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The thermodynamics of irreversible nonspecific protein adsorption at a solid-aqueous interface Liu, Susan Marisa 1997

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THE THERMODYNAMICS OF IRREVERSIBLE NONSPECIFIC PROTEIN ADSORPTION AT A SOLID-AQUEOUS INTERFACE by SUSAN MARISA LIU B.Eng., McGill University, 1993 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n THE FACULTY OF GRADUATE STUDIES Department of Chemical and Bio-Resource Engineering and The Biotechnology Laboratory We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA April 1997 © Susan Marisa Liu, 1997 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia Vancouver, Canada Date DE-6 (2/88) ABSTRACT Nonspecific adsorption of protein to interfaces is pervasive in nature and has both positive and negative consequences which are of interest to scientists and engineers. Previous studies on protein adsorption have indicated that adsorption is driven by a complex set of subprocesses rather than a single effect, and that the overall process is usually irreversible as verified by the lack of traceability between the ascending isotherm (increasing bulk protein concentration) and the descending isotherm (decreasing bulk protein concentration). These irreversible energetic effects have been neglected in current models describing protein adsorption which are entirely based on reversible thermodynamics. The objective of this thesis is to develop a thermodynamic framework describing the energies associated with nonspecific adsorption of protein to a liquid/solid interface, incorporating both the apparently reversible (quasi-equilibrium) and irreversible components of the process. To demonstrate the theory, a model system was chosen: the adsorption of hen egg-white lysozyme, to particulate silica in 50-rnM KC1 at pH 7 and 37°C. Isothermal titration calorimetry, differential scanning calorimetry and isotherm measurements are combined with our thermodynamic framework and a theory by Everett to show that two major subprocesses, restructuring of the protein upon adsorption and formation of multiple contacts between the protein and sorbent surface, are the major contributors to the irreversibility of the process. iii TABLE OF CONTENTS ABSTRACT ii TABLE OF CONTENTS iv TABLE OF FIGURES vi LIST OF TABLES ix ACKNOWLEDGEMENTS x 1. INTRODUCTION 1 1.1 Significance of protein adsorption 1 1.2 System components and their properties 9 1.2.1 Water and the hydrophobic effect 10 1.2.2 Proteins 13 1.2.2.1 Chemistry and basic structural elements 13 1.2.2.2 General properties of globular proteins 18 1.2.2.3 Globular protein stability and factors affecting it 21 1.2.3 Low molecular weight ions 25 1.2.4 Sorbent surfaces 26 1.3 Protein adsorption subprocesses 29 1.4 Complexity of the protein adsorption process 34 2. MODEL DEVELOPMENT 38 2.1 Protein adsorption isotherms and quasi-equilibrium theory 38 2.2 Interpretation of protein adsorption thermodynamics 43 2.3 Entropy 45 3. MATERIALS AND METHODS 48 3.1 Chemicals 48 3.2 Preparation of base salt solution 49 3.3 Preparation of protein solution 50 3.4 Preparation of silica 50 3.5 Cold adsorption and desorption isotherms * 53 3.6 125I-Radiolabelling of lysozyme 54 3.7 Hot adsorption and desorption isotherms 59 3.8 Isothermal titration calorimetry experiments 61 iv 3.8.1 AadsHmeasurements for lysozyme on silica 64 3.8.2 AadsCp measurements 65 3.9 DSC (lysozyme on silica) 66 3.10 DSC (lysozyme on PSS-HC) 67 4. RESULTS AND DISCUSSION 69 4.1 Selection and properties of the model system 69 4.1.1 Selection of the model system 69 4.1.2 Physico-chemical equivalence of radiolabelled and unlabelled lysozyme 71 4.1.3 Detection limit 73 4.2 Binding isotherm data 74 4.2.1 Ascending isotherm at 37°C 75 4.2.2 Temperature dependence of ascending isotherm and initial slopes 79 4.2.3 pH dependence of ascending isotherm 82 4.2.4 Descending isotherm data 84 4.3 Isothermal titration microcalorimetry and the enthalpy of adsorption 86 4.3.1 Instrument calibration and raw data 86 4.3.2 Heat of adsorption Aac&.r7 88 4.3.3 Heat capacity of adsorption Aa&Cp 95 4.4 Quantifying protein denaturation by differential scanning calorimetry 100 4.4.1 Denaturation thermodynamics for hen egg-white lysozyme in solution 101 4.4.2 Conformation of lysozyme adsorbed to silica (37°C, pH 7) 104 4.4.3 Conformation of lysozyme adsorbed to a highly charged polystyrene latex....107 4.5 Model calculations and analysis 110 4.5.1 Quasi-equilibrium Gibbs energies, enthalpies and entropies of adsorption 110 4.5.2 Compressed ball model for ascending isotherm conditions 113 4.5.3 Descending isotherms: Everett analysis and irreversible entropy production. 115 4.5.4 Quasi-equilibrium and irreversible contributions to AadsHand A^S 119 4.5.5 Descending isotherms: defining the metastable state and AadsGir 120 5. CONCLUSION 124 NOMENCLATURE 127 REFERENCES 130 V TABLE OF FIGURES Figure 1.1: Adsorption isotherm for closed-circular supercoiled pUC-18 DNA (deoxyribonucleic acid) on silica particles in 6-M perchlorate (pH 8, 37°C).5 Figure 1.2: Gibbs energy (AG), enthalpy (AH) and entropy (AS) of transfer of benzene into water. AC/> is assumed to be temperature-independent for the range given. [Adapted from Privalov and Gill, 1988.] 12 Figure 1.4: Schematic of a condensation reaction between two amino acids to form a peptide bond 15 Figure 1.5: Space-filled model of lysozyme contrasting polar residues (lighter shade) with non-polar residues (darker shade). Each diagram represents a perspective of the protein rotated at various degrees around the y-axis: a)0°, b) 90°, c) 180°, and d) 270°, respectively. [Adapted from the Brookhaven Protein Databank; Malcolm et al, 1990; Wilson et al, 1992.] 19 Figure 1.6: Space-filled model of lysozyme at pH 7 contrasting positively charged (dark shade) with negatively charged residues (medium shade). Each diagram represents a perspective of the protein rotated at various degrees around the y-axis: a) 0°, b) 90°, c) 180°, and d) 270°, respectively. [Adapted from the Brookhaven Protein Databank; Malcolm et al, 1990; Wilson et al, 1992.]20 Figure 1.7: Schematic of a Gouy-Stern model of the electric double layer. Electrostatic potential, <|>, is plotted against distance from the sorbent surface, x. An explanation of the symbols is given in the text. [Adapted from Haynes and Norde, 1994.] 28 Figure 1.8: Adsorption isotherm at pH 7.0 and 25°C for hen egg-white lysozyme on negatively charged polystyrene latex in 50-mM KC1 solution. [Adapted from Haynes et al, 1994.] 35 Figure 2.1: Adsorption isotherm for bovine serum albumin on silica. [Adapted from Haynes and Norde, 1995.] 39 Figure 3.1: BET isotherm data used to measure the specific surface area of particulate silica. See text for details 52 Figure 3.2: Schematic diagram of the Iodobead radiolabelling mechanism 56 Figure 3.3: A typical calibration curve used to determine the specific radioactivity for a lysozyme sample. The gamma count (background subracted) is plotted against the protein concentration for a 10-pL sample 60 vi Figure 3.4: A schematic diagram of the Calorimetry Sciences Corp. Model 4200 Isothermal Titration Calorimeter. [Adapted from the CSC ITC manual.]..62 Figure 3.5: An example of raw titration data taken to calibrate the ITC. This particular titration shows measurements of a series of 500-uJ electrical pulses delivered to the sample cells using a 1000-Q internal block heater. The sample and reference cells each contained 1 mL of degassed, deionized water 63 Figure 4.1: A comparison of binding characteristics between labelled and unlabelled lysozyme. Surface concentrations are measured by radioactivity counts 72 Figure 4.2: Ascending isotherm binding data for radiolabeled hen egg-white lysozyme on silica in 50-mM KC1 solution at pH 7 and 37°C. The open and closed squares show separate runs of the same experiment 75 Figure 4.3: Ascending isotherm binding data for radiolabeled hen egg-white lysozyme on silica in 50-mM KC1 at pH 7 and 22°C 80 Figure 4.4: A comparison of the initial slopes of isotherm binding data for radiolabeled hen egg-white lysozyme on silica in 50-mM KC1 solution at 37°C at 22°C81 Figure 4.5: A plot showing saturated surface concentration (Tpl) versus pH for hen egg-white lysozyme adsorbed onto particulate silica in 50-mM KC1 at 37° 83 Figure 4.6: Data showing the sequential dilution of free protein starting from an ascending departure point at 0.29Tp/ for radiolabeled hen egg-white lysozyme adsorbed onto particulate silica in 50-mM KC1 at pH 7 and 37°C 84 Figure 4.7: Desorption isotherms of hen egg-white lysozyme adsorbed to particulate silica in 50-mM KC1 solution at pH 7 and 37°C. The departure points of the descending isotherms correspond to 0.29^, 0.46rp/, 0.74rp/, and 1.01*'. ..85 Figure 4.8: Calibration data for the ITC showing the titration of 1.0-mM KC1 standard into 250-mM Tris buffer. Both the reference cell and sample cell contained 1 mL of degassed Tris buffer. Each injection was 10 uL in volume 87 Figure 4.9: ITC thermogram for the titration of 50-mM KC1 (pH 7) into 1 mL of 50-mM KC1 solution containing 5.4 mg of particulate silica at pH 7 and 37°C 90 Figure 4.10: ITC thermogram for the titration of hen egg-white lysozyme solution in 50-mM KC1 (3.5 g/L, pH 7) into 1 mL of 50-mM KC1 solution containing 5.4 mg of particulate silica at pH 7 and 37°C 91 vn Figure 4.11: The differential heat of adsorption, 8Q, plotted against the free protein concentration for the adsorption of hen egg-white lysozyme in 50-mM KC1 (pH 7) into particulate silica in 50-mM KC1 (pH 7) at 37°C 92 Figure 4.12: The cumulative calorimetric heat, Q, plotted against the unbound protein concentration, [P], for the adsorption of hen egg-white lysozyme adsorbed onto particulate silica in 50-mM KC1 at pH 7 and 37°C 93 Figure 4.13: Double reciprocal plot of calorimetric heat data taken from ITC experiments. Plotted are the inverse cumulative heat of adsorption versus inverse protein concentration 95 Figure 4.14: Plot of ACp data for various globular proteins versus their relative total nonpolar atomic surface areas (ANP-ASA) 97 Figure 4.15: DSC thermogram of the denaturation of hen egg-white lysozyme in 50-mM phosphate buffer containing 50-mM KC1 102 Figure 4.16: Plot of A.N-DG, &N-DH, and A-N-DS for hen egg-white lysozyme as a function of temperature 103 Figure 4.17: DSC thermogram for a silica suspension in 50-mM phosphate buffer at pH 7 containing no adsorbed protein 105 Figure 4.18: DSC (background subtracted) denaturation thermogram for hen egg-white lysozyme