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Complexing behaviour of bishydroxycoumarin with macromolecules Cho, Moo Jung 1970

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THE COMPLEXING BEHAVIOUR OF BISHYDROXYCOUMARIN WITH MACROMOLECULES by MOO JUNG CHO B.S.P., SEOUL NATIONAL UNIVERSITY SEOUL, KOREA, 1966 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN PHARMACY in the Division of Pharmaceutical Chemistry of the Faculty of Pharmaceutical Sciences We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA MAY, 1970 In presenting th i s thes is in pa r t i a l f u l f i lment o f the requirements fo r an advanced degree at the Univers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make i t f r ee l y ava i l ab le for reference and study. I fu r ther agree tha permission for extensive copying of th i s thes is for scho lar ly purposes may be granted by the Head of my Department or by his representat ives. It is understood that copying or pub l i ca t ion of th i s thes i s fo r f inanc ia l gain sha l l not be allowed without my wri t ten permiss ion. Department of 'phaM^hCcuii'Ca.I <sC/€>iCg5> The Univers i ty of B r i t i s h Columbia Vancouver 8, Canada Date Apr*/. >X, I 7 <? This thesis, in the opinion of the examiners, exceeds the usual standards considered necessary for research at the M. Sc. level. It i s , in many respects, equal to investigations carried out at the Ph. D. level and reflects the student's a b i l i t y to carry out research at these more advanced levels. - i = ABSTRACT The strong binding of bishydroxycoumarin to serum albumin was f i r s t reported about 20 years ago. However, the mechanism of binding has not been studied. In this investigation, attempts have been made to reveal the mechanism. The work was extended to some other synthetic macromolecules including polyvinylpyrrolidone. The literature survey covers the physicochemical properties and the complexing behaviours in aqueous solution of the individual substances examined. The theory of multiple equilibria, which i s fundamental to an understanding of the binding process, has been summarized. Spectrophotometric, solubility, dynamic and equilibrium dialyses, and viscometric methods were used and their theoretical back-ground has been reviewed and discussed. Some physicochemical properties of BHC, necessary for the interpretation of binding data, were estimated. Maximum binding capacities of macromolecules and association constant of each binding site were obtained from the binding data. The nature of the site and intermolecular forces were characterized from thermo-dynamic analysis. This abstract represents the true contents of the thesis submitted. Supervisor TABLE OF CONTENTS - i i -Page I. INTRODUCTION 1 II. THEORY 3 III. METHODOLOGY 22 1. Spectrophotometry 23 2. Phase Solubility 26 3. Equilibrium Dialysis 28 4. Viscometry 33 IV. THE CHEMICAL AND BIOLOGICAL CHARACTERISTICS OF THE SUBSTANCES USED IN THIS INVESTIGATION 38 1. Bishydroxycoumarin (BHC) 38 2. Human Serum Albumin (HSA) 41 3. Polyvinylpyrrolidone (PVP) 44 4. Dextran, Starch, and Hydroxyethyl Starch (HES) .... 51 V. EXPERIMENTAL 53 1. Apparatus 53 2. Chemicals and Reagents 53 3. Determination of Apparent pKa Values for BHC 55 4. Solubility Measurements on BHC 57 5. The Solubility of BHC as a Function of Macro-molecule Concentration 58 6. Spectrophotometrie Analysis 60 7. Equilibrium Dialysis 61 8. Viscometric Analysis 66 - i i i -Page VI. RESULTS AND DISCUSSION 68 1. Intramolecular Hydrogen Bonding in BHC 68 2. Apparent pKa Values of BHC 71 3. Solubility 85 (a) Effects of pH, Ionic Strength and Buffer Components 85 (b) Effect of Macromolecule 91 i) Starch Sol and HES 91 i i ) HSA and PVP 94 4. Spectrophotometry 96 (a) Absorptivity Values of BHC 96 (b) Absorbance Contribution of HSA and PVP 96 (c) Depression of BHC Absorbance in the Presence of HSA and PVP 98 (d) Spectrophotometry Analysis of Complex Formation 98 5. Dynamic Dialysis 106 6. Equilibrium Dialysis 112 (a) Binding of BHC to Cellophane Membrane 112 (b) Permeability of Membrane to PVP 112 (c) Donnan Effect 114 (d) Free Drug Concentration and Volume Ratio 116 7. Interpretation of Binding Data 118 (a) Langmuir-Type Plot 118 (b) Scatchard Plot 123 (c) Double Reciprocal Plot 123 8. Thermodynamic Analysis and Mechanism of Interaction 126 (a) HSA-BHC Interaction 126 i ) Enthalpy, Entropy, and Free Energy Changes .. 126 i i ) Possibility of Ionic Interaction 128 i i i ) Possibility of Pre-Existing Binding Site 129 iv) Nature of Binding Site and Effect of Binding on Water Structure 131 (b) PVP-BHC Interaction 132 i ) Enthalpy, Entropy, and Free Energy Changes .. 132 i i ) Analysis of Enthalpy of Binding 135 i i i ) Possibility of Hydrophobic Bonding 138 iv) Nature of the Intermolecular Forces and of the Binding Site 139 - iv -Page 9. Viscometry 142 10. Comparison of Methods Used to Evaluate Binding 149 VII. SUMMARY AND CONCLUSION 155 VIII. REFERENCES 157 BIOGRAPHICAL INFORMATION 174 LIST OF TABLES - v -Table Page 1. The Complexing Behaviour of PVP with Various Types of Drugs 47 2. Absorptivity Values for BHC in a pH - 7.4 Buffer .... 96 3. Estimate of Molar Absorptivity Ratio of Bound BHC to Free BHC 104 4. Analysis of Spectrophotometric Data for PVP-BHC Interaction in 0.02$ PVP (5 umole/L.) 104 5. Calculated Data for the Dynamic Dialysis of BHC i n the Presence of PVP 109 6. Calculation Procedures for (Df) and r Value (Equili-brium Dialysis for HSA-BHC Interaction) 117 7. Calculation Procedures for (Df) and r Value (Equili-brium Dialysis for PVP-BHC Interaction) 117 8. Effect of Changes in Temperature on the Binding of BHC to HSA 128 9. Thermodynamic Data for the Binding of D-Phenyl-(p-azobenzoylamino)-acetate by Purified Antibody Specific for the Compound, in 0.02M Phosphate Buffer of pH 7.4 Containing 0.15M NaCl (from Karush, 1956) .. 130 10. Thermodynamic Functions for the Binding of One Mole of BHC by One Mole of Vacant Binding Site on PVP 135 11. Calculation Procedure for Estimating Specific and Reduced Viscosities of PVP Solution at 10°C in the Presence and Absence of BHC 142 12. Influence of BHC Binding on the Rheological Pro-perties of PVP at Various Temperatures 144 LIST OF FIGURES - v i -Figure Page 1. Schematic Diagram of a Macromolecule with n Sites for the Attachment of a Simple Molecule 7 2. Schematic Diagram of a Macromolecule with Two Sets of Binding Sites 14 3. Hypothetical Binding Curve for a Macromolecule with Two Groups of Binding Sites 15 4. Schematic Diagram of Changes in Water Structure Accompanied by an Interaction Between M and D 21 5. Hypothetical Curves for Changes in Absorbance (of Small Molecule) as a Function of M Concentration 24 6. Calculated Values of R as a Function of Salt Concentra-tion in the M-Free Compartment (from Bull, 1964a) 30 7. Chemical Structure of BHC 38 8. Chemical Structure of Monomer of PVP, N-Vinylpyrro-lidone 44 9. Diagram of a Plexglas Block and an Assembled Dialysis Ce l l 62 10. A Set-Up for Dynamic Dialysis Method 63 11. A Water Bath with a Tumbler Used in Solubility and Equilibrium Dialysis Studies 65 12. Infrared Spectrum of BHC in KBr 69 13. Chemical Structure of BHC showing Two Intramolecular Eight-Membered Chelations 70 14. Three Dimensional Structure of BHC 70 15. Resonance Structure of BHC after the Fi r s t Ionization .. 72 16. Titration Curves for BHC in 40$ v/v DMF in Water 74 17. Ultraviolet Spectra Showing the Second Dissociation of BHC 76 18. Absorbance-pH Curves for BHC 78 - v i i -Figure Page 19. Ultraviolet Spectra Showing the Second Dissociation of BHC i n 20$ v/v DMF 80 20. Absorbance-pH Curves for BHC at 276.5 and 315 mu 82 21. Apparent pKa Values of BHC as a Function of Per Cent DMF 83 22. Tautomerism of a BHC Molecule 84 23. Effect of pH on the Apparent Solubility of BHC at 30°C .. 86 24. Effect of Ionic Strength (Chloride Ion) on the Apparent Solubility of BHC at 30°C 87 25. Buffer Value of Tris Buffer Solutions 90 26. Two Dimensional Structure of Tris Showing Intramolecular Hydrogen Bonds 91 27. Effect of Various Concentrations of HES and Potato Starch Sol on the Apparent Solubility of BHC at 30°C in Tris Buffer 92 28. Chemical Structure and Molecular Configuration of HES .. 93 29. Effect of HSA and PVP Concentrations on the Apparent Solubility of BHC in Tris Buffer at 20°C 95 30. Absrobance Measurements at 304 mu for HSA and PVP Solutions in Tris Buffer 97 31. Absorption Spectra for BHC in the Presence and Absence of 0.1$ HSA 99 32. Absroption Spectra for BHC in the Presence and Absence of 0.4$ PVP 100 33. Predominating Chromophore ( oi,/9 -Unsaturated Lactone) in the BHC Molecule 101 34. Absorbance Depression of BHC as a Function of HSA Concentration 102 35. Absorbance Depression of BHC as a Function of PVP Concentration 103 36. Absorbance Differences for BHC Solutions in the Absence and Presence of Constant Amount of Macromolecules as a Function of Total BHC Concentration 105 37. Loss of Free BHC from Inside a Dialysis Bag in the Absence and Presence of 0.4$ HES and Dextran in Tris Buffer at 30°C 107 - v i i i -Figure Page 38. Loss of Free BHC from Inside a Dialysis Bag in the Absence and Presence of 0.4 and 0.2$ PVP in Tris Buffer at 30°C 108 39. Estimate of the Extent of Adsorption of BHC to Cellophane Membrane at Three Different Temperatures .... 113 40. Colorimetric Determination of PVP 115 41. Plot of r Values versus the Concentration of Free BHC for HSA-BHC Binding at Two Temperatures 119 42. Plot of r Values versus the Concentration of Free BHC for PVP-BHC Binding at Four Temperatures 120 43. Binding Curves at 20°C for HSA-BHC and PVP-BHC Inter-actions in Tris Buffer 122 44. Scatchard Plot for HSA-BHC Interaction at 20 and 40°C ... 124 45. Scatchard Plot for PVP-BHC Interaction at 10, 20, 30, and 40°C 125 46. Double Reciprocal Plot for PVP-BHC Interaction 127 47. Van't Hoff Plot for the PVP-BHC Interaction 133 48. Schematic Illustration of the Binding Processes Between BHC and PVP Molecules 136 49. Molecular Model of PVP Chain Segment with Eight Monomer Units 140 50. Proposed Configuration of PVP-BHC Complex 141 51. Densities of PVP Solutions 143 52. Reduced Viscosity of PVP as a Function of PVP Concen-tration at Various Temperatures 145 53. Effect of Temperature on the Intrinsic Viscosities of PVP i n the Presence and Absence of BHC 148 54. Comparison of Binding Data Obtained from Spectrophoto-metric Analysis with Those from the Equilibrium Dialysis Method for the HSA-BHC Interaction at 20°C 150 55. Comparison of Binding Data Obtained from Spectrophoto-metry Analysis with Those from the Equilibrium Dialysis Method for the PVP-BHC Interaction at 20°C 152 ACKNOWLEDGEMENTS - ix -The author would like to thank his supervisor, Dr. M. Pernarowski, for his guidance and encouragement during the course of this investigation. He would also like to express his gratitude to Dr. A.G. Mitchell for his advice and pro-fessional understanding of the problems associated with this study. The author i s grateful to the many professors and friends in the Faculty of Pharmaceutical Sciences, University of British Columbia, for their assistances at the various stages of this investigation. In particular, he would like to thank Dr. B. Roufogalis for his help in interpreting thermo-dynamic data, Dr. C.T. Rhodes for his guidance in general physical chemistry, Dr. F.S. Abbott and Mr. J. Coates for their counselling in organic chemistry, and Dr. J.O. Runikis for assigning one of his summer students (Miss K.G. Tom) to help with the viscometric experiments. The author would also like to express his gratitude to Mr. A.J. Leathern for his cooperation and help with many of the technical aspects invol-ved in this investigation. This study was financed, at least in part, by funds made available to the author by the Faculty of Pharmaceutical Sciences. The author would, therefore, like to thank the Dean of the Faculty, Dr. B.E. Reidel, not only for these funds but also for confidence in the author's capabilities to embark on a M. Sc. program at this university. I. INTRODUCTION Many investigators have studied the interactions between drugs and a wide variety of organic and inorganic molecules which are associated with a therapeutically active substance in either an jLn vitro or In vivo system. It i s known that drugs form 'complexes' with plasma proteins, enzymes, other drugs and many of the adjuvants which are added to dosage forms. The physi-cochemical properties of these complexes differ significantly, in many instances, from those observed for the interacting drug. Although these properties can be determined, they are not based, in general, on the complex i t s e l f but on studies in which the complex, the drug, and the interacting molecule are associated with each other in some In vitro system. A complex i s a co-ordination compound which arises from a Lewis acid-base reaction. This classical definition includes those complexes which are formed by reacting the drug with a metallic ion or an organic molecule. For the purposes of this thesis, the latter definition i s broader than necessary. The word 'complex', as used herein, i s defined as that substance formed by a reversible chemical reaction in which equilibrium rates are much higher than any of the rates associated with the measuring process. Chemical (covalent) bonds are not formed and the long range forces which hold the interacting molecules toge-ther are much weaker than those found in most chemical compounds. Bishydroxycoumarin (BHC) i s strongly bound to plasma proteins. It has been suggested that the interaction leads to erratic therapeutic results and that binding of drugs to macromolecules may affect the in vivo activity of the substance. The object of this study i s , therefore, to investigate the mechanism of interaction between this drug and human serum albumin (HSA), starch sol, polyvinylpyrrolidone (PVP), dextran, and hydroxyethyl starch (HES). The latter three substances have been used as plasma expanders. Complex formation may be studied by u t i l i z i n g a wide variety of methods. However, only the equilibrium and dynamic dialyses, solubility, spectrophotometric, and viscometric methods w i l l be used in this investigation. Quantitative information on the interactions may be obtained from equations which are based on the law of mass action. The nature of the intermolecular forces between the molecules i s derived from thermodynamic data obtained during the investigation. Although studies of this type have been carried out by many investigators, the significance of their observations has not always been evident. The bulk of the papers on the subject appeared in the literature during the 1950's but, in recent years, many investigators have again begun to study complex formation. This i s due, in part, to the possibility that both the s t a b i l i t y of the drug and i t s in vivo activity may be affected by other drugs or adjuvants in the dosage form. The results in this thesis are not directly related to the latter problem but do offer additional proof that therapeutically significant drugs bind easily to macromolecules. II. THEORY A general discussion of the principles and concepts fundamental to the binding capacity of proteins with various substances may be found in the papers by Scatchard (1949; and others, 1954), Klotz (1946a; 1949a; 1953a), Edsall and Wyman (1958c), Foster (1960), Tanford (1965), and Weber (1965). The mathematical theory associated with such studies i s dis-cussed in detail by Kruger-Thiemer, et al.(1964), Hart (1965), Sandberg, et a l . (1966), and Rosenthal (1967). Scatchard (1949; and others, 1954) stated that four questions should be answered at the conclusion of any study on the interaction between a protein and a small molecule. These are: "How many molecules are bound to the protein?" "How tightly are the molecules bound to the protein?" "Where does the binding occur?" "Why does the binding occur?" The answers to these questions deal, therefore, with the number of binding site, the equilibrium constant at the site, and the type of interaction between the molecule and the functional group or groups on the protein. If the functional groups on the large molecule act independently, the law of mass action may be used to explain the interaction with a small molecule and the binding strength can be expressed as a constant. If the protein (M) combines with a molecule (D) to form a single complex (MD), then M + D = MD (Eq. 1) - 4 -The association constant (K) i s defined by the following equation. (Db) K = (Eq. 2) (Mf) (Df) The quantities i n parentheses represent the concentrations of the respective species and the subscripts (b and f) indicate bound or complexed and free or unbound species, respectively. However, (Mt) = (Db) + (Mf) (Eq. 3) (M^), in Eq. 3, indicates the total concentration of macro-molecule. Rearrange Eq. 2 and substitute (M^) - (Db) for (Mf). (D b) = K(Df) £(M t) - (Db) (Eq. 4) Divide both sides of Eq. 4 by K(D f)(D b) and rearrange. (Db) 1 - (Eq. 5) (M+) 1 1 + K(Df) The molar ratio of bound drug to total macromolecule i s equal to r. This ratio indicates the extent of binding. (Db) r r= 2— (Eq. 6) (M+) Substitute the above into Eq. 5 and rearrange. - 5 -r = K (Df) 1 + k (Df) (Eq. 7) Interactions between macro and simple molecules are usually more complex than that indicated above. If there are n binding sites, i f each site i s not influenced by i t s neighbor, and i f each has the same intrinsic a f f i n i t y for D, then the successive interactions and their corresponding constants may be represented in the following way. M •+ D f = MD MD + D f = MD2 MD2 -f- D f = MD3 MDi_1 + D f = MD^  MD n-1 + D_p = MD n (MD) k l ^ (M)(Df) (MD2) (MD)(Dj) (MD3) (MD2)(Df) k, -(MD±) (MD|_ j)(D f) (MDn) (MDn_!)(Df) (Eq. 8) - 6 -Furthermore, the step association constants are not independent of each other. However, the r e l a t i o n s h i p s between constants can be stated mathematically by applying the rule s of combination and permutations. A schematic diagram of a macromolecule i s shown i n Figure 1. The equilibrium constant for the association between D and s i t e 1 on M i s the same as that for the reaction between D and any other p o s i t i o n on the molecule. Therefore: M + D f = gMD M + D f = ±MD y (Eq. 9) K = (jMD) (2MD) (M)(D f) (M)(D f) (nMD) (M)(D f) (Eq. 10) Therefore: k 1 = nK (Eq. 11) since (MD) = (,MD) + (0MD)+ + ( MD) (Eq. 12) i d n Similarly, n - 1 k 2 = ( J K (Eq. 13) 0 Figure 1. Schematic diagram of a macromolecule with n sites for the attachment of a simple molecule (D). and r n- i+1 K (Eq. 14) i This, then, i s the general relationship between the step association constant (k i) for the formation of the MDi complex and the intrinsic association constant (K). The coefficient of K in Eq. 14 i s frequently called the 's t a t i s t i c a l factor' since this may also be derived on the basis of s t a t i s t i c a l consider-ations. The value of r may now re-defined. (MD) + 2(MD2)-r3(MD3)^ ... *i(MDi)+ ... +n(MDn) (Eq. 15) r = (M)+- (MD)+ (MD2)+ ... +(MDi)+ ... 4 (MDn) The (MD) terms in Eq. 15 may now be appropriately expressed by K, (M) and (D^) terms in Eq. 8. (Df) f r = (Eq. 16) f The f and f represent the denominator of Eq. 15 and i t s f i r s t derivative with respect to (D^). Substitute the appropriate terms of the l e f t side of Eq. 14 into the corresponding step association constant terms involved in Eq. 16 and rearrange on the basis of the binomial theorem.* Thus r can be expressed without using step association constant terms. n K (Df) r= (Eq. 17) 1 + K (Df) Therefore, i f there are n independent binding sites, the extent of binding i s n times that for a single site and the intrinsic association constant i s the same as that in Eq. 7. Rearrange Eq. 17. 1/r = 1/n + l/nK(Df) (Eq. 18) Therefore, a plot of 1/r versus l/(D f) i s a straight line with a slope value of 1/nK and an intercept value of 1/n. Both the binding constant and the number of binding sites can, therefore, be determined. Enzymologists refer to this method of presenting * Eq. 16 and 17 are not derived herein. The equations leading to these may be found in the papers published by Klotz (1946a; 1953a) or by Edsall and Wyman (1958c). - 9 -data graphically as the Lineweaver - Burk plot (Lineweaver and Burk, 1943). The main problem with this double reciprocal plot i s that a few low solute concentrations w i l l outweigh many high solute concentrations. Small extrapolating errors at high (Df) wi l l result i n large errors in the n value (Goldstein, 1949; Dowd and Riggs, 1965). Klotz, Walker, and Pivan (1946b) used this method of plotting in their investigations into the binding of azosulfonic acids with bovine serum albumin. Scatchard (1949), on the other hand, plotted his data in a different manner. The 'Scatchard equation', which may be derived from Eq. 17, i s r/(D f) = Kn - Kr (Eq. 19) A plot of r/(Dj) versus r i s , therefore, a straight line. The intercept value on the abscissa yields n; the intercept value on the ordinate i s equal to Kn. This equation lays less stress on the values of r at very low (Df) values than does the double reciprocal plot (Eq. 18). In addition, i t gives a more even relative weight to the different points on the curve. Eq. 17 i s similar to the equation that was derived by Langmuir (1918) to describe certain adsorption isotherms. The equation i s bkC m= (Eq. 20) 1 +kC where m i s the number of grams of solute adsorbed by one gram of adsorbent; C i s the total concentration of solute - 1 0 -in solution. The constants in this equation (b and k) arises from the mathematical derivation of the isotherm. Although Eq. 17 and 20 are similar, i t i s not correct to assume that binding and adsorption are identical processes. The equations are similar because both have been derived from the law of mass action. The subject i s discussed in detail by Goldstein (1949) and Klotz (1953a). The Freundlich isotherm i s one of the f i r s t equations proposed to explain adsorption phenomena. m s k C 1 / n (Eq. 21) This isotherm can not be used i f the concentration of adsorbate with respect to adsorbent i s too high. The isotherm i t s e l f i s empirical. Patel and Foss (1965) described the binding of benzoic acids by polysorbate 80 and cetomacrogol 1000 in terms of a Freundlich-type adsorption relationship. Many binding systems cannot be described mathematically by using the simple mass action equation based on the assumption that there i s but one intrinsic association constant. Attempts have been made to correct for electrostatic interactions between the binding sites on M. If charged ions are bound to M, the f i r s t ion tends to reduce the af f i n i t y of M for the second oncoming ion because of electrostatic repulsion between species of like charge. Eq. 17 i s , therefore, no longer valid even i f the intrinsic a f f i n i t y of each site on M i s the same for the small ion. - 11 -If electrostatic forces are significant, there i s a relationship between two successive binding constants and . The correction procedure described by Klotz, Walker, and Pivan (1946b) i s similar to that used by Kirkwood and West-heimer (1938) in their study of the f i r s t and second ionization constants of a dibasic acid. The equation for the free energy changes for the reaction MDi_2 + 2 MD. = 2 M D ^ _ ( E q . 