridging configuration. The i n i t i a l agglutination rates, as estimated by the i n i t i a l slopes of the absorbance-time curves are given in Figure 32 at different equilibrium antibody concentrations for the various BSA surface coverage. The semilogarithmic plots show that the i n i t i a l rates vary weakly with equilibrium concentration of antibody. Increasing the density of BSA coverage on the particle surface shifts the curves to higher equilibrium concentration of antibody, again indicating that significantly higher concentrations of antibody are required to produce agglutination of a given rate as the BSA coverage on the particle surface increases. A l l the curves appear to reach the same maximum value at this shear rate, however. Some of this data i s presented numerically in Table XV. For a given equilibrium concentration of antibody, the difference in i n i t i a l agglutination rates for the various BSA coverage on the particle surface i s significantly higher at low equilibrium antibody concentrations than at high equilibrium antibody concentrations. This can be clearly seen in Figure 32 and is further illustrated in Table XV below, for two different equilibrium concentrations. 165 T a b l e XV I n i t i a l rate of change of absorbance at two equilibrium antibody concentrations for different BSA surface coverages as given in Table X (Chapter Three) for the sulfate latex. I n i t i a l rate of change of absorbance Equilibrium at given BSA surface coverage IgG 2.72 x 10 1 0 8.11 x 10 1 0 3.64 x 10 1 1 1.05 x 10 1 2 (mg/ml) 2 (molec/cm ) 2 (molec/cm ) 2 2 (molec/cm ) (molec/cm ) -(dA/dt) -(dA/dt) . -(dA/dt) -(dA/dt) 1.5 x 10"3 3.36 x 10"3 2.10 x 10"3 1.17 x 10"3 4.80 x 10"4 6.0 x 10"2 3.79 x 10"3 4.05 x 10"3 3.27 x 10"3 3.87 x IO - 3 The maximum degree of agglutination, as represented by the minimum absorbance, is not as sensitive to IgG concentration at different BSA coverages as is the i n i t i a l agglutination rate. Evidently there is sufficient Ab bridging at long times to allow equivalent sized aggregates to form. The i n i t i a l rates suggest the probability of bridge formation at short times is strongly dependent on Ag coverage, however. Apparently 900 seconds is sufficient time to allow either lower probability bridges to form at higher BSA coverages, or is sufficient to allow some rearrangement of bound Abs to allow interparticle bonds to form. The fact that the i n i t i a l agglutination rate at high BSA coverage (Figure 32) can be increased to the same level as that observed at low Ag surface concentrations i f enough IgG is present supports the former explanation, however. The rate at which lower probability events occur would be expected to increase as the concentration of potential bridging molecules is increased at constant Ag coverage, as observed. 166 4.0 3.0 -CD O C o 2.0 O cn < 1.0 -(A) 0.0 A 1—i i i r i | T ' "' I ™ "t 1 'i "'I I 111 0.001 0.01 Equilibrium IgG Concentration ( m g / m l ) 8.0E-003 6.0E-003 -o a ^ 4.0E-003 : < "D 2.0E-003 -0.0E+000 0.001 0.01 Equilibrium IgG Concentration (mg/ml) Figure 33 (a) and (b). P l o t s of absorbance (900 seconds) (a) and i n i t i a l a g g l u t i n a t i o n rate (b) vs e q u i l i b r i u m antibody concentrat ion for shear a g g l u t i n a t i o n at (q) 14, (5ft 28 and ( « ) 81 s _ 1 of s u l f a t e la tex with BSA coverage of 1.05 x 10 molecules cm . 167 4.3 (c) (ii) The Effect of Varying Shear Rate Figures 33 (a) and (b) illustrate the effect of shear rate on agglutination reaction of sulfate latex with a BSA surface density of 12 —2 1.05 x 10 molecules cm . The absorbance (at 900 seconds) and i n i t i a l rates plotted against equilibrium antibody concentrations in Figure 33 (a) and (b) were obtained from the optical absorbance vs time plots of Appendix 10 (c). The agglutination at each antibody concentration was studied for three different shear rates: 14 s 1, 28 s 1, and 81 s !. The results show that doubling the shear rate from 14 s 1 to 28 s 1 significantly reduces the Ab concentration at which the degree of agglutination at 900 seconds is half maximum. However at earlier times, the degree of agglutination is much more reduced at 81 s 1 than between 14 s 1 and 28 s 1 (see Appendix 10 (c)). Thus for a given surface coverage of BSA, increasing the shear rate in this range decreases the Ab concentration necessary to produce a given degree of agglutination. It seems unlikely shear would alter the binding of Ab, since no dependence on s t i r r i n g rate was observed. It is possible that the more energetic interparticle collisions that occur at higher shear rates allow configurations of bound Ab to bridge that would be ineffective at lower shear rates. In effect, smaller energy barriers to agglutination could be overcome by shear. The further increase in shear rate to 81 s 1 did not appreciably increase the sensitivity to Ab concentration, however, so the above effect occurs only at relatively low shear rates. As the shear rate is raised both energy and frequency of interparticle collisions is increased. If the c o l l i s i o n efficiency is independent of shear rate the i n i t i a l c o l l i s i o n rate should be directly proportional to i t [218]. The data in Figure 33 (b) does not show this 168 _3 proportionality, however. For instance at « 6 x 10 mg/ml IgG the rates are 1:1.8:3.5, while the shear rates increased as 1:2:5.8. The effect of shear rate appears to be a roughly equal factor at a l l IgG concentrations within the uncertainty of the data, the relative increase in sensitivity to Ab between 14 s 1 and 28 s 1 observed i f Figure 33 (a) not being in evidence in the rate data. The reason for this difference is not clear. Although higher shear rates mean more frequent collisions and greater chances of antibody bridge formation, there w i l l be some value of shear rate above which the rate of aggregate formation w i l l not increase since large shear forces in the f l u i d w i l l tend to disrupt the aggregates. The value w i l l depend on the strength of the interparticle bonds and their a b i l i t y to resist the forces which shear exerts on the aggregates as they grow. Up to this point, however, i t is to be expected that increasing the shear rate w i l l increase the agglutination rate. Based on the absorbance values in Figure 33 (a), i t is evident that larger aggregates are formed at the higher shear rate 28 and 81 s - 1 than at the lower shear rates 14 s 1 i f comparisons are made after the same length of shear exposure. 4 .3 (c) (iii) The Effect of varying BSA-coated Latex Concentration The effect of varying the amount of BSA-coated latex was studied at a constant shear rate of 28 s 1 for sulfate latex with BSA surface 12 2 density of 1.05 x 10 molecules cm at five different equilibrium _3 antibody concentrations ranging from 3.0 x 10 mg/ml to 6.0 x _2 10 mg/ml. The experimental data of absorbance vs time plots are given 1 6 9 i n A p p e n d i x 10 ( d ) , and t h e p l o t s o f i n i t i a l a g g l u t i n a t i o n r a t e s v s e q u i l i b r i u m a n t i b o d y c o n c e n t r a t i o n s a r e g i v e n i n F i g u r e 3 4 . 5.0E-003 4 .0E-003 -< 2.0E-003 : I 1.0E-003 : 0.0E+00O Equilibrium IgG Concentration (mg/ml) Figure 34. P l o t s o f i n i t i a l r a t e o f change o f a b s o r b a n c e v s e q u i l i b r i u m a n t i b o d y c o n c e n t r a t i o n s f o r d i f f e r e n t c o n c e n t r a t i o n o f p a r t i c l e p e r u n i t o . Q i n 10 v o l u m e : (O) 4 . 5 9 x 10 , ( * ) 9 . 0 9 x 10 , ( • ) 1 . 8 2 x 10 , ( • ) 2 . 6 9 x 10 m o l e c u l e s p e r cm . 