adsorbed to particulate silica at surface saturation (pH 7, 50-mM phosphate buffer) 106 Figure 4.19: DSC (background subtracted) denaturation thermograms for hen egg-white lysozyme adsorbed on particulate silica at surface coverages of 0.46rp/ and 0.201^ (pH 7, 50-mM phosphate buffer) 107 Figure 4.20: DSC (background subtracted) denaturation thermogram for hen egg-white lysozyme adsorbed at 0.9^' to negatively-charged polystyrene-sulphonate latex particles (PSS-HC) in 50-mM phosphate buffer at pH 6 108 Figure 4.21: DSC data showing AA-DH as a function of surface coverage for PSS-HC adsorbed to silica particles in 50-mM phosphate buffer at pH 6 and 37°C109 Figure 4.22: Plot of ascending and descending isotherm data at surface saturation for the adsorption of I-lysozyme on silica in 50-mM KC1 (pH 7, 37°C) in the form of the Everett equation 117 viii LIST OF TABLES Table 1.1: Interactions governing the structural stability of globular proteins. A N - D G refers to the Gibbs energy of denaturation for the protein 22 Table 3.1: Physicochemical properties of hen egg-white lysozyme 48 Table 4.1: ACp data for various globular proteins versus their relative total nonpolar atomic surface areas (ANP-ASA) 96 Table 4.2: Quasi-equilibrium parameters from ascending isotherm data for hen egg-white lysozyme adsorbed onto silica in 50-mM KC1 at pH 7 I l l Table 4.3: Comparison of denaturation thermodynamics for lysozyme in aqueous solution with adsorption thermodynamics for lysozyme on silica 114 i x ACKNOWLEDGEMENTS I am indebted to my advisor, Chip Haynes, whose encouragement, tireless enthusiasm, and insight made this thesis possible. I am proud to be the first graduating student of what promises to be a remarkable scientific career. I am also grateful for the friendship and good advice of Louise Creagh. Her kindness will always be remembered. I would like to thank Don Brooks and his lab for the generous use of their facilities for the radiolabelling work in the project. My special appreciation goes to Andrew Olal for his guidance and patience while performing these experiments. Much of my thanks goes to my coworkers in the Bioprocess Engineering section of the Biotechnology Lab. Their help, support, humour and friendship has made the lab a truly exceptional place to work in. Finally, my gratitude goes to my parents and sisters for always being there for me. 1. Introduction 1.1 Significance of protein adsorption The adsorption of protein to interfaces is pervasive in nature and has both positive and negative consequences. Scientists and engineers ,(in particular, chemical engineers) have developed processes which take advantage of protein adsorption. For example, the stabilization of foams and microemulsions and the production of pharmaceutical creams and lotions utilize the adsorption of proteins to a liquid/liquid interface. Adsorption of therapeutic proteins to site-targeted liposomes is an example of the application of protein adsorption in drug delivery [Chonn et al., 1992; Zellmer, S. and Cevc G., 1996]. Many methods of protein purification, including hydrophobic-interaction and reverse-phase chromatography use adsorption of proteins to a solid matrix as a separation mechanism. There are detrimental effects as well. The most common example is plaque formation on teeth, which is initiated by adsorption of food and saliva proteins. The clouding of contact lenses also results from adsorption of tear proteins adhering to the solid lens surface. The fouling of bioprocessing equipment, naval equipment, kidney dialysis membranes and biosensor membranes are just a few examples of costly industrial problems associated with protein adsorption. Another unfortunate, and perhaps more severe, consequence of protein adsorption is the fouling of biomedical implants. The use of biomedical implants has become common clinical practice throughout North America and the world [Ratner, 1992]. Types of 1 implants range from bone cement to artificial heart valves to intraocular lenses. Protein adsorption to such devices often leads to severe medical problems. It is believed that the adsorption of specific blood proteins such as serum albumin, thrombin and fibrinogen to implants triggers a biochemical cascade which results in the formation of a blood clot, or thrombus. Thrombus formation is a health risk in that it can enlarge to form an occlusion in the vessel to which it adheres. It may also break off and form an embolus, a free blood clot carried throughout the circulatory system. Depending on where the embolus is delivered to, tissue damage, aneurysm, pulmonary edema, or congestive heart failure may result. In order to avoid the problems encountered with protein adsorption, biomedical implants have been constructed from a vast range of synthetic polymers and inorganics with the goal of rendering them biocompatible. Ratner [1992] defines biocompatiblity as "...the exploitation by materials of the proteins and cells of the body to meet a specific performance goal." Unfortunately, none of the existing synthetic materials utilized for implants or blood contacting applications meet these criteria. Therefore, the fields of biomedical engineering, chemical engineering and biotechnology continue to work toward satisfying the demand for better-engineered implant materials. Research in the area of protein adsorption to biomedical implants can be divided into two general classes. The first class approaches protein adsorption from a trial-driven point of view. In this case, potential implant materials are directly contacted with whole blood or blood proteins either in vivo or in vitro. The state of the implant and host after exposure are then assessed and correlated with the known characteristics of the material. Through 2 this type of research, some general trends regarding biocompatibility have been observed and some useful materials have been developed. However, none of the materials developed so far have shown long-term sustainability. The second class of research involves the development of biocompatible materials through a more fundamental approach which seeks to establish a thorough understanding of the fundamental driving forces and mechanisms associated with protein adsorption. This approach is aimed at answering the question: Why do proteins prefer interfaces? Substantially less work has been carried out from this point of view, which is regrettable since a clear understanding of the fundamental nature of protein adsorption appears necessary for the construction of any truly biocompatible material. Protein adsorption from a fundamental perspective involves both kinetic and thermodynamic considerations. The kinetics of protein adsorption includes the study of rates of adsorption, the arrangement of proteins on the surface, and the exchange of adsorbed proteins with proteins in solution [Bornzin & Miller, 1982; Jonsson et al, 1982; MacRitchie, 1987; McGuire et al, 1995a; McGuire et al, 1995b; Ramsden, 1995]. Models of protein adsorption kinetics have been developed using several approaches, including self-exchange reactions [Lundstrom et al, 1987; Lundstrom and Elwing, 1989] exchange with other molecules [Lundstrom and Elwing, 1989], adsorption of a second layer of proteins [Lundstrom, 1985], and adsorption sites and surface/protein interactions of multiple types [Sevastianov et al, 1991]. Important questions concerning, for instance, the sequence of blood protein adsorption to polymer implants (known as the Vroman effect) [Leonard et al, 1987] and the progression of thrombosis have been partially answered through this approach [Wojciechowski, et al., 1986; Cuypers et al., 1987; Slack and Horbett, 1989]. Often, radiolabeled proteins have been used to carry out competitive adsorption studies of blood protein mixtures on polymers [Horbett, 1987; Fabrizius-Homan and Cooper, 1991] allowing one to track the position of the protein in a complex multicomponent system. Thermodynamic studies of protein adsorption attempt to quantify the overall energy change in the system and the forces and subprocesses that contribute to it. For a spontaneous reaction to occur, the Gibbs energy of the system, AG, must decrease during the process such that AG = AH-TAS <0 (1.1) Determination of the Gibbs energy change for the system will therefore predict whether or not the reaction can occur. Evaluation of the enthalpy and entropy changes (AH and AS, respectively) then provides a basis for analysing the nature of the driving force for the reaction. For reversible adsorption, both A ^ G and AadsH can be determined experimentally by using known reversible adsorption models and AadsS then calculated from Equation 1.1. The heat capacity change upon adsorption AadsCp can also be measured to provide the temperature dependence of the system and thus a complete thermodynamic description of the adsorption process. The subscript "ads" refers to the change due to the adsorption process. For instance, Aa^H, refers to the enthalpy of the system before adsorption 4 subtracted from the enthalpy of the system after adsorption. Figure 1.1 shows the adsorption isotherm for closed-circular supercoiled pUC-18 DNA (deoxyribonucleic acid) on silica particles in 6-M perchlorate at pH 8 and 37°C [Melzak et al., 1996]. For reversible adsorption, the ascending (increasing pUC-18 DNA concentration) and descending (decreasing pUC-18 DNA concentration) branches of the isotherm must overlap at all concentrations. This is the case for supercoiled pUC-18 DNA adsorption to silica, allowing Aa<&G to be directly calculated from the isotherm using the appropriate equilibrium isotherm relation. O C/3 CN Q it O U U . U 1 1 1 1 1 1 • 1 • i 1 1 1 1 1 1 1 1 1 500.0 -• o Ascending isotherm '. Descending isotherm ~. 400.0 ( * > • • 300.0 : & '• 0 -200.0 ; 8 -100.0 '• o -0.0 i i i 1 — i — i i i i i i ' ' 0 10 15 20 c (jag DNA/mL) Figure 1.1: Adsorption isotherm for closed-circular supercoiled pUC-18 DNA (deoxyribonucleic acid) on silica particles in 6-M perchlorate (pH 8, 37°C). 