22)* consists of two terms. It takes into consideration the free energy change of the interaction in the absence of electrostatic effect and the electrostatic free energy change ( AGe^) which can be estimated from the Born and Debye-Hiickel Theory. K i - 1 LG = RT In = RT In k i n-(i-2)i N n- ( i - l ) i - l - &G ei (Eq. 23) In order to calculate any constant k^, k-^  must f i r s t be obtained from a suitable extrapolation of experimental data. The kg value may be calculated from Eq. 23. By using a similar procedure, k o may be calculated from the k g value. Other constants are obtained in a similar manner. If successive binding constants are known, r values can be estimated by using Eq. 16. * Eq. 22 i s the summation of two successive reactions to produce the complexes MD^_j and MD^ . - 12 -Scatchard (1949) corrected for the electrostatic effect by using the following equation. e 2 w r = Kn - Kr (Eq. 24) The w term may be calculated from theory or an approximate value may be determined empirically. The Debye-Huckel equation for a charge spread uniformly over the surface of a sphere of radius b which excludes small ions to a radius a i s given below. w = 2DkBT Ik 1/b (Eq. 25) 1 + Ika D i s the dielectric constant of the medium, kg i s the Boltzmann constant, T i s the absolute temperature, £ i s the electronic charge, z i s the valence of the small molecule, and Ik i s defined by the Debye-Huckel Theory. Tanford, Swanson, and Shore (1955a) reported that, in the hydrogen ion t i t r a t i o n of bovine serum albumin, empirical values of w are independent of pH between pH values of 4.3 and 10.5 but change drastically when pH values are outside the latter limits. Karush and Sonenberg (1949) found that the binding of bovine serum albumin with three alkyl sulfates could not be described mathematically by using the mass action equation even a correction i s made for electrostatic interaction. They assumed that the free energies of binding at the various sites obeyed a Gaussian distribution and from this deduced a theoretical expre-ssion which adequately described their data. - 13 -In a second study on the interaction between bovine serum albumin and an anionic azo dye, Karush (1950) found that the data failed to f i t the Gaussian distribution hypothesis. Experi-mental results could, on the other hand, be explained by assuming the existence of two different groups of binding sites. Inter-actions between macro and simple molecules are probably more com-plex than that indicated in Eq. 17. Most macromolecules probably contain several sets or groups of sites with different a f f i n i t i e s for the simple molecule. If the macromolecule contains m different sets of sites, the f i r s t set with n^ equivalent and independent binding sites, each with intrinsic association constant K^ ,. the second set with n^ such sites, each with an intrinsic association constant Kg, and so forth, then the mean number of sites occupied by D i s ™ n ^ D f ) r = > , (Eq. 26) i . 1 1 + K ±(D f) The KJL in this equation i s an intrinsic association constant and is different from the step equilibrium constant (designated as k^) in Eq. 8. The K values have the following order; K^^ Kg> •••^ K m' The total number of binding sites are defined by Eq. 27. m n = > \ n ± (Eq. 27) i = 1 In order to further i l l u s t r a t e the effect of more than one set of binding sites, a schematic diagram of a macromolecule with two sets of sites i s shown in Figure 2. - 14 -Figure 2. Schematic diagram of a macromolecule with two sets of binding sites. The molecule contains four sites with an association constant equal to and eight sites with an association constant equal to Kg. Eq. 26 may now be re-written on the basis of two sets of binding sites illustrated in Figure 2. 4^ (Df) 1 + K 1 (Df) 8K2 (Df) 1 + K 0 (D.) (Eq. 28) The m term, for the example cited, is equal to two. There are twelve sites on the macromolecule. - 15 -r Figure 3. Hypothetical binding curve for a macromolecule with two groups of binding sites. n 1=4,.K 1s 4000; n 2=8, K 2 = 1000. Sandberg, et a l . (1966) and Rosenthal (1967) showed how an experimental curve obtained from a Scatchard equation can be resolved into two or more straight lines, each of which represents a different set of binding sites. This graphical approach to the treatment of binding data i s illustrated in Figure 3. The K-^  and K 2 values for this hypothetical system are 4000 and 1000 respectively. If line 1 represents the f i r s t binding system and line 2 the second system, then curve 1 illustrates experimental data. Any point P on curve 1 i s the sum of the binding coordinates of system 1 at point Pj and of system 2 at point P 2. Points Pj, P2, and P are so chosen - 16 -that they l i e on a straight line which passes through the origin. Consequently, the geometric relationship OP = 0P1 + 0P 2 (Eq. 29) i s obtained. Experimental data i s resolved by drawing straight lines under the curve so as to satisfy the relationship shown in Eq. 29. For systems with more than two sets of binding sites, the mathematical procedures for calculating K have been worked out by Hart (1965). Scatchard et a l . (1950), in their study on the interaction between the thiocyanate ion and human serum albumin (HSA), obtained a binding curve which when resolved indicated the presence of two sets of binding sites with n values of 10 and 30 and K values of 1000 and 250. Karush (1950), in his study on the interaction between bovine serum albumin (BSA) and an anionic azo dye, used the mathematical approach described by Scatchard et a l . (1950) but did not correct for electrostatic effects between binding sites. Binding studies may also be carried out in the presence of two or more substances, both of which can attach themselves to the same site on M. If the two reacting species C and D have corresponding association constants KQ and KD, then the binding of D in the presence of C i s explained mathematically by the following equation. n K D (Df) (Eq. 30) r ° = 1 + K D(D f) + K^Cj) If the n sites are equivalent and independent, then n KD' (D„) r D = . i (Eq. 3 1 ) 1 + Kp' (Df) K D ' i s defined by Eq. 3 2 . K ' = (Eq. 3 2 ) 1 + K (C ) The above equations imply that, in the presence of a constant concentration of C, the binding of D to M follows the same pattern as that indicated in Eq. 17 , except that the K ^ ' value w i l l be lower than that observed for and i s a function of (C). If KJJ, or K i n Eq. 17, i s known, and K D ' i s determined for a known value of (C), then K^. can be calculated from an equation which i s derived from Eq. 3 2 . 1 / K D Kp = - 1 (Eq. 3 3 ) (C f) \ V * Klotz et a l . ( 1 9 4 8 ) studied the effects of salicylate, dodecylsulfate, and other anions on the binding of methyl orange by serum albumin and found that their results could be explained by using Eq. 3 3 . Cogin and Davis ( 1 9 5 1 ) studied, by use of Eq. 3 3 , the competition in the binding of long chain fatty acids and methyl orange to BSA. - 18 -It has also been observed that, in many instances, the binding of anions by albumin does not decrease over the pH range of 6 to 9 to the extent that would be expected from the increased negative charge on the protein. Karush (1951) observed an increase in binding a b i l i t y of albumin for methyl orange when the pH was increased from 6.4 to 7.6. The net charge changes, under these conditions, from -8 to -16. These discrepancies have been a t t r i -buted to a failure of the Debye-Huckel Theory when applied to complex protein molecules or to the possible configurational changes which may occur in the albumin molecule over the 6 to 9 pH range. Such configurational rearrangements could change n and K values in a direction which could compensate for the repulsive electrostatic effects of an increasing pH. Binding studies at more than one temperature have resulted in a thermodynamic evaluation of complexes. Enthalpy of binding, AH°, can be computed from the temperature depencence of associ-ation constant. The standard free energy of binding, AG° , at equilibrium can be estimated from a knowledge of binding constants at various temperatures. (Eq. 34) &G° = - RT In K (Eq. 35) For isothermal changes in a system, the variation of free energy with temperature i s expressed by the Gibbs-Helmholtz equation. - 19 -AG°- AH 0 T (Eq. 36) Since association constants are dependent on the composition of the buffer, the standard state includes the buffer employed in the experiment. Thermodynamic parameters are, therefore, sub-ject to possible error which would arise i f the buffer ion binds significantly to M and varies considerably with temperature. Thermodynamic data helps to explain the nature of the intermolecular forces responsible for binding (Karush, 1950; Klotz and others, 1949a; 1949b; 1953b). Temperature changes do not appear to affect greatly the extent of binding of ions with serum albumin. However, Klotz and Ayers (1952) have shown that there i s a marked temperature-dependent binding between p-aminoazobenzene and bovine serum albumin. For any equilibrium reaction which is not affected significantly by temperature, the heat of reaction i s small. It follows from Eq. 36 that, i f AH°is small, the magnitude of AG0 at any fixed temperature i s determined primarily by the value of AS° the entropy change in the reaction. The favorable free energies of binding (i.e., negative AG°value) which have been observed for many ion-albumin complexes seem, therefore, to be a result of a favorable entropy change (i.e., positive AS°value) during binding rather than to be any favorable heat effect (i.e., negative AH°value). - 20 -The positive and relatively high values of AS°are in themselves unique because the reactions as written in Eq. 8 and 9 are association reactions for which one would expect unfavorable entropy changes. One explanation for this pheno-menon i s given below. Although an anion i s usually written as D~, i t has been claimed that this ion has several polarized water molecules 'frozen' to i t in aqueous solution. The subject has been extensively discussed by various investigators: Frank and Evans (1945), Claussen and Polglase (1952), Master-ton (1954), Buswell and Rhodebush (1956), Feates and Ives (1956), Frank and Wen (1957), Klotz (1958), Nemethy and Scheraga (1962a; 1962b), Nemethy, Steinberg, and Scheraga (1963), Mohammad (1965), and Bernal (1965). Similarly, the protein molecule i s highly hydrated.* This probably occurs around the charged l o c i of the cationic nitrogen atoms which seem to be directly involved in the binding process. Consequently, the formation of a bond between these two oppositely charged species would release some of the 'frozen' water molecules. The system, therefore, becomes more randomized and i t becomes reasonable to expect an increase in the entropy of the system. This implies that, at the molecular level, there would be an increase in the number of molecule species upon formation of the anion-protein complex rather than a decrease as indicated in the M + D » MD equation. A schematic diagram of the changes in water structure around M and D i n the M + D = MD reaction i s shown in Figure 4. * It i s well known that, in aqueous solution, macro and small molecules are hydrated. However, Frank and Evans (1945) were probably the f i r s t researchers to emphasize the importance of 'iceberg' around solute molecules in water. - 21 -ice-like' water melted' water Figure 4. Schematic diagram of changes in water structure accompanied by an interaction between M and D. Karush (1950), in his study on the interaction between an anionic azo dye and BSA, reported AS° values of 8.7 e.u. and 3.3 e.u. for the f i r s t and second groups of binding sites, respectively. He attributed the differences in AS* values to the structural differences between the two binding groups. It was suggested that the cationic group 1 sites are not bonded intramolecularly. Group 2 sites, on the other hand, are linked to nearby anionic carboxyl groups. Therefore, the binding of the anionic dye by group 2 sites would require the breaking of these bonds and would be accompanied by the release of an equal number of carboxyl groups. Binding on group 1 sites would involve a net neutralization of charge and this would result in a positive AS° value because water molecules are liberated from the ions. Such an entropy increase would not be observed at group 2 sites. I I I . METHODOLOGY Goldstein (1949), in his paper on the interaction between drugs and plasma proteins, has reviewed the methodology asso-ciated with binding studies. Similar papers have been published by Klotz (1953a). More recently, Meyer and Guttman (1968a) have reviewed those methods (e.g., kinetic, or dynamic, dialysis, partitioning, gel f i l t r a t i o n , u t i l i z a t i o n of isotopes, nuclear magnetic resonance, and fluorescence quenching techniques) which have been developed during the past several years. These methods f a l l into one of two categories. The f i r s t group depends upon the properties of the interacting molecule; the second, on the behavior of the macromolecule. Quantitative investigations must be based, therefore, on a method which w i l l yield numerical values for two of the three unknowns, (D^), (D b), and (Dt) and for (Mt). These symbols are an inherent part of Eq. 17. Of the many methods described in the literature, only those based on spectrophotometry, solubility analysis, equilibrium and dynamic dialysis methods, and viscometry w i l l be discussed here. Except viscometry, these methods measure changes in the properties of D, the interacting molecule. 1. Spectrophotometry The spectrum of D i s frequently changed by the macro-molecule, M. These spectral changes have been used by many investigators to determine the extent of binding of a wide variety of substances with macromolecules (Job, 1926; Robinson and Hogden, 1941; Klotz, 1946c; 1947; Benesi and Hilderbrand, 1949; Oster and Immergut, 1954; Worley and Klotz, 1966; Connors and Mollica, 1966). If the concentration of M i s low, the total absorbance at a specified wavelength of free and bound D i s defined by Eq. 37. A i s the absorbance; b i s the c e l l length; and £ i s the molar absorptivity of the specified forms of D. The term oL i s defined by Eq. 38. A - £ fb(D f) + £ bb(D b) (Eq. 37) (Eq. 38) The fraction of D^ , F f, i s expressed by the following equations. F f * £ f(D t) - A \ € F ( D T ) - * € F ( D T ) > (Eq. 39) or app - 24 -The apparent molar absorptivity in Eq. 39 i s defined by Eq. 40. A = Gapp ( D t > ( E < 1 - 4 0 > Molar absorptivity values for the bound drug may be deter-mined by extrapolating absorbance values for D in the presence of increasing quantities of M. At high M concentrations, i t i s assumed that D i s completely bound to M. The hypothetical curves in Figure 5 ill u s t r a t e absorbance changes as a function of M concentration. 0 m b CONCENTRATION OF MACROMOLECULE Figure 5. Hypothetical curves for changes in absorbance as a function of (M). £ b values can be estimated from asymptotic values. At (M) = 0, m, b; F f = 1, jt, 0, respectively. - 25 -The precision of this method depends on the magnitude of the difference in absorption produced by the presence of M. Binding data obtained in this way must be complimented by data obtained in other ways because D concentrations are restricted by Beer's Law (i.e., they are too low and too narrow). Further-more, M should not absorb energy at the wavelength at which the absorbance change for D due to the presence of M i s maximum. In spite of these disadvantages, this method is important because small quantities of D can be determined with accuracy. Moreover, i t i s not necessary to separate a r t i f i c i a l l y and as in the equilibrium dialysis technique. Klotz (1946c), in his paper on the interaction between an azo dye and BSA, reported good agreement between the spectro-photometric method and the equilibrium dialysis technique in the region in which the two methods overlap. Oster and Immergut (1954) found that the absorbance of iodine at 290 nyu changed drastically in the presence of polyvinylpyrrolidone (PVP). This increase in absorbance in the presence of increasing PVP concentrations resulted in a sigmoidal curve similar to that in the upper part of Figure 5. However, at lower PVP concentrations, the curves changed slowly. This appears to indicate that the f i r s t few molecules of iodine are bound to PVP with d i f f i c u l t y but that further molecules are more easily taken up by the polymer. 2. Phase Solubility This technique has been discussed in detail by Higuchi and Connors (1965). It involves the addition of an equal quantity (in excess of i t s normal solubility) of D into each of several solutions containing successively increasing amount of Jfl. The solutions are brought to equilibrium at a constant temperature and then analyzed for D^ .. A phase diagram i s con-structed by plotting the amount of D in solution versus (Hj.) . If there i s no interaction between D and M, there w i l l be no changes in (D) i n the presence of M. If a soluble complex i s formed, (Dj.) w i l l increase as (M^ .) increases within a range of concentrations which i s a characteristic of both the small and macro molecules. Increased quantities of D in the presence of M represent Dfe since (Df) i s a fixed constant under specified conditions and i s in equilibrium with (Db) throughout the (M) range. When the theory of multiple equilibria i s applied to the data, the method becomes a 'spot' analysis because only one value for (D f), or the solubility of D in the absence of M, i s used throughout the experiment. Furthermore, this method i s suitable only for substances of relatively low solubility. Certain aspects of the binding process can, however, be easily studied by u t i l i z i n g phase solubility analysis. For example, the method has been used to investigate the effects of various solvents, pH, ionic strength, and temperature on the extent of binding. The value of r (see Eq. 6) i s a constant under controlled - 27 -conditions and therefore a comparison of r values, under different conditions, gives information about the binding mechanism. The thermodynamic parameters obtained from solubility analysis need not be corrected for disorientation entropy, because the interacting molecules possess no rotational freedom in the crystalline or bound state (Sahyun, 1964). In some methods (e.g., dialysis method), however, binding occurs in an unsaturated system, which implies that the bound molecules possess fewer degrees of freedom (Tanford, 1950; McMenamy and Seder, 1963). Therefore comparison of thermodynamic data from different methods should be carried out after corrections have been made for differences in the standard state. Many investigators and in particular Higuchi and his co-workers have used this technique to study a wide variety of intermolecular reactions. The papers covering these interactions are not specifically referenced here but are liste d in detail in the 'REFERENCES' section of this thesis (Higuchi and others, 1953a; 1953b; 1954a; 1954d; 1954e; 1954f; 1959; 1961; 1964;1965; Mader, 1954; Kostenbauder and Higuchi, 1956; Poole and Higuchi, 1959; Dittert and others, 1961; Breuninger and Goettsch, 1965; Wadke and Guttman, 1965; Wolfson and Banker, 1965; Singh and others, 1967). Most of these papers have no direct bearing on this study. However, several w i l l be briefly reviewed in order to i l l u s t r a t e the applicability of the method. Higuchi and Lach (1954d) reported that an insoluble complex was formed between phenobarbital and polyethylene glycol. Their results indicated that a 2:1 complex was formed (i.e., two - 28 -ethylene oxide units reacted with one phenobarbital molecule). Mansour and Guth (1968) studied the complexing behaviour of starch and starch fractions with benzoic acid, some of i t s derivatives, sorbic acid, and other selected molecules. Breu-ning and Goettsch (1965) studied the interactions between p-chlorometaxylenol and various synthetic polymers. The method has not been used extensively to study the interaction between macromolecules. Laurent (1963) reported a relative decrease in the solubility of human serum albumin, y-globulin, and fibrinogen in the presence of various types of dextran. He studied the effect of ionic strength and pH and showed that the solubility of proteins in the presence of dextran increased with an increase i n the size of the protein. 3. Equilibrium Dialysis Interactions between small and macro molecules may be studied quantitatively by u t i l i z i n g the equilibrium dialysis technique.* A container i s divided into two compartments by a semi-permeable membrane. A macromolecule solution i s placed in one compartment; a solution containing the small molecule i s placed in the second compartment. The small molecule passes through the membrane but the macromolecule is retained in i t s own compartment. At equilibrium, the total number of small * The kinetic or dynamic dialysis technique (Andreoli and others, 1965, Stein, 1965; Agran and Elofsson, 1967; Reuning and Levy, 1968; Meyer and Guttman, 1968b; 1970a; 1970b) w i l l be briefly discussed in the 'RESULTS AND DISCUSSION' section of this thesis. - 29 -molecules in the M compartment w i l l exceed that in the M-free compartment. The difference between these two concentrations i s a measure of (D^). Two possible sources of error, the Donnan effect, and membrane binding of small molecules must, however, be taken into consideration before applying this technique. When a charged macromolecule i s retained in one of the two compartments, at equilibrium, the concentration of diffusible ions i s no longer identical across the membrane. This phenomenon has been described as the Donnan equilibrium (Gverbeek, 1956). The ion ratio characterizing the distribution of diffusible ions across the membrane (R) i s expressed by Eq. 41 when both anion and cation are univalent. The subscripts, F and M, represent the M-free and M compartments, and the parentheses represent the concentrations of the specified ion species. Values of R may be expressed as a function of the concentra-tion of the neutral salt in the M-free compartment, ( C + ) F , the valence on the macromolecule, ZM, and (M) in molality (Bull, 1964a). R . ( C + ) F (Eq. 41) (Eq. 42) Figure 6 illustrates the relationship between R and ( C 4 ) F when the M-compartment contains 10 grams of the macromolecule per 1000 grams of solvent. The molecular weight of M i s 40,000; the valence, - 30 -2.5 2.0 R 1.5 1.0 0 0.2 0.4 0.6 ( c + ) F Figure 6. Calculated values of R as a function of salt concentration in the M-free compartment. See Bull (1964a) in one series of experiments, i s -10 and in the other i s -40. In a dilute solution of M, the Donnan effect can be neglected only i f the concentration of the diffusible ion i s reasonably high and the valence of M i s f a i r l y low. In a solvent system of high ionic strength and pH at which the macromolecule has a small valence charge, the abnormal distribution of small molecules across the membrane due to the Donnan equilibrium can be neglected. The dialysis membrane may act as a binding site for the small molecule and a correction must be made for this interaction. Most corrections are made by using a control in which no macro-molecule i s present in the apparatus. It i s then possible to - 31 -measure the 'loss' of small molecule from the solution. It has been either observed or assumed that the extent of membrane binding i s proportional to the amount of small molecule added to the system. Osborne (1906), at the turn of the century, studied the interaction between salt and proteins by u t i l i z i n g the dialysis method. The procedure was refined by Klotz, Walker, and Pivan (1946b) and, of approximately 400 papers on protein binding reviewed by Meyer and Guttman (1968a), more than 130 papers reported the use of dialysis thechnique. Its main advantage i s that an interaction can be studied through a range of small molecule concentrations. Nearly complete saturation of the macromolecule with a given D can often be achieved. It i s one of the few methods which are conducive to quantitative work and i s thermodynamically sound. By using this method, i t i s possible to cover a wider range of r value (see Eq. 6) and thus obtain more information about the interaction. Karush and Sonenberg (1949) covered an r range from 0 to 10 in a study of the interaction between alkyl sulfates and bovine serum albumin. In a similar study, Pollansch and Briggs (1954) studied r values up to 40. They used volume ratios of protein compartment to protein-free compartment of 1 to 79 and 1 to 9. By using the former ratio, they were able to u t i l i z e a large quantity of detergent in their study. The maximum amount of detergent which could be used was limited only by the solubility of the detergent in the protein-free compartment. - 32 -Equilibrium dialysis would be carried out by equilibrating the macromolecule solution in a cellophane bag with an external solution containing the small molecule. However, the concentra-tion of the small molecule i s frequently limited by i t s solubi-l i t y . Consequently, a large volume of solution containing a small quantity of the small molecule i s required to cover the whole range of interaction. Under these conditions, a long period of time i s required to equilibrate the system. Yang and Foster (1953) used a 1 to 100 volume ratio of protein compartment to protein-free compartment in their study on the interaction between dodecylbenzenesulfonate (SDBG) and bovine plasma albumin. However, even after a one-month time interval, dialysis equilibrium was not attained. They, therefore, modified their procedure by storing the mixed solutions for at least two days at 1 to 3° C and then dialyzing against an equal volume of the buffer used for an additional two days. The amount of free SDBG was then determined in the dialyzate. Patel and Foss (1964) used a dialysis c e l l consisting of two plexiglas blocks separated by a semi-permeable membrane. Eide and Speiser (1967a) used a similar apparatus but stirred the solutions in the chambers with a magnetic s t i r r e r . By using these approaches, a better control of membrane binding was attained because the surface area of the membrane i s more or less constant throughout the study.