170 5.0E-003 -r 4.0E-003 H 73.0E-0O3 H < 2.0E-003 -1.0E-003 A O.OE+000 l i i n i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i | i i i i i i i n i i i n i i i i i | O.OE+000 1.0E+010 2.0E+010 3.0E+010 BSA-coa ted P S L / m l Figure 35. Pl o t s of i n i t i a l rate of change of. absorbance vs number of p a r t i c l e s per unit volume f o r d i f f e r e n t equilibrium antibody concentrations : (Q)_ 3.0 x 10 - 3, &|0 7.50 x IO - 3, ( 0 1.5 x IO - 2, (1ft) 3.0 x 10~2, (D) 6.0 x 10 2 mg/ ml. 171 It can be seen that when the number of BSA-coated latex particles per unit volume is very low, the initial rate of absorbance change is virtually unaffected by an increase in equilibrium concentration of antibodies. At a low ratio of antibody molecules to number of BSA-coated particles per unit volume, there is a rapid increase in the rate. As this ratio increases, the rate levels off over a wide range of equilibrium antibody concentrations. At higher ratio of the antibody molecules to number of BSA-coated particles per unit volume, the rate of change of absorbance begins to decrease, suggesting that there is an optimal antibody concentration at a given number of coated particles per unit volume for which agglutination attains a maximum rate. This optimal value is probably dependent on particle surface coverage and shear rate. The data is replotted in Figure 34, specifically illustrating the particle concentration dependence. The tendency towards saturation at high particle concentration is likely due to the complex optical path and the increase in overlap of aggregates in the light beam as the fraction of solids increases. 4.4 Structure Formation in PSL Dispersions In the course of our studies with PSL, we have observed a new type of structuring in particle suspensions undergoing simple shear flow in the concentric cylinder device (aggregometer) used in our kinetic studies of latex coagulation and agglutination. 172 It was observed that when a dilute suspension of polystyrene latex spheres containing a sufficient amount of salt to cause aggregation was subjected to a uniform shear flow of 14 s *and 28 s 1 in our shearing device, the randomly distributed, freely-moving particles produced an i n i t i a l l y cloudy suspension. As the shearing was continued, however, small aggregates began to form as a result of collisions taking place between particles. The aggregates continued to build as more single particles and smaller aggregates collected in the growing masses. After a characteristic time lag that was dependent on the shear rate and latex concentration such that the aggregates had attained a certain size (~ 0.5mm), they began to arrange themselves into lines of approximately equally spaced aggregates that were roughly parallel to the stream lines in the shearing device. A steady state was observed at roughly 10 minutes after the onset of structuring. Thereafter the pattern gradually degraded as the aggregates sedimented. The size of the aggregates in the structure increased with an increase in latex and/or salt concentrations, but decreased with an increase in shear rate. Although the structure became more defined at higher shear rates, for example at 28 s - 1 compared to 14 s 1, i t was completely lost at 81 s X, presumably due to shear-induced breakdown of the aggregates. An example of the development of the structure formation is given in Figure 36 for coagulation of sulfate latex (diameter = 1.073 pm), concentration 0.05% latex in 1.44M NaCl at a shear rate of 21.6 s"1. 173 Figure 36. Structure formation in coagulating sulfate latex suspensi under shear (21.6 s ) at room temperature. 174 Comparison is made in Figure 37 with formation of aggregates during shear agglutination of BSA-coated sulfate latex, concentration 0.05% BSA-coated latex at 21.6 s 1 in 0.06 mg/ml anti-BSA IgG, after the same length of shear exposure. It can be seen that under these conditions no pattern appears. This may be because agglutination does not lead to formation of aggregates large enough to produce pattern formation, as observed with coagulating sulfate latex, even after long periods of shearing. Instead many more smaller aggregates are formed, as can be seen in Figure 37. This may be because the aggregates formed under agglutination by antibody bridges are more shear sensitive due to their open structure, than aggregates formed by coagulation, low shear (21.6 s 1) being sufficient to break down the aggregates. Increasing the concentration of BSA-coated latex does not significantly increase the aggregate size formed during agglutination and no structuring i s observed at higher concentrations of BSA-coated latex. At extremely low shear rates the aggregates formed during agglutination are slightly bigger, and coarser in shape (see Appendix 12), but no structuring is observed at this shear rate either. Similar behaviour is observed for flocculation of BSA-coated latexes with salt solutions, i.e., no structure formation is observed at a l l , although the absorbance signal indicates that flocculation i s s t i l l occurring; the size of the aggregates formed are small compared with those for naked latex coagulating at similar volume fractions. It appears, therefore, that adsorbed protein or macromolecules on the surface of latexes greatly affects the formation of aggregate structures and patterns that are observed with coagulation of naked latexes. The presence of protein or macromolecules on the surface of particles apparently hinders the growth of aggregate size and this 175 probably explains the failure of structure formation under these conditions. 9 min. 15 min. 20 min. 30 min. 40 min. 45 min. Figure 37. Floe formation in agglutinating BSA-coated sulfate latex suspension under shear (21.6 s~ ) at room temperature. 176 Although different size aggregates and patterns were observed for the coagulation and flocculation of latex particles by salt and antibodies, the absorbance signal did not show any effect of pattern formation. This is probably due to the large optical source s l i t of the HP 8450A UV/VIS Spectrophotometer (50 micrometer wide) and the fact that each absorbance reading recorded was an average of ten one-second measurements. 4 .5. Summary: Antibody-induced Aggregation of PSL (1) . Low surface coverage of latex particles by protein may cause latex in s t a b i l i t y by both bridging and charge neutralization mechanisms. Increasing surface density of protein on latex particles increases the s t a b i l i t y of the particles. (2) . Addition of a sufficient amount of specific antibody to antigen-coated latex suspensions causes agglutination to occur. Non-specific antibody does not cause agglutination at any concentration. (3) . For low surface coverage of latex particles by protein antigen, relatively low concentrations of specific antibodies are required to cause agglutination. The numbers of antibodies bound under thses conditions represent a small fraction (»5%) of Ab saturation, and demonstrating that very few Abs per unit area can cause agglutination. 177 (4) . Increasing surface density of protein antigen on latex surface requires significantly higher concentrations of specific antibodies to produce agglutination, presumably because at higher protein surface density, antibody binding occurs with both sites occupied on the same surface, reducing the probability of a bridging configuration. (5) . Fluid motion caused by shear is an important factor in agglutination reactions, because of the increase in number of collisions between particles. However, high shear rates may cause aggregate break-up, thus producing smaller aggregates that may not be clearly visible and higher optical absorbance. (6 ) . There is a remarkable structure formation that is exhibited by latex coagulation in salt under intermediate shear rates. This structure formation does not occur during antibody-induced agglutination under shear probably because the aggregates formed are relatively easily broken down by shear. 