5 In many reversible systems, adsorption obeys the Langmuir isotherm model, which is given by, rplK c r= 1 (1.2) l + KLc where c is the free sorbate concentration at equilibrium, Ypl is the surface concentration of pUC-18 DNA at saturation, and KL is the Langmuir equilibrium constant, which is given by AabG = -RTlnKL (1.3) AadsH can then be found either by using the Gibbs-Helmholtz equation or by direct measurement using a calorimeter. The Gibbs-Helmholtz equation, which describes the dependence of the Gibbs free energy on temperature, is related to the change in enthalpy in the system as follows: dhiKL T KJi (L4) R JP Finally, the heat capacity change for adsorption, AadsCp, can be measured by calorimetry through application of the difference form of the fundamental thermodynamic relation, 6 An adsorption system cannot be considered reversible if the ascending and descending branches of the isotherm do not trace each other exactly. In such instances, adsorption hysteresis is observed. Most protein adsorption systems have been found to be irreversible; however, thermodynamic analyses of these systems have rarely reflected this fact. An example of the common, but questionable use of reversible thermodynamics in an irreversible case is the use of Young's equation to describe the free energy of interaction between a solid and a biopolymer [van Oss, 1991]. Application of reversible thermodynamics to adsorption or contact angle data typically results in Aa<&G values in the range of -10 to -50 kJ/mol. One of our goals in this work is to validate whether the values obtained through application of reversible thermodynamic theories are accurate or even approximate representations of the Aa<&G for real protein adsorption processes, which are typically irreversible. As with reversible adsorption, A ^ / / for the irreversible process can be directly measured using calorimetry. The change in entropy, however, is a more complicated term to quantify. Much of the theoretical work on quantifying the change in entropy for an irreversible adsorption process has been carried out by Everett [1967]. Everett used domain theory to mathematically describe adsorption hysteresis. He proved that the area between the ascending and descending curves (i.e. the hysteresis loop) of an irreversible process is a measure of the irreversible entropy change accompanying the process: (1.6) where AadsSir is the irreversible entropy change for the process,/? is the universal gas constant, T is the specific surface concentration, T* is the surface concentration at the departure point of the desorption curve, and c is the concentration of protein in the bulk solution in moles of protein per unit volume. Everett's theory does not consider the reversible component of the overall irreversible process and therefore our analysis on protein adsorption will require that some assumptions be made and reversible thermodynamics be used to determine the reversible parameters of the process. A second goal of this work is therefore to combine Everett's theory with reversible thermodynamics to obtain a more realistic thermodynamic model describing protein adsorption. With our thermodynamic framework, we will attempt to estimate the change in enthalpy, entropy and Gibbs energy for a well-characterized "model" protein adsorption process. We acknowledge that some of the calculations may lead only to a semi-quantitative estimate of the actual values; however, it is hoped that the theory will give further insights into the energetics of the process and therefore provide a more appropriate framework for analysis. It is also hoped that the model will lead to further understanding of the forces driving protein adsorption. How relevant is the irreversible component to the overall Gibbs energy? To what extent does the irreversible change in enthalpy contribute to the energy? 8 Is the adsorption of proteins to surfaces entropically driven? And if so, what physical mechanisms does this entail? The model system chosen for these experiments is the adsorption of hen egg-white lysozyme on silica from a 50-mM KC1 solution. This model system was chosen for its simplicity; both hen egg-white lysozyme and silica are common materials, and relatively well-characterized. Through X-ray crystallography studies, the 3-dimensional structure of hen egg-white lysozyme has been determined [Wilson et al., 1992; Malcolm et al., 1990]. Use of a specific model system allows us to determine the validity of the theoretical framework developed throughout the thesis. By utilizing a simple model system, we hope to be able to draw comparisons between our irreversible approach and those based on reversible thermodynamic theories. Before proceeding with a more detailed description of the new thermodynamic framework for analyzing irreversible protein adsorption, we present a discussion of the properties of the basic components involved in typical protein adsorption systems with the aim of identifying dominant factors and characteristics influencing adsorption. 1.2 System components and their properties The simplest possible protein adsorption system, often called a model adsorption system, is comprised of four components: the charged protein macromolecule, the (usually charged) sorbent surface, water, and low-molecular-weight ions, including added salts and protein counterions. Although rarely of medical or technological importance, model 9 systems, because of their relative simplicity, have provided the most meaningful data on the thermodynamics of protein adsorption. They are the basis for most of the general principles which are thought to govern the protein adsorption process. However, even for these simple systems, a complete picture of the adsorption mechanism has not emerged. All mechanistic features which have been identified, however, are intimately linked with an understanding of the properties of the system components, particularly the stabilities and structural properties of globular proteins. 1.2.1 Water and the hydrophobic effect The contribution of water to protein adsorption processes cannot be underestimated. Liquid water, despite being the most common solvent, is one of the most poorly understood. Its unique properties come, at least in part, from the extensive network of hydrogen bonds formed in both liquid water and ice. At low to ambient temperatures, liquid water is a random hydrogen-bonded network where microscopic clusters of molecules participate in hydrogen bonds (of varying energy) with four nearest neighbours to form a fluid tetrahedral structure. The consequence of these bond networks is a percolating effect, where, due to its associative nature, disturbances to the solvent are detected over macroscopic distances, not just adjacent to the affected area [Stillinger, 1980]. Both spectroscopic measurements and bond-percolation simulations indicate that the density of hydrogen bonds (or total hydrogen bond strength per molecule) is strongly temperature dependent, decreasing with increasing temperature in a nearly linear fashion 10 [Franks, 1972; Luck and Ditter, 1970]. Stanley and Teixeira [1980] report correlated bond-percolation model results which suggest that the connectivity of the hydrogen bond network in liquid water is lost above a percolation threshold temperature of ca. 85°C whereas ca. 60% of all possible H-bond sites are filled at ambient conditions. The relatively open, loosely ordered structure of liquid water is easily altered by the presence of cosolutes despite the strong solvent-solvent hydrogen bond forces. Ions with very high charge densities, for instance, tend to promote local ordering of water molecules which results in a strongly negative excess entropy of mixing. The solubility of these ions is due to strong ion-dipole interactions which lead to an exothermic heat of mixing [Burgess, 1988]. Addition of uncharged hydrophobic solutes also leads to a pronounced local enhancement in solvent structure which allows water molecules adjacent to the solute to maximize hydrogen bonds. At ambient conditions, formation of this highly structured solvent shell leads to a substantial decrease in entropy and a large positive change in heat capacity which together, are the central thermodynamic criteria of the "hydrophobic effect". Figure 1.2 shows the Gibbs energy, enthalpy and entropy of transfer of benzene from a pure benzene phase to an aqueous solution. The positive value of A G indicates that for the temperature range shown, benzene is immiscible in water. At lower temperatures, miscibility is limited by the large negative entropy of transfer, a direct consequence of the hydrophobic effect. As the temperature increases, the water molecules, which were once ordered around the solute surface in order to maximize hydrogen bonding, "melt" away 11 250 300 350 400 Temperature (K) 450 Figure 1.2: Gibbs energy (AG), enthalpy (AH) and entropy (AS) of transfer of benzene into water. ACp is assumed to be temperature-independent for the range given. [Adapted from Privalov and Gill, 1988.] into the bulk solvent, resulting in an increased entropy of transfer. The removal of ordered water from the solute interface is an additional energy storage mechanism for the solvent which consequently results in a large positive change in heat capacity for the 12 system. At high temperatures, the benzene remains immiscible in the aqueous solution due to the enthalpy of transfer which is endothermic at elevated temperatures. Any protein adsorption theory must therefore account for the unique hydrogen-bonding properties of water and the resulting hydrophobic effect. 1.2.2 Proteins Proteins are biological macromolecules found in abundance in all living systems. They have many functions: transportative, contractile, hormonal, immunogenic, and structural. They also function as biological catalysts, or enzymes. The complexity and diversity of proteins have been known for a long time, and studies into their structure and function have helped to recognize the important role of proteins in biological systems. More recently, these unique structural and stability features have been shown to be important in the protein adsorption process [Norde and Lyklema, 1991; Haynes and Norde, 1994]. 1.2.2.1 Chemistry and basic structural elements Proteins are complex heteropolymers. Unlike many other types of macromolecules, proteins in solution retain specific structures, called the native state, which are essential to their function. The native state is stabilized relative to an ensemble of denatured states by a close balance of energies, involving the protein and its surrounding solvent. A shift in this balance of energies, possibly through the introduction of a surface, can lead to dramatic changes in structure. One objective of this thesis is to explore the occurrence and contribution of these structural changes to the driving force for protein adsorption. 13 Threonyl Tryptophanyl Tyrosyl Valyl H"hr] [Trp] [Tyr] [Val] Figure 1.3: Chart of the twenty most common amino acid side chains. 