* * Goldstein (1949) reported that loss of small molecules due to membrane binding i s not only large (for example, to 20 per cent of total methylene blue in his study) but also variable from bag to bag. - 33 -A dialysis membrane is a very thin layer of a specified substance or mixture of substances. Various types of membranes are described by Craig (1965). Kostenbauder et a l . (1969) dis-cussed the use of nylon membranes. Nylon reacts with phenolic compounds, however, and Mitchell and Brown (1966) used rubber latex membranes in a study of the interaction between p-chloro-metaxylenol and a non-ionic surfactant. Most investigators, however, use cellophane membranes. These membranes are usually marketed in r o l l s and are stored in plastic bags to prevent drying. They contain glycerin and small amounts of other solutes but these can be easily removed by washing. When stored in a refrigerator, their porosity remains f a i r l y constant over long periods of time. The main advantage of this type of membrane i s that i t i s relatively free of fixed charges which would be ion selective (Craig, 1965). 4. Viscometry A dilute solution of concentration C w i l l have a slightly higher viscosity (^) than the solvent i t s e l f C7 0) . The relative viscosity i s defined by Eq. 43. °?rel - °7 / (Eq- « ) The relative viscosity i s , therefore, slightly more than one and includes the effect of solvent (unity) and solute. Specific viscosity, which isolates the solute effect, i s defined by Eq. 44. - 34 -^ s p = ^ r e l " 1 <E(1- 4 4> Specific viscosity depends on concentration, i s small number, and i s related the reduced viscosity. Vred = ^sp / c (Bq. 4 5> The reduced viscosity i s a large number, does not change much with concentration in dilute solutions, and measures the increase in viscosity per unit concentration in a slotuion of concentration C. If the above value i s determined at several low concen-trations, an extrapolation to zero concentration w i l l yield a value which i s due to the solute at i n f i n i t e dilution per unit concentration. This value i s called the intrinsic viscosity and i s the value which i s quantitatively important in solute-solvent interactions. C°?3= c ^ O Isp / C (Eq. 46) Huggins (1942) related concentration to reduced viscosity by using Eq. 47. ^ s P / c = (*}]•• V T O 2 C (EQ- 4 7 ) - 35 -K J J i s a constant, i s known as Huggins parameter, and i s determined experimentally.* Intrinsic viscosity depends on hydration and molecular shape. The relationship between particle assymetry and viscosity are complex but Mysels (1959), Yang (1961), and Flory (1953) have discussed the changes in intrinsic viscosity due to structural changes in macromolecules. Miller and Hamm (1953) studied the properties of polyvinyl-pyrrolidone (PVP) by measuring viscosity, sedimentation velocity, and diffusion. Configurational changes in bovine serum albumin have been investigated by Yang and Foster (1954) by measuring intrinsic viscosity and specific rotation over a 1.3 to 7.0 pH range. They concluded that viscosity changes are due to swelling rather than coulombic repulsion and suggested that the expansion reaction i s an all-or-none rather than a stepwise phenomenon which i s fast and completely reversible. A similar study was carried out by Tanford and Buzzell (1956). They concluded that the expansion process was much more complicated than that suggested by Yang and Foster (1954). Doty et a l . (1957) measured the intrinsic viscosity of poly-L-glutamic acid as a function of pH i n 0.2 M sodium chloride-dioxane (2:1). They concluded that the polypeptide exists in an -helix below a pH of 5.5 and as a random c o i l at pH values in excess of 6.5. * Kraemer (1938) proposed a similar equation; ln°? r el/C • £ . " 1 ) - K ' C H 2 C (Eq. 48). K H and K' are related by each other in the following way; K H + K' = 0.5 (Eq. 49). Both Eq. 47 and 48 indicate that a plot of ^ gp/C and ln°?rel/C versus C should yield the same intercept, C1? 3 ,and the limiting slopes at C = 0 should satisfy the Eq. 49 relationship. By using both equations, intrinsic viscosity can be determined with some confidence. - 36 -Changes in viscosity have been used to detect interactions between small and macro molecules. Frank et a l . (1957) measured the reduced viscosity of PVP in the presence of dye. In the absence of salt, the reduced viscosity was increased by the dyes and a sharp viscosity maximum was observed. The reduced viscosity increased with a decrease in PVP concentration. This appears to be typical polyelectrolytes because electrostatic repulsion of identical charges w i l l lead to an unfolding of the polymer mole-cule. As the PVP concentration was decreased in the presence of a constant quantity of dye, the concentration of unbound 'gegen-ions' (counterions) increased. This increase w i l l tend to suppress the eleetroviscous effect. A viscosity increase in the presence of salt was explained by assuming a cross-linking effect due to aggregation of dye ions. A similar study was carried out by Molyneux et a l . (1961b). Their results indicated that, in general, the polymer expands in the presence of anionic cosolutes. With non-ionic cosolutes, the polymer contracts and, in the presence of cationic cosolutes, no appreciable viscosity effects were observed. The influence of buffers and complexing substances on the rheological properties of PVP has been studied by Eide and Speiser (1967b). The properties of PVP, in water and in salt solution, were determined by Goldfarb and Rodriguez (1968) by measuring heat capacities, specific volumes, and reduced viscosities. They concluded that the decrease in intrinsic viscosity of aqueous PVP with increased temperature was due to the progressive c o i l -ing of the molecule. Interactions between dodecyl sulfate - 37 -anions and BSA at high pH have been studied by Lovrien (1963). He maintained pH at a value at which the protein has a large negative charge. Under such conditions, an increase in hydrody-namic volume would be expected. However his viscometric data indicated that the detergent reduces expansion. The hydrocarbon portion of the molecule appears to induce conformational changes which counter unfavorable electrostatic energy changes. Complexation has been studied by using capillary viscometers. The operating characteristics of these viscometers have been described by Van Wazer et a l . (1963). Specifications may be found in documents issued by the American Society for Testing and Mat-erials (A.S.T.M., 1966a; 1966b). The viscosity equation applicable to capillary viscometers i s based on Poiseuille's Law. ^ / f = Ct - B/t (Eq. 50) f> i s the density of the liquid; t i s the flow time in seconds; the constant C and B have been characterized by Cannon et a l . (1960); the quantity B/t i s called the kinetic energy correction factor. In a well designed viscometer, B/t i s usually a small per cent of the Ct term. When the correction factor can be neglected, the calibration constant C i s determined by measuring the flow time of a standard liquid of known kinematic viscosity. It may also be determined by comparing the flow time of a liquid in an uncalibrated viscometer with that observed in a master viscometer with a known C value. IV. THE CHEMICAL AND BIOLOGICAL CHARACTERISTICS OF THE SUBSTANCES USED IN THIS INVESTIGATION 1. Bishydroxycouraarin Bishydroxycoumarin (BHC), was f i r s t synthesized by Link (1943-1944), and i s o f f i c i a l in the U.S.P. It i s also described as dicoumarin or dicumarol. Its chemical name i s 3,3'-methylene-bis-(4-hydroxycoumarin) or 3,3'-methylene-bis-(4-hydroxy-l,2-benzopyrone). BHC i s a white crystalline or amorphous powder practically insoluble in water. It i s a weak dibasic acid and soluble in alkaline solutions. Burns, Wexler, and Brodie (1953) reported a pKa value of 5.7. This value was obtained by titrating 10 ml. of a 90$ ethanolic solution (containing 20 mg. of BHC) with 0.025N sodium hydroxide solution. Nagashima, Levy and Nelson (1968a) obtained a value of 6.5 by using a partitioning technique. In alkaline solution, BHC absorbs a maximum of radiant energy at 314 mu.. The pH of the solution affects the spectrum and isosbestic points are observed at 254 and 286 mu (Findlay OH OH Figure 7. Chemical structure of BHC. - 39 -and others, 1965). The molecular weight of BHC i s 336.29. Melting points of 287-293°C (Merck Index, 1968) and 288-290°C (Nagashima, Levy, and Nelson, 1968a) have been reported. French and Wehrli (1965) published the infrared spectra of some of the coumarin anticoagulants, including BHC. The f i r s t c l i n i c a l t r i a l s u t i l i z i n g BHC were carried out in the early 1940•s. Ingram (1961) and Douglas (1962) reviewed the use of BHC in the treatment of myocardial infarction, angina pectoris, rheumatic heart disease, cerebrovascular disease, venous thrombosis, and pulmonary embolism. The pharmacological properties of coumarin anticoagulants have been reviewed by Levine (1967). Owren (1963a; 1963b) discussed the use of anti-coagulant medication. The importance of dissolution rate on c l i n i c a l effect was f i r s t reported by Lozinski (1960). Findlay et a l . (1965) reported that the particle size distribution i s a major factor governing dissolution rate. O'Reilly, Aggeler, and Leong (1964) observed that the absorption of BHC from solution (or when administered as a powder) was rapid but that absorption was slow when whole tablets were administered to the patient. Weiner et a l . (1950) studied the physiological disposition of BHC in man. They reported a strong interaction between the drug and plasma albumin. A similar study was initiated by Lee et a l . (1950) but the test animals in this instance were mice and rabbits. O'Reilly et a l . (1964) carried out a pharmacodynamic study of BHC and warfarin in man. Other investigations u t i l i z i n g different animal species were carried out by Jaques et a l . (1957), - 40 -Christensen (1964), Solomon et a l . (1967), and Nagashima et a l . (1968b; 1968c; 1968d). The metabolism of BHC was investi-gated by Christensen (1966). The in vitro binding of warfarin to albumin was exten-sively studied by O'Reilly et a l . (1966; 1967; 1968; 1969). In addition to equilibrium dialysis, they used a heat burst micro-calorimeter to measure the heat evolved in the inter-action (O'Reilly and others, 1968). The exothermic and non-ionic nature of the interaction was observed. The introduction of a polar hydroxy group on the coumarin ring during metabolism reduced i t s hydrophobic binding surface and thus decreases albumin binding (O'Reilly and others, 1969). During their investigation of the analysis of BHC in biological fluids, Nagashima et a l . (1968a) observed a decrease in plasma albumin binding at pH 4. It i s at this pH that the plasma albumin undergoes a largely reversible structural alteration from compact to expanded form. The configurational expansion results in a disruption of non-polar clusters located in the interior of the albumin molecule and thus causes a decrease in binding strength. 2. Human Serum Albumin Human serum albumin (HSA) i s characterized by i t s solubility in water or by i t s electrophoretic behaviour. Its physicochemical properties may be explained in terms of an elongated ellipsoid with a molecular weight of 69,000, a length of 150 A, and a diameter of 38 A. Certain investigators report a molecular weight of 65,000. The arguments for or against these values are given by Putnam (1965). Uti l i z i n g intrinsic viscosity measurements, Tanford and Buzzell (1956) obtained an axial ratio of about 3 to 1. HSA appears to be made up of amino acid residues but their primary sequence has not been established. The residues are joined together by a single long peptide chain which i s internally cross-linked by 17-18 disulfide bridges. These disulfide linkages contribute greatly to the st a b i l i t y of the configuration. The importance of such cross-links i n protein structures has been discussed by Edsall and Wyman (1958a). A fractionation procedure for the isolation of albumin has been worked out by Cohn et a l . (1950). This 'Conn Fraction V i s mainly albumin and i s prepared by precipitation at pH of 4.8 and an ethanol concentration of 40$. Spectrophotometric and turbidi-metric (Layne, 1956), Kjeldahl and isotopic techniques (Hauro-witz, 1963) have been used to analyze proteins. Although serum albumin i s available in crystalline form, the substance i t s e l f i s micro-heterogeneous. This heterogeneity may be established by examining the substance electrophoretically at low ionic strength, chromatographically, interferometrically, or serolo-gical l y . Foster (1968) has written a review on this subject. - 42 -Because of i t s availability, HSA i s one of the most widely investigated proteins. Its ion binding behaviour, i t s amphoteric heterogeneity at low pH, and i t s denaturation have been investi-gated. Foster (1960) reviewed these characteristics. Titration curves have been evaluated by Tanford et a l . (1950; 1955a; 1955b). They estimated the number of dissociable groups and calculated their intrinsic dissociation constants. A satisfactory agreement was obtained with regard to the amino acid contents. They and Foster et a l . (1956), Aoki et a l . (1957) and Clark et a l . (1962) observed that both HSA and bovine serum albumin exhibited an anomalous t i t r a t i o n behaviour below the isoelectric point, 4.7, and beginning at about a pH of 4. Yang and Foster (1954), on the basis of a study of the effect of pH on optical rotation and viscosity, concluded that an isotropic expansion of the albumin molecule ocurred in acid solution. They attributed the molecular expansion to a mutual repulsion of the positively charged ammonium groups. This phenomenon was confirmed by Tanford et a l . (1955b; 1956). They proposed that the expansion takes place through an intermediate expandable form - the so-called 'F form'. Foster and Clark (1962) presented evidence that the native form (the ' N form') has a large number of carboxylate groups that are masked and that isomerization to the F form leads to the normalization of a l l carboxylate sites. Because i t has a strong a f f i n i t y for ions and other substances, albumin has been used to elucidate protein-ion interactions. Klotz (1953a) was the f i r s t investigator to review this subject. Karush (1950) attributed the high reactivity of albumin with a - 43 -variety of anions tb the particular configurational adaptability of the molecule. Serum albumin interacts readily with detergents ions such as dodecyl sulfate. Interaction of this type have been investigated in various laboratories (Putnam, 1945; Karush, 1949; Pollansch and Briggs, 1954; Lovrien, 1963) and reviews on the subject have been published by Foster (1960) and Ray (1968). The clas s i c a l review on drug-albumin interactions was published by Goldstein (1949). More recently, Meyer and Guttman (1968a) have re-reviewed this particular aspect of serum albumin binding. The physilogical consequences of ion binding and the af f i n i t y of serum albumin for dyes, drugs, and similar molecules have been emphasized by Bennhold (1961). The effect of drug-albumin interactions on the absorption, distribution, and excretion of the drug has been discussed by Martin (1965). Wishnia and Pinder (1964) observed that the extent of binding of alkanes (Cg to Cg) to the F form of bovine serum albumin i s much lower than that obserbed for the N form. They concluded that the large hydrophobic clusters in the interior of the protein are responsible for the interaction. Nagashima et a l . (1968a) observed a similar decrease in binding capacity of BHC to HSA in the acid range. The role of hydrophobic bonding in relation to physicochemical behaviour of protein solutions, has been discussed by Kauzmann (1959), Klotz (1958; 1960), Scheraga (1961; 1963), Nemethy et a l . (1962c; 1963), and Cecil (1967). In this context, studies on water structure have been made by various investigators (see p. 20). Solvent effects on the binding or organic ions by proteins have been discussed by Klotz and Luborsky (1959). 3. Polyvinylpyrrolidone Polyvinylpyrrolidone (PVP) i s a water soluble, high molecular weight polymer. It may be represented structurally in the following way. N H2C H2C 0 I CH CHg-Figure 8. Chemical structure of monomer of PVP, N-vinylpyrrolidone (C6H9ON - 111.14). Because of i t s chemical and physical properties, the polymer has been used as a plasma extender. The molecular weight of PVP i s defined in terms of the viscosity of a dilute solution. For this purpose, the Fikentscher K F value i s commonly used (G.A.F., 1957). The average molecular weight of the PVP which i s used as a plasma extender i s approximately 40,000 (K F = 30). This value i s derived from ultracentrifugation and osmosis measurements. Its physicochemical properties were investigated by May et a l . (1954). An aqueous solution of PVP i s slightly acidic (pH of 4) but has no buffering action. Using light scattering measurements and assuming that the PVP molecule i s a random c o i l , Hengstenberg et a l . (1952) reported a mean square molecular diameter of 360 A corresponding - 45 -to a molecular weight of 249,000. A similar study was carried out by Miller and Hamm (1953). Assuming an elongated ellipsoid shaped model, they obtained an axial ratio of 22 to 1 and a root mean square distance of 169 A for PVP of molecular weight of 41,500. At a lower temperature, PVP was believed to be more tightly coiled.* Drugs, dyes, and toxins bind with PVP. References on this particular subject and to i t s physicochemical and physiological properties are available from the manufacturer of the polymer (G.A.F., 1967). Oster and Immergut (1954) studied the iodine-PVP complex and this complexation process has been used quantitatively to determine PVP (Campbell, 1953). Scholtan (1953) expressed the binding process of PVP with dyes by use of Langmuir adsorption isotherm. His thermodynamic data indicated that in one case the a f f i n i t y of the binding process was determined preferably by the entropy, in the other (meta-benzopurpurin 4B) preferably by the heat of reaction. In solutions containing PVP, albumin and dyes simultaneously, a complexation balance was formed. Theoretical relations were given between these three components. The calculated and experimental values showed a close agreement. Spitzer and McDonald (1956) studied the interactions between bovine serum albumin and PVP with bromophenol blue (BPB). There was no evidence of an electrostatic factor with respect to the exothermic PVP-BPB binding. Frank et a l . (1957) studied the interaction between PVP and azo dyes. Orange II and benzo-purpurin 4B appear to be bound to the chain segment of seven * This statement i s in contradiction to that appeared on p. 36 (Goldfarb and Rodriguez, 1968). See 'RESULTS AND DISCUSSION' section of this thesis for more detail. - 46 -or ten monomer units. Molyneux and Frank (1961a; 1961b) studied the interaction of PVP with a large number of aromatic compounds. They observed entropy gains in almost a l l systems and concluded that hydrophobic bonding ocurred. Infrared spectra of dry PVP films containing varying concentrations of cosolutes indicated the presence of polymer-cosolute hydrogen bonds (1961a). Using light scattering and viscometric methods, they concluded that anionic cosolutes expand the polymer, nonionic cosolutes contract the molecule, and cationic cosolutes had no effect on molecular size (1961b). Worley and Klotz (1966) studied the effect of PVP on the near infrared spectra of H20 - DgO solutions. They suggested that PVP exhibits a structure making character. Goldfarb and Rodriguez (1968), however, found no evidence for the existence of more 'structural water' in the v i c i n i t y of the PVP molecule. PVP has several properties which makes i t of particular interest to the pharmaceutical scientist. PVP forms water soluble or water dispersible complexes with a wide variety of water insoluble drugs (G.A.F., 1967). References covering these com-plexation studies are given in Table 1. Binding depends not only on the nature of the simple molecule but also on the concen-tration of the macromolecule (Edsall and Wyman, 1958c). In most of the investigations cited in Table 1, at a fixed total drug concentration, concentration ratio of total to free (or vice  versa) i s a linear function of macromolecule concentration. The ratio can, therefore, be an approximation of the extent of binding. Ratios at 1$ PVP concentration are shown in Table 1. - 47 -Table 1. The Complexing Behaviour of PVP with Various Types of Drugs. Drug oc Solvent (Dt)xlO 3 System mole/L. $PVP (Dt) (Df) Methodology and Reference Sulfathiazole 0 Water .393 1.0 1.42 Equilibrium Dialysis, Higuchi and Kuramoto (1954b). Sodium Salicylate 0 Water 12.49 1.0 1.1 Equilibrium Dialysis, Higuchi and Kuramoto (1954b). Procaine HC1 0 Water 5.56 1.0 1.00 Equilibrium Dialysis, Higuchi and Kuramoto (1954b). Chloram-phenicol 0 Water 1.547 30 Water 1.547 30 Water 3.095 1.0 1.0 1.0 1.05 1.05 1.05 Equilibrium Dialysis, Higuchi and Kuramoto (1954b). Benzyl Penicilin 0 Water 2.68 1.0 1.00 Equilibrium Dialysis, Higuchi and Kuramoto (1954b). Mandelic acid 0 Water 6.619 1.0 1.08 Equilibrium Dialysis, Higuchi and Kuramoto (1954b). Caffeine Theophylline Cortisone No Evidence of Complex Formation Equilibrium Dialysis, Higuchi and Kuramoto (1954b). Benzoic Acid 0 Water 5.74 1.0 1.13 Equilibrium Dialysis and Solubility, Higuchi and Kuramoto (1954c), Guttman and Higuchi (1956). S a l i cylic Acid 0 Water 3.62 1.0 1.22 Equilibrium Dialysis and Solubility, Higuchi and Kuramoto (1954c), Guttman and Higuchi (1956). m-Hydroxy Benzoic Acid 0 Water 1.81 0 Water 7.25 1.0 1.0 1.43 1.47 Equilibrium Dialysis and Solubility, Higuchi and Kuramoto (1954c), Guttman and Higuchi (1956). p-Hydroxy Benzoic Acid 0 Water 1.82 0 Water 7.25 1.0 1.0 1.40 1.40 Equilibrium Dialysis and Solubility, Higuchi and Kuramoto (1954c), Guttman and Higuchi (1956). p- Ami no Benzoic Acid 0 Water ? 