178 CHAPTER FIVE GENERAL CONCLUSIONS This study was designed to provide some general information on the physicochemical factors important in latex agglutination caused by Ag-Ab reactions. The results delineated some interesting effects both in protein adsorption and the agglutination response. It was found that Ag adsorption, in this case BSA, is markedly influenced by the properties of the latex surface. In most cases hydrophobic interactions between the hydrophobic amino acids of the protein and the hydrophobic regions of the PSL surface are responsible for protein adsorption. Hence latexes with high hydrophobic surface areas maximize adsorption. Latexes with opposite charge to that of the adsorbing protein may show enhanced adsorption due to superimposition of electrostatic and hydrophobic effects. Although the amount of protein adsorbed w i l l vary with the protein used, these findings have practical implications when considering the the use of latex particles for applications that require immobilization of proteins onto the latex surface, such as in immunological procedures. There is a clear need to establish in each the most appropriate latex to be used. Desorption or exchange of proteins during storage of prepared reagents w i l l obviously affect results obtained by solid-phase immunoassay. The desorption of albumin molecules from PSL surfaces was found, to a limited extend, to be dependent on the type of latex. Latexes that maximize adsorption lose the lowest fraction of molecules following extensive pure buffer wash. The addition of more protein or other macromolecules did not displace the adsorbed albumin from the 179 s u r f a c e o f t h e l a t e x e s o v e r a r e l a t i v e l y s h o r t p e r i o d o f t i m e . However , p a r t i a l d e s o r p t i o n was a c h i e v e d b y t h e a d d i t i o n o f t h e s u r f a c e a c t i v e a g e n t , sod ium d o d e c y l s u l f a t e . I t a p p e a r s t h a t p r o t e i n s p r e - a d s o r b e d t o h y d r o p h o b i c s u r f a c e s r e m a i n s t a b l y b o u n d , a t l e a s t o v e r t h e t i m e c o u r s e s used i n t h i s s t u d y , so t h a t d e s o r p t i o n a n d / o r e x c h a n g e , b e i n g s l o w p r o c e s s e s do n o t o c c u r s i g n i f i c a n t l y o v e r t h i s t i m e p e r i o d . S i n c e s u r f a c e a c t i v e a g e n t s such as SDS can d i s p l a c e and s o l u b i l i z e p r o t e i n s f r o m t h e s u r f a c e o f l a t e x , t h e use o f s u r f a c t a n t s t a b i l i z e d l a t e x p r e p a r a t i o n s c o u l d r e d u c e t h e a d s o r p t i o n o f p r o t e i n s because o f c o m p e t i t i o n b e t w e e n t h e s u r f a c e a c t i v e a g e n t s and p r o t e i n s . The a d s o r p t i o n o f p r o t e i n s c o n t a i n i n g o l i g o m e r s and o r m i x t u r e s t o PSL depends on t h e c o n c e n t r a t i o n o f b o t h t h e p r o t e i n s and l a t e x . Fo r p r o t e i n s c o n t a i n i n g o l i g o m e r s , t h i s s t u d y shows t h a t h i g h e r amounts p e r u n i t a r e a a d s o r b i n s u s p e n s i o n s c o n t a i n i n g l o w e r t o t a l s u r f a c e a r e a s . The a d s o r b e d l a y e r i s e n r i c h e d i n t h e h i g h e r m o l e c u l a r w e i g h t o l i g o m e r s , r e l a t i v e t o t h e i r c o n c e n t r a t i o n s i n t h e s t o c k s o l u t i o n . T h i s e n r i c h m e n t may be due t o p r e f e r e n t i a l a d s o r p t i o n o f h i g h e r p o l y m e r i c s p e c i e s o r t o t h e f o r m a t i o n o f t h e s e h i g h e r p o l y m e r i c s p e c i e s on t h e p a r t i c l e s u r f a c e s as a consequence o f c o n f o r m a t i o n a l changes o c c u r r i n g upon a d s o r p t i o n . T h i s r e s u l t f u r t h e r c o m p l i c a t e s t h e a n a l y s i s o f p r o t e i n a d s o r p t i o n on p o l y s t y r e n e l a t e x e s . However , t h e p r e s e n c e o f o l i g o m e r s o r c o m p e t i n g p r o t e i n s on t h e l a t e x s u r f a c e may have no e f f e c t on t h e immunoassay o f a p r o t e i n o f i n t e r e s t as l o n g as t h a t p r o t e i n i s p r e s e n t i n s u f f i c i e n t amoun ts . The b i n d i n g o f p o l y c l o n a l a n t i b o d i e s t o a n t i g e n i m m o b i l i z e d on t h e s u r f a c e o f l a t e x e s i s c o m p l i c a t e d by t h e f a c t t h a t p o l y c l o n a l a n t i b o d y p r e p a r a t i o n s c o n t a i n a m i x t u r e o f s p e c i e s w i t h d i f f e r e n t a f f i n i t i e s f o r bound a n t i g e n a n d / o r t h e b a r e s u r f a c e o f l a t e x e s . A consequence o f t h i s 180 i s t h a t a v a r i e t y o f e f f e c t s can be e x p e c t e d , d e p e n d i n g on t h e c o n c e n t r a t i o n o f a n t i g e n on t h e PSL s u r f a c e and on t h e a v a i l a b i l i t y o f t h e a r e a n o t o c c u p i e d by t h e a n t i g e n t o n o n s p e c i f i c a l l y a d s o r b a n t i b o d y m o l e c u l e s . The r e s u l t s o f b i n d i n g s t u d i e s show t h a t t h e a d s o r p t i o n a t a l l b u t t h e l o w e s t a n t i b o d y c o n c e n t r a t i o n s i n c r e a s e s as t h e s u r f a c e c o n c e n t r a t i o n o f a n t i g e n i s d e c r e a s e d , i . e . t h e amount o f IgG bound i s g r e a t e r t h e s m a l l e r t h e f r a c t i o n o f t h e PSL s u r f a c e o c c u p i e d b y t h e a n t i g e n and t h e l a r g e r t h e b a r e s u r f a c e a r e a . T h i s i m p l i e s t h a t more n o n s p e c i f i c b i n d i n g o f a n t i b o d y t o b a r e PSL o c c u r s t h a n s p e c i f i c b i n d i n g t o a n t i g e n a t most a n t i b o d y c o n c e n t r a t i o n s . As t h e s u r f a c e c o n c e n t r a t i o n o f a n t i g e n i n c r e a s e s , a n t i b o d y b i n d i n g d e c r e a s e s , c o n s i s t e n t w i t h t h e r e d u c t i o n i n t h e a r e a a v a i l a b l e f o r n o n s p e c i f i c b i n d i n g and t h e i n c r e a s i n g e f f e c t o f s p e c i f i c b i n d i n g o f a n t i b o d y t o a n t i g e n . A t h i g h e r s u r f a c e a n t i g e n c o n c e n t r a t i o n s t h e s l o p e s o f t h e S c a t c h a r d p l o t s i n c r e a s e mean ing t h a t t h e a f f i n i t y o f a n t i b o d y b i n d i n g i n c r e a s e s . T h i s i s c o n s i s t e n t w i t h t h e c o n t r i b u t i o n o f h i g h a f f i n i t y a n t i b o d y b i n d i n g i n c r e a s i n g as b a r e s u r f a c e a r e a o f l a t e x i s r e d u c e d . T h i s s u p e r i m p o s i t i o n o f n o n s p e c i f i c a d s o r p t i o n o f a n t i b o d y on t h e s p e c i f i c b i n d i n g t o a n t i g e n means t h a t a d i r e c t b i n d i n g measurement o f t h e t o t a l a n t i g e n i c b i n d i n g s i t e s p e r l a t e x p a r t i c l e s becomes amb iguous , s i n c e d i f f e r e n t r e s u l t s can be o b t a i n e d i n t h e same s y s t e m d e p e n d i n g on t h e m a g n i t u d e s o f t h e d i f f e r e n t a f f i n i t i e s p r e s e n t . I t a l s o c o m p l i c a t e s c o m p a r i s o n s o f t h e number o f s u r f a c e a n t i g e n i c s i t e s on d i f f e r e n t l a t e x p a r t i c l e t y p e s u s i n g , s a y , t h