14 L-amino acids are the building blocks of a protein. The fundamental structure of an amino acid is RCH(NH3+)C02 " , where R represents one of 20 naturally occurring side-chains. A chart of the amino acid side chains is shown in Figure 1.3. As shown in the figure, side chains vary in size, flexibility, charge and hydrophobicity. Current protein structure theories indicate that when linked together to form a protein, the sequence of the amino acids, or residues, in the linear polymer determine the eventual structure, and consequently the function, of the folded protein [Dewey, 1996; Rost and Sander, 1996; Friesner and Gunn, 1996; Russell et al, 1996]. The sequence of amino acids in a protein is referred to as its primary structure. R 2 I I H3N - c - CO," + +H3N - C - C 0 2 i H R, ° R 2 I ' ll i UN - C - C - N - C - C 0 2 + H20 H H H Figure 1.4: Schematic of a condensation reaction between two amino acids to form a peptide bond. 15 Amino acids are attached together by peptide bonds. A peptide bond is formed from a condensation reaction between the carbonyl and amino groups of two adjacent amino acids as shown in Figure 1.4. The peptide bond is highly rigid due to its partial double bond character. Because of the inflexibility of peptide bonds throughout the protein and steric hindrance experienced by the side chains, a polypeptide chain can adopt only a limited number of configurations. Ramachandran plots suggest that the total possible configurations of the two remaining flexible bonds and <|)) per peptide is about 4 when the polypeptide chain is in a fully random-coil configuration and 1 when the protein is in its native (fully functional) state. In most cases, amino side groups are found in a trans configuration. In the folded native-state protein, there can be areas where the linear conformation of the chain is either highly regular or irregular in conformation, depending on the extent and sequence of hydrogen bonds formed. These localized structures are referred to as the secondary structure of the protein. The most common ordered secondary structures are the a-helix and the parallel and antiparallel P-sheets, which are found mainly in the interior of the protein. Tertiary structure refers to the overall conformation of the polypeptide chain. It is the tertiary structure that defines a protein's function, total surface area, surface hydrophobicity, and number of titratable groups exposed to the solvent. It, along with the primary sequence, also define the isoelectric point, or pi, of the protein which corresponds to the pH where the sum of the charges originating from (de)protonation of 16 the amino acid residues and from low molecular weight ions bound within the hydrodynamic slipping layer around the protein is zero. Finally, there exists a higher level of organization for proteins consisting of more than one polypeptide chain (multimers). The interaction between the polypeptides and their supporting structures is referred to as its quaternary structure. A common example of a multimer is hemoglobin, the active protein component in red blood cells, which has four folded polypeptide chains centred around a prosthetic heme group. Regrettably, we are only now beginning to formulate a meaningful model of adsorption of single-domain proteins [Haynes and Norde, 1994]. Thus, although multimers are important to many biological processes, their use in protein adsorption studies has typically led to confusion rather than insight. Single polypeptide chain proteins can be divided into three broad categories according to their tertiary structure: a) expanded coil structures: flexible and highly solvated, b) fibrillar proteins: mainly consisting of regular secondary structures such as oc-helices and P-sheets c) globular proteins: compact proteins that are made up of both random and structured parts, all folded into a roughly spherical configuration. Most proteins of interest, such as enzymes and antibodies, are globular proteins. For this reason, they are the focus of our protein adsorption studies. 17 1.2.2.2 General properties of globular proteins Globular proteins in an aqueous solution have a number of general characteristics [Creighton, 1993]. Many of these traits are evident in hen egg-white lysozyme (MW = 14388 Da) which is typical of a small globular protein. Figures 1.5 and 1.6 show various perspectives of space-filled models of lysozyme. Analysis of these figures, as well as similar data for other globular proteins, reveals the following general properties: 1) Globular proteins are roughly spherical in shape with diameters of the order of angstroms to nanometres. The size of lysozyme is 4.6 x 3.0 x 3.0 nm3 [Malcolm et al, 1990; Wilson et al, 1992]. 2) Hydrophobic side groups have a tendency to reside in the interior of globular proteins to avoid contact with water, the solvent. This does not mean that all hydrophobic residues are sheltered from the aqueous surroundings or that the interior is composed entirely of hydrophobic groups. Internal hydrophobicity is limited, for instance, by the presence of the hydrophilic polypeptide backbone. In the case of hen egg-white lysozyme (MW=14388 D), approximately 50-60% of the water accessible surface area consists of apolar atoms [Lee and Richards, 1971] while 60% of the interior is apolar [Miller et al, 1987]. From molecular graphic images of the protein in Figure 1.5, it can be seen that polar and apolar atoms are fairly evenly distributed, and consequently there are no noticeable hydrophobic or hydrophilic patches on the surface. 18 Figure 1.5: Space-filled model of lysozyme contrasting polar residues (lighter shade) with non-polar residues (darker shade). Each diagram represents a perspective of the protein rotated at various degrees around the y-axis: a)0°, b) 90°, c) 180°, and d) 270°, respectively. [Adapted from the Brookhaven Protein Databank; Malcolm et al, 1990; Wilson et al, 1992.] 19 b) d) Space-filled model of lysozyme at pH 7 contrasting positively charged (dark shade) with negatively charged residues (medium shade). Each diagram represents a perspective of the protein rotated at various degrees around the y-axis: a) 0°, b) 90°, c) 180°, and d) 270°, respectively. [Adapted from the Brookhaven Protein Databank; Malcolm et al, 1990; Wilson etat, 1992.] 20 3) Charged groups are found predominantly on the exterior of the protein, while the very few charged groups in the interior are almost always found in ion pairs. As shown in Figure 1.6, most of the charged residues on the water-accessible surface of hen egg-white lysozyme carry a positive charge, and consequently, lysozyme has a pi of 11.1. 4) Globular proteins are very densely packed, i.e. comparable to densities for close-packed equal-sized spheres. The atomic packing fraction of a protein is about 75%. This can be compared to the packing fraction of liquid water which is 58% at 25°C and 1 atm. 1.2.2.3 Globular protein stability and factors affecting it A folded protein is a densely packed molecule stabilized by an intricate network of energy relationships. Thermodynamic investigations carried out by Privalov [Privalov, 1989] measured the stabilization energy of a globular protein to be 30-70 kJ/mol, comparable to the energy of 2 to 6 hydrogen bonds. Lysozyme, for instance, is a single-chain globular protein composed of 140 amino acid residues which are tightly folded to form a nearly spherical molecule with a packing density of about 73%. In this type of arrangement, it can be estimated that each amino acid residue has direct contact with about 3 other residues [Cantor and Schimmel, 1980]. Table 1.1 summarizes favourable and unfavourable forces known to affect the stabilities of protein dissolved in aqueous solutions. The table shows that hydrophobic dehydration, 21 dispersion forces and possibly hydrogen bonding drive the folding of the native protein. Compensating those forces are the loss of conformational entropy and distortions of bond lengths and bond angles. Coulombic forces can be favourable or unfavourable to the native structure, depending on the overall pH of the system relative to the isoelectric point of the protein. Table 1.1: Interactions governing the structural stability of globular proteins. A N - D G refers to the Gibbs energy of denaturation for the protein. Type of Interaction Contribution Comments to A N . D G Hydrophobic « 0 dehydration Hydrogen bonding < 0 (?) Deydration of polar < 0 groups Electrostatic forces > or < 0 Dispersion forces < 0 Conformational » 0 entropy Distortion of covalent > 0 bond lengths and bond angles An increase in entropy results from the release of water molecules contacting hydrophobic residues. Intramolecular hydrogen bonding, especially in ordered secondary structures, may contribute to stability. Deydration of polar groups may contribute up to 5 kJ/(mol amino acid). Contribution is dependent on the pH of the system relative to the pi of the protein. Favourable due to the dense packing of the atoms in a protein structure. A substantial loss of conformational freedom from folding and the formation of highly ordered secondary structures. Unfavourable strains existing to accommodate other, more dominant interactions. 