1.0 1.23 Equilibrium Dialysis and Solubility, Higuchi and Kuramoto (1954c), Guttman and Higuchi (1956). Phenobarbital 30 Water 2.58 30 Water 4.31 1.0 1.0 1.19 1.19 Equilibrium Dialysis and Solubility, Higuchi and Kuramoto (1954c), Guttman and Higuchi (1956). C i t r i c Acid Aminopyrine No Evidence of Complex Formation Equilibrium Dialysis and Solubility, Higuchi and Kuramoto (1954c), Guttman and Higuchi (1956). Phenol 0 Water 200.0 0 Water 160.0 .37 .12 1.19 1.23 Equilibrium Dialysis and Solubility, Higuchi and Kuramoto (1954c), Guttman and Higuchi (1956). Chlorobutanol 15 Water 28.5 30 Water 28.7 30 Water 57.7 45 Water 28.8 1.0 1.0 1.0 1.0 1.06 1.08 1.08 1.11 Equilibrium Dialysis, Bahal and Kos-tenbauder (1964). Benzyl Alcohol Phenylethyl Alcohol No Evidence of Complex Formation (Continued on next page.) - 48 -(Table 1. Continued) Drug °C Solvent (D t)xl0 5 $PVP (Dt) Methodology System mole/L. (Df) and Reference p-Chlorometa- 30 Water .113 2.0 1 .13 xylenol *a 30 Water .140 2.0 1 .17 Equilibrium 30 Water .197 2.0 1 .19 Dialysis and 30 Water .225 2.0 1 .18 Solubility, 30 Water .283 2.0 1 .18 Breuninger et 30 Water .401 2.0 1 .15 a l . (1965). Methylparaben 27 Water 6.12 1.0 1 .15 Eqm. Dialysis, Propylparaben 30 Water 1.23 1.0 1 .30 Miyawaki et a l . Hexylresor- (1959), P o l l i sinol 23 Water .858 .05 3 .00 et a l . (1969). Tannic Acid Kabadi et a l . *b Soluble Complex Formed (1966). Benzoic Acid 22 Ionized 33.0 1.0 1 .02 22 pKa 13.7 1.0 1 .03 22 pKa 36.3 1.0 1 .03 22 Union. 10.1 1.0 1 .11 Phenol 22 pKa 22.5 1.0 1 .02 W M 22 pKa 45.1 1.0 1 .05 0- C 22 Union. 32.4 1.0 1 .07 Aniline 22 Ionized 35.8 1.0 1 .00 h-1 P H* 22 pKa 38.5 1.0 1 .02 3 cr 22 pKa 74.3 1.0 1 .02 22 Union. 33.9 1*0 1 ,04 09 P w g Nitrobenzene 22 Union. 3.52 1.0 1 .03 (6 H> O p-Nitrophenol 22 Union. 13.3 1.0 1 ,11 CO H-p-Nitrobenzo- 22 Ionized 4.49 1.0 1 .02 (D P ic Acid 22 pKa 1.32 1.0 1 .02 .—, u) 22 pKa 3.82 1.0. 1 .03 22 Union. 1.02 1.0 1 .06 co co cn-p-Hydroxy P Benzoic Acid 22 Ionized 13.5 1.0 1 .08 22 rpKa of 12.5 1.0 1 .11 22 tcocr 33.7 1.0 1 .13 22 Union. 1.51 1.0 1 .25 p-Amino Benzoic Acid 22 -cocr 12.1 1.0 1 .08 22 fpKa of 12.3 1.0 1 .09 22 ICOO" 21.5 1.0 1 .11 22 rpKa of t-NH3+ 11.9 1.0 1 .11 (Continued on next page.) - 49 -(Table 1. Continued) Drug °C Solvent System (Dt)xlO 3 mole/L. $PVP (Dt.) (Df) Methodology and Reference Bezocaine 22 pKa of -NH3-Union. 1.09 2.25 1.13 1.0 1.0 1.0 1.11 1.12 1.13 Equilibi Eide et Methylparaben 22 22 22 pKa pKa Union. .74 2.66 1.32 1.0 1.0 1.0 1.09 1.11 1.10 Equilibi Eide et Butylparaben 22 Union. .517 1.0 1.20 •ium Dialysis, al. (1967a). Propylparaben 22 22 22 pKa pKa Union. 1.06 1.59 .875 1.0 1.0 1.0 1.13 1.15 1.18 •ium Dialysis, al. (1967a). Methyl-be nzoate 22 Union. ? 1.0 1.02 •ium Dialysis, al. (1967a). Ethylbanzoate 22 Union. 4.1 1.0 1.03 •ium Dialysis, al. (1967a). Procaine HC1 22 Ionized 8.16 1.0 1.02 •ium Dialysis, al. (1967a). *a - Insoluble complex i s formed up to PVP concentrations of 0.4$, after which solubility increases linearly with regard to PVP concentration. *b - The presence of dextrose slightly enhances the complexation. Some investigators presented their results in graphical form and i t was necessary, therefore, to make approximations directly from these graphs. Similarly, the different concen-tration terms in the various publications necessitated a conversion to an identical concentration term. Several of the factors affecting binding are illustrated by the results in Table 1. Bezoic acid, for example, i s more weakly bound to PVP than i t s derivatives. Orthohydroxy benzoic acid (Sali-c y l i c acid) has a lower binding tendency than does the meta or para forms. The former substance has a higher internal coordination or chelation between -OH and -COOH groups. - 50 -The lesser complexing tendency of the corresponding para-amino compound i s probably due to the weaker electrophilic nature of amino hydrogen as compared with the hydroxyl hydrogen. This results in weaker hydrogen bond formation (Higuchi and Kuramoto, 1954c). The effect of temperature i s illustrated by the studies of the PVP-chlorobutanol complex. Binding strength increases with temperature. This indicates an endothermic reaction. Bahal et a l . (1964) concluded that the large positive entropy change accompanying the binding was due to the formation of hydrophobic bonds. If the PVP concentration i s fixed, the extent of interaction i s often enhanced by increasing total drug concentration (Breuninger and Goettsch, 1965; Eide and Spei-ser, 1967a). This concentration dependency i s not, however, observed in most investigations. The results obtained by Eide and Speiser (1967a) strongly suggest that the nonionic species react more readily with PVP. The low interaction tendency of the ionic compounds i s most lik e l y due to the hydrophobic nature of the substances. The increased complexing tendency of ionic compounds containing -OH, -NHg, or -COOH groups indicates that hydrogen bonding also plays a significant role in reactions of this type. Buffer substances (Eide and Speiser, 1967b) and third components in the solvent system (Kabadi and Hammarlund, 1966) w i l l also alter PVP-drug binding. Simonelli et a l . (1969) reported that the apparent solubility and rate of solution of sulfathiazole - 51 -from compressed tablets containing PVP i s greatly increased i f the drug i s f i r s t coprecipitated with the polymer. These investigators developed methods for the preparation of these coprecipitates in water and in 95$ alcoholic solution. 4. Dextran, Starch, and Hydroxyethyl Starch Dextrans are polysaccharides and consist of a variety of oC-polyglucosans produced by Leuconostoc mesenteroides and closely related bacteria under suitable environmental conditions. Synthetic procedures have been developed by Ruckel and Schuerch (1966). The concentration of dextran in solution may be deter-mined by heating the carbohydrate with anthrone in sulfuric acid (Scott and Melvin, 1953). Arond and Frank (1954) studied the molecular weight distribution of native dextran by u t i l i z i n g light scattering techniques and the intrinsic viscosity in aqueous solution. Granath (1958) studied the properties of branched dextran in solution. By measuring viscosity, light scattering properties, and sedimentation rates, Granath was able to obtain a more complete picture of the hydrodynamic behaviour of dextran molecule. Gronwall (1957) discussed the use of dextran solutions as plasma extenders. It i s generally recognized that as the molecular weight of dextran increases i t s interaction with proteins increases. In this context, Ricketts (1966) published data on the molecular composition of dextran solutions which are currently used as plasma extenders. Reese et a l . (1966) compared the extent of - 52 -branching of the synthetic dextran with that of the natural product. Enzymatic analysis confirmed the basic similarity of the two forms. More recently, Laurent and Granath (1967) fractionated dextran by using Sephadex G-200 packed into chromatographic columns. Greenwood (1956) reviewed the physicochemical properties of starch. BeMiller (1965) bri e f l y discussed complexation of carbo-hydrates with organic substances. Analytical procedures for deter-mining starch sol have been described by Launer (1963) and Whistler et a l . (1965). Saito (1957) reported that anionic surfactants are readily adsorbed on various nonionic polymers including starch and PVP, especially above the c r i t i c a l micelle concentration. They suggested that the polar part of the anion i s probably adsorbed on the oxygen atom in the polymer. However, l i t t l e attention has been given to this complexation phenomenon. Gray and Schoch (1962) studied the influence of various fatty adjuvants on the swelling behavior of several starches. Goudah et a l . (1965) and Mansour et a l . (1968) studied the solubility characteristics of benzoic acid derivatives in the presence of various starch sols. They concluded that amylose i s the main complexing component in starch. Hydroxyethyl starch (HES) i s a waxy or branched starch which has been hydroxyethylated to retard intravascular hydrolysis. The substance i s being promoted as a plasma substitute. However, not much i s known about the physicochemical properties of HES solutions. Most publications deal with the in vivo behaviour in animals and have been collected by the National Academy of Sciences (N.A.S. - N.R.C., 1965). V. EXPERIMENTAL 1. Apparatus (a) Spectrophotometers Beckman DU Beckman DU-2 Bausch & Lomb Spectronic 505 Beckman IR-10 (b) Fisher Accumet 310 pH Meter (c) International Equipment Company HN Centrifuge (d) American Laboratory Sterilizer (e) Westphal Balance (f) Blue M Electric Company Refrigerated Bath (g) Cannon-Fensk Viscometer (Size 50) (h) Haake Thermoregulator (Type FE) (i) B-D Cornwall Continuous Pipetting Outfit with Swinny F i l t e r Adopter. MF-Millipore (WP) F i l t e r Paper (pore size, 0.65 ± 0.30 ji) was used with the apparatus. 2. Chemicals and Reagents (a) Bishydroxycoumarin, U.S.P., (BHC). The melting point of the substance was 287-288 °C. The drug was obtained from Abbott Laboratories Limited, Montreal, Quebec and was identified by infrared spectrophotometry. (b) Polyvinylpyrrolidone (PVP). Plasdon C was purchased from the General Aniline Corporation, New York, N.Y. The Kj. value range i s 28 to 32 (upper 15$ not higher than Kp, 41; lower 25$ not less than Kp, 16) and the molecular weight is 40,000. To remove monomer, the PVP was extracted with - 54 -anhydrous ether in a soxhlet apparatus for 24 hours. The PVP was then dried in an oven, under vacuum and at a temperature of 35-40°C for 12 hours. May (1954) reported that the monomer could be extracted with methylene chloride. It was found, however, that this solvent dissolved the polymer and for this reason, anhydrous ether was used to extract the monomer (see Higuchi et a l . , 1954b). The water content of PVP was determined from the loss in weight after drying in an oven at 110-115°C for 24 hours. Five such determinations were carried out. The average value was 3.79$ (range, 0.28$). (c) Dextran-75. The sample was obtained from Abbott Lab., Montreal, Quebec. Its molecular weight was 75,000 ± 15,000. Its water content was determined in the manner indicated above. The average value was 2.24$ (range 0.6$). (d) Human Serum Albumin (Cohn Fraction V, HSA). The albumin was obtained from Pentex Inc., Kankakee, 111. No loss i n weight on drying was detected. (e) Hydroxyethyl Starch (HES). The starch was obtained from McGaw Lab., Glendale, C a l i f . The company also supplied a 6$ solution containing 0.9$ sodium chloride. (f) Potato Starch. The starch was purchased from Baker and Adamson Products, New York, N.Y. (g) Tris(hydroxymethyl)aminomethane (Tris). Reagent Grade. (h) 0.1N I 2 T.S., IN HC1, IN NaOH, U.S.P. (i) Buffer Components. Reagent Grade. (j) Dimethylformamide(DMF). Reagent Grade. 3. Determination of Apparent pKa Values for BHC (a) Potentiometric Titration . Dissolve an accurately weighed sample of BHC (approximately 140 mg.) in 200 ml. of DMF. To a 10.0 ml. aliquot of this solution, add 2.5 ml. of 0.01N HC1, 30.0 ml. of DMF, and s u f f i -cient water to make 100.0 ml. of solution. Titrate the solution with 0.01N NaOH, using a glass-calomel combination electrode to follow pH changes. Perform a blank t i t r a t i o n . (b) Spectrophotometric Determination. Add 400 ml. of 0.01N NaOH to an accurately weighed sample of BHC (approximately 50 mg.). Shake u n t i l dissolved (approximately 2 hours) and dilute to 500.0 ml. with 0.01N NaOH. Dilute this solution to give a fin a l concen-tration of approximately 10 mg./L. A series of buffer solutions were prepared (pH range of 2.5 to 10.5) by u t i l i z i n g Perrin's buffer tables (Perrin, 1963). The ionic strength of these solutions was 0.0i. The pH difference between buffer solutions was 0.5 units except in the case of the buffers in the 4.0 to 7.0 range. For these solutions, the pH interval between solutions was of the order of 0.2 units. Chloroacetic acid - KOH gave a 2.5 to 3.0 range; formic acid -KOH, a 3.2 to 4.2 range; acetic acid - KOH, a 4.4 to 6.2 range; phosphates, a 6.4 to 7.6 range; Tris - HC1, an 8.0 to 8.8 range; borates, a 9.0 to 9.7 range; and carbonates, a 10.0 to 10.5 range. A 2.5 ml. aliquot of the BHC stock solution (BHC concen-tration of approximately 10 mg./L.) was diluted to 50.0 ml. with buffer. Visual observation indicated the BHC remained in solution over the entire pH range. Actual pH values were determined by using a pH meter. - 56 -Absorbance values were determined by the trace analysis technique (Reilley and Crawford, 1955; Pernarowski, 1969) at 276.5 and 315 mu. For convenience, a BHC solution of 0.01N NaOH (BHC concentration of approximately 3 mg./L.) was used to adjust zero per cent transmittance (0$ T) at both wavelengths. Absorbance values were determined in the following manner. Select wavelength and adjust instrument to read 0$ T. Place reference solution in the light beam. Turn the selector switch on the Beckman DU spectrophotometer to the one position and zero the instrument using the dark current control knob. Return selector switch to the check position. Place buffer solution in the beam and set the instrument to 100$ T. Determine the ab-sorbance of a solution containing the drug. Absorbance was plotted versus pH. The pH values at the inflection points corresponds to the apparent pKa values. The mathematical basis for the calculation i s given in Eq. 51. (ionized form) pKa = pH - log (Eq. 51) (unionized form) The solubility of BHC in buffer solutions of low pH i s the limiting factor in the determination of pKa^ value. However, the second pKa value can be more easily determined since the drug i s more soluble at higher pH values. In determining pKa.^  value, BHC concentration of approximately 0.5 mg./L. was used to a pH of 7. The absorbance values of such solution were determined at 276.5 mjx by the trace analysis method. Two more runs were made in buffer-DMF systems which containing 1.0 and 0.8 mg. drug per l i t e r of solution containing 2.5 and 10.0$ v/v DMF, respectively. - 57 -The pKag value was determined by using solutions containing 10 mg. drug per l i t e r . The spectrum-wavelength curves of these solutions (pH range of 6.0 to 10.5) were recorded by using a B & L Spectronic 505 spectrophotometer. The procedure was repeated with solutions containing 5 and 20$ v/v DMF. 4. Solubility Measurements on BHC (a) Effect of pH on the Solubility of BHC. Buffer solutions (pH range of 6.4 to 8.0) were prepared by using Tris and hydro-chloric acid. The buffers were prepared in the following manner. Dilute 50.0 ml. of IN HC1 with water. Insert glass-calomel electrodes into the solution and tit r a t e with 0.5M Tris solution to the desired pH. Dilute with water to make 250 ml. and re-determine the pH. The ionic strength of these buffers was 0.2. Solubility measurements were carried out in the following manner. Transfer 50 mg. of BHC to a 125-ml. glass bottle and add 100 ml. of buffer. Tumble in a water bath at 30°G at a rotational speed of approximately 30 rpm. After 24 and 48 hours, withdraw aliquots f i l t e r e d through a Swinny f i l t e r adaptor and deter-mine the absorbance at 286 mu, the isosbestic point for BHC. The solutions must be diluted prior to measurement, the extent of dilution depending on the pH of the buffer. The f i l t e r i n g device must be maintained at 30°C i n order to prevent drug from precipitating from solution. The pH values of the solutions were determined both before and after solubilization. - 58 -(b) The Effect of Ionic Strength on the Solubility of BHC. Hydrochloric acid solutions were prepared from IN HC1. The pH of each of these solutions was adjusted to 7.2 with either 0.1 or 0.5M Tris solution. The ionic strength of each of the solutions was calculated from the amount of hydrochloric acid used to prepare the buffer. The solubility of BHC in these buffer solutions was determined in the manner described in the previous section. 5. The Solubility of BHC as a Function of Macromolecule Concentration (a) Starch Sol. A starch sol was prepared by a procedure similar to that described by Goudah and Guth (1965). Prepare a slurry, in a 100-ml. beaker, containing 25 Gm. of potato starch with Tris buffer (pH of 7.2; ionic strength, 0.2). Slowly add the slurry to 350 ml. of hot buffer at 90-95°C. Agitate continuously for five minutes in a boiling water-bath. Transfer the starch sol to an autoclave and heat for three hours at approximately 125°C. Remove the sol from the autoclave, cool, and adjust the pH, i f necessary, to 7.2 with 0.1M T r i s . Make volume to 500 ml. with Tris buffer. Calculate the starch concentration on the basis of the amount of starch weighed i n i t i a l l y . Solubility measurements were carried out in the following manner. Prepare starch solutions by diluting the sol with Tris buffer. To each solution, add excess BHC. Tumble these preparations in closed containers in a 30°C water-bath for 40 hours. F i l t e r the solutions through a coarse sintered glass f i l t e r . Maintain the f i l t e r i n g apparatus at 30°C prior to use. Dilute the samples, i f necessary, and determine the absorbance of the solution at 286 mu. Place a starch solution of the same concentration as that in the test sol in the reference beam of the B & L Spectronic 505 spectrophotometer. - 59 -(b) HES. Solubility measurements were carried out in the following manner. Prepare a 3$ HES solution by diluting a 6$ solution containing 0.9$ sodium chloride with Tris buffer. Add hydrochloric acid solution to obtain an ionic strength of 0.2 and a pH of 7.2. Typical quantities are list e d below. 6$ HES i n 0.9$ NaCl 500.0 ml. IN HC1 123.0 ml. IM Tri s 134.6 ml. Water q.s. to 1000.0 ml. Calculate the ionic strength from the quantity of hydrochloric acid and sodium chloride in the solution. Prepare a series of HES solutions containing various concentrations of HES by diluting with Tris buffer. Add an excess of BHC to each solu-tion and determine the solubility in the manner described in the previous section. (c) PVP. Solubility measurements were carried out in the following manner. Prepare a 4$ PVP solution by dissolving the substance in Tris buffer (pH of 7.4; ionic strength, 0.15). Dilute this stock solution with Tris buffer to prepare solutions con-taining various concentrations of PVP. Add excess BHC to 25.0 ml. of each of these solutions. Transfer the sealed 30-ml. cen-trifuge tubes to a 20°C water-bath and tumble for 40 hours. Transfer aliquots to a second series of centrifuge tubes. Centrifuge for 20 minutes at 2,500 rpm. Withdraw aliquots, dilute with Tris buffer and determine the absorbance at 304 mu using Beckman DU-2 spectrophotometer. Use Tris buffer as the blank solution. Correct measured absorbance for PVP content and absor-bance depression due to complex formation (a typical calibration curve w i l l be shown later). (d) HSA. The procedures for determining solubility were the same as that given above (a typical calibration curve w i l l be shown later). 6. Spectrophotometric Analysis (a) Infrared Spectrum of BHC. Prepare a KBr pellet and record the spectrum on a Beckman IR-10 spectrophotometer. (b) The Absorptivity Value of BHC. Weigh accurately 100.0 mg. of BHC and dissolve in 500.0 ml. of 0.01N NaOH. Dilute aliquots with 0.01N NaOH to give f i n a l concentrations of 2 to 18 mg./L. Prepare five such solutions from three different stock solutions. Record spectrum on a B & L Spectronic 505 spectropho-tometer and calculate absorptivity values at 286 mu. Repeat the procedure but dilute the stock solution with Tris buffer of pH 7.4. Prepare ten solutions from each of four different stock solutions in such a way that the f i n a l concentration varies from 4 to 12 mg./L. Check the pH of the solutions both before and after reading the absorbance on a Beckman DU and DU-2 spectrophotometers set at 304 mu. Calculate the absorptivity value at 304 mu. (c) Absorbance Values of HSA and PVP Solutions. Prepare 4$ stock solutions using Tris buffer. Prepare a series of solutions by diluting the stock solution with Tris buffer. Determine the absorbance on a Beckman DU-2 spectrophotometer set at 304 mu. Prepare calibration curves by plotting absorbance versus the per cent con-centration of macromolecule i n solution. (d) Determination of Changes in Absorbance at a Fixed  BHC Concentration as a Function of Macromolecule  Concentration. Shake an excess of BHC with Tris buffer for one hour. F i l t e r through a Milipore f i l t e r paper. To each of a series of 50-ml. volumetric flasks, add different amounts of 4$ macromolecule solu-tion and a constant amount of the BHC stock solution. To two flasks, add only BHC stock solution. Dilute to volume with Tris buffer. - 61 -(e) Determination of the Changes in Absorbance at a  Fixed Macromolecule Concentration as a Function of  BHC Concentration. Add varying quantities of the BHC stock solution (see previous section) to fixed amounts of the macromolecule* Dilute and record absorbance as indicated above. Calculate the theoretical absor-bance value of each solution from the amount of BHC in solution. Subtract the observed value from the theoretical value and plot the difference against the observed value. Prepare solutions to contain 0.02$ PVP and use different BHC concentrations. Data from (d) above and that obtained here i s used to prepare the calibration curves. 