e same a n t i b o d y p r e p a r a t i o n , s i n c e t h e n o n s p e c i f i c a d s o r p t i o n i s d e p e n d e n t on t h e h y d r o p h o b i c i t y o f t h e l a t e x s u r f a c e s . E s t i m a t e s o f t h e number o f a n t i g e n i c s i t e s a v a i l a b l e p e r p a r t i c l e f o r a g i v e n a n t i g e n s u r f a c e c o n c e n t r a t i o n a r e o f i m p o r t a n c e i n d e t e r m i n i n g t h e number o f a n t i b o d y 181 molecules required to effect agglutination which, in turn, subsequently determines the ultimate sensitivity achievable by latex immunoassys. While the apparent affinity constant for antibody binding to BSA is higher than for binding to the bare latex surface, the number of antigenic sites available per unit area is evidently much lower on adsorbed BSA than is the density achievable by nonspecific binding, by about a factor of three according to the model presented in Appendix 7. Only three molecules of antibody bind specifically per molecule of BSA. The kinetic results in this study show that very low surface coverage of latex surface by protein may cause latex instability and the addition of any level of antibody to such systems produces an agglutination response that is indistinguishable from the nonspecific flocculation caused by bridging and charge neutralization by the antigen molecules in the absence of antibody. At higher antigen surface coverage, the latex is stable in the absence of the antibodies. This indicates the importance of distinguishing pure immunochemical effects (agglutination) from non-specific aggregation caused by flocculation or coagulation. For surface coverage of latex particles by protein antigen which is low but sufficient to produce a stable suspension, relatively low concentrations of specific antibodies are required to to cause agglutination. Increasing the surface density of protein antigen on the latex surface requires significantly higher concentrations of specific antibodies to produce agglutination. Presumably the difference is due to the nature of antibody binding, i.e. whether it increases or reduces the probability of bridge formation. These results indicate that antigen adsorption effective for agglutination is achieved at concentrations much lower than that necessary to saturate the latex particle surfaces. 182 T h e r e f o r e , f o r a g i v e n p r o t e i n a n t i g e n , i t i s d e s i r a b l e t o e s t a b l i s h t h e c o n c e n t r a t i o n a t w h i c h s t a b i l i t y o f t h e l a t e x i s a c h i e v e d and above w h i c h i t r e d u c e s t h e p r o b a b i l i t y o f a b r i d g i n g c o n f i g u r a t i o n . The r e s u l t s o f a g g l u t i n a t i o n o f l a t e x e s a t d i f f e r e n t s h e a r r a t e s i l l u s t r a t e t h e s t r o n g e f f e c t s t h a t l o c a l f l o w c o n d i t i o n s can have on t h e r a t e a t w h i c h a g g l u t i n a t i o n o c c u r s . I n c r e a s i n g s h e a r r a t e s i n c r e a s e t h e number o f c o l l i s i o n s be tween p a r t i c l e s , t h u s i n c r e a s i n g t h e p r o b a b i l i t y o f b r i d g e f o r m a t i o n . However , e x t r e m e l y h i g h s h e a r r a t e s may cause a g g r e g a t e b r e a k - u p . The i n i t i a l r a t e s s u g g e s t t h a t t h e p r o b a b i l i t y o f b r i d g e f o r m a t i o n i s s t r o n g l y dependen t on a n t i g e n c o v e r a g e . The maximum d e g r e e o f a g g l u t i n a t i o n , as r e p r e s e n t e d by minimum a b s o r b a n c e , i s n o t as s e n s i t i v e t o a n t i b o d y c o n c e n t r a t i o n s a t d i f f e r e n t BSA c o v e r a g e s as i s t h e i n i t i a l a g g l u t i n a t i o n r a t e . Under s h e a r c o n d i t i o n s l o w e r p r o b a b i l i t y b r i d g e s f o r m i n r e l a t i v e l y s h o r t p e r i o d s o f t i m e i f s u f f i c i e n t a n t i b o d y i s p r e s e n t . Thus u n d e r s h e a r a g g l u t i n a t i o n may i n c l u d e c o n t r i b u t i o n s f r o m a n t i b o d y m o l e c u l e s o f low a f f i n i t i e s , w h i c h a r e n o r m a l l y assumed t o c o n t r i b u t e o n l y t o e q u i l i b r i u m t i t r e s . 183 Glossary of Terms Adsorpt ion The spontaneous enrichment (accumulation) of one or more components at a surface or in an interfacial layer. Adsorption Isotherm The relation between the quantity adsorbed and the composition of the bulk phase under equilibrium conditions at constant temperature. Affinity The number and total strength of the bonds between an individual antibody binding site and antigenic determinant. Agglutination The process by which suspended particles (bacteria, cells, latex, etc) are caused to adhere and form into clumps due to specific macromolecular briding, as in the case of antibody-antigen interaction. Antibody Antibody i s one of many classes of immunoglobulins present in blood serum or body fluids of an animal, which are produced in response to an antigenic stimulus. Antigen Is any foreign substance (e.g. microorganism) that, as a result of comning into contact with appropriate tissues of an animal, induces the body to produce another substance (an antibody) which reacts with the antigen. Coagulation and Flocculation The formation of aggregates is called coagulation or flocculation. Coagulation implies the formation of compact aggregates and flocculation implies the formation of loose or open network aggregates (or floes). Colloidal Refers to a state of subdivision, implying that the molecules or polymolecular particles dispersed in a medium have at least in one direction a dimension roughly between lnm and lum. Colloidal Aggregate An aggregate i s , in general, a group of particles (atoms or molecules) held together in any way. Colloidal aggregates describe the structure formed by the cohesion of colloidal particles. Colloidal Dispersion A system in which particles of colloidal size of any nature (gas, liquid or solid) are dispersed in a continous phase of a different composition (or state). 184 Collodal Stability Implies the particles in a colloidal system do not aggregate at a significant rate. Colloidal Suspension A suspension is solid particles dispersed in a liquid; a colloidal suspension is one in which the size of the particles l i e in the colloidal range. Emulsion Liquid droplets dispersed in a liquid. Latex (plural = latices or latexes) is an emulsion or sol in which each colloidal particle contains a number of macromolecules. Lyophobic and Lyophilic Terms used to describe the character of interaction of a material with the medium. Qualitatively, lyophobic means "solvent rejecting" and lyophilic means "solvent prefering". Colloidal dispersions may be lyophobic (hydrophobic, i f the dispersion medium is an aqueuos solution) or lyophilic (hydrophilic). Monodisperse If a l l particles in a colloidal system are of (nearly) the same size the system is called monodisperse. If they are not of (nearly) the same size, i t is called heterodisperse and i f many particles sizes occur polydisperse. Perikinetic and Orthokinetic aggregation The rate of aggregation is in general determined by the frequency of collisions between the particles and the probability of cohesion during collision. If the collisions are caused by Brownian motion, the process is called perikinetic aggregation; i f by hydrodynamic motions (e.g. convection, sedimentation or shear forces) then the process is called orthokinetic aggregation. Sent itization and Protective Action Addition of small amounts of a hydrophilic colloid to a hydrophobic colloid, sol may make the hydrophobic sol sensitive to flocculation by electrolyte. This phenomenon is called sentitization. When higher concentration of the hydrophilic colloid protects the hydrophobic sol from flocculation, then the phenomenon is called protective action. Sol Colloidal system composed of two or more componenets, e.g. protein sol, gold sol and an emulsion. Surface active agent (= surfactant) A substance which lowers the surface tension of the medium in which i t i s dissolved and/or the interfacial tension with other phases. 