22 Hydrophobic dehydration is believed to be one of the dominant driving forces for protein folding in aqueous solutions [Privalov and Gill, 1988; Dill, 1990; Haynes and Norde, 1994]. It refers to the change in solvation of the hydrophobic amino acid side chains of a protein in its folded (native) state relative to its unfolded (denatured) state. When a protein is fully denatured, most, if not all of its side chains are exposed to the aqueous solvent. This results in a high degree of solvation which requires the solvent molecules to locally arrange themselves around the apolar solute (in this case, the denatured protein) in a relatively ordered shell favouring solvent hydrogen bonding at the solvent/solute interface. In general, the folded native-state structure has considerably less hydrophobic side chains exposed to the solvent since a majority of the apolar groups fold into the interior of the protein. Entropy gained from dehydration of these buried apolar groups is believed to be one of main driving forces stabilizing the folded native state of a protein. Intramolecular hydrogen bonding may also make a substantial contribution to the stability of the native state. Creighton [1993] proposes that hydrogen bonding contributes ca. 30-45% of the energy driving folding, along with less significant contributions from van der Waals and electrostatic interactions. The significance of electrostatic forces to the state of the protein can be estimated by observing the dependence of protein stability on changes in pH and ionic strength. For example, at extreme pH, the charge density of a folded protein becomes very high, and there is a tendency for the protein to unfold. Specific electrostatic interactions such as ion pairing within a protein have an opposite effect in that they usually lead to the stabilization of the native protein. A rough gauge of the degree of electrostatic interaction 23 occurring at the surface of the protein is given by the local water density adjacent to the protein surface: an ion of significant charge density increases the molar density of water directly surrounding it [Burgess, 1988]. Dispersion forces, which are highly dependent on the distance between atoms (T a r"6), are likely important for local protein structure due to the dense atomic packing in a typical protein. The total magnitude of stabilization energy from dispersion effects, however, is thought to be small relative to the effects of hydrophobic dehydration and possibly hydrogen bonding [Dill, 1990]. Counteracting all the positive stabilization forces is one main destabilizing force: the loss of conformational entropy resulting from the folding of the polypeptide chain [Haynes and Norde, 1994; Dill, 1990]. Creighton has estimated that for a polypeptide chain in a random coil, approximately 4 distinct backbone conformations exist per peptide unit [Creighton, 1993]. Assuming that a peptide unit has only one backbone conformation when involved in an a-helix or [3-sheet, the loss of entropy per peptide unit is R In lA = -11.53 J mol"1 K"1. For a protein consisting of 100 residues, the loss in entropy is approximately 1200 J/K per mole of protein due to freezing of the backbone structure. This results in a Gibbs free energy gain of 350 kJ/mol at 300 K. Additional entropy losses occur from reductions in conformational freedom of side chains within the interior of the folded protein. A somewhat less significant force opposing the native state is the distortion of covalent bond lengths and bond angles as determined by energy minimization calculations 24 [Creighton, 1993; Levitt, 1978]. These distortions, which add approximately 4 to 8 kJ per distorted bond to the native state energy, are believed to be necessary to optimize the various interactions (hydrophobic, dispersive and peptide-peptide hydrogen bonding) required for a tightly packed, compact molecule. 1.2.3 Low molecular weight ions Counterions and ions of added electrolyte (e.g. buffer ions) are present in all protein adsorption processes, and contribute to the adsorption process in two fundamental ways: (1) by disrupting local and possibly long-range solvent structure, and (2) by participating in electrostatic screening and charge neutralization at the various macro- and microinterfaces of the system. The presence of low molecular weight ions in an aqueous solution can disrupt the extensive network of hydrogen bonding through the formation of strong ion-dipole interactions between the ions and water molecules. Ion solvation requires proximal water molecules to arrange themselves in an ordered layer similar to that which characterizes the hydrophobic effect. Addition of ions to water tends to increase the hydrophobic effect. The resulting decrease in free water reduces solubilities of apolar molecules in aqueous electrolyte solutions relative to those in pure water [Tanford, 1961]. The relatively low dielectric environment formed at the interface during protein adsorption requires overall neutralization of charge within the layer. If the protein macro-ion and the sorbent surface carry the same charge sign, this neutralization must be 25 accomplished by coadsorption of protons or other low molecular weight ions [Haynes and Norde, 1994]. In unbuffered systems, the extent to which protons from the bulk solution are incorporated into the protein surface interface can be detected by the pH change of the system. The total number of ions involved with the adsorbed protein layer can be estimated using charge density values (usually determined by electrophoretic measurements) of the bare sorbent, the protein in solution and the protein/sorbent complex. 1.2.4 Sorbent surfaces Studies on protein adsorption have determined that whether or not a protein adsorbs to a surface is highly dependent on the characteristics of the surface itself [Horbett and Brash, 1987; Haynes and Norde, 1994; Norde, 1986; Park and Cooper, 1985; Young et al, 1988]. Some of the properties which are known to influence adsorption are structure of the surface, surface area, hydrophobicity and charge on the surface [Haynes and Norde, 1994; Absolom et al, 1987; Chuang, 1978; Baszkin and Lyman, 1980; Park et al, 1990]. For example, a continuous planar surface ususally binds proteins more strongly than does a series of fibres of the same area. This preference is believed to originate from the fact that sorbent and protein dehydration effects are stronger at the planar surface. Techniques such as BET isotherms, dye-binding studies, photon-correlation light scattering and electron microscopy techniques can be used to measure surface area [Haynes and Norde, 1994; Nakai and Li-Chan, 1988]. Although these techniques are 26 usually quite reliable in providing relative values, the heterogeneity of the surface often leads to discrepancies in absolute values determined by the different techniques. Proteins prefer surfaces of intermediate hydrophobicity, as suggested by studies which compared initial slopes and plateau values of isotherms measured for proteins adsorbed to solids of varying hydrophobicities [Norde, 1986; van Oss, 1991; Baszkin and Lyman, 1980]. Contact angle measurements are the most common method for measuring surface hydrophobicity. From the contact angle of a sessile drop of water or saline on a planar surface, the Gibbs energy of hydration can be calculated using the Young-Dupre equation [Adamson, 1990]: A G i W = -rw(l + cos0) (1.7) where AG™ is the reversible work of hydration per unit surface area of solid-water interface (mJ/m ), yw is the surface tension of pure water (mJ/m ), and 6 is the measured contact angle (degrees). Surface charge on the sorbent surface can originate from the association or dissociation of ions (including protons) to covalently bound surface groups, or the specific adsorption of low-molecular-weight ions from the aqueous solution [Haynes and Norde, 1994]. To satisfy the energetic requirement of an overall null-charge equilibrium in the fluid adjacent to a charged surface, there must also exist a nonuniform arrangement of electrostatic charges in the solution. This arrangement is known as the electrical double layer. The Gouy-Stern model, which is diagrammed in Figure 1.7 is one of the most widely accepted models describing charge-distribution in the double layer [Adamson, 27 1990]. In it, sorbent charges are located at the immediate surface boundary (x=0) and specifically adsorbed ions are in contact with the surface with centrepoints x=m away from the surface. In the case of a surface without specifically adsorbed ions Figure 1.7: Schematic of a Gouy-Stern model of the electric double layer. Electrostatic potential, <|>, is plotted against distance from the sorbent surface, x. An explanation of the symbols is given in the text. [Adapted from Haynes and Norde, 1994.] 28 the hydration of counterions prevents direct contact between the counterion and the surface. Consequently, a charge-free layer, the Stern layer, exists in the region 0<x<d where d is the plane of closest approach of the centrepoints of the hydrated counterions. Outside the layer of counterions (x=d), a diffuse net charge which neutralizes the sorbent charge extends into the bulk aqueous solution (x>d) such that the differential potential in each element dx decays exponentially to 1/e its surface value at a distance 1 /K (the Debye-length) from the surface. Adsorption of proteins to a charged surface therefore requires that the forces driving adsorption, whether electrostatic or non-electrostatic, interact with and disrupt this electric double layer. Various analytical tools can be used to determine surface composition. Common methods used for the characterization of polymers include electron spectroscopy for chemical analysis (ESCA), [Perez-Luna et al, 1994; Gombotz et al., 1991; Barbucci et al, 1993; Brunstedt et al, 1993], wide angle X-ray scatter (WAXS) [Barbucci et al, 1993], infared spectroscopy [Barbucci et al, 1993], and secondary ion mass spectroscopy (SIMS) [Perez-Luna et al, 1994]. 1.3 Protein adsorption subprocesses It is believed that three subprocesses are the leading driving forces for adsorption of protein on a surface [Haynes and Norde, 1994; Norde and Lyklema, 1991]: 1) structural rearrangements of the protein 29 2) dehydration of the sorbent and protein surface, and 3) redistribution of charged groups at the protein/sorbent interface. In aqueous solution at ambient conditions, a protein in its native state is marginally stable due to the close balance between the entropic gain associated with dehydration of its hydrophobic residues (favouring a structured protein) and the conformational entropy favouring structural freedom. The introduction of a sorbent interface can disrupt this balance by directly interacting with the protein and by altering the organization and distribution of the solvent and added electrolytes [Haynes and Norde, 1994]. When a protein adsorbs to a surface, new interactions take place between the sorbent surface and the protein, and a new quasi-stable complex is formed with the surface. There is some evidence that conformational changes occur when proteins adsorb onto planar surfaces. For instance, the observed maximum surface concentration of protein is often significantly lower than the concentration predicted for an unperturbed protein adsorbed in a side-on configuration [Haynes et al., 1994]. This indicates either the formation of incomplete monolayers at the surface, or a change in structure of the proteins such that each adsorbed protein occupies greater sorbent surface area [Haynes and Norde, 1994]. Most evidence points to the latter. Norde and Favier observed changes in conformation for bovine serum albumin and hen egg-white lysozyme adsorbed onto silica particles using circular dichroism [Norde and Favier, 1992]. They found that both proteins experienced a considerable loss in their ot-helix structure at low surface coverages and that the magnitude of the structural change 30 depended on surface coverage and charge contrast between the protein and the sorbent. A