7. Equilibrium Dialysis (a) Dialysis C e l l . A diagram of a dialysis c e l l i s shown in in Figure 9. Cells of this type are described in detail by Patel and Foss (1964). Total volumes in the dialysis c e l l may be changed by adding additional spacers on either side of the membrane. (b) Preparation of the Cellophane Membrane. Immerse dialyzer tubing (flat width is equal to 1.735 inches) in d i s t i l l e d water for several minutes. Unfold, cut to size, and transfer to 1.5 l i t e r s of water. Shake the container for approximately ten hours and, at hourly intervals, replace the water with fresh water. Store in a refrigerator at 0-5°C and use within two weeks. Prior to use, immerse the membrane in Tris buffer. Remove the membrane from the buffer, drain but do not allow drying to occur, and attach the membrane to the c e l l . - 62 -Rubber Cellophane 'O' Ring Membrane Figure 9. Diagram of a plexiglas block and an assembled dialysis c e l l . (c) Dialysis Equilibrium and Membrane Binding of BHC. Prepare three solutions containing varying concen-trations of BHC. Transfer a portion of the solution to one side of. the dialysis c e l l and dialyze against Tris buffer in the other compartment. Remove aliquots and analyze for BHC. Continue the process u n t i l the BHC concentration in both compartments i s the same for at least two sampling periods. On the basis of the data obtained, determine the time required for equilibration in the c e l l . Membrane binding of BHC was determined in the following manner. Transfer a solution containing a known quantity of BHC to the c e l l . Dialyze u n t i l both compart-ments contain the same amount of drug. Calculate the total amount of drug in solution. Subtract this value from the amount of drug added to the c e l l . Calculate the per cent recovery and estimate membrane binding. In experiments involving macromolecules, a control c e l l containing no macromolecule was maintained under the conditions specified for that study. Thus additional information on membrane binding was obtained throughout the investigation. - 63 -(d) Dynamic Dialysis. A diagram of the apparatus used i s shown in Figure 10. The procedure has been used by Meyer and Guttman (1968b) to study protein binding with drugs. Add excess of BHC to a solution containing a macromolecule. Shake for four to five hours. F i l t e r the solution through Millipore f i l t e r paper. Analyze for BHC in a similar manner described previously (see p. 59). To the cellophane bag, transfer 50.0 ml. of the macromolecule solution nearly saturated with BHC. Add 500.0 ml. of Tris buffer to the apparatus. Stir this external solution with a magnetic s t i r r e r . Stir the macromolecule solu-tion within the bag in the manner indicated in Figure 10. At specified times, remove 50.0 ml. of solution from the main part of the apparatus. Immediately replace this solution with the same volume of Tris buffer. Calculate the amount of drug in the cellophane bag by subtracting the amount of drug removed from i n i t i a l amount added to the system. Motor Holes for Introduction and Removal of Solution Rubber Stopper To a Constant-Temperature Water Bath BHC-Macromolecule Stock Solution t Cellophane Bag Tris Buffer Magnetic Stirring Device Figure 10. A set-up for dynamic dialysis method. - 64 -(e) Permeability of PVP through the Cellophane Membrane. Prepare PVP solutions in Tris buffer (0.1 to 0.4$). Transfer aliquots to one of the compartments in the dialysis c e l l and dialyze against Tris buffer for 40 hours. Analyze the Tris buffer compartment for PVP, following the method of Campbell et a l . (1953). To a 10.0 ml. of sample of the solution, add 0.1 ml. of 0.1N iodine in 0.1M potassium iodide solution. After 12 to 15 minutes, read the absorbance of the solution on a Beckman DU-2 spectrophotometer set at 500 mu. Dilute the iodine test solution to 10.0 ml. of Tris buffer and use as the blank solution. Calculate concentration from a calibration curve based on solutions containing known amount of PVP. (f) .Equilibrium Dialysis Studies. Prepare a series of BHC and BHC-macromolecule solutions (see p. 63). Determine BHC concentration in these solutions (see p. 59). Transfer 20.0 ml. (or 40.0 ml., depending on compartment volume) of the BHC solution to the dialysis c e l l and dialyze versus the BHC-macromolecule solution or macro-molecule solution containing no BHC. Also dialyze BHC-macromolecule solution against Tris buffer. In one run of experiment, use six to twelve c e l l s depending on the experiment and the number of control c e l l s required. Attach the c e l l s to the shaft of the water bath and tumble at 30 rpm for 40 hours (a diagram of the apparatus i s shown in Figure 11). Remove aliquots from the BHC compartment, store in a water bath at 20°C, and analyze for BHC content. Dilute the aliquots, i f necessary (dilution factors of from 1:1 to 1:10), with Tris buffer. Carry out at least two analyses on each aliquot taken from the BHC compartment. PVP studies were carried out at 10, 20, 30, and 40°C and at PVP concentrations of 0.1, 0.2, and 0.4$. Similar HSA concen-trations were used but studies were carried out at 20 and 40°C only. HES studies were carried out at 30°C and at a concentration of 0.5$ HES. Since HES does not significantly increase BHC solubility, BHC-HES stock solutions were not used i n the - 6 5 -Figure 11. A water bath with a tumbler used in solubility and equilibrium dialysis studies. investigation. Dialyses were based on BHC and HES solutions only. Temperature fluctuations during dialysis were less than 0.1°C. 8. Viscometric Analysis (a) Calibration of the Viscometer. Calibrate seven Cannon-Fenske Viscometers in the manner described in an A.S.T.M. bulletin (1966b). Use freshly d i s t i l l e d water as the reference standard. Viscosity and density values for water at various tempera-tures are given in the literature (Bull, 1964b; Weast, 1969). With respect to the viscosity values for water, the values from Bull's textbook were used i n the calculation. The viscometers were f i l l e d and allowed to stand in a water bath for at least two hours. Flow time was determined to 0.1 seconds. At least five determinations were made for each viscometer. The average flow time for each viscometer was substituted into Eq. 50 along with the two water constants and the instrument constant at the specified temperature was calculated. Temperature variation in any experiment was less than 0.1°C. (b) Density Measurement. Calibrate a Westphal balance at each temperature with d i s t i l l e d water. Maintain the specified temperature by immersing the glass cylinder of the balance in a water bath (800 ml.) set to the desired temperature. Make calibration both before and after measurement of PVP solutions. The repro-ducibility was 0.0002 density units. Prepare a series of PVP solutions and determine density. Note that the apparatus measures apparent specific density but, for the purposes of the experiment, the two terms were considered to be synonymous. (c) Viscosity Measurements of PVP Solutions in the  Presence of BHC. Dissolve PVP i n a BHC stock solution to yield a fin a l PVP concentration of 4$. Dilute with BHC stock solution to yield solutions which contain the same quantity of BHC and from 0.2 to 3.0$ PVP. - 67 -Prepare seven such solutions. Determine flow-times in the manner described in (a) above. Substitute the mean flow-time, the density value, and the instrument constant into Eq. 50 and cal-culate, the viscosity. Calculate relative viscosity by dividing each viscosity value by that of the BHC solution without PVP.* Calculate reduced and specific viscosities by using Eq. 44 and 45. Determine intrinsic viscosity and Huggins parameter from the intercept and slope of the graph obtained by plotting reduced viscosity versus PVP concentration. * This implies that the relative viscosity of the BHC solution was considered to be unity (see Eq. 43). VI. RESULTS AND DISCUSSION 1. Intramolecular Hydrogen Bonding in BHC The infrared spectrum of BHC i s shown in Figure 12 and i s similar to that published by French and Wehrli (1965). The vibrational frequency corresponding to an -OH stretch occurs at approximately 3500 Cm.-* The f i r s t overtone i s usually observed at 7000 Cm.-1 If chelation occurs with the carbonyl group in phenols through the formation of an intra-molecular hydrogen bond, the former frequency value becomes less but the extent of change depends on the strength of the hydrogen bond. The band i s broad and, at times, very weak (Nakanish, 1964; Dyer, 1965). With BHC a broad absorption band occurs at approxi-mately 3100 Cm.~* and this may indicate an intramolecular hydrogen bond. The molecular model for BHC suggests the possible formation of two intramolecular hydrogen bonds between the carbonyl group at Cg and the -OH group at C^t (or vice versa). Solubility data (see later) appear to support this conclusion. These two internal eight-membered chelations (see Figure 13) appear to restrict the rotation of the one-sided moiety of the methylene bridge and fix i t s configuration. The most probable three dimensional structure of BHC i s shown in Figure 14. - 70 -Figure 13. Chemical structure of BHC showing two intramolecular eight-membered chelations. Figure 14. Three dimensional structure of BHC Black, red, and white bars represent carbon, oxygen, and hydrogen atoms, respectively. The black bar below the model has a length of 4 A 2. Apparent pKa Values of BHC If a dibasic acid i s symmetrical with respect to the two ionizable hydrogen atoms and i f the negative charge on the f i r s t ionizable group i s sufficiently removed from the remaining hydro-gen atom, then the effect on the second group i s negligible and the f i r s t ionization constant i s approximately four times as large as the second constant (Robinson and Stokes, 1968). In general, however, the effect of the negative charge does make i t more d i f f i c u l t for the second hydrogen to ionize. For example, for oxalic acid, the f i r s t constant i s approximately 1000 larger than the second. On the other hand, there i s only a six fold difference for azelaic acid (C00H(CH2)7COOH). Kirkwood and Westheimer (1938), under reasonable assumptions with respect to the size and configuration of the molecules, discussed the effect of electrostatic interaction between ionizable groups on the cosecutive ionization constants.* Although pKa values have been reported for BHC (Burns and others, 1953; Nagashima and others, 1968a), the uncertainties associated with the determination and the absence of values for the total ionization process made i t necessary to study the ionization behaviour of this drug. The molecule has two ionizable hydrogen atoms and both are involved in the internal hydrogen bond. As shown in Figure 15, the negative charge on the oxygen * This study formed the basis for the theory of multiple equilibria i n the complexation process in the presence of electrostatic interactions between binding sites (see p. 11). - 72 -Figure 15. Resonance structure of BHC after the f i r s t ionization. atom produced by the f i r s t ionization i s expected to make the oxygen atom in the carbonyl group more negative by an electronic shift through the conjugated chain. This increase in electro-negativity apparently increases i t s a b i l i t y to form hydrogen bond with the remaining hydrogen atom (Pauling, 1967). The strengthened hydrogen bond w i l l , therefore, make i t more d i f f i -cult for the second hydrogen atom to ionize. For this reason, and the fact that the s t a t i s t i c a l considerations of two successive ionization constants would appear to be sound when applied to long and thin molecules but not to shorter and more spherical molecules (Robinson and Stokes, 1968) like BHC, the ratio of the f i r s t to the second ionization constants for BHC should be at least 1000:1. It i s rather surprising, therefore, that only single ionization constants for BHC have been reported i n the literature. The pK values of acids and bases may be determined in many different ways (Albert and Serjeant, 1962). BHC i s , however, very insoluble in acidic solution and the basic titrimetric approach - 73 -in aqueous media cannot be u t i l i z e d . However, solubility can be increased by u t i l i z i n g an organic solvent - water mixture and potentiometric and spectrophotometric titrations can be carried out in such systems. Alcohol, dioxane, and DMF have been recommended in such systems (Parke and Davis, 1954). Attempts were made, therefore, to measure the apparent pKa values of BHC i n DMF-water systems containing varying quantities of DMF. These values may be extrapolated to zero per cent DMF in order to determine the value in water alone. Garrett (1963) studied the variation of pKa values of tetra-cyclines in a DMF-water system in a similar manner. A solution containing 706.0 mg. BHC per l i t e r of DMF was prepared. A 10.0 ml. aliquot of this solution was transferred to a 100 ml. volumetric flask. When 2.5 ml. of 0.01N HC1 were added to the flask, the solution became turbid but the turbidity disappeared when 30.0 ml. of DMF was added. Addition of water to 100.0 ml. produced no further turbidity (see p. 55). It became necessary to consider the following factors when preparing BHC sample solutions for titration; pH of the solution before titra t i o n , strength of titrant, concentration of BHC, size of sample, and per cent DMF. The results in Figure 16 were obtained when a 100.0 ml. sample of BHC (70.6 mg. per l i t e r of a 40$ solution of DMF i n water) solution containing 2.5 ml. of 0.01N HC1 was titrated with 0.01N NaOH. The blank t i t r a t i o n curve was obtained by titrati n g 100 ml. of 40$ DMF solution containing 2.5 ml. of 0.01N HC1 with 0.01N NaOH. The blank t i t r a t i o n curve was subtracted u X)—-• < • 1 • 1 4 5 6 7 8 9 10 PH - 75 -volumewise from the BHC curve and the difference converted to equivalents of OH ion per mole of BHC and plotted as a function of pH. The pH range covered in these titrations was from 3.5 to 10. Because BHC i s insoluble in acidic media, titrations could not be carried out below pH 3.5 and no potentiometric break i s observed. One endpont region (pH 5 to 8) i s present; the second region f a i l s to appear on the curve. It i s impossible, therefore, to report quantitative pKa values for BHC in this system. However, the difference curve does show the presence of two pKa values, the one below pH 4, the other, above pH 9. No further attempts were made to determine pKa values in this way because i t would have been necessary to increase DMF concentrations and hence operate much further from the zero per cent DMF point. The low solubility of BHC i n aqueous media caused similar d i f f i c u l t i e s during the spectrophotometric determination of pKa values. The solubility of the unionized BHC (AHg form) i s approxi-mately 0.5 mg./L. (1.5 x 10"6 mole/L.). At these concentrations, the spectral characteristics of the unionized species cannot be obtained. However, the change from the AH- to the A form can be followed. These spectrophotometric curves are shown in Figure 17. Each solution contained 10.0 mg. BHC per l i t e r of the specified buffer. As the pH decreases, an absorption maximum appears at 276.5 mu; with increasing pH, a peak i s observed at 315 mu. 330 320 310 300 290 280 270 260 250 Wavelength, mu If a similar spectral change occurs when AH2 i s converted to AH~ and H~, the most suitable wavelengths for analysis would appear to be 276.5 or 315 mu. A series of solutions were prepared to contain 0.5 mg. BHC per l i t e r of buffer. To prevent spectral distortion, the ionic strength of each solution was kept as low as possible (Sager and others, 1945). Perrin (1963) describes buffers of this type. They have a low ionic strength (0.01), cover the 2.2 to 11.6 pH range, and absorb very l i t t l e energy in the ultraviolet region of the electromagnetic spectrum. The absorbance of a solution containing small quantities of drug can be determined in one of two ways. First, a long spectrophotometrie c e l l may be used in the determination and, secondly, precision spectrophotometry (trace analysis) may be used to analyze the solutions. Sager et a l . (1945) used a 5-Cm. c e l l to determine the pKa values of some esters of p-hydroxy-benzoic acid. The s o l u b i l i t i e s of these esters ranged from 10" 4 to 10"^ molar. Precision spectrophotometry (Reilley and Craw-ford, 1955; Pernarowski, 1969) has not been used to determine such values. By using the principles inherent in precision spectrophoto-metry, the absorbance values of a series of BHC solutions were determined at 276.5 and 315 mu and plotted versus pH values. These plots are shown in Figure 18. Absorbance values did not exceed 0.1 absorbance unit even though the absorbance scale was expanded to a maximum by appropriate use of reference standards. A slight turbidity was observed in those BHC solutions i n 0.01N HC1. No turbidity was observed in the solutions with higher pH .09 .08 -.07 " .06 Figure 18. Absorbance-pH curves for BHC. Circles and triangles indicate readings at 276.5 and 315 mu, respectively. Closed and open symbols were obtained from separate experiments. .05 .04 -.03 " .02 . A A O .01 • A - 79 -values but undetected over-saturation may be the cause of the scattered values below pH 4 in Figure 18. Absorbance changes show clearly the two ionization steps. The calculated values from the curves i n Figure 18 are 4.6 and 4.2 for pKa^ and 7.75 and 7.9 for pKag. The former values were obtained from absor-bance readings at 276.5 mu; the latter, from readings at 315 mu. Average values are 4.44 and 7.83.* Figure 18 also shows that the spectral changes due to the f i r s t ionization i s apparently different from those associated with the second ionization. At both 276.5 and 315 mu, absorbance increases as pH increases from 3 to 5 (compare with Figure 17). This implies that no isosbestic point occurs between these two wavelengths on the f i r s t ionization process. The pKa 2 value may be determined directly by measuring absorbance values of buffered solutions of BHC, because BHC has a reasonable solubility at that pH range (see later). Solutions containing 10.0 mg. of drug per l i t e r of buffer, 5$ DMF i n buffer, and 20$ DMF in buffer were prepared. Absorbance-wavelength curves were recorded on B & L Spectronic 505 spectro-photometer. Figure 19 shows spectral changes occurred in the presence of 20$ DMF. However, at low pH values, drug solubility must be increased by the addition of DMF. This solvent does not affect the pH of the buffer and absorbs l i t t l e energy at the two analytical wave-lengths. Solutions containing 0.5 mg. of drug per l i t e r of buffer, 1.0 mg. of drug per l i t e r of 2.5$ DMF i n buffer, and 0.8 mg. * The mean of 4.2 and 4.4 i s 4.44 because a log scale i s being used. Antilog values for the pair are added. An average value i s the log of the value obtained divided by two. Similarly the average of 7.75 and 7.9 i s 7.83. Figure 19. U l t r a v i o l e t spectra showing the second d i s s o c i a t i o n of BHC i n 20$ v/v DMF. Solution pH values are: 1, 11.30; 2, 10.75; .80 .75 t-70 .65 .60 1.55 > |.50 w o cr P .45 g © .40 • .35 " .30 .25 4.20 340 330 320 310 300 290 280 Wavelength, mu 270 260 250 - 81 -of drug per l i t e r of 10$ DMF i n buffer were used in determining pKa^ value. Absorbance values of these solutions were measured at 276.5 mu by means of precision spectrophotometry (see p. 56). Results are shown in Figure 20. The relationship between pKa values and per cent DMF i s shown in Figure 21. Values obtained from this data are 4.4 for pKa^ and 8.2 for pKa 2. The dielectric constant for DMF i s reported to be 36.7 (Leader, 1951). As the solvent becomes less polar by addition of DMF the f i r s t ionization occurs more easily and the weak acid behaves as a stronger acid in this system. In aqueous media, the BHC molecule i s believed to exist in the enol form which i s more acidic than keto form (see Figure 22).* The enol-keto ratio would be greater when the polarity of the environment decreases (Gould, 1963). The increase in the mole fraction of enol form may be partly responsible for the increased acidity of BHC in the DMF system. The extent of solvation around the monoionized BHC molecule would be expected to decrease as the polarity of the solvent decreases (i.e., re-moval of charges become more d i f f i c u l t ) . As a result, the second ionization constant increases slightly when DMF content i s in-creased. These results and those obtained by potentiometric t i t r a t i o n (see p. 75) indicate pKa values of the same magnitude. * After this work had been completed, a study on the structure of BHC and a related compounds appeared in the literature. Hutchinson and Tomlinson (1969) proposed a hydrogen-bonded structure for BHC, identical to ours (Figure 13), from a study of nuclear magnetic resonance and infrared spectra. They also made the conclusion that in tautomeric structures similar to Figure 22 4-hydroxycoumarin i s preponderantly in the enolic form both in the solid state and in solution in polar solvent. We had further inferred that enol:keto ratio increases with decrease in polarity of solvent. We are grateful to Mr. J. Coates for bringing this paper to our attention. Absorbance at 276.5 mu Measured by Precision Spectrophotometry ro , CM •a cn .. cn Absorbance at 315 mu C M —»- — cn cn — t — 03 —»-CD S3 co . o 3 \ CD f 3 • rt 01 O • H» o 01 CD a P 3 a cn CD P 3 a cd 8 rt-ro ->i cn o CD 3 0) ><! I-O I—1 01 f t . . ro • cn cn p 3 TO M CD CO P P 3 a Figure 21. Apparent pKa values of BHC as a function of per cent DMF. Values were obtained spectrophotometrically. - 84 -O O Keto Form Figure 22. Tautomerism of a BHC molecule. From a l l of the data obtained herein, i t i s reasonable to assign a pKaj value of 4.4 and a pKa 2 value of 8.0 to BHC. By means of non-logarithmic linear t i t r a t i o n curves, Levy (1969) obtained values of 4.6 and 7.7. However, in order to obtain these values, he assumed a solubility of 0.2 mg./L. for the unionized BHC. 3. Solubility (a) Effects of pH, Ionic Strength and Buffer Components. The effect of pH on the apparent solubility of BHC at 30°C i s shown in Figure 23. A Tris-HCl buffer system (ionic strength, 0.2) was used in the determinations. Solubility increases rapidly with increase in pH from 7.6 to 8.0. BHC appears to be unstable in 0.1N NaOH solutions, since they turn yellow after standing at room temperature for three days. Low aqueous solubility strongly indicates that the hydroxyl groups at C^ and C4« do not contribute to solubility by forming hydrogen bonds with water. A parallel situation exists with s a l i -c y l i c acid in which the -OH group i s involved in an intramolecular hydrogen bond (Martin, 1968b). Solubility i s expected to increase after the f i r s t ionization since an intramolecular hydrogen bond, in which the ionized hydroxyl group has been involved, i s no longer present. However, a marked change in solubility (such as observed around pH 8) i s not expected, because the molecule i s s t i l l more or less r i g i d l y fixed by one remaining internal hydrogen bond to allow l i t t l e interaction-with water. After complete ionization, a significant ion-dipole interaction between BHC and water can be expected and this w i l l result in a marked increase in solubility. The effect of ionic strength on the apparent solubility of BHC i s shown in Figure 24. The pH of each solution was maintained at 7.2. If neutral salts are used to alter ionic strength, organic molecules w i l l , in general, show a decreased water solubility - 86 -Figure 23. Effect of pH on the apparent solubility of BHC at 30°C (ionic strength, 0.2). Solubility was determined after 24 (O) and 48 (•) hours. 7.4 7.6 — i — 7.8 8.0 pH - 87 -Figure 24. Effect of ionic strength (chloride ion) on the apparent solubility of BHC at 308C (pH, 7.2), after 24 (O), 48 ( • ) , and 72 (A) hours. - 88 -because of the 'salting out' effect.