185 Glossary of Symbols and Abbreviations a radius of particle a and b major and minor semi-axes of prolate spheroid a specific surface area of latex (cm /g) s A Absorbance (A , initial absorbance at t = 0) o A Hamaker constant of particles ii A Hamaker constant of medium 22 Ab antibody Ag antigen BSA bovine serum albumin molar concentration of the ith ionic species C initial concentration of BSA (mg/g ) i s o l n . C equilibrium concentration of BSA (mg/g ) e s o l n C equilibrium protein concentration p 3 C number of particles per cm CCC critical coagulation constant c.f.c. critical flocculation concentration c.f.T. critical flocculation temperature CMC critical micelle concentration CML carboxyl modified latex diffusion constant of a spherical particle DEAE diethylaminoethyl -(dn)/(dt) rate of diffusion-controlled coagulation (dA/dt) rate of change of absorbance with time DNA deoxyribonucleic acid FPLC fast protein liquid chromatography G = (dv/dr) velocity gradient (shear rate) AG free energy of attraction A A G r free energy of repulsion A G t Total free energy of interaction between two particles H distance of separation between the centres of particles hCG human chorionic gonadotropin HSA human serum albumin 2 I = 1/2 Szt = ionic strength IgG immunoglobulin G J° Brownian collision frequency J° Shear-induced collision frequency k Boltzmann's constant k rate constant for diffusion-controlled coagulation kf rate constant for fast coagulation k rate constant for slow coagulation s k forward reaction rate -> k reverse reaction rate <-186 k efective rate constant e f f k experimental rate constant exp K , K , & K are the intrinsic association constants for the binding 1 2 1 each class of antibody binding site K equilibrium binding constant K and K intrinsic association constants i II > K light extinction cross-section 1 optical path length M monomer m mass of latex (g) M primary minimum M2 secondary minimum M relative molar mass r N Avogadro's number A n number of particles per unit volume P primary maximum PCS photon correlation spectroscopy PDMS polydimethylsiloxane PS polystyrene PSL polystyrene latex PVT polyvinyl toluene R radius of bob (inner cylinder) b R radius of cup (outer cylinder) c Rf relative electrophoretic mobility RNA ribonucleic acid s number of antigenic binding sites S surface area of adsorbent S geometric function e l S geometric function mix SDS sodium dodecyl sulfate SANS small-angle neutron scattering t time T Absolute Temperature T Transmittance TCA trichloroacetic acid TEMED tetramethylethylne diamine V potential energy of interaction V solution volume AV energy barrier to coagulation V R steric interaction energy V solvent molecular volume l V 2 polymer molecular volume W coagulation s t a b i l i t y ratio Wp polar component of work of adhesion 187 dispersion component of the work of adhesion z^ valency of the ith ionic species T amount adsorbed per unit area 2 T plateau adsorption value (mg/cm ) max r amount of nonspecific IgG bound to BSA-coated latex per unit area n s r° amount of nonspecific IgG bound to naked latex per unit area n s T amount of nonspecific IgG adsorbed at high T n s , s B S A T amount of specific anti-BSA IgG bound to BSA adsorbed on latex s p particle T amount of specific anti-BSA bound to BSA adsorbed on PSL plus s p , s nonspeific adsorption of anti-BSA IgG to bare surface of PSL * 2 r nonadsorbed amount per unit area (mg/cm ) * r"BsA surface BSA concentration above which nonspecific and specific IgG binding to PSL saturates e dielectric permittivity of medium s C q permittivity of free space C, zeta potential i) viscosity of continous phase K reciprocal Deby-Huckel electrical double layer thickness v moles of IgG bound per gram of latex p density of latex (g/cm ) p(z) adsorbed polymer segment concentration profile x turbidity (x i n i t i a l turbidity) X Flory polymer/solvent interaction parameter, w revolution per second angular velocity ypQ surface electrostatic potential <f> volume fraction of particles 188 Appendix 1 Procedure f o r electrophoretic analysis of BSA samples i n the stock solu t i o n , supernatant solution, and that eluted from latex surfaces. The o v e r a l l approach to gel preparation was that due to Fairbanks et. al [75]. Concentrated stock solutions were prepared i n the proportions given i n Table IA. The 4% gel stock s o l u t i o n was then poured into glass tubes of 5mm inner tube diameter, 12.5 cm long, that had been cleaned by soaking i n chromic acid , rinsed thoroughly i n d i s t i l l e d water and dri e d i n an oven. Each gel column was o v e r l a i d gently with overlay s o l u t i o n (Table IA) and when polymerization was complete (about one hour at room temperature), the tops of the gels were rinsed with d i s t i l l e d water and o v e r l a i d with electrophoresis buffer. The supernatant and stock BSA s o l u t i o n from adsorption studies were prepared f o r electrophoresis by mixing lOOu.1 of the pro t e i n s o l u t i o n with lOOul of Fairbanks sample reagent (Table IA). The BSA adsorbed onto the latex surface was eit h e r eluted with 200ul portions of 2% SDS and then mixed with an equal portion of Fairbanks sample reagent f o r electrophoresis analysis, or d i r e c t l y eluted, from the latex surface, with 200ul portions of Fairbanks sample reagent. These samples were then b o i l e d f o r 5 minutes and allowed to cool to room temperature, and 20ul of each were, separately, discharged gently to the top of a g e l , using a micropipette. Normally, electrophoresis was performed at a constant current of 3 mA/gel f o r about 2.5 hr. When the tracking dye band, pyroriin Y, had come to the bottom of the gels, the electrophoresis was stopped and the tubes removed from the electrophoresis apparatus. The gels were removed from the tubes and the p o s i t i o n of the tracking dye was 189 marked in each gel by pricking i t with a needle dipped in black ink. The gels were then stained as described below. Table IA Solutions used to make 47. SDS PAGE gels FAIRBANKS SAMPLE REAGENT 10X TRIS-HCL BUFFER Tris-HCl 0.02 M Tris -HC1 24.23 g EDTA 0.002 M S odium Acetate 13.61 g SDS 2.0% w/w EDTA 3.72 g Sucrose 14.0 7. H 0 2 up to 500 i ml Pyronin Y 0.004 7. 47. GEL STOCK 10X ACRYLAMIDE:BIS 10X Acrylamide:bis 4 ml Acrylamide 40 g 10X Tris-HCl buffer 3 ml Bis 1.5 g HO 17 2 ml H 0 2 up to 100 ml 47. SDS 1.5 ml 0.57. TEMED 1.5 ml 1.5% Ammonium 3 ml Persulphate OVERLAYING SOLUTION RESERVOIR BUFFER This was made as the 4% gel 10X Tris-HCl 200 ml solution with the acrylamide:bis 47. SDS 100 ml replaced with H20. H 0 2 1700 ml The gels were stained for protein with coomassie blue. They were placed in a gel stain/destainer plastic mold with a compartment slotted to hold 12 gel rods; to which was added the staining, fixing and destaining solutions given below: 190 Table IB Solutions for staining, fixing and destaining electrophoretic gels Coomassie Blue Stain: Coomassie Blue G-250 0.200 g Methanol 28 ml Glacial Acetic acid 5 ml Perchloric acid 25 ml HO up to 500 ml 2 Methanol Fix Solution: Methanol 300 ml Acetic acid 50 ml H 0 650 ml 2 Destaining Solution ( 7% Acetic acid ): Acetic acid 70 ml HO 930 ml 2 The gels were stained in coomassie blue stain solution for ^  1 hr. , followed by = Ihr. of methanol f i x solution and then destained in 7% acetic acid until a clear background was obtained. They were then stored in glass tubes f i l l e d with water. The bands on the gels were recorded by scanning them on a Beckman Model 25 Spectrophotometer with a rod gel scanning adaptor at 590nm and integrated as described in Chapter 2, section 2.3 (d). 