similar study was carried out by Chan and Brash who detected a 50% loss in helicity in human fibrinogen desorbed from Pyrex glass by exposure to 1-M Tris at pH 7.35 for 3 hours [Chan and Brash, 1981]. Their results, however, were unclear as to whether the changes in conformation were due to the protein-glass interactions or to the elution effects. Proton titrations have been used to study conformational changes of adsorbed proteins. Haynes, Sliwinski and Norde [1994] used proton titrations to demonstrate substantial differences in the titration curve of a-lactalbumin adsorbed onto negatively charged polystyrene relative to that in solution. Differences in the titration curves clearly suggested changes in the structure of the protein. Galisteo and Norde [1994] compared proton titrations of lysozyme and a-lactalbumin adsorbed onto poly(styrenesulphonate) with titrations of the same proteins denatured by SDS and guanidinium hydrochloride. Their results showed that when adsorbed at low surface coverages, lysozyme has characteristics similar to those of SDS-denatured lysozyme. At high surface coverages however, proton titrations showed the structure of adsorbed lysozyme to be similar to that of native lysozyme. For a-lactalbumin, the proton titration of the adsorbed protein was similar to the titration of the SDS-denatured a-lactalbumin, regardless of the surface coverage. Differential scanning calorimetry, a tool often used to measure the thermodynamic stabilities of proteins in solution, has also been used to detect loss of stability in proteins 31 adsorbed to surfaces. For example, Haynes and Norde [1995] studied the stability changes of hen egg-white lysozyme and bovine milk a-lactalbumin when adsorbed to negatively-charged polystyrene latex and hematite. Their calorimetric studies allowed them to determine the enthalpies of denaturation associated with the adsorbed molecules and compare them to enthalpies of denaturation for native-state proteins. The relatively low denaturation enthalpies for the adsorbed proteins indicated that significant losses of stability, and therefore structural changes of the proteins, occurred during the adsorption process. Several other analytical tools have been utilized to characterize the structure of adsorbed proteins. Fluorescence spectroscopy [Andrade et al., 1984; Horsley et al., 1986; Anderson et al., 1986], nuclear magnetic resonance (NMR) [Benko et al., 1975], electron paramagnetic resonance (EPR) [Panitz, 1986; van Dulm et al., 1981] and infared spectroscopy (IR) [Ball and Jones, 1995; Pireaux, 1992; Muller et al., 1996; Buijs et al, 1996; Chittur et al, 1986; Jakobsend and Wasacz, 1986] have all identified changes in protein conformation after adsorption to a surface. Only microcalorimetry, however, has provided any quantitative insights into the energetics associated with these conformational changes. The conformational change of a protein on a surface is thought not to be from a compact protein to a completely random coil, but rather to a less structured molecule with similar dimensions as the native-state [Norde and Lyklema, 1991]. Ellipsometry studies suggest that the thickness of adsorbed protein layers is comparable in thickness to the diameters 32 of native proteins in solution, indicating that conformational changes during the process do not lead to a gross unraveling of the chain [Cuypers et al., 1977; Cuypers et al., 1978]. In certain cases, mainly those involving very hydrophilic sorbents, adsorption has little effect on enzymatic activity of the protein. Barnett and Bull observed that the activity of ribonuclease is unchanged when adsorbed to glass [Barnett and Bull, 1959]. As well, the pH of optimal activity was unchanged indicating that any conformational changes experienced by the protein had no effect on its catalytic site. Conformational change of an adsorbed protein is therefore not universal, but dependent on the environmental conditions and type of system involved. By analogy with the hydrophobic effect, dehydration of hydrophobic areas on both the sorbent surface and the exterior of the protein increases the overall entropy of the system. Similar to the forces stabilizing a protein in solution, attachment of a hydrophobic protein to a surface results in the release of ordered, water molecules arranged around the hydrophobic areas, which is an energetically favourable process. Protein adsorption also involves the overlap of the electric double layers of the protein and the surface. Because of the requirement of electroneutrality, ions from solution are incorporated into the protein/solid interface. For example, Haynes, Sliwinski and Norde [1994] measured titration curves of a-lactalbumin adsorbed onto negatively-charged polystyrene beads in an unbuffered system. The average charge of the adsorbed protein was about 11 units higher than the protein in solution and the overall pH of the system 33 increased from 4.0 to 4.1. Both observations indicate that a net positive transfer of protons to the adsorbed phase originated from the bulk solution. 1.4 Complexity of the protein adsorption process Quantitative behaviour of an adsorption system is commonly presented using adsorption isotherms, where the surface concentration of protein, T, is plotted against the bulk protein concentration, c, at apparent equilibrium. An example is given in Figure 1.8 where the adsorption isotherm of hen egg-white lysozyme on negatively-charged polystyrene latex at pH 7 and 25°C in 50 mM KC1 solution is shown. Analysis of adsorption isotherms such as Figure 1.8 has been the most common approach to elucidate those factors which drive protein adsorption. The initial slope of the adsorption isotherm is a clear indication of the affinity of the protein for the surface. For homopolymer adsorption, Fleer and Lyklema [1983] conclude that high-affinity isotherms occur when multiple contacts can be made between a sorbate and a surface. For example, a high initial slope is usually observed for the adsorption of a random coil polymer to a surface. This is not always the case for protein adsorption, however; both sharp or shallow initial slopes are seen. Based on this type of data, Norde and Lyklema [1991] have outlined a number of effects that contribute to the affinity of a protein for a surface; affinity increases if: 1) the sorbent surface is more hydrophobic, 34 3 .0 - r [mg m"2] c [g dm- J] Figure 1.8: Adsorption isotherm at pH 7.0 and 25°C for hen egg-white lysozyme on negatively charged polystyrene latex in 50-mM KC1 solution. [Adapted from Haynes et al, 1994.] 2) the protein exterior is more hydrophobic, 3) the protein is structurally more unstable, 4) the overall charge potential of the protein is opposite to that of the surface, 35 5) a minimum number of ions are incorporated into the protein/surface interface, i.e. the magnitude of protein surface charge density is exactly neutralized by that at the sorbent surface, 6) ions in the system have a relatively high valency and low (negative) Gibbs energy of hydration. Numerous analyses of the dependence of the adsorption plateau on system variables have indicated that adsorption is driven by a complex set of subprocesses rather than by a single effect. For instance, electrostatics are a significant driving force for protein adsorption, but not the singular dominating force, as shown by the studies of hen egg-white lysozyme, bovine pancreas ribonuclease, myoglobin and calcium-containing a-lactalbumin adsorbed onto positively charged polystyrene at pH 7 [Haynes and Norde, 1994; Arai and Norde, 1990]. The proteins mentioned are of similar size and shape, but differ in isoelectric points and hydrophobicities. Adsorption plateaus for the proteins on PS+ follow their electrostatic characteristics; that is, proteins with the highest electrostatic attraction (the ones most negatively charged) adsorb to the highest surface concentration. The same is observed for negatively charged polystyrene, where a higher adsorption plateau is associated with the more positively charged proteins. Inconsistencies exist however, which point to the fact that effects other than electrostatic ones are important. For instance, a-lactalbumin adsorbs strongly to negatively charged polystyrene despite being negatively charged itself at pH 7. As well, plateau values for ribonuclease adsorbed 36 onto positively and negatively charged polystyrene at pH 7 are essentially the same even though ribonuclease is positively charged at the given pH. What is clear from these isotherm studies is that the adsorption process is irreversible with respect to dilution at otherwise constant conditions (i.e. the thermodynamic test for reversibility). A thermodynamic framework is now required which provides a basis for understanding the energetics which result in this observed irreversibility. 37 2. Model Development The main objective of this thesis is to estimate the Gibbs energy of protein adsorption, AadsG, using a thermodynamic model incorporating both the reversible and irreversible components of the process. In this chapter, the proposed model for determining AacjsG and its derivation are presented. The estimate will be compared to results of past models which are based on the assumption that protein adsorption is entirely reversible. The results of our model will therefore not only estimate the magnitude of the irreversible component and its contribution to the total force driving protein adsorption, but may also provide an estimate of the errors associated with treating the process reversibly. 2.1 Protein adsorption isotherms and quasi-equilibrium theory Figure 2.1 shows a schematic of the adsorption isotherm for bovine serum albumin on silica particles [Norde and Haynes, 1995]. The direction of the arrows on the curves shown in Figure 2.1 indicate whether the data reflect the ascending isotherm where the total protein concentration is progressively increased, or the descending isotherm where the free protein concentration is diluted at otherwise constant conditions. Several isotherm features are seen which are generally observed in globular protein adsorption. First, adsorption isotherms for proteins on solid surfaces are complex. Second, both ascending and descending isotherms are time invariant, indicating that at a given free protein concentration, the system can exist in more that one (quasi-)equilibrium state. 