* The results for BHC do not follow this pattern. However, the ionic strength of these solutions was governed by HC1 content and the study may, there-fore, be nothing more than the specific effect of chloride ion on the solubility of BHC. According to Frank and Wen (1957), halide ions except fluoride ion are water structure breakers. Fewer 'icebergs' would be expected around the chloride ion and this should enhance BHC-water interaction, i.e., the number of unbound water molecules i s greater in the presence of chloride ion and this provides more cavities for the solution of the hydrocarbon (Nemethy and Scheraga, 1962b; Mohammad, 1965). A l l drug-macromolecule interactions were studied in buffer systems. Buffer composition i s , therefore, an important part of the investigation. For example, the ionic strength of the buffer arises from the hydrochloric acid added to the buffer. This implies that buffer with a low ionic strength contains less buffer component. Consequently, the buffer capacity of the Tris buffer ( f3) i s lower at low ionic strength. ' Ka C (IT) (Eq. 52) d(b) B = « 2.303 ' d(pH) Ka (H+) + (H*-) + (OH") (Ka + (H*)] 2 * Hydrocyanic acid and glycine, which are alike in that their aqueous solution have higher dielectric constants than pure water, become more soluble in the presence of salts. The data herein may reflect such a 'salting in' effect (Edsall and Wyman, 1958b), but evidence for this i s lacking because the dielectric constant of the BHC solution was not determined. - 89 -In Eq. 52, Ka and C are the ionization constant of the buffer component and i t s concentration, respectively, and b i s the number of gram equivalents of a l k a l i added to one l i t e r of buffer solution (Bates, 1961). As shown in Eq. 52, buffer capacity i s a function of pH and the concentration of the buffer component. These relationships between buffer capacity and pH for Tris buffer i s shown in Figure 25. As expected, maximum buffer capacity i s obtained at a pH equal to the pKa of T r i s . The value reported in the literature i s 8.075 (Bates, 1961). The Tris buffer used in this investigation i s 0.063M with respect to Tris and 0.15N with respect to hydrochloric acid. The buffer capacity i s 0.021. Buffer components may interact with macromolecules. Tris, however, has an intramolecular hydrogen bond as shown in Figure 26 (Benesch and others, 1955) and should not react significantly with macromolecules. For example, Higuchi and Kuramoto (1954c) claimed that complexation of s a l i c y l i c acid with PVP i s less than observed between p-hydroxy-benzoic acid because a strong internal hydrogen bond exists in the former drug (see pp. 49-50). Chloride ions, on the other hand, may also interfere with BHC-macromolecule interaction. Klotz (1953a) briefly reviewed the binding of chloride ion to serum albumin. However, these effects were neglected in this investigation because competitive interaction of chloride ion with the macromolecule would be far less than that usually observed drug-macromolecule interactions. A typical example of correction for competitive effect of buffer components may be found in the paper published by Klotz and Urquhart (1949c). Using Eq. 33, they corrected for the contribution of phosphate to the interaction between methyl orange and albumin. - 90 -Figure 25. Buffer value of Tris buffer solutions in the pH range from pKa - 1.3 to pKa + 1.1. Total Tris concentrations are 0.2M (a), 0.1M (b), and 0.05M (c). See Bates (1961). Open c i r c l e represents the buffer capacity of Tris buffer used in this investigation. - 91 -Figure 26. Two dimensional structure of Tris showing intramolecular hydrogen bonds. See Benesch and Benesch (1955). (b) Effect of Macromolecule - i) Starch Sol and HES. The binding tendency of BHC to potato starch sol and HES in Tris buffer (pH, 7.2; ionic strength, 0.2) i s illustrated in Figure 27. A l l solutions were euilibrated for at least 40 hours at 30°C. Concentration ratio of total to free BHC i s plotted against macro-molecule concentration. When linear relationship i s observed the slope (r value in Eq. 6) can be an approximation of binding capacity (see p. 4 and 46). If the drug and macromolecule do not interact, a straight line with zero slope passing through the unity should be obtained. This type of presenting solubility and equilibrium dialysis data has been frequently used in the literature (see, for example, Higuchi and Kuramoto, 1954b). Results in Figure 27 show that approximately 60 and 72$ of the total BHC exist ;in the; complexed form when the drug i s equili-brated with 3$ starch sol and HES solutions, respectively. - 92 -Figure 27. Effect of various concentrations of HES (A) and potato starch sol ( • ) on the apparent solubility of BHC at 30°C i n Tris buffer (pH, 7.2; ionic strength, 0.2) 4.5 4.0 3.5 3.0 2.5 2.0 J 1.5 1.0 % Macromolecule - 93 -Figure 28. Chemical structure (a) and molecular configuration (b) of HES. The chemical structure of HES i s shown in Figure 28 (a). Its molecular configuration, illustrated in Figure 28 (b), i s believed to be similar to that of amylopectin in that both molecules have many dilated branches. The average number of hydroxyethyl groups per glucose unit has been reported to be 0.7 to 0.9 (N.A.S. - N.R.C., 1965). Potato starch consists of 20$ amylose and 80$ amylopectin (Greenwood, 1956) whereas HES has no amylose-type configuration. It has been reported that amylose i s more likely to undergo a side-by-side association with organic molecules than amylopectin (BeMiller, 1965; Goudah and Guth, 1965; Mansour and Guth, 1968). The starch sol should, therefore, have a slightly higher a f f i n i t y - 94 -for BHC than HES and this i s confirmed by the results shown in Figure 27. Unfortunately, the limited results obtained do not lend themselves to an interpretation of mechanisms. Mansour and Guth (1968) assumed that benzoic acid, derivatives of benzoic acid, and sorbic acid form complexes with starches i n a manner similar to that observed for the starch-iodine and starch-n-butanol systems. There appears to be an entrapment of the 'guest' molecule in the <*-helical structure of amylose with a supplimentary stabilization of dipole-dipole interactions (Stein, 1948). A similar mechanism might explain BHC-starch and BHC-HES interactions. (b) Effect of Macromolecule - i i ) HSA and PVP. The apparent solubility of BHC i n Tris buffer (pH, 7.4; ionic strength, 0.15) at 20°C as a function of either HSA or PVP concentration i s i l l u s -trated in Figure 29. Solutions were analyzed for BHC spectrophoto-metrically. Corrections were made for depression of BHC absorbance due to complex formation in a manner described elsewhere in this thesis (see pp. 59-60 and 104-105). In 1.0$ HSA or PVP solution, apparent solubility i s enhanced by approximately 5.4 and 21.5 times, respectively. In these solutions, approximately 84.4 and 95.6$ of total BHC exist in the complexed form. In low macromolecule concentration range (up to 1.0$ for HSA and 0.4$ for PVP), linear relationship i s observed between change in solubility and macromolecule concen-tration. When BHC-PVP binding a f f i n i t y i s compared with that for other drugs (see Table 1), this interaction i s unusually strong. Interaction mechanisms w i l l be extensively discussed later. - 95 55 50 45 40 35 30 25 P 4-> S 20 Figure 29. E f f e c t of HSA ( c i r c l e s ) and PVP ( A ) concentrations on the apparent s o l u b i l i t y of BHC i n T r i s buffer (pH, 7.4; ionic strength, 0.15) at 20°C. Analyses for BHC concentration were ca r r i e d out a f t e r 40-hour s o l u b i l i z a t i o n . Each t r i a n g l e i s average of three d i f f e r e n t experi-ments. Open and closed c i r c l e s represent separate experiments. 15 -10 0 0 .5 1.0 1.5 2.0 2.5 $ Macromolecule 3.0 3.5 4.0 4. Spectrophotometry (a) Absorptivity Values of BHC. BHC concentrations were determined spectrophotometrically. Absorbance readings were carried out at either 304 mu, the wavelength at which BHC exhibits maximum absorption in pH 7.4 buffer, or at 286 mu, an isosbestic point. Absorptivity values (a g) are reported in Table 2. Molar absorptivity values may be obtained by multiplying a g values by 336.29, the molecular weight of BHC. N S s \ ^ Wavelength Instrument 286 mu 304 mu B & L 505 Beckman DU Beckman DU-2 47.35 * 0.26 48.38 * 0.48 55.5 ± 0.57 Table 2. Absorptivity Values for BHC in a pH-7.4 Buffer. (b) Absorbance Contribution of HSA and PVP. HSA and PVP absorb some radiant energy at the above wavelengths. It i s necessary to correct for this absorption by using appropriate calibration curves, before calculating BHC concentrations in the presence of these macromolecules. Such curve i s shown in Figure 30. Both HSA and PVP obey Beer's Law over the concen-tration range investigated. HSA appears to absorb 10 time more energy than PVP, when both macromolecule solutions are expressed on a w/v percentage basis. Under experimental conditions, - 97 -Figure 30. Absorbance measurements at 304 mu for HSA ( • ) and PVP (O) solutions in Tris buffer (pH, 7.4). Each point represents the average of at least two determinations on Beckman DU-2. , _ , * ==^-»— » TF • r, r : r 1 2 3 4 5 6 7 8 9 10 % Macromolecule, xlO PVP and xlO 2 HSA - 98 -absorbance values corresponding to the macromolecule concen-tration in the solution, were determined from this curve and subtracted from the values obtained for the BHC-macromolecule solution. (c) Depression of BHC Absorbance in the Presence of HSA  and PVP. The spectrophotometrie characteristics of bound BHC differ from those observed for the free drug. Spectral changes in the presence of HSA and PVP are illustrated i n Figures 31 and 32. The reference solution, in both instances, contained the same quantity of macromolecule as the BHC solution. The spectra are, therefore, due to BHC i n the solution. For comparison, spectra of BHC i n the absence of macromolecule are also shown in Figures 31 and 32. Because the absorption maximum at 304 mu i s depressed, i t i s probable that the functional group producing this absorption i s involved i n the complexation process. It i s d i f f i c u l t to relate ultraviolet maximum to configuration. However, the chromophore in BHC i s probably the d,-unsaturated lactone structure (see Figure 33). As the pH of the solvent changes, the -OH group in the /3-carbon position has a tendency to ionize and cause the type of electronic shift shown in Figure 15. This implies that the energy repuired for the elctronic transition w i l l be altered resulting in a shift of the spectrum. (d) Spectrophotometrie Analysis of Complex Formation. Since absorbance i s depressed, attempts were made to evaluate these spectral changes quantitatively. The procedures used are similar to those described by Klotz (1946c) and Oster and Immergut (1954). A series of BHC solutions containing identical Figure 32. Absorption spectra for BHC in the presence ( ) and absence ( ) of 0.4$ PVP. .6 — i > . 1 1 1 1 . i 1 1 1 1 , 1— 330 320 310 300 290 280 270 260 Wavelength, mu - 101 -Figure 33. Predominating chromophore ( <A,(3 -unsaturated lactone) i n the BHC molecule. quantities of BHC but varying amount of HSA and PVP were prepared and absorbance values were determined at 304 mu. The depressions in absorbance values, plotted as a function of macromolecule concentration, are illustrated in Figures 34 and 35. Beyond a certain macromolecule concentration, there i s no further depression, which implies that a l l BHC molecules are in the bound form. Molar absorptivity values of bound BHC were estimated from the known per cent depression of absorbance readings. The results are summarized in Table 3. The £ f and € b values represent molar absorptivities for the free and bound species, respectively. The per cent depression i s equal to oL value in Eq. 38. In Figure 36, absorbance depression at a constant macro-molecule concentration was plotted as a function of BHC concen-tration. Most of the results illustrated are from the experiments used to produce the plots in Figures 34 and 35. A linear relation-ship was observed between the difference in absorbance in the absence and presence of macromolecule and the observed absorbance. From this, i t i s possible to obtain information which can be used — 102 — Figure 34. Absorbance depression of BHC as a function of HSA concentration. BHC concentra-tions are 26.7 (a), 23.7 (b), 15.4 (c), and 9.1 (d) xlO" 6 mole/L. .06 .08 .10 % HSA A - 103 -Figure 35. Absorbance depression of BHC as a function of PVP concentration. BHC concentrations are 26.5 (a) and 16.9 (b) xlO" 6 mole/L. (a) (b) -+— -5 .2 • 3 .4 % PVP .6 .7 .8 - 104 -i n the law of mass action. From Eq. 37 to 40, (D f) and r values can be estimated. The c a l c u l a t i o n procedure i s i l l u s t r a t e d i n Table 4, when PVP concentration i s equal to 0.02$ ( i . e . , 5 x l 0 - 6 mole/L.). Experiment € f(D t) *b<V $ Depression Average HSA-BHC (a) (b) (O (d) .499 .442 .288 .170 .443 .402 .256 .155 88.8 90.0 88.9 91.1 89.9 PVP-BHC (a) (b) .493 .315 .400 .252 81.1 80.0 80.5 Table 3. Estimate of Molar Absorptivity Ratio of Bound BHC to Free BHC. € f(D t) A304 irai Observed AA (D b) (D f) r .0985 .0895 .009 5.28 2.47 2.81 0.494 .197 .180 .017 10.56 4.67 5.89 0.934 .246 .224 .022 13.18 6.04 7.14 1.21 .315 .284 .031 16.88 8.52 8.36 1.70 .394 .355 .039 21.11 10.72 10.39 2.14 .493 .445 .048 26.41 13.19 13.22 2.64 .616 .553 .063 33.00 17.31 15.69 3.46 Table 4. Analysis of Spectrophotometrie Data for PVP-BHC Interaction i n 0.02$ PVP (5 umole/L.). Absorbance observed i s average of a pair of separate measurements on sample solutions separately prepared. The concentration terms are i n jimole/L. C^ , = 0.805 €f = 0.805 x 18,660 (see Table 3). Figure 36 was also used to correct for the presence of macromolecule i n BHC analyses. For example, i f a BHC soluti o n i n 0.02$ PVP has an absorbance value of 0.400, the correcti o n factor (0.043, read d i r e c t l y from the ordinate i n Figure 36) i s added, and the new value i s divided by 6^ to y i e l d the molar concentration of BHC i n the sol u t i o n . - 105 -Figure 36. Absorbance differences for BHC solutions in the absence and presence of constant amounts of macro-molecules as a function of total BHC concentration. Closed symbols: HSA-BHC; open symbols: PVP-BHC. Macro-molecule concentrations are: squares, 0.004$; triangles, 0.01$; circles, 0.02$. Absorbance Observed 5. Dynamic Dialysis The results of the dynamic dialysis experiments are illustrated in Figures 37 and 38. On the basis of molecular weights of 75,000 and 450,000, the systems contained 53.3 and 8.89 micromoles dextran and HES per l i t e r of Tris buffer, respectively. In studies of the PVP-BHC interaction, two different PVP concentrations (50 and 100 jimole/L.) were used. In the absence of macromolecule, dialysis of BHC follows Fick's law of f i r s t order kinetics. This i s indicated by the straight line obtained when log concentration i s plotted versus time. The interactions of BHC with dextran and HES appear to be weak. On the other hand, the dialysis rate of BHC in the presence of PVP i s significantly different from that observed in the absence of the macromolecule. Quantitative analysis of this data can be carried out by ut i l i z i n g Eq. 21 and Eq. 53 given below. Dialysis rate i s pro-portional to the concentration of free BHC inside the dialysis bag. d(D t) - = k d (D.) (Eq. 53) dt 1 The concentration of unbound (i.e., free) BHC in the macromolecule compartment at any total BHC concentration can be calculated from Eq. 53. The k^ value i s obtained from the slope of the semilog plot of (D.J.) versus time in the absence of macromolecule. The instantaneous rate at a value of (D^) in the presence of macro-molecule can be estimated from a plot of (Dt) versus time on linear graph paper. - 107 -Figure 37. Loss of free BHC from inside a dialysis bag in the absence (O) and presence of 0.4$ HES ( • ) and dextran (A) i n Tris buffer (pH, 7.4; ionic strength, 0.15) at 30°C. j 150.-•* +-— — • — » 1 1 1 1 1 0 1 2 3 4 Hours (c) Figure 38. Loss of free BHC from inside a dialysis bag in the absence (d) and presence of 0.4$ (a and c) and 0.2$ (b) PVP in Tris buffer (pH, 7.4; ionic strength, 0.15) at 30°C. Hours t-—*—t—t—t—r 10 11 - 109 -The first-order rate constant (k d), which characterizes the diffusion process and incorporates the area and thickness of the membrane, was found to be 5.71 x 10"3 Cm.2/min. Calculations of (Df) and r values for the experiment (b) i n Figure 38 are illustrated in Table 5. The i n i t i a l BHC concen-tration was 828x10"6 mole/L. and PVP concentration was 0.2$ (i.e., 50xl0~ 6 mole/L.). The second colume shows BHC concen-trations at a given time in the PVP-free compartment which contains 500 ml. of Tris buffer. These values were converted to amount terms and subtracted from the total amount of drug in the PVP compartment which contains 50 ml. of PVP-BHC solution. The amount of BHC remaining inside the bag was re-converted to a concentration term and this value i s shown in column three. The fourth column i s the slope of a tangent line at a given time obtained from a plot of (D+) versus time. Time (Hour) (C) (Dt) k d(D f) (Df) (Db> r 0 0 828 —. 1 4.7 781 .756 132 649 13.0 2 8.8 735 .631 111 624 12.5 3 11.5 700 .578 101 599 12.0 4 13.6 667 .554 97 570 11.4 5 15.5 635 .475 83 • 2 552 11.0 6 16.6 608 .460 80.5 527 10.5 7 17.4 583 .413 72.5 510 10.2 8 18.2 558 .387 67.8 490 9.8 9 18.4 537 .363 63.5 473 9.5 10 18.8 515 .350 61.3 454 9.1 Table 5. Calculated Data for the Dynamic Dialysis of BHC i n the Presence of PVP. The concentration terms are in jimole/L. PVP concentration was 50 umole/L. See the text for more detail. - 110 -A single dynamic dislysis experiment would f a i l to cover a wide range of r values or (Df) (especially when the binding a f f i n i t y is remarkably high as in the case of PVP-BHC interaction). It i s , therefore, necessary to repeat the procedure several times with different experimental conditions (e.g., use of much lower macromolecule concentration) in order to obtain data covering a wider range of r values or (D f). For example, the results illustrated in curves (a) to (c) in Figure 38 cover a (Df) range from 36.8 to 68.9, from 61.3 to 132.0, and from 6.3 to 14.7 umole/L., respectively. In terms of r value, they are from 7.4 to 8.8, from 9.1 to 13.0 (see Table 5), and from 1.19 to 1.22. These ranges could be extended by dialyzing for longer periods of time but analytical errors w i l l increasev' with time and result in unreliable data. These d i f f i -culties are mentioned by Stein (1965) but not by Meyer and Guttman (1968b; 1970a; 1970b). For this reason, the experimental design (i.e., volume ratio of the two compartments, concentration of drug and macro-molecule, size of sample, duration of dialysis, etc.) i s c r i t i c a l when this technique i s used to study completely unknown drug-macromolecule interactions. However, this method can be effi c i e n t l y used for a study of well known binding systems such as albumin-dye complexations (Meyer and Guttman, 1970b). Data obtained for HES-BHC and dextran-BHC interactions failed to cover a wide range enough (Df) range to permit an evaluation of the mechanism of the interaction. Because of this, the data obtained for these macromolecules i s not reported here. - I l l -Dynamic dialysis experiments confirm the reversibility of binding of BHC with the macromolecules investigated. Continuous dialysis appeared to remove a portion of the BHC which had been bound to the macromolecule within the dialysis bag. For example, in 0.2$ PVP solution, solubility data indicates that approxi-mately 84$ of the total BHC exists in the bound form (see Figure 29). This value i s not necessarily equal to that in the i n i t i a l stages of the dynamic dialysis experiment (b) in Figure 38 because extent of binding depends on BHC concentration. However, i f i t i s assumed that they are approximately equal,* then 133 (i.e., 828-828x0.84) umole/L. exists in the unbound form at time zero. After ten hours of continuous dialysis, the BHC concentration inside the bag was reduced to 515 umole/L. (see Table 5). This means that 313 umole/L. have been removed from the bag in this period of time. This, of course, i s much greater than the value of 133 umole/L. and indicates dissociation of the PVP-BHC complex during the experiment. * This assumption seems to be valid, since the PVP solution for the dynamic dialysis experiment (b) was nearly saturated with BHC (see p. 63). 6. Equilibrium Dialysis (a) Binding of BHC to Cellophane Membrane. One of the main sources of error in the dialysis method i s the irregular adsorption of small molecules by the membrane (see pp. 30-32). It was necessary, therefore, to correct for this binding on an experimental basis.* Extent of binding of BHC to membrane (and also possibly to the plexiglas c e l l ) was studied at three different temperatures. Results are shown in Figure 39. No significant differences in binding were observed at the three temperatures. Although the same procedure for membrane preparation was used throughout the study, the extent of binding varied. However, on the basis of a l l the data, a correction factor of four per cent of the total BHC was used throughout this investigation. (b) Permeability of Membrane to PVP. Hengstenberg and Schucht (1952) reported that the permeability of PVP molecule through the membrane can be neglected only i f i t s molecular weight i s greater than 10,000. However, Spitzer and McDonald (1956) found that some PVP molecules cross the membrane even i f the molecular weight i s higher than 40,000. By using differential titration, they confirmed that the dialyzable PVP i s titratable species which i s either a sub-fraction of the PVP or an impurity (or impurities) arisen during synthesis of the polymer. * When the concentration of small molecules i s analyzed on both compartments, the correction for membrane binding i s unnecessary. However in this work only macromolecule-free compartment was analyzed for BHC concentration. - 113 -Figure 39. Estimate of the extent of adsorption of BHC to the cellophane membrane at three different temperatures: 10 ( A ) , 20 (•), and 40 (• ) C. - 114 -Although the PVP used in this investigation was purified by extraction with anhydrous ether, experiments were carried out to determine i f the polymer passed through the membrane. Analysis of the PVP-free compartment was carried out spectrophotometrically using the iodine-PVP reaction. A calibration curve i s shown in Figure 40. When 20 ml. of a 0.4$ PVP solution was added to one of the compartments and dialyzed for 40 hours against Tris buffer, approximately 10 mg./L. PVP was detected in the PVP-free compart-ment. This implies that approximately 0.25$ of the total amount of PVP used can pass through the membrane. This value i s so small that i t can be neglected. (c) Donnan Effect. In equilibrium dialysis, an appropriate ionic strngth must be maintained in order to prevent Donnan equilibrium across the membrane (see p. 30). The alternative i s to use low macromolecule concentrations. HSA has a net negative charge of 18 at pH 7.4 (White and others, 1968). The ionic strength in the Tris buffer used i s 0.15 and the highest HSA concentration used in the investigation was 0.4$ (5.8 x 10~5 mole/L.). When these values are substituted into Eq. 42, the distribution ratio of univalent anions across the membrane (R value in Eq. 42) i s equal to 1.0035. It i s possible, therefore, to neglect the abnormal distribution of BHC anion due to the Donnan effect. PVP has no el e c t r i c a l charge at pH 7.4 (May and others, 1954). The Donnan effect can, therefore, be neglected.