191 Appendix 2a The following is an outline of the procedure used to calculate the amount of BSA adsorbed per unit area of PSL and error estimates associated with the calculations. The amount of BSA adsorbed per unit area of latex is given by: r = c x v (2A) a x m s where T = amount of protein adsorbed per unit area (mg cm ) C = C - C i e C = initial concentration of BSA before binding (mg/g ). 1 s o l n . C = equilibrium concentration of BSA (mg/g ). e s o l n . V = amount of liquid phase (g). 2 a = specific surface area of latex (cm/g). s m = mass of latex (g). Measured Quantities: A = CPM/g solution of BSA for calibration c = CPM/g solution of BSA before adding latex A = CPM/g solution of BSA in supernatant e W = wt. of BSA stock solution i W = wt. of BSA solution + wt. of latex suspension e W = total wt. of fluid f W = wt. of buffer b Wj = wt. of stock latex suspension w = wt. of supernatant for counts s (3^  = mass fraction of stock latex suspension /3 = equilibrium mass fraction of latex suspension e 192 (a) The in i t i a l concentration of BSA in each sample was determined from the amount of BSA solution added in each sample and the specific radioactivity of stock BSA: The specific activity of BSA is given by: A = A /C , ( C = concentration of BSA (g /g ). BSA c BSA BSA BSA soln. The in i t i a l concentration of BSA is then given by: C = A /A (g /g . ). i i BSA BSA S O l n . (b) The equilibrium concentration of BSA in each sample was determined from the activity of the supernatant of each sample and the specific radioactivity of the stock BSA: C = A /A (g /g ). e e BSA BSA soln. (c) The mass of latex in each sample was determined from the mass fraction of the stock latex suspension: m = (0 x W ). e e ( d ) The specific area of the latex was determined from: 4 - 3 a = 6 x 10 /dp, p = 1.055 g cm , d = diameter of latex particle. s The probable error in the amount of BSA adsorbed per unit area, Af, as calculated by Equation 2A is given by: Af (V/a m)2(AC)2 + (C/a m)2(AV)2 + (CV/a2m)2(Aa ) 2 s s s s 1/2 (CV/a m2)2(Am)2 s where AC is the uncertainty in the difference in the initial concentration of BSA before adsorption and the equilibrium concentration of BSA, AV is the uncertainy in amount of fluid, Aa is the uncertainty s in the specific surface area of latex, and Am is the uncertainty in the mass of latex used in each sample. 193 Appendix 2b A d s o r p t i o n i s o t h e r m s o f r e p e a t e d measurements o f BSA a d s o r p t i o n t o s u l f a t e l a t e x u n d e r s i m i l a r c o n d i t i o n s as t h o s e g i v e n i n F i g u r e 6 , C h a p t e r Two. The e r r o r b a r s shown a r e t h e s t a n d a r d d e v i a t i o n o f t h e mean v a l u e s o f amount a d s o r b e d p e r u n i t a r e a as o b t a i n e d f r o m r e p e a t e d measurements . I t can be seen t h a t t h e r e p r o d u c i b i l i t y i s low f o r i s o t h e r m s o b t a i n e d a t r e l a t i v e l y low t o t a l s u r f a c e a r e a s : A p p e n d i x 2b ( I ) and ( I I ) where t h e s t a n d a r d d e v i a t i o n o f t h e mean r a n g e f r o m ~ ±2-15%. T h i s p r o b a b l y r e f l e c t s t h e u n c e r t a i n t y i n d e t e r m i n i n g t h e r e l a t i v e l y s m a l l change i n t h e c o n c e n t r a t i o n o f BSA s o l u t i o n due t o t h e f a c t t h a t t h e r e i s r e l a t i v e l y low s u r f a c e a r e a exposed f o r p r o t e i n a d s o r p t i o n . On t h e o t h e r h a n d , when r e l a t i v e l y h i g h s u r f a c e a r e o f l a t e x i s exposed t o t h e same BSA s o l u t i o n , t h e r e p r o d u c i b i l i t y o f t h e a d s o p t i o n i s o t h e r m s i s much i m p r o v e d as i n d i c a t e d by t h e low v a l u e s o f t h e s t a n d a r d d e v i a t i o n o f t h e mean (< ± 3 . 5 % ) : A p p e n d i x 2b ( I I I ) . 194 Appendix 2b (I) Repea ted a d s o r p t i o n i s o t h e r m s f o r BSA t o s u l f a t e l a t e x a t room t e m p e r a t u r e f r o m 0.01M p h o s p h a t e b u f f e r , pH 7 . 2 0 . The t o t a l s u r f a c e a r e a used i s 240 cm . CM £ 5.00E-004 i O 4.50E-004 -\ cn E 4.00E-004 TD 3.50E-004 -CD ~G 3.00E-004 H O - § 2.50E-004 -O < 2.00E-004 H CO CD 1.50E-004 -O 1.00E-004 • o C 5.00E-005 -D O 0.00E+000 t 0.00 0.20 0.40 0.60 0.80 1.00 < Equilibrium BSA concentration (mg/ml) 195 Appendix 2b (II) Repea ted a d s o r p t i o n i s o t h e r m s f o r BSA t o s u l f a t e l a t e x a t room t e m p e r a t u r e f r o m 0.01M p h o s p h a t e b u f f e r , pH 7 . 2 0 . The t o t a l s u r f a c e a r e a used i s 712 cm . CM I £ 5.00E-004 - i ( J 4.50E-004 H cn £ 4.00E-004 -TJ 3.50E-004 -CD "2 3.00E-004 H O -§ 2.50E-004 -D . 2.00E-004 -<C 00 CD 1.50E-004 H O 1 -OOE-004 -"c 5.00E-005 -2 0.00E+000 o t 0.00 0.20 0.40 0.60 0.80 1.00 < Equilibrium BSA concentration (mg/ml) 196 Appendix 2b (III) R e p e a t e d a d s o r p t i o n i s o t h e r m s f o r BSA t o s u l f a t e l a t e x a t room t e m p e r a t u r e f r o m 0.01M p h o s p h a t e b u f f e r , pH 7 . 2 0 . The t o t a l s u r f a c e a r e a used i s 1200 cm . CN I £ 5.00E-004 - i O 4.50E-004 -E^/.OOE-004 -TJ 3.50E-d) -004 -T_ 3.00E-O -§ 2.50E--004 -•004 -O . 2.00E-< 00 CD 1.50E--004 --004 -VQ 1.00E--004 -* C 5.00E-005 2 0.00E+000 . . . •£ 0.00 0.20 0.40 0.60 0.80 1.00 < Equilibrium BSA concentration (mg/ml) 197 Appendix 3 4% SDS-PAGE electrophoresis of polyclonal IgG fraction used in antibody binding to antigen-coated PSL and agglutination of antigen-coated PSL. A l l protein samples were reduced with 5mM 2-mercaptoethanol. 1 2 3 4 5 6 Lane 1. Low molecular weight standards. Lane 2. High molecular weight standards. Lane 3. Reduced polyclonal (anti-BSA) IgG preparation. Lane 4. Non-reduced polyclonal (anti-BSA) IgG preparation. Lane 5. Reduced nonspecific IgG. Lane 6. Non-reduced nonspecific IgG. 198 A p p e n d i x 4 Calculation of amount of polyclonal anti-BSA IgG bound per unit area of BSA-coated PSL. (1) . The procedure outlined in Appendix 2 (see above) for the calculation of the amount of BSA adsorbed per unit area of latex was used to calculated the amount of IgG bound per unit area of latex. (2) . For the Scatchard plots the values v = moles of IgG bound per gram of PSL and the ratio i>/[Ab] were calculated from the amount of IgG bound per unit area of latex and equilibrium concentration of IgG (W = 1.5 x r 105) as follows: v = (r x 10"3/ 1.5 x 105) x a (moles of IgG/g ) s latex and [Ab] = C/1.5 x 105 (moles/litre) (3) . The amount of IgG bound at saturation was estimated from the intercept of the Scatchard plots and converted into molecules of IgG bound per unit area as follows: 2 Amount bound (molecules/cm ) = Intercept (moles of IgG/g ) x latex 2 23 1/specific surface area of latex (cm /g ) x 6.023 x 10 latex (molecules/mole of IgG). (4) . The probable error in the amount of IgG bound (molecules/cm ), as estimated from the intercepts of the Scatchard plots, was estimated using the standard deviation of the residuals assuming that the residuals are a sample of actual experimental errors. 