38 These states are characterized by local minima in Gibbs energy which are separated by energy barriers that prevent the transition from one state to the other; hence, the overall adsorption process is prevented from following a reversible path. Third, for a given ascending isotherm there are an infinite number of descending isotherms, each of which is defined by the departure point from the ascending curve. Finally, to the lowest free protein concentrations measured to date, there is no evidence that the descending isotherms rejoin the ascending isotherm at low protein concentrations. 39 True thermodynamic equilibrium requires that all descending isotherms trace exactly the ascending isotherm. This trait is not observed in the adsorption isotherms of BSA on silica. In the context of protein adsorption, irreversibility, or hysteresis is apparent when the protein surface concentration 'lags behind' with respect to changes in the bulk protein concentration. Although hysteresis is not considered to be a thermodynamic equilibrium state, it is stable by nature, and therefore is often referred to as a metastable, quasi-stable or quasi-equilibrium state. The time-independence of hysteresis allows it to be treated as a state function [Neumann, 1973]. What is required then is a comprehensive adsorption theory which includes those effects (or subprocess) leading to the observed hysteresis in adsorption isotherms. This observation is not new. What has to date prevented the development of such a theory is the apparent intractable nature of the problem if one correctly acknowledges that reversible thermodynamics cannot be used to describe an adsorption process in total when hysteresis is observed. In this thesis, we offer a methodology, based on the assumption that quasi-equilibrium theory can be applied to the ascending adsorption isotherm, for establishing an appropriate thermodynamic framework to describe all energetics of a protein adsorption process, including those that lead to binding hysteresis and the related irreversible state of the adsorbed protein. This assumption is justified by two experimental observations which appear to hold for all protein adsorption processes. First, ascending isotherms for protein adsorption to solids show features consistent with equilibrium adsorption processes and associated theories. In particular, free protein can be detected in solution prior to reaching surface saturation. This observation, combined 40 with the overall Langmuir-type shapes of ascending isotherms, has motivated a number of equilibrium thermodynamic treatments of the protein adsorption process. Second, provided solute dilution is not allowed, the shape of the ascending isotherm is independent of the number and size of solute concentration step increases used in measuring the curve. To apply quasi-equilibrium theory to adsorption data such as that shown in Figure 2.1, we divide the Gibbs energy change A a ^G describing the overall adsorption process at any adsorption condition (i.e., any free protein concentration) into a quasi-equilibrium component AadsGqe, and a residual irreversible component AadsGir so that ^ G = A a d s G q e + A a d s G i r (2.1) We assume that the ascending isotherm describes a quasi-equilibrium between free protein and a specific but uncharacterized adsorbed state which we will attempt to characterize; AadsGqe can then be determined directly from the 'quasi-equilibrium' binding constant Ka regressed from the ascending isotherm =-RT In Ka (2.2) By definition, AadsGqe (per mole of protein) is a state function which does not depend on free (or adsorbed) protein concentration, but does depend on temperature, pH and all other system variables. 41 What remains then is to evaluate AadsGir at any adsorption condition. Since the trajectory of the descending isotherm is unique to the departure point from the ascending isotherm, AadsG,r is a function of free protein concentration. The entropic contribution A^SV to this compositional dependence has been determined by Everett [1954], who applied domain theory to the description of the irreversible entropy gain generated in hysteretic adsorption of benzene onto activated carbon [Everett and Whitton, 1955]. For adsorption from liquid solvents, Aa<&S,r has the following functional dependence [Everett, 1954; Jennissen, 1985] A^S^RJ^rdWP] (23) where [P] is the free protein concentration, T([P]) is the surface concentration, and T* is the surface concentration at the departure point from the ascending isotherm. The integration is over the closed loop defined by the descending and ascending isotherms and is therefore a unique function of the departure point. Knowing A^S^P]) allows for the evaluation of AaarjG,r([P]), the irreversible Gibbs energy loss which accompanies a protein adsorption process at any specified condition. AadsGtr and AadsSir are related by the fundamental equation for the Gibbs ensemble A^G,([P]) = A^//,([P]) - 7A^,([P]) (2.4) which can be rewritten as ^G,r([P]) = (AadsH([P]) - AadsHqe) - TA^S^P]) (2.5) 42 All terms on the right-hand side of Equation 2.5 can be determined experimentally, allowing one to arrive at a reasonable estimate of AadsGir, and through Equation 2.1, A a ^G at any adsorption condition. The enthalpy of adsorption, A.adsH, can be measured directly using an isothermal titration microcalorimeter (ITC). The quasi-equilibrium component of the adsorption enthalpy AadsHqe, can be determined through the Gibbs-Helmholz equation using the temperature dependence of the binding constant of the ascending isotherm: Accurate evaluation of AadsHqe requires adsorption isotherm experiments to be carried out at two closely spaced temperatures. 2.2 Interpretation of protein adsorption thermodynamics As outlined in the last section, we propose that the enthalpy of adsorption can be quantified using a combination of quasi-equilibrium theory and direct calorimetric measurements. Some of the most thorough studies into the interpretation of binding enthalpies were carried out by Norde and Lyklema [1978; 1979] and Haynes and Norde [1994], who developed models expressing the overall heat of adsorption as a sum of the enthalpies of five subprocesses: a In A: a qe R (2.6) 43 &adsH = + A A ( F C / / M + k a d s H H + + AadsHion_coad + A^H,, (2 .7 ) where AadsHstr-Pr is the enthalpy of adsorption due to structural changes in the protein, AadsHhyd is the enthalpy change due to changes in the hydration of the interface, A A ^ / Y / / + is the enthalpy change due to dissociation of protons from charged residues on the protein or sorbent surface, AadsHion.coads is the enthalpy change due to incorporation of ions into the adsorbed layer, and AadsHei is the enthalpy change due to electrostatic contributions which include the overlap of electric fields and lateral interactions between proteins. Their model suggests that the two most influential terms in Equation 2 .7 are those accounting for structural changes in the protein (endothermic) and the last three terms on the right-hand side related to the rearrangement of charge at the interface (exothermic). As suggested by Figure 1.2, AadsHhyd is relatively small in magnitude, but may nevertheless be significant if the leading two subprocesses are fully compensating. Of the subprocesses contributing to the enthalpy of adsorption, only that related to changes in protein conformation is clearly irreversible. As shown in Chapter 4 , the protein at the surface often differs from the protein in solution structurally, as shown by spectroscopic techniques, and thermodynamically, as demonstrated by differential scanning calorimetry. The remaining four factors of Equation 2.7 involve the shifting of protons, ions and water molecules, all of which are likely to be reversible processes due to the low-molecular weights and high internal energy of the principal components. 44 Analogous to Equation 2.1, we are free to divide the state function Aa&H into its quasi-equilibrium and irreversible contributions: ^ H = AadsHqe+AadsHir (2.8) Irreversible adsorption subprocesses which may contribute to AadsH include (1) the breakdown of ordered secondary structure in the protein, and (2) the adaptation of protein structure to facilitate formation of multiple solvent-free contacts with the sorbent surface. Thus, if the surface topology of the native state allows for formation of multiple contacts with the sorbent, adsorption may still be irreversible despite being accompanied by only a minor, possibly undetectable change in protein structure. At least a semi-quantitative analysis of the enthalpy change associated with these irreversible adsorption subprocesses can be obtained through the use of a differential scanning calorimeter (DSC). Using a DSC, the enthalpy of denaturation of a protein on a surface can be compared to the enthalpy of denaturation of a protein in solution. The difference between the two values is the change in stability of the protein from its native to adsorbed state. 2.3 Entropy It is not altogether surprising that protein adsorption is irreversible. Conformational changes known to occur during protein adsorption allow the protein backbone to more easily form multiple contacts with the sorbent surface. Evidence of these interactions was first noted by Morressey and Stromberg [1974], who, by detecting shifts in infrared 45 frequencies of adsorbed albumin and fibrinogen on silica, found that multiple contacts are formed between protein carbonyl groups and the sorbent. Binding ranged from 77 contacts per albumin molecule to 703 contacts per fibrinogen molecule. Jennissen, in his studies on phosphorylase B adsorbed onto butyl-Sepharose noted that the degree of hysteresis of a system can be correlated with its multivalency [Jennissen, 1978; Jennissen andBotzet, 1979]. The types of contact taking place between an adsorbed protein and a sorbent surface, (namely, hydrogen bonding, hydrophobic and electrostatic interactions) are relatively weak compared to a covalent bond, and are likely reversible. However, the probability that all the contacts will dissociate at the same time is relatively small, suggesting that the combined effect of multiple contact formation is to render the process irreversible. For instance, if a protein forms on average 150 contacts with a surface at the strength of 1.5 kT per contact, the energy of attachment due to the contacts would approximately equal that of a carbon-carbon covalent bond. Two other theories, both forwarded by Jennissen [1985], have been proposed to explain irreversible protein adsorption. The first is based on the capillary condensation model of Zsigmondy [1911] for describing hysteresis observed in water-vapour adsorption to silica. To quantitatively apply this model to protein adsorption, Jennissen assumed that the adsorbed protein undergoes a transition at the sorbent surface to form a gelatinous phase which cannot desorb. The model successfully represents hysteresis observed at high surface coverages, but cannot explain observed hysteresis at low surface densities (where a gelatinous phase cannot form). Moreover, the model is inconsistent with the negative 46 cooperativity effects observed in irreversible protein adsorption systems such as the adsorption of phosphorylase b to agarose. The second concept, based on surface dynamics theory, is qualitative in nature and cannot be used to directly evaluate adsorption thermodynamics. A more plausible theory, forwarded here, regards irreversibility of protein adsorption as the result of reorientation and reconfiguration of adsorbed proteins. Reorientation refers to the movements of the molecule as a whole, where rotations and shifting on the surface take place to optimise interactions between proteins and the sorbent. Reconfiguration refers to the changes in the protein structure, namely denaturation of the protein on the surface. Evidence of this has been provided by studies using differential scanning calorimetry, proton titration and other analytical methods as discussed in the previous chapter [Haynes and Norde, 1995; Haynes et al, 1994; Norde and Favier, 1992; Andrade et al, 1984; Ball and Jones, 1995]. 