* * PVP w i l l also behave as a polyelectrolyte after binding with the BHC anion. However this characteristic w i l l not be remarkable i n a solution of high ionic strength (see Frank and others, 1957, for example). - 115 -Figure 40. Colorimetric determination of PVP. mg. PVP / L. - 116 -(d) Free Drug Concentration and Volume Ratio. In order to study binding mechanisms, i t i s necessary to cover a wide range of (Df) or r values. Pollansch and Briggs (1954) claimed that maximum efficiency i s obtained by assigning appropriate volume ratios to the macromolecule to macromolecule-free compartments. Furthermore, the total amount of BHC that can be handled under given conditions can be enhanced by dialyzing BHC solutions against macromolecule solutions which have been nearly saturated with BHC. Yang and Foster (1953) used this approach in their binding studies (see pp. 31-32). Typical design and results of a dialysis experiment are shown in Tables 6 and 7. Calculations can be carried out on the basis of either concentration or amount term. If 1:1 volume ratio i s used, i t i s more convenient to use concentration term. However, in this investigation at least one of the dialysis c e l l s had a 2:1 volume ratio. It i s , therefore, more convenient to use amount term.* The corrected total amount of BHC (D^ . in the f i f t h column of the tables) i s obtained by multiplying D^, the un-corrected i n i t i a l amount of BHC, by 0.96, the correction factor for membrane binding. The BHC content of the macromolecule-free compartment i s determined spectrophotometrieally and converted to the amount present in either 20 or 40 ml. The i n i t i a l BHC concen-tration in the macromolecule compartment was determined from the correction curves illustrated in Figure 36. * Attention must be paid to term used in the calculation procedure. In the literature, some investigators failed to convert concentration term to amount term, although they used volume ratio rather than 1:1. For example, O'Reilly and Kowitz (1967) showed a typical miscalculation of r values. It was pointed out by Meyer and Guttman (1970b). - 117 -Designing Results No. ml.of Stock Solutions IA 40(BHC/1) 7.65 IB 20(H-B) 4.41 2A 20(BHC/1) 3.83 2B 20(H-B) 4.14 3A 20(BHC/2) 1.91 3B 20(HSA) 0 4A 20(BHC/4) 0.96 4B 20(HSA) 0 5A 20(BHC/5) 0.765 5B 20(HSA) 0 6A 40(BHC/10) 0.765 6B 20(HSA) 0 DH D.F, l304 (Df) D, D» 11.58 7.91 1.85 0.92 0.734 0.734 10 5 1 1 1 1 .241 129.1 7.75 .427 114.4 4.58 10.6 0.42 .198 .039 .031 .047 3.83 6.60 3.33 5.74 1.42 2.45 2.1 0.084 0.834 1.44 1.67 0.064 0.67 1.16 2.52 0.15 0.58 1.01 Table 6. Calculation Procedures for (Df); aridrr Value. Compartment B contains HSA. The BHC concentration of the stock solution (BHC/1) was 191.3 umole/L. Denomi-nator represents the dilution factor (D.F.) of the stock solution. HSA stock solution nearly saturated with BHC i s designated by H-B, for which the BHC con-centration i s 220.7 umole/L. HSA concentration i s 0.2$ (28.98 umole/L. = 0.58 umole/20 ml.). Temperature was maintained at 20°C. The concentration terms are in umole/L. The amount terms are in jumole. Designing Results No. ml.of Stock Solutions D± D t IA 40(BHC/1) 7.87 16.77 IB 20(P-B) 9.60 2A 40(3BHC/4) 5.90 14.88 2B 20(P-B) 9.60 3A 20(3BHC/4) 2.95 12.05 3B 20(P-B) 9.60 4A 20(BHC/2) 1.97 11.10 4B 20(P-B) 9.60 5A 20(Tris) 0 9.22 5B 20(P-B) 9.60 6A 20(3BHC/4) 2.95 2.83 6B 20(PVP) 0 D.F. A304 (Df) D f D b r 10 .243 130.0 7.80 8.97 17.94 10 .216 115.5 6.93 7.95 15.9 10 10 5 5 .206 .189 .370 .300 110.4 100.2 80.4 4.42 4.01 3.22 7.64 7.10 6.00 15.27 14.19 12.00 1 .429 23.0 0.92 1.91 3.82 Table 7. Calculation Procedures for (Df) and r Value. Compartment B contains PVP. The BHC concentration of the stock solution (BHC/1) was 196.6 umole/L. The frac-tional expression gives the dilution factor for the stock solution. PVP stock solution nearly saturated with BHC i s designated by P-B, for which the BHC concentra-tion i s 480.1 umole/L. PVP concentration i s 0.1$ (25 jimole/L. = 0.5 umole/20 ml.). Temperature was main-tained at 20°C. 7. Interpretation of Binding Data (a) Langmuir-Type Plot. The simplest way to handle binding data i s to plot r value versus (D^). The curve obtained from Eq. 17, which i s applicable only to a binding system containing a single set of binding sites, i s a segment of a rectangular hyperbola passing through the origin. If (Df) in Eq. 17 becomes inf i n i t e , the r value approaches n as a limit, r = n ( E q - 5 4 ) and a t r s n/2, (Df) - K - 1 (Eq. 55) In Eq. 55, K - 1 represnts the intrinsic 'dissociation' constant. These two equations indicates the importance of a wide range of ( D f ) values. For example, Dowd and Riggs (1965) pointed out that many investigators chose unsuitable substrate concentration ranges in studies of enzyme-substrate complexation. They discussed the significance of the Michaelis-Menton equation which i s similar to Eq. 17 or 20. Binding data for BHC to HSA and PVP i s illustrated i n Figures 41 and 42. For the ( D f ) range studied, both macromolecules failed to show saturation of binding sites. As illustrated in Figure 41, at lower BHC concentrations the drug i s more easily bound to HSA than at high concentrations. However, with PVP the curve does not change as ( D f ) increases. In other words, the ( D f ) range investigated i s too narrow to permit an evaluation - 119 -Figure 41. Plot of r values versus the concentration of free BHC for HSA-BHC binding at two temperatures; 20°C (closed symbols) and 40°C (open symbols). Values were obtained from three different HSA concentrations; 0.1$ (triangles),0.2$ (circles), and 0.4$ (squares). 7 -I 1 , \ » 1 1 1 1 1 1 1 1 1 1 < >— 0 20 40 60 80 100 120 140 160 (Df) x 10 b mole/L. - 120 -10 ( D f ) x 10 b m o l e / L . - 121 -of binding mechanisms. It was impossible, from equilibrium dialysis method, to obtain data at a higher (Df) range, even though attempts were made to saturate binding sites with BHC prior to dialysis experiments. However, solubility method can give information at high (Df). The r values calculated from, solubility data at 20°C are 6.8 for HSA-BHC and 20.2 for PVP-BHC interactions.* For PVP-BHC interaction, a further equilibrium dialysis experiment was carried out in which the PVP concentration was reduced from 0.4$ to 0.1$ to get addi-tional data at a high (Df) range. These results at 20°C and results from solubility data are shown in Figure 43. For HSA-BHC interaction, complete saturation of the binding sites was reached. The curve shows that about six or seven binding sites occur on the HSA molecule (see Eq. 54). The intrinsic association constant i s approximately 3.5 x 10 4 L./mole (see Eq. 55). However these results are valid only i f there i s a single set of binding sites for BHC (for further discussion, see p.123). In case of PVP-BHC interaction, even the data obtained from solubility method failed to show complete saturation of binding sites. It was, therefore, impossible to interprete the binding curve quantitatively. * From Figure 29, i t can be seen that up to 1$ HSA and 0.4$ PVP, the apparent solubility of BHC changes linearly with respect to macromolecule concentration. Therefore in this range of macromolecule concentrations, the r value (slope of a line) i s a constant and independent of macromolecule concentration. The r values reported was obtained in this range of macromolecule concentrations. The fact also ex-plains why data obtained from dialysis studies in which 0.1, 0.2, and 0.4$ HSA were used, produced identical bind-ing curves as shown in Figure 41. 20 j Figure 43. Binding curves at 20°C for HSA-BHC (closed symbols) and PVP-BHC (open symbols) interactions i n Tris buffer. Data obtained from solubility analysis (large open circles) are included on the curves. Data for 0.1, 0.2 and 0.4$ macromolecule are represented as triangles, c i r c l e s , and squares, 16 t respectively. 'A 12 --4-20 -»-40 -4-60 -4 80 100 120 (Df) x 106 mole/L< - 123 -(b) Scatchard Plot. The binding curves for HSA-BHC interaction illustrated in Figures 41 and 43 are replotted on the basis of Eq. 21 in Figure 44. At both 40 and 20°C, the binding data follows a curvilinear course that bends sharply near the abscissa. This indicates that more than one set of binding sites i s present in the HSA molecule. The values of n, the average number of the f i r s t set of binding sites, 2.8 at 40°C and 3.0 at 20°C, was rounded off to the nearest whole number. This rounding-off procedure has been used by Scatchard et a l . (1957). The intercepts of the curves on the ordinate, nK, are 51 x 10^ and 105 x 10^, which yield intrinsic association constants of 17 x 10^ and 35 x 10^ (L./mole) at 40 and 20°C, respectively. The association constant at 20°C i s nearly twice that at 40°C. The second set of binding sites w i l l not be considered in this discussion because the intrinsic a f f i n i t y of the BHC molecule for these sites i s far smaller than that for the f i r s t set. Binding data for the PVP-BHC interaction at various temper-atures plotted according to the Scatchard equation (Eq. 21) i s illustrated i n Figure 45. Although the data i s scattered, differ-ences in binding strength at various temperatures can be seen. Straight lines were drawn on the assumption that there are 50 identical binding sites on the PVP molecule irrespective of temperature (for further discussion, see p.126). The point marked with an arrow i s the value obtained from the solubility analysis. (c) Double Reciprocal Plot. Because of error inherent in the double reciprocal plot, i t i s preferable to use the Scatchard plot for quantitative analysis of binding whenever possible. However in the case of PVP-BHC interaction i t was d i f f i c u l t to no •-ioo 90 -80 " 70 !o 60 D 50 40 -30 •• 20 10 •• r s (Db)/(HSA) 21 20 19 Figure 45. Scatchard plot for PVP-BHC interaction at 10 (•), 20 (O), 30 ( A ) , and 40 (A) *C. Data obtained from solu-b i l i t y i s indicated by an arrow. 18 17 16 15 " 11 1 10 9 8 8 9 10 11 12 13 W 15 16 17 18 19 20 r = (Db)/(PVP) 126 -derive accurate binding parameters from the Scatchard plot. Hence a double reciprocal plot (see Eq. 20) was used, Figure 46. These curves pass through approximately the same point on the ordinate (i.e., 0.02). The reciprocal of the intercept (i.e., 50) was taken as the average number of binding sites on the PVP molecule and used in the extrapolation of the Scatchard plot (see Figure 45). Intrinsic association constant at various temperatures was calculated from the slopes of the curves. 8. Thermodynamic Analysis and Mechanism of Interaction (a) HSA-BHC Interaction. that there i s no significant temperature dependence of enthalpy change within the temperature range in which the interaction was carried out, i t i s possible to estimate the standard enthalpy change ( AH°) for the association of one mole of BHC to one mole of the binding sites of the f i r s t set on the HSA molecule. The calculation i s shown below. Standard free energy ( AG") and entropy (AS 0) changes were calculated using Eq. 35 and 36, and are reported in Table 8. Because of possible competitive role of the buffer ions during binding, the K values must be regarded as being dependent on buffer composition. With respect to the thermodynamic quantities, this implies that the standard state includes the Tris buffer i) Enthalpy, Entropy, and Free Energy Changes. Assuming (Eq. 56) - 128 -K x 10~5 AH 0 AG° AS 0 °c (L./mole) (Kcal/mole) (e.u.) 20 3.5 - 6.58 - 7.43 42.90 40 1.7 - 6.58 - 7.49 + 2.91 Table 8. Effect of Changes in Temperature on the Binding of BHC to HSA. used in the investigation. This approach to calculation i s that used by Karush (1950). The decrease in binding strength of HSA for BHC with increasing temperature i s characteristic of exothermic reaction. Similar decreases have been observed for many protein interactions with a wide variety of substances (see, for example, O'Reilly and Kowitz, 1967). The negative sign for AG° means that the binding process i s spontaneous. The AS° value, the disorder factor of thermodynamic changes, i s positive. This i s in agreement with observations for most of albumin-anion interactions. However, the magnitude of AS° i s small compared with that observed for the interaction between albumin and azo dye anions. i i ) Possibility of Ionic Interaction. At pH 7.4, the HSA molecule has a net negative charge of 18 (White and others, 1968). On the basis of the determined pKa values (see p. 84), 80 and 20$ of total BHC exists as the monoionized and di-ionized species, respectively. This does not mean that the possibility of ionic interaction between these substances can be ruled out. A net negative charge on the protein molecule merely implies an excess of negative charges over positive residues. There i s evidence in the literature to substantiate the view that cationic centers on the protein at a pH 7 are intimately involved in the binding - 129 -with anionic molecules (Klotz, 1949a). Thermodynamic changes for the HSA-BHC interaction indicate an unusually large contribution to the - AG°value by the - A H ° value. In general, anion-protein interactions have shown l i t t l e temperature dependence (Klotz and others, 1949b). A small temper-ature coefficient i s a characteristic of an interaction between oppositely charged species (Klotz and others, 1952). If the nature of the HSA-BHC interaction were largely electrostatic, i.e., i f the ionic part of the BHC molecule combined with the cationic o parts of the HSA molecule, the main source of the - AG value would be a large positive AS° value with l i t t l e contribution o from the A H factor. It i s very unlikely, therefore, that the HSA-BHC interaction i s ionic in nature. O'Reilly et a l . (1967;1969) proposed similar suggestions for the interaction between HSA and warfarin. i i i ) Possibility of Pre-Existing Binding Site. In the absence of information about attendant conformational changes, most interpretations of binding processes make the assumption that pre-existing binding sites are involved (Lovrien, 1963). On the other hand, Karush (1950) postulated that serum albumin possesses 'configurational adaptability' for a variety of small molecules. It i s clear from Karush's discussion that there i s a strong possibility that some proteins might form binding sites during the binding process. Using this hypothesis, Karush (1956; 1957) satisfactorily interpreted the differences in thermodynamic parameters usually observed in non-specific anion-albumin and specific hapten-antibody interactions. - 130 -The positive AS 0 associated with many reaction involving proteins are usually attributed to disorientation and unfolding of the protein molecule. This does not appear to be a satis-factory explanation for the HSA-BHC interaction because the enthalpy changes observed are very negative whereas a process of unfolding presumably requires the breaking of several bonds and should, therefore, result i n an endothermic reaction of appreciable magnitude (Klotz and others, 1949b). It i s , therefore, preferable to postulate that the HSA molecule may have some kind of pre-existing site for the BHC molecule. This site may be more or less r i g i d as the binding sites of antibody for haptens. Thermodynamic data obtained for the HSA-BHC interaction i s compared, in Table 9, with that obtained by Karush (1956) for antibody-anionic hapten binding. K x 10~ 5 AH* AG° AS° °c (L./mole) (Kcal/mole) (e ,u.) 7.1 4.4 - 6.7 -(7.1 - 7.3) -(7.24 - 7.48) + (0.3 - 0 .7) 25 2.1 - 3.1 -(7.1 - 7.3) -(7.25 - 7.50) + (0.3 - 0 .7) Table 9. Thermodynamic data for the binding of D-phenyl-(p-azobenzoylamino)-acetate by purified antibody specific for the compound, in 0.02M phosphate buffer of pH 7.4 containing 0.15M NaCl (from Karush, 1956). Free energy changes, for both interactions, are of the same magnitude. In the specific binding between antibody and haptens, the free energy change i s due almost entirely to the enthalpy. The contribution of the entropy term i s negligible. - 131 -iv) Nature of Binding Site and Effect of Binding on  Water Structure. The BHC combining region on the HSA molecule probably consists of an inter-helical cavity whose van der Waals contour i s closely complementary to, and therefore selective for the BHC molecule. In this respect, the interaction may be considered specific, and i s explained by a large contribution of enthalpy to free energy changes and by a relatively sharp change in slope of the binding curves near the abscissa (see Figure 44). The change in slope i s similar at both 20 and 40°C which implies that there i s no significant change in the average number of binding sites at the two temperatures. Presumably the cavity i s not completely r i g i d , as in case of an antibody for haptens, and cannot resist the disruptive tendencies of intra-molecular electrostatic repulsions to which the protein i s subjected at extreme values of pH, e.g., a pH value of 3. Therefore, as Nagashima and others (1968a) have observed, the HSA-BHC interaction would be much less at pH ranges where N to F conversion of the protein takes place (see p. 42). The cavity can, therefore, be easily disrupted by expansion of the albumin molecule. The HSA-BHC binding involves a transfer of a hydrophobic molecule from an aqueous environment to a region with a lower dielectric constant. After binding occurs, a hypothetical hole, previously occupied by the BHC molecule, remains and this w i l l then be f i l l e d with an equal volume of hydrogen-bonded water molecules (Karush, 1956). The number of hydrogen bonds formed in this way w i l l exceed the number of hydrogen bonds which - 132 -the free BHC molecule previously formed with i t s neighboring water molecule.* On the basis of this explanation, complex formation would be exothermic and should be associated with a substantial decrease in the enthalpy of the system, which w i l l exceed the endothermic nature of the heat of fusion of icebergs around the BHC and HSA molecules. The melting of iceberg-structured water around BHC and HSA molecules w i l l result in an increase in randomness (i.e., positive AS 0). The BHC molecule w i l l lose rotational and transitional degrees of freedom after binding to yield a higher ordering (i.e., negative AS°). Formation of a bonded-water cluster at the hypothetical hole l e f t by the BHC molecule w i l l give an ordering effect (Nemethy and Scheraga, 1962a). The two disordering effects mentioned f i r s t probably exceed the last two ordering effects and the result i s a net entropy change of + 2.9. In more specific interactions (such as antibody-hapten interactions), the loss of degrees of freedom would be highly significant and could result in a net negative change (Karush, 1957). (b) PVP-BHC Interaction. i ) Enthalpy, Entropy, and Free Energy Changes. Intrinsic association constants are shown in Figure 47, a van't Hoff type plot, as a function of temperature. The enthalpy change appears to be temperature dependent. A similar temperature dependence has been observed in other studies (see, for example, Hymes and others, 1969). From the slope of a tangent line at a given temperature the standard enthalpy change was estimated. Thermody-namic parameters were calculated by u t i l i z i n g Eq. 35 and 36. * From low aqueous solubility of BHC, i t was assumed that BHC molecule has l i t t l e hydrogen bonds with neighboring water molecules (see p. 85). - 133 -Figure 47. Van't Hoff plot (log K versus 1/T) for the PVP-BHC interaction. - 134 -Results are listed in Table 10. If the concentration used in calculating the association constant are expressed in moles per l i t e r , A S 0 i s the entropy change when one mole of BHC and one mole of a binding site on a PVP molecule, each at a concen-tration of one mole per l i t e r , react to give one mole of the complex, again at concentration of one mole per l i t e r . If differ-ent concentration units are used, A S 0 w i l l have a different value. It i s desirable to eliminate this rather arbitrary factor before trying to interpret the magnitude of AS 0 in terms of the molecular structures present in the solution. If we assume that the A S ° values listed in Table 10 are determined from measurements at sufficiently high dilution, the so-called 'unitary (or contact)' entropy change ( /_u) for the reaction can be calculated from Eq. 57 (Gurney, 1953; Kauzmann, 1959). ASu » _S° + 7.98 (Eq. 57) The unitary entropy change depends, therefore, only on those factors which involve the interaction of the BHC molecule and the binding site on a PVP molecule with the solvent and with each other and not on the contribution due to randomness of the mixing with the solvent. The 'cratic' term (7.98 e.u.) originates from the expression, - R In (1/55.6), where 55.6 (mole/L.) i s the concentration of water in a highly diluted aqueous solution. This term takes into account the reduction in number of independent solute species by one on the combina-tion of a BHC molecule with a PVP molecule (Molyneux and Frank, 1961a). In order to compare this data with that for the inter-- 135 -actions between PVP and a variety of organic substances (Molyneux and Frank, 1961a), the unitary values for PVP-BHC interaction are also listed in Table 10. °c K x 10"2 (L./mole) (Kca AG° 1/mole) AS° (e .u ASu .) 10 3.64 -2.74 -3.32 + 2.05 +10.03 20 3.05 -2.96 -3.33 + 1.28 + 9.26 30 2.48 -4.69 -3.32 -4.53 + 3.45 40 1.72 -8.57 -3.20 -17.14 - 9.16 Table 10. Thermodynamic functions for the binding of one mole of BHC by one mole of vacant binding site on PVP. i i ) Analysis of Enthalpy of Binding. Emphasizing the 'iceberg' concept of water structure (Frank and Evans, 1945) around the BHC and PVP molecules, i t i s possible to divide the binding enthalpy into the following five contributions (Molyneux and Frank, 1961a). The corresponding binding processes are schematically illustrated in Figure 48. (1) Heat i s needed to break (or bend) hydrogen bonds in the icebergs neighboring the polymer and BHC molecules. (2) Enthalpy w i l l also have to be provided to overcome any specific interactions (e.g., true hydration) between the water and PVP and between the water and BHC. (3) The actual binding process between the 'dehydrated' entities w i l l be exothermic. (4) The interaction between the complex formed and the neighboring water (i.e., reformation of true hydration) w i l l be exothermic. (5) Enthalpy w i l l , finally, also be gained by the reforming of hydrogen bonds in the ice-bergs associated with the complex. - 136 -(1) AH^ (+) AHg (+) V (2) (3) A H 3 (-) AH 4 (-) (4) (5) AH 5 (-) Figure 48. Schematic i l l u s t r a t i o n of the binding processes between BHC and PVP molecules. Small cir c l e s represent a hydrogen bonded water cluster indicating the formation of a partial cage around a solute. - 137 -The net enthalpy change associated with the purely hypothe-t i c a l binding processes illustrated in steps two to four in Figure 48 was reported to be essentially a constant (-5 Kcal/mole) for interactions of PVP with a variety of substances (Molyneux and Frank, 1961a). If this value i s applied to the data herein, the net enthalpy changes associated with the f i r s t and f i f t h steps would be approximately +2.3, +2.0, +0.3, and -3.6 Kcal/mole at 10, 20, 30, and 40°C, respectively. Total changes are shown in Table 10. As temperature increases, the enthalpy change decreases to a negative value at 408C. The mole fractions of various water species in the f i r s t layer around an aromatic hydrocarbon were estimated as a function of temperature by Nemethy and Scheraga (1962b) on the basis of their theory of water structure (Nemethy and Scheraga, 1962a). For example, the fraction of unbroken hydrogen bonds changes from 59.3$ at 10°C to 49.0$ at 40°C. On this basis, the decreasing tendency of the enthalpy changes, associated with the f i r s t and f i f t h binding processes, with increasing temperature can be easily explained. At a given temperature, the absolute value of the enthalpy change associated with the breaking hydrogen bonds in the icebergs around the solutes, H^-p w i l l exceed that for the formation of hydrogen bonds in the icebergs around the complex, ^Hg, since the number of hydrogen bonds around the solutes before binding would exceed the number of hydrogen bonds around the complex. However, the difference becomes less impor-tant as temperature increases. The value approaches zero and f i n a l l y becomes negative at 40°C. - 138 -i i i ) Possibility of Hydrophobic Bonding. The so-called 'iceberg' concept (Frank and Evans, 1945) assumes that hydrocarbon groups, such as those present both in the polymer and in the BHC molecules, are surrounded in aqueous solution with one or more layers of water molecules which are more highly ordered than the molecules in ordinary liquid water. Entropy gains in protein (Klotz, 1958; Kauzmann, 1959; Nemethy and Scheraga, 1962c; Nemethy and others, 1963; Cecil, 1967; Hymes and others, 1969) and PVP (Molyneux and Frank, 1961a; Bahal and Kostenbauder, 1964; Eide and Speiser, 1967a) interactions with a variety of small molecules or ions have been attributed to increased disorderness of the iceberg structure due to complex formation. The positive unitary entropy change observed over the room temperature range (see Table 10) can be explained in a manner similar to that above. It i s postulated, therefore, that the PVP-BHC complex i s accompanied by either a less ordered iceberg or by an iceberg containing a smaller number of water molecules as compared with the iceberg of the two separate entities. The release of water molecules from the ordered structure should produce a proportional gain in entropy. The free energy change associated with PVP-BHC interaction shows no significant temperature dependence. The contribution to the free energy of entropy term becomes more important as temperature increases from 17.5$ at 10°C to 38.5$ at 40°C. A similar trend has been observed for the formation of a typical hydrophobic bond between leucine and isoleucine (Nemethy and Scheraga, 1962c) although, in the case, the magnitude of i t s contribution i s approximately - 139 -eighty per cent. At a high temperature (e.g., 40°C), hydrophobic bonding seems to play a lesser role in the PVP-BHC interaction. The exothermic reaction here i s enhanced by temperature whereas the formation of hydrophobic bonds i s essentially endothermic in nature (Nemethy and others, 1963). This inference i s also supported by the decrease in the favorable entropy change with increase in temperature. iv) Nature of the Intermolecular Forces and of the  Binding Site. The PVP molecule has no ionizable groups (May and others, 1954) and i t i s , therefore, unlikely that electrostatic interactions would play an important role in i t s binding with BHC anion. The high temperature dependence of binding strength also rules out the possibility of significant electrostatic interactions (see p. 129). However, the lactam bond in the pyrrolidone ring represents a dipole, which is likely to under-go ion-dipole interaction with BHC anion. It w i l l aid the binding of the anion in such a way as to supply the necessary attraction force to bring the two components into close contact (Frank and others, 1957). After the close contact of the two entities by ion-dipole force, which varies with the inverse f i f t h power of the distance, van der Waals forces* w i l l stabilize the complex. The photograph in Figure 49 shows a molecular model of a PVP chain segment with eight repeating units and i s similar to that proposed by Frank et a l . (1957). To avoid unnecessary complications, a l l hydrogen atoms are omitted. Pyrrolidone * The term 'van der Waals forces' i s often used without explanation. In this context, the dipolar forces of Keesom (dipole-dipole), Debye (dipole-induced dipole), and London (induced dipole-induced dipole) are called van der Waals forces. The forces vary inversely with the seventh power of the distance (Martin, 1968a). - 140 -Figure 49. Molecular model of PVP chain segment with eight monomer units. Black, blue, and red colours represent carbon, nitrogen, and oxygen atoms, respectively. rings appear to make a channel-type of cavity in both sides of the paraffin backbone which i s apparently accessable for complexation with BHC. A PVP molecule of molecular weight, 40,000, has approximately 360 monomer units, since the molecular weight of the latter i s about 111. The binding data shown in Figure 46 indicates an average number of binding sites on a PVP molecule of approximately 50, irrespective of temperature. This implies that on the average, 7.2 repeating units provide a binding site for BHC molecule. As shown in Figure 50, a BHC molecule f i t s quite well on approximately eight pyrrolidone rings. As pointed out earlier (p. 85), a monoionized BHC molecule is expected to have less rotational degrees of freedom around the methylene bridge than a fully ionized molecule. A model - 141 -Figure 50. Proposed Configuration of PVP-BHC complex. of the PVP-BHC complex indicated that a better f i t of monoionized BHC molecule may require a slight bending, or folding, of the PVP molecule toward the BHC anion. However, no such requirement i s necessary in case of binding of the di-ionized BHC species, since the high degrees of freedom would allow the anion to have a suitable form for f i t t i n g to PVP. The possibility of binding of another BHC anion on the other side of the PVP molecule (below the plane of the paper in Figure 50) can be ruled out by an expected repulsive forces between BHC anion bound to the polymer and an oncoming BHC anion. 9. Viscometry Any changes in hydrodynamic volume as a result of confi-guration 1 changes in the macromolecule during the binding process should alter the reduced viscosity. The reduced viscosity was calculated using Eq. 43 to 45 in the presence and absence of BHC. The BHC concentration was 185 mg./L. (550 x IO - 6 mole/L.). Results of the density measurements for PVP solution necessary for the calculation of reduced viscosity are shown in Figure 51. Table 11 shows the calculation procedure for specific and reduced viscosities from measurements of flow time and density. In Figure 52, the reduced viscosity was plotted against PVP concentration. Slopes and intercepts were calculated using the method of least squares. Table 12 shows slope and intercept (i.e., intrinsic viscosity) values for each line. The correlation coefficient, Rc, was calculated between the two variables, reduced viscosity and PVP concentration. From the slope, the Huggins constant, KH, was also estimated (Eq. 47). $PVP AxlO 5 ? (Gm./ml.) t (sec.) °1 ^sp ^sp/C 4.0 2.72 1.0184 1274.6 .03531 1.5312 38.28 3.0 2.71 1.0161 1034.7 .02849 1.0423 34.74 2.0 2.64 1.0138 847.9 .02269 .6265 31.33 1.5 2.48 1.0127 804.6 .02021 .4487 29.91 1.0 2.47 1.0115 716.3 .01790 .2832 28.32 0.4 2.46 1.0102 620.8 .01543 .1061 26.53 0 2.42 1.0092 571.3 .01395 0 -Table 11(a). Calculation procedure for estimating specific and reduced viscosities of PVP solution at 10°C i n the absence of BHC. See pp. 33-37 for definition of terms used. - 143 -1.020 1.002 1.000 - 144 -$PVP AxlO 5 ? (Gm./ml.) t (sec.) °7 sp *?sP/C 4.0 2.72 1.0184 1260.9 .03493 1.5220 38.05 2.0 2.71 1.0183 820.9 .02255 .6282 31.41 1.5 2.64 1.0127 747.9 .02000 .4440 29.60 1.0 2.48 1.0115 705.5 .01770 .2780 27.80 0.4 2.47 1.0102 611.3 .01525 .1011 25.28 0 2.42 1.0092 . 566.9 .01385 0 -Table 11(b). Calculation procedure for estimating specific and reduced viscosities of PVP solution at 10°C in the presence of 550 umole/L. BHC. See pp. 33-37 for definition of terms used. °c In the Absence of BHC In the Presence of BHC (550 umole/L.) V Slope KH Rc Slope KH Rc 10 339.0 .55 24.81 1.048 343.5 .58 24.32 .980 .98 20 305.1 .56 23.35 1.004 330.3 .65 22.54 1.001 .97 30 271.2 .54 22.38 1.003 303.8 .67 21.28 .995 .95 40 248.6 .55 21.22 .991 290.6 .73 20.02 1.015 .94 Table 12. Influence of BHC binding on the rheological properties of PVP at various temperatures. Intrinsic viscosity ( t°73 ) units are ml./Gm. Rc i s the correla-tion coefficient. V i s the intrinsic viscosity ratio (Eq. 58). See pp. 33-37 for definition of other terms. In the absence of BHC, the intrinsic viscosity of PVP decreases with increase in temperature (Table 12). The same temperature effect was reported by Goldfarb and Rodriguez (1968). This finding may be interpreted in terms of a progressive coiling of the polymer with an increase in temperature.* It may be postulated that the van der Waals contour of the binding site i s changed by the configurational change in an unfavorable way for BHC binding which results in lower binding a f f i n i t y at higher temperature. * Miller and Hamm (1953) found that the diffusion coefficient of PVP i s higher at 5°C than at 21.4°C. From this they pos-tulated that the PVP molecule i s more tightly coiled at the lower temperature. In this respect, our data and that obtained by Goldfarb et a l . (1968) contradict that of Miller et a l . The Fikentscher's Kp- value was 30 in each case. 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 - 145 -Figure 52. Reduced viscosity of PVP as a function of PVP concentration at various temper-atures; 10 (circles), 20 (squares), 30 (triangles), and 40 (hexagons) °C. Solid and dotted lines repre-sent the viscosities in the presence and absence of BHC (550 umole/L.), respectively. .5 1.0 1.5 2.0 % PVP 2.5 3.0 3.5 4.0 - 146 -At a l l temperatures studied, binding of BHC i s accompanied by a slight but significant decrease in intrinsic viscosity. The shrinking of the polymer c o i l , indicated by the reduction in intrinsic viscosity, supports the postulate previously made (see p. 141). Molyneux and Frank (1961b) employed the 'intrinsic viscosity ratio' (V), defined in Eq.58, as a direct indication of the effect of cosolute on the size of the polymer molecule in solution. C1?) i n the Presence of Cosolute V = (Eq. 58) (*]) in the Absence of Cosolute The ratio for BHC-PVP binding at 30°C (see Table 12) i s in the same order as that for the interactions of sodium hydrogen phthalate and sodium-p-hydroxy benzoate with PVP studied by Molyneux and Frank (1961b). In solutions of high ionic strength, expansion due to the coulombic repulsion between the BHC anions bound to the polymer c o i l i s believed to be greatly reduced by the 'screening' effect of the free counterions, Tris of RH^4-form, within the Tris buffer solution encompassed by the polymer molecule. In other words, van der Waals forces stabilizing the PVP-BHC complex probably exceed repulsive forces and hence a slight degree of coiling can be maintained. Molyneux and Frank (1961b) also observed shrinking of the polymer c o i l in the presence of nonionic cosolutes such as phthalic acid and benzoic acid. The bulky nonionic part of BHC molecule may also have such an effect and cooperate to the shrinking of PVP. - 147 -Changes in intrinsic viscosity caused by the cosolute are generally not a linear function of the concentration of the latter (Eliassaf and others, 1960). In the present study, measurements were made at only one BHC concentration, a concentration which i s near the solubility limit. Therefore, the changes measured only serve to ascertain the existence of an effect at that concentration and the general nature of this effect. As shown in the last column in Table 12, the extent of c o i l -ing of PVP due to complexation with BHC becomes greater as the temperature increases. The variation of intrinsic viscosity with temperature i s more clearly demonstrated in Figure 53, i n which Eq. 59 analogous to the Arrhenius equation of kinetics (Martin, 1968c) i s used to i l l u s t r a t e the data. «9 - A e E v / R T (Eq. 59) A i s a constant and depends on the solution being studied. Ev i s the 'activation energy' required to i n i t i a t e flow of the solution. As shown in Figure 53, the data obtained f i t s the equation well. From the slope, the activation energy was calculated to be 0.92 and 1.13 Kcal/mole in the absence and presence of BHC, respectively. The Huggins constant i s some function of the solute-solvent interaction (Huggins, 1942; Yang, 1961). As the temperature increa-ses, the parameter for the polymer in the presence of BHC anion shows a gradual but significant deviation from the average value of 0.55 for the polymer in the absence of BHC. No attempt has been made to interpret these findings, since the deviations are, i n general too irregular for them to be correlated with any definite molecular effect (Molyneux and Frank, 1961b). - 148 -26 3.1 3.2 3.3 3.4 3-5 3.6 1 3 - ^ r x i o 5 Figure 53. E f f e c t of temperature on the i n t r i n s i c v i s c o s i t i e s of PVP i n the pre-sence and absence of BHC. Symbols have same meanings as those i n Figure 52. 10. Comparison of Methods Used to Evaluate Binding In the present work, five different methods have been used to investigate the mechanism of binding of BHC to various macro-molecules; spectrophotometric, dynamic and equilibrium dialyses, solubility, and viscometric methods. The f i r s t four methods are based on the analysis of changes in properties of BHC due to complex formation. Viscometry measures changes in properties occurring in the macromolecule. The data from the spectrophotometric method i s , in general, of doubtful value. The main d i f f i c u l t y i s estimation of absorpti-vity value of bound drug (Klotz, 1953a). As shown in Table 3, the per cent depression of BHC absorbance i s reproducible in the presence of excess amount of macromolecules. However, i t can be expected that bound BHC w i l l have different molar absorptivity values i f binding sites on a macromolecule shows heterogeneity (e.g., HSA) because the actual binding environment w i l l be different from one set of sites to another set of sites. Figure 54 compares the spectrophotometric data with that obtained from the equilibrium dialysis method for the HSA-BHC interaction. A l l points are from the absorbance depression measured in 0.04$ HSA (see Figure 34 for data and Table 4 for calculation procedure). Different values are assigned for molar absorptivity of bound drug. It i s surprising to note that the largest deviations occur when the experimentally determined absorptivity value (closed c i r c l e s in Figure 54) i s used. - 150 -' • ~ • 3.2 • « 3.0 • 2.8 • 2.6 • 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 (Df) x 10 6 mole/L. Figure 54. Comparison of binding data obtained from spectrophotometric analysis (closed symbols) with those from the equilibrium dialysis method (open circles) for the HSA-BHC interaction at 20°C. Various values were given to ot in Eq. 38; 0.899 (• , experi-mentally determined), 0.880 (A, arbi t r a r i l y chosen), and 0.805 (•, value for PVP-BHC interaction). See Table 3 for more detail. - 151 -Figure 55 shows the comparison for the PVP-BHC interaction. At extremely low concentration range of free drug, data from both methods agree. The agreement may be due to the fact that the PVP molecule has only one set of binding sites for BHC. However, the precision of the spectrophotometric method f a l l s off rapidly at higher concentrations of free drug and the data cannot be used by i t s e l f . Klotz (1946c) arrived at a similar conclusion. The dynamic dialysis method i s based on the fact that non-diffusible macromolecule-drug complexes are 'reversibly' formed in the macromolecule compartment and that the rate of loss of drug molecule from that compartment i s directly proportional to the free drug concentration, provided that care i s taken to ensure that 'sink' conditions are maintained for the diffusing species. The main advantage of this method i s that i t i s less tedious and time-consuming and requires fewer individual measurements to define binding behaviour. However, in order to prevent back diffusion of drug molecule into the macromolecule compartment, large amounts of buffer are required. In addition, i t i s d i f f i c u l t to obtain the experimental conditions for an unkown binding system over a wide range of free drug concentration. Numerical comparison of the data from this method under a specified condition (see p. 63) has been made already (see p. 110). Equilibrium dialysis i s one of most suitable methods for binding studies. The volume ratio of the two compartments must be appropriately assigned in order to cover a wide range of free drug concentration (or to improve precision of analysis). A dialysis c e l l which has a fixed volume (e.g., plexiglas block used by Patel and Foss, 1964) i s not completely satisfactory for the study of very insoluble compounds. - 152 -Figure 55. Comparison of binding data obtained from spectrophotometric analysis (closed symbols) with those obtained from the equilibrium dialysis method (open circles) for the PVP-BHC interaction at 20°C. Data are from absorbance depression measured in 0.02$ (•) and 0.1$ (A) PVP. - 153 -Solubility analysis has been widely used to study molecular interaction in solution. If there i s a sharp break in the solubility curve, the overall step st a b i l i t y constant can be estimated (Higu-chi and Connors, 1965; Connors and Mollica, 1966).* However, in the present work, the macromolecules studied have appreciable aqueous solubility and formed soluble complexes with BHC; the solubility curves were non-linear and failed to show a break. The r value obtained from the linear portion i s a constant (see p. 121). Hence the method gives only one point on any type of binding curve (i.e., Langmuir, Scatchard, and double reciprocal plots). For the PVP-BHC interaction, the r value was approximately 20 compared with a value of 50 obtained from equilibrium dialysis (see p. 121 and p. 126). The molecular model of the PVP-BHC complex supports the value of 50 identical binding sites per PVP molecule (see pp. 140-141). It i s apparent, therefore, that a l l the binding sites are not accessible to BHC molecules and that uptake of BHC * The overall step stability constant (k 0y) i s defined by x>v (MDn) (M)(D)n (Eq. 60) for the reaction, nD + M = MD n (Eq. 61) The right-hand side of Eq. 60 can be obtained by multiplying Eq. 14 by i t s e l f from i=l to n. Eq. 62 then shows the rela-tionship between overall step st a b i l i t y constant ( k o v ) , step st a b i l i t y constant (k_), and intrinsic association constant (K) k o v s k_.k2«kg.••-kn = K n . ^ ) . ^ ) . . . . ^ ) (Eq. 62) - 154 -interferes with the interaction at other sites. Interference due to repulsion of bound BHC anion for unbound BHC anion i s unlikely because of the screening effect of high ionic strength (see p. 146). Viscometry does not provide quantitative information about binding and i n the present study i t s applicability was limited by the low solubility of BHC. However, a configurational change in PVP was detected from measurements made at one BHC concentration. Coiling of the polymer, as a result of binding (see p. 146), i s a possible explanation of the inaccessibility of a l l binding sites to BHC molecules. VII. SUMMARY AND CONCLUSION 1. Physicochemical Properties of BHC i n Aqueous Solutions Potentiometric and spectrophotometric methods were used to determine the apparent pKa values of the weak dibasic acid, BHC. BHC i s very insoluble i n ac i d i c solutions and i t was necessary to modify the usual t i t r a t i o n approach to pKa determinations. Values obtained were 4.4 and 8.0 for pKa^ ^ and pKag, respectively. The e f f e c t of ioni c strength (chloride ion) and pH on the apparent s o l u b i l i t y of BHC was investigated. Increase i n solu-b i l i t y of BHC with increase i n chloride ion concentration was explained i n terms of water structure. The e f f e c t of pH on the BHC s o l u b i l i t y was interpreted on the basis of intramolecular hydrogen bonding. This view was supported by the infrared spectrum of the drug i n KBr d i s c . 2. Binding Studies Data obtained by u t i l i z i n g the s o l u b i l i t y analysis and dynamic d i a l y s i s methods indicated that binding strength of BHC increases i n the order dextran, HES and potato starch s o l . HSA and PVP possess much greater a f f i n i t y for BHC than the others and for these two macromolecules the mechanism of in t e r -action with BHC was investigated i n d e t a i l . The following conclusions were reached. - 156 -( a ) W i t h r e s p e c t t o b o t h H S A - B H C a n d P V P - B H C i n t e r a c t i o n s : i ) B o t h i n t e r a c t i o n s a r e e x o t h e r m i c a n d o c c u r s p o n t a n e o u s l y u n d e r t h e e x p e r i m e n t a l c o n d i t i o n s , i i ) T h e ol,/3 - u n s a t u r a t e d l a c t o n e s t r u c t u r e i n BHC i s i n v o l v e d i n t h e c o m p l e x a t i o n s . ( b ) W i t h r e s p e c t t o H S A - B H C i n t e r a c t i o n : i ) A h e t e r o g e n e i t y o f b i n d i n g s i t e s w a s o b s e r v e d . T h e a v e r a g e n u m b e r o f b i n d i n g s i t e s o f t h e f i r s t s e t w a s a p p r o x i m a t e l y t h r e e , i i ) T h e i n t r i n s i c a s s o c i a t i o n c o n s t a n t i s e q u a l t o 17 x 1 0 ^ a n d 3 5 x 1 0 ^ L . / m o l e a t 40 a n d 2 0 ° C , r e s p e c t i v e l y , i i i ) T h e b i n d i n g s i t e s a r e b e l i e v e d t o b e i n t e r - h e l i c a l c a v i t i e s w h o s e v a n d e r W a a l s c o n t o u r a p p r o x i -m a t e s , a n d i s t h u s i n a s e n s e s e l e c t i v e f o r , t h e BHC m o l e c u l e , i v ) T h e s e l e c t i v i t y o f t h e b i n d i n g s i t e s w a s s u p p o r t e d b y t h e l a r g e c o n t r i b u t i o n o f A H 0 t o t h e AG 0 v a l u e , v ) T h e m a i n b i n d i n g e n e r g y i s d e r i v e d f r o m n o n - i o n i c s o u r c e s . ( c ) W i t h r e s p e c t t o P V P - B H C i n t e r a c t i o n : i ) A P V P m o l e c u l e w i t h a m o l e c u l a r w e i g h t o f 4 0 , 0 0 0 p r o v i d e s a p p r o x i m a t e l y 50 i d e n t i c a l b i n d i n g s i t e s f o r BHC m o l e c u l e s . T h i s i m p l i e s t h a t o n e b i n d i n g s i t e c o n s i s t s o f s e v e n o r e i g h t monomer u n i t s o f P V P . i i ) T h e i n t r i n s i c a s s o c i a t i o n c o n s t a n t i s i n t h e o r d e r o f 1 0 2 L . / m o l e . i i i ) I o n - d i p o l e a n d v a n d e r W a a l s f o r c e s p l a y a n i m p o r t a n t r o l e i n t h e b i n d i n g p r o c e s s , i v ) A t l o w t e m p e r a t u r e s , t h e t h e r m o d y n a m i c d a t a i n d i c a t e s t h a t h y d r o p h o b i c b o n d f o r m a t i o n p l a y s a s i g n i f i c a n t p a r t i n t h e p r o c e s s , v ) I n t r i n s i c v i s c o s i t y d a t a i n d i c a t e s t h a t c o i l i n g o f t h e p o l y m e r t a k e s p l a c e d u r i n g t h e b i n d i n g p r o c e s s . VIII. REFERENCES Agran, A. and Elofsson, R. (1967). Acta Pharm. Suecica, 4, 281. Complex Formation Between Macromolecules and Drugs. I. Dialysis Studies of Phenols and Polyethylene Glycol. 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