199 The standard deviation of N residuals is given by 1/2 S N r t h where N is the number of data points, r i s the residual of the i data point and is defined for a linear function as: r = y - a x -a 1 i 1 i 2 where and are the slope and intercept of the linear function respectively. Using the fact that at the 95% confidence level, the error in the dependent variable, Ay, lie s within 1.96 standard deviation of the mean i f the standard normal distribution holds, the expected error in the intercept of the Scatchard plots assuming that the error in the dependent variable is not known is given by 1/2 Aa (1.96s ) r where D = NS x2 N S = V x ; and x i i=i S N u i 1=1 200 Appendix 5 Binding isotherms of polyclonal rabbit anti-BSA IgG to BSA-coated PSL with different surface coverage of BSA. The labels (a), (b)^ (c), and (d) correspond to the number of molecules of BSA bound per cm for each latex type as given in Table XVI (see page 202). Equilibrium Concentration of IgG (mg/ml) Equilibrium Concmtrotlon of IgG (mg/ml) 1.60 x 1.20 -| 0.80 o m '8 0.40 c 0.00 BSA-Cooted Carboxyl Modified latex I I I I I I I | I I I I I I I I I | I I I I I I I I I | I I I I I I T T T 0.000 0.005 0.010 0.01 S 0.020 Equilibrium Concentration ef IgG (mg/ml) 3.00 • i i i i i • i i i i i i i • i i I i i i i i i i i i 0.000 0.009 0.010 0.013 Equilibrium Concentration of IgG (mg/ml) 201 Appendix 6 S c a t c h a r d p l o t s o f i s o t h e r m s g i v e n i n A p p e n d i x 5. The l a b e l s ( a ) , ( b ) , ( c ) , and (d ) c o r r e s p o n d t o t h e number o f m o l e c u l e s o f BSA bound p e r cm' f o r each l a t e x t y p e as g i v e n i n T a b l e XVI (see page 2 0 2 ) . 1.2OE+0OQ n N _ BSA-CocUd SuJphcU Late* o 8.COE+0O3 ; * O s * x oV« 4.00E+005 -aooE+ooo \ v N N O0E+000 N \ \ N \ \ I I I I I I I I I I . r -4.0E-008 X N X N N M l I f 8.0C-00S S.00E+00S K 3 e.ooe+009 : N BSA—Coat « i Carbo^ lot«* 3.00E+003 • 1.2E-007 V O OOF+OOO • I I I I I I I I I | h i f i i i i i n | i i i r t i i n l i | a OXE+bob' eXE^OOB 1JE-007iiE-0072.46-^07 V 6.00E+005 i 4A0E+009 " Z0OE+00S aooE+ooo. aoooE+ooo BSA-Ceated CUL N X 1. * N . X . ^ x ^ X X N N > V X 5 3.00E+006 ZO0E+O0« 1.00E+00B • BSA-Cooted Ajnfcfln* (•) laUoi «W X \ > X \ * N N x N X N X N \ N XX \ \ W •N n| i i i i1 i*i V:r^-^'''''''''aoo^-ooa a o o E + < £oEi«)6 iOE-007 tsii^m ix^m 1.2E-** 2 0 2 Table XVI Amounts of BSA and and 6 . IgG bound per cm 2 for the data plots in Appendix 5 BSA-Coated latex Amount of Bound. BSA Amount IgG bound at saturation. (from Scatchard plots) 2 (molecules/cm ) 2 (molecules/cm ) Sulfate ( 1 3 4 cm2/ml) (a) 2 . 7 2 ± 0 . 1 5 X i o 1 0 1 . 2 0 ± 0 . 0 6 x i o 1 2 (b) 8 . 11 ± 0 . 2 3 X i o 1 0 9 . 3 2 ± 0 . 8 3 x i o 1 1 (c) 3 . 6 4 ± 0 . 1 7 X i o 1 1 5 . 5 7 ± 0 . 3 2 x i o 1 1 (d) 1. 0 5 ± 0 . 1 4 X i o 1 2 4 . 5 5 ± 0 . 2 3 x i o 1 1 Carboxyl ( 1 2 1 cm2/ml) (a) 2 . 15 ± 0 . 1 1 X i o 1 0 2 . 4 2 ± 0 . 0 9 x i o 1 2 (b) 7 . 2 9 ± 0 . 2 0 X i o 1 0 2 . 1 1 ± 0 . 0 5 x i o 1 2 (c) 3 . 5 6 ± 0 . 2 3 X i o 1 1 1 . 4 8 ± 0 . 0 6 x i o 1 2 (d) 9 . 9 5 ± 0 . 1 8 X i o 1 1 1 . 3 1 ± 0 . 0 4 x i o 1 2 CML ( 1 0 6 cm2/ml) (a) 3 . 16 ± 0 . 1 7 X i o 9 4 . 2 1 ± 0 . 1 4 x i o 1 1 (b) 4 . 5 3 ± 0 . 2 9 X i o 9 4 . 9 5 ± 0 . 1 8 x i o 1 1 (c) 2 . 7 5 ± 0 . 1 6 X i o 1 0 6 . 3 2 ± 0 . 2 4 x i o 1 1 (d) 2 . , 3 5 ± 0 . 1 7 X i o 1 1 5 . 6 8 ± 0 . 1 5 x 1 0 1 1 Amidine (+) ( 1 6 0 cm2/ml) (a) 2 . , 0 8 ± 0 . 1 0 X i o 1 0 4 . 6 1 ± 0 . 1 0 x i o 1 2 (b) 6 . , 5 6 ± 0 . 1 5 X i o 1 0 4 . 2 5 ± 0 . 0 7 x i o 1 2 (c) 4 . , 4 8 ± 0 . 1 8 X i o 1 1 2 . 9 5 ± 0 . 0 9 x i o 1 2 (d) 1. , 2 4 ± 0 . 0 9 X i o 1 2 2 . 5 9 ± 0 . 1 1 x i o 1 2 203 Appendix 7 A model for the stoichiometry of specific and non-specific binding of polyclonal anti-BSA IgG to latex coated with various surface concentrations of antigen. (Personal communication, D.E Brooks, Departments of Pathology and Chemistry, University of British Columbia, B.C., Canada.) It i s evident from Figure 22 that the non-specific binding of IgG to the latex surface is strongly reduced by pre-adsorbed BSA whether or not specific antibody to BSA is present in the polyclonal mixture. In the following model i t is assumed that the IgG binding is saturated at each equilibrium point and that depletion effects and binding differences due to variations in a f f i n i t y within the IgG fraction are negligible. When the BSA surface concentration, T , is low, assume that a BSA constant number of molecules of non-specific IgG, n , is displaced per n s molecule of pre-adsorbed BSA. Near the origin of Figure 22, then, the surface concentration of IgG containing no Ab against BSA, T , w i l l be ns given by: r = r° - n r (A7.i) ns n s n s BSA where r° is the surface IgG concentration adsorbed at saturation to the ns bare latex surface. If the IgG fraction contains antibodies specific for BSA, assume n IgG molecules bind specifically to epitopes on the s p antigen. In this case, again when T is low, pre-adsorption of BSA BSA w i l l both replace non-specifically adsorbed IgG and bind n IgG molecules s p per BSA molecule. Therefore, the total amount of IgG bound per unit area, T , w i l l be: s p 204 r = r - n r + n r sp ns ns BSA sp BSA (A7.2) Hence, the i n i t i a l slopes AfBSA r Af and sp AfBSA provide estimates for n and n , since from Equations (A7.1) and (A7.2) above: ns sp f Ar 1 ns AfBSA = -n (A7.3) and sp AfBSA (n - n ) sp ns (A7.4) The i n i t i a l slopes in Figure 22 give: n = 8 and n = 3 ns sp At high BSA coverage, since each BSA molecule replaces about 8 IgG molecules from the surface, the regions from which they exclude IgG w i l l overlap and reduction in IgG binding saturate above some surface BSA * • concentration, T . For T >T , T w i l l remain constant as more BSA BSA BSA ns BSA is put on the surface within the regions from which IgG is excluded. If BSA packing on the surface was perfectly regular, T would be zero ns * above T . However, this i s not the case and there is a small amount of BSA non-specific adsorption remaining at high T , T BSA ns, s Due to s t a t i s t i c a l and geometric effects the transition between the linear decrease in T , and i t s saturation at T is not sharp, but ns ns,s T can be estimated by making the simplifying assumpt on that T obeysBSA ns 205 the following conditions: T = T* - n T ; for r « r* (A7.5) n s n s n s B S A B S A B S A r = r ; for r » r* (A7.6) n s n s , s B S A B S A * Hence T can be estimated from the intersection of the two lines to be B S A * 12 2 T ~ 0.15 x 10 molecules/cm B S A In the case in which specific Ab binding is present as well as replacement a similar analysis can be applied. At low T , T is B S A s p assumed to decrease linearly with increasing T . At high T , IgG B S A B S A binding again saturates, in this case at the higher value , T s p , s associated with the specific binding of Ab added to the remnant non-specifically bound material. That T approaches the constant value s p r suggests that surface bound BSA can exclude specifically bound IgG s p , s as well as non-specifically adsorbed antigen. Again, the transition of r from a linear decrease to a constant value i s assumed to occur at the s p some value V . Intersection of the appropriate linear regions on B S A Figure 22 gives: ' 12 2 r ~ 0.15 x 10 molecules/cm B S A This is in good agreement with V , suggesting that the above model is B S A reasonable. It follows that the difference (T T ) represents the n s s p amount of antibody specifically bound to surface adsorbed Ag; i t s concentration dependence is shown as the solid line in Figure A7 below. 206 2.00 n CN X 1.50 H CM E o BSA-Coated Sulphate Latex 1.00 H co D o _a> o E S^0.50 \0 W I • Wl M \ [o) Total anti-BSA IgG Total nonspecific IgG - O 0.40 0.80 1.20 BSA molecules/cm X10 -12 1.60 Figure A 7 . Plots according to Equations A7.1 and A7.2. 207 Appendix 8 (a) Absorption spectra of PSL at different volume fractions. The range of volume fractions for each latex type can be seen from the abscissa of the Beer-Lambert plots of the same data in Appendix 8 (b). 208 Appendix 8 (b) Beer-Lambert plots at different wavelengths (400-800nm) for plots of absorption spectra of different PS1 given in Appendix 8 (a). 4JBD AM i xoo V u c o •fiioo o to xi < Amldlrw krtex (0.489M) 209 Appendix 9 (a) Plots of optical absorbance at various times (0-180 min.) vs wavelength for coagulating PSL, in the absence of shear. Each curve represents a 20 minute interval. i i i 210 Appendix 9 (b) P l o t s of o p t i c a l absorbance at d i f f e r e n t wavelengths vs time (min.) f o r coagulating PSL i n a 1 cm x 1 cm quartz cuvette. 2.40 1J0 • O o c o •fil.40 O 01 < O.M -i Sulphate ( 1 . 0 7 3 / * ) Latex H i ! ' l l l l 0.40 "ST \a ; i o " " Time (min.) 2.40 v u c a -£ 1-40 O 0) < 0JO • 200 0.40 - T T Carboxyl latex (0.984/i) • • • ' * t 4 . .:•:??** ' I l | i SO tOO l 4 6 2 0 0 Time (min.) 2.40 CML ( 0 . 8 6 5 M ) I JO • u u c o •0 1.40 ^ . o n 5 0J0 -• • • a 40• 90 • 100 " " 130 Time (min.) 2.40 1J0 V u c o •fil.40 O on 0J0 200 0.40 Amidln* latex (0.4S9p) * • • . • ' • 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 j 1 1 1 1 1 1 1 1 1 1 loo . iso 90 Time (min.)200 (+) 400 nm, (*) 500 nm (•) 600 nm (•) 700 nm (£) 800 nm) 211 Appendix 10 (a) Optical absorbance vs time (sec.) plots for agglutination of BSA-coated sulfate latexes with different surface densities of BSA:(A) 2.72 x 10_ , (B) 8.11 x 1010, (C) 3.64 x 10 1 1, and (D) 1.05 x 10 1 2 molecules cm 2. The effect of varying anti-BSA IgG concentration. The equilibrium concentration of antibodies for the curves identified are given on page 212. 4.0 cu O3.0 c o jQ 0.0 BSA-coated Sulphate latex (A) Agglutination at 20 RPM 180 ""ieo" Time 540 (sec.) 726' ' 900 4.0 a> O3.0 c 0.0 BSA-coated Sulphate latex (B) Agglutination at 20 RPM 11111111 • 1111111 180 360 Time 540 (sec.) 11111 7: 111111 20 4.0 0) O3.0 c o JQ 0.0 BSA-coated Sulphate latex (C) Agglutination at 20 RPM 1111111111 • 1B0 • 1111111 360 Time T T "3o; (sec.) 1 • 11111 • • 720 4.0 O3.0 c o XI l_ o to .0 2.0 < 900 0.0 BSA-coated Sulphate latex (0) Agglutination at 20 RPM 111 1111 180 • 111111 • 11 360 Time 5 4 6 " ' (sec.) 726' 9C 212 Summary of equilibrium concentrations of IgG for data shown in Appendix  10 (a). Sample: (A) (1) 4.3 x 10"5, (2) 1.95 x 10"4, (3) 3.99 x 10~4, (4) 1.5 x IO - 3, (5) 3.08 x 10"3, (6) 9.05 x IO - 3, (7) 1.48 x 10 _ 2, (8) 2.72 x 10~2, (9) 5.99 x 10"2 (mg/ml). Sample: (B) (1) 4.3 x 10"5, (2) 1.99 x 10"4, (3) 3.76 x 10~4, (4) 1.54 x IO - 3, (5) 3.07 x 10"3, (6) 6.15 x 10~3, (7) 1.19 x IO - 2, (8) 1.82 x 10~2, (9) 5.99 x 10"2 (mg/ml). Sample: (C) (1) 3.9 x 10"4, (2) 1.52 x 10"3, (3) 6.17 x 10~3, (4) 1.2 x 10 _ 2, (5) 1.82 x 10"2, (6) 6.01 x 10"2 (mg/ml). Sample: (D) (1) 1.9 x 10"4, (2) 1.5 x 10"3, (3) 2.54 x 10~3, (4) 6.2 x IO - 3, (5) 8.97 x 10"3, (6) 1.21 x IO"2 (7) 6.011 x IO - 2 (mg/ml). 213 Appendix 10 (b) Plots of optical absorbance at various agglutination times as a function of equilibrium IgG concentrations for shear agglutination at 28 s of BSA-coated sulfate latex with surface coverage (a), (b), (c), and (d) as given in Figure 28 (see page 156). (O) 120 min., (%) 300 min. and (#) 900 min. 214 Appendix 10 (c) Optical absorbance vs time (sec.) plot for agglutination of BSA-coated sulfate latex (1.05 x 10 molecules cm" ). The effect of varying shear rates. The equilibrium concentrations of antibodies for the curves identified are given on page 215. 215 Summary of equilibrium concentrations of IgG for data shown in Appendix 10 (c). Data for agglutination at 10 rpm (14 s *) (1) 3.8 x 10"4, (2) 7.5 x 10"4, (3) 1.57 x 10~3, (4) 3.0 x IO - 3, (5) 6.03 x 10"3, (6) 9.1 x 10"3 (7) 1.50 x IO - 2 (mg/ml). Data for agglutination at 20 rpm (28 s *) (1) 3.84 x 10"4, (2) 7.5 x 10"\ (3) 1.57 x 10 _ 3, (4) 3.0 x IO - 3, (5) 6.03 x 10"3, (6) 9.1 x 10"3 (7) 1.50 x IO - 2 (mg/ml). Data for agglutination at 60 rpm (81 s *) (1) 3.85 x 10 4, (2) 7.7 x 10 \ (3) 1.6 x 10 3, (4) 3.05 x 10 3, (5) 6.07 x 10"3, (6) 9.08 x IO - 3 (7) 1.53 x IO - 2 (mg/ml). 216 Appendix 10 (d) Optical absorbance vs time (sec.) plots for agglutination of BSA-coated sulfate latex (1.05 x 10 molecules cm ). The effect of varying BSA-coated latex 4.59 x 109; (2) concentration 9.09 x IO9; and equilibrium IgG (3) 1.82 x 10 1 0 and concentration: (1) (4) 2.69 x 10 BSA-coated particles/ml. 4.0 Equilibrium concentration: [IgC] - 0.003 ma/ml *.0 3.0 Equilibrium concentration: [IgG] - 0.015 may ml 360 Time (sec . ) 360 T i m e 900 217 Appendix 11 (a) Optical absorbance vs time (sec.) plot for agglutination of BSA-coated amidine ( + ) latex (0.45 mg m" ). The effect of varying shear rates. 400 800 1200 Time (sec.) 2,3.4 400 800 Time (sec.) 1200 1600 1 • Apendix 11 (a):Amidine ( + ) latex: BSA surface coverage * 0.45 mg m" - l Equilibrium concentration of IgG (mg/ml) for agglutination at 28 s" (1) 0.0048; (2) 0.0097; (3) 0.0188; (4) 0.028; (5) 0.0470 and (6) 0.0940 Equilibrium concentration of IgG (mg/ml) for agglutination at 81 s"1: (1) 0.0048; (2) 0.0097; (3) 0.0188; (4) 0.028. 218 2. Apendix 11 (b):Amidine (+) latex: BSA surface coverage ~ 0.60 mg m"2. Equilibrium concentration of IgG (mg/ml) for agglutination at 14 s"1: (1) 0.0000; (2) 0.0016; (3) 0.0056; (4) 0.0116; (5) 0.0226; (6) 0.0336 Equilibrium concentration of IgG (mg/ml) for agglutination at 28 s"1: (1) 0.0000; (2) 0.0016; (3) 0.0056; (4) 0.0116; (5) 0.0226; (6) 0.0336 Equilibrium concentration of IgG (mg/ml) for agglutination at 81 s - 1: (1) 0.0000; (2) 0.0016; (3) 0.0056; (4) 0.0116; (5) 0.0226 219 4.00 ~*So eoo 1200 Time (sec.) 400 BOO 1200 1600 Time (sec.) 3. Appendix 11 (c):Amidine ( + ) latex: BSA surface coverage » 0.75 mg m - l Equilibrium concentration of IgG (mg/ml) for agglutination at 14 s 1 (1) 0.00 (2) 0.002 (3) 0.009 (4) 0.018 (5) 0.035 (6) 0.173 Equilibrium concentration of IgG (mg/ml) for agglutination at 28 s (1) 0.000 (2) 0.002 (3) 0.009 (4) 0.017 (5) 0.035 (6) 0.174 Equilibrium concentration of IgG (mg/ml) for agglutination at 81 s (1) 0.00 (2) 0.0017 (3) 0.087 (4) 0.0175 (5) 0.174 - l 220 Appendix 11 (d) Optical absorbance vs time ^sec.) plot for agglutination of BSA-coated amidine ( + ) latex ( 1.8 mg m ). The effect of varying shear rates. 600 1200 Time (sec.) 3.00 -o c D XI o X I < 2.00 1.00 0.00 3.00 -E00 1200 Time (sec.) 1.00 0.00 1200 Time (sec. ) 18 4. Appendix 11 (d):Amidine ( + ) latex: BSA surface coverage « 1.80 mg m . Equilibrium concentration of IgG (mg/ml) for agglutination at 14 s X: (1) 0.012; (2) 0.018; (3) 0.024; (4) 0.036; (5) 0.048; (6) 0.121 Equilibrium concentration of IgG (mg/ml) for agglutination at 28 s : (1) 0.006 (2) 0.012; (3) 0.0318; (4) 0.024; (5) 0.036; (6) 0.048; (7) 0.121. Equilibrium concentration of IgG (mg/ml) for agglutination at 81 s : (1) 0.00; (2) 0.0088; (3) 0.018; (4) 0.035; (5) 0.052; (6) 0.070; (7) 0.070, (8) 0.084; (9) 0.173. 2 2 1 Append ix 12 Floe formation i n a g g l u t i n a t i n g BSA-coated s u l f a t e l a t e x at constant volume f r a c t i o n but d i f f e r e n t shear rates : 3.7 s and 21.6 s . A g g l u t i n a t i o n at 3.7 s : 10 min. 15 min. 30 min. A g g l u t i n a t i o n at 21.6 s 10 min. 15 min. 30 min. 222 References 1 . Singer, J.M. and Plotz, CM. (1956). The latex fixation test. I. Apllication to the serological diagnosis of rheumatoid a r t h r i t i s . Am. J. Med., 2 1 , 888. 2 . Hechemy, E.K., and Michaelson, E.F. (1984). 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