47 3. Materials and Methods 3.1 Chemicals Hen egg-white lysozyme (catalogue #L6876) was purchased from Sigma Chemical Company (St. Louis, MO) and was used without further purification. Some important physical properties of lysozyme are shown in Table 3.1. Table 3.1: Physicochemical properties of hen egg-white lysozyme. Property Molar mass (g/mol) 14388 Dimensions (nm3) 4.6x3.0x3.0 Diffusion coefficient (m2/s) 1.04 x 10"10 Isoelectric point 11.1 Total hydrophobicity (J/g)a -7.6 0, % of protein surface which is apOlarb 59 AN-D CT (J/g) Thermal0 +4.1 Denaturanf +4.0 Secondary structure % a-helix 42 % (3-sheet " a: [Eisenberg and MacLachlan, 1986] b: [Lee and Richards, 1971] c: [Privalov, 1979] 48 Microcrystalline silica particles (Sigma Chemical) were used having a size distribution of 0.5 pm to 10 pm, with over 80% of the particles between 1 to 5 microns. The silica surface is hydrophilic and has a point of zero charge between pH 2 and 4 [Van Wagenen et al., 1976]. Reagent grade sodium persulfate was purchased from BDH Limited (Poole, England). Concentrated sulfuric acid was purchased from Fisher Scientific (Nepean, ON). All water used was distilled and filtered through a Sybron/Barnstead NANOpure JJ system. Potassium chloride and potassium hydroxide used for the base salt solution were reagent grade and purchased from J.T.Baker, Inc. (Philipsburg, NJ). Reagent grade hydrochloric acid was purchased from Fisher Scientific (Nepean, ON). Reagents required for I-radiolabelling of lysozyme were as follows. I as sodium iodide in dilute NaOH solution (pH 7-11) was purchased from Amersham Canada Ltd. (Oakville, ON). Methanol and acetone used for TLC analysis were purchased from Fisher Scientific (Nepean, ON). Iodobeads™ were purchased from Pierce Scientific (Rockford, IL). 3.2 Preparation of base salt solution Base salt solutions containing 50-mM KC1 were prepared and adjusting to pH 7.0 by adding aliquots of 50-mM HC1 or 50-mM KOH. 49 3.3 Preparation of protein solution Protein stock solution was prepared by dissolving hydrated lysozyme powder into a 50-mM KC1 solution and adjusting to pH 7.0. The concentration of the protein was measured by taking a sample of the solution and measuring its spectral absorption at a wavelength of 280 nm using a Milton Roy Spectronic 601 spectrophotometer. The extinction coefficient is s(l cm, 280 nm) = 2.483 mL mg"1 cm"1 as found by a calibration curve. This value agrees well with extinction coefficients found in the literature [Worthington, 1977]. The spectrophotometer is within 1% precision, based on repeated measurements of a 0.05-mg/mL lysozyme solution at 22°C. 3.4 Preparation of silica Microcrystalline silica particles were cleaned overnight by stirring in a solution of 0.7 % sodium persulfate in concentrated sulphuric acid. The mixture was then transferred to pyrex glass tubes, and spun down at 10000 rpm in a Beckman J2-21 centrifuge at room temperature for 20 minutes. The supernatant was discarded and replaced with distilled Nanopure water. The silica pellet was resuspended using a suction bulb to continually draw the silica/water solution up and down a glass pasteur pipette while the tube was immersed in a Branson 3200 sonicating bath. Once the silica appeared to be evenly suspended in the water, the solution was centrifuged at 10000 rpm for 5 minutes and the water discarded. This water wash procedure was repeated an additional 5 times. After the final rinse, the silica was placed in a Precision vacuum oven overnight at 85°C and 50 under a vacuum of 4.9 in.Hg. The dried and cleaned silica was stored in a dessicator at room temperature until use. Before each set of isotherm experiments was conducted, a 0.12-g/mL stock solution of silica in 50-mM KC1 was prepared. The solution was adjusted to pH 7 using titrations of 50-mM KC1 or 50-mM KOH. To evenly suspend the silica in the salt solution, the mixture was placed in a sonic bath for 5 minutes. Sonication effectively suspended the silica particles but resulted in no measurable change in specific surface area. The specific surface area of the silica particles were determined by multipoint BET measurements with nitrogen gas using a Quantisorb instrument (Quantachrome Corporation). BET theory is an extension of the Langmuir adsorption model to include multilayer formation on a surface. It assumes the evaporation-condensation properties of the first layer to be that defined by Langmuir theory, and the properties of the second and higher layers to be identical to those of the adsorbate in the condensed liquid state. These assumptions lead to the BET isotherm equation [Adamson, 1990]: 1 + v(/>0 - p) vmc 2- (3-D Po where p is the partial pressure of the nitrogen gas, p0 is the saturation pressure, v is the total volume of gas adsorbed, vm is the volume of gas adsorbed when the entire adsorbent surface is covered with a complete monolayer, and c = exp RT (3.2) 51 where Hi is the heat of adsorption of the monolayer, H% is the heat of liquification of the gas, and R and T are the universal gas constant and temperature, respectively. By constructing a BET plot of p/v(p0-p) versus p/p0, the values of vm and c can be calculated from the intercept and slope. The most widely used method to measure surface area of solids is the adsorption of nitrogen gas at -195°C where the projected surface area of a nitrogen molecule is approximately 16.2A2 [Adamson, 1990]. Figure 3.1 shows the results of BET isotherms measured to determine the specific surface area of the 160-140-120-100-CL 1 o CL 8 0 -CL 6 0 -4 0 -2 0 -0.05 Figure 3.1: BET isotherm data used to measure the specific surface area of particulate silica. See text for details. 52 particulate silica. It can be observed from the data that for the values of p/p0 used, the data fall within the linear region of the equation. The equation is known to be in a linear range betweenp/p0 values of 0.05 and 0.35 [Osipow, 1972]. The specific surface area of silica, As, was found to be 5.6 ±0.45 m2/g silica. 3.5 Cold adsorption and desorption isotherms All cold adsorption isotherms were performed in 10-mL Oakridge polycarbonate centrifuge tubes. To each tube, 12% w/w silica stock solution was added to a total surface area of 1 m . The required amounts of lysozyme stock solution (2 mg/mL) and base salt solution (50-mM KC1, pH 7.0) were then added to create a total volume of 5 mL. The tubes were placed in a 37°C or a 22°C incubator and rotated end-over-end for 18 hours. This incubation period was more than sufficient to allow the system to come to steady state (~ 20 to 30 min). Adsorption to the tube walls was insignificant. Isotherm data were obtained by the depletion method. After the incubation, the tubes were centrifuged at 10000 rpm for 20 minutes at 25°C. The supernatants were then individually drawn off using a glass pasteur pipette and filtered through a 0.2-um Gelman Sciences Acrodisc syringe filter into a pyrex test tube. The purpose of the filter was to remove small pieces of silica which could interfere with the absorbance measurements without removing any of the protein. Previous experiments have demonstrated that the Acrodisc filter does not adsorb protein [Norde and Anusiem, 1992]. The free protein concentration in the filtered supernatant was determined by absorbance measurements at 53 280 nm. Specific surface concentrations of lysozyme on the silica were then calculated using a protein mass balance. Independence of the shape of the ascending isotherm to the protein-concentration step size used was analyzed by constructing a set of ascending isotherm experiments in which a given total protein concentration was reached in either a single step or in a series of steps. In the latter case, each sample was incubated for 18 hours between protein concentration steps. Desorption experiments were also carried out at 37°C and 22°C to examine the reversibility of adsorption in terms of adsorption hysteresis. The ascending isotherms at the two temperatures were measured as described above. For a resulting 5-mL sample at a given point on the ascending curve, descending isotherm data were obtained by either serial-dilution or supernatant-replacement with 50-mM KC1 (pH 7). Jennissen and Botzet [1979] have shown that isotherm data generated by the serial-dilution and solvent-replacement methods are equivalent. Diluted samples were incubated at constant temperature for 18 hours and then analyzed by the same procedure used for the ascending isotherms. 3.6 125l-Radiolabelling of lysozyme l25I-labelling of hen egg-white lysozyme used Iodobeads™ from Pierce Scientific (Rockford, IL), which catalyze the selective substitution of protons at positions ortho to the tyrosine hydroxyl with 1 2 5I. The Iodobead method for radiolabelling was selected 54 because it is a well-proven, mild technique which does not denature or significantly perturb the native structure of lysozyme (or other globular proteins). Thus, the structural and functional properties of the radiolabeled protein are indistinguishable from the unlabelled protein. Hen egg-white lysozyme has three tyrosines, all situated on the exterior of the molecule. Up to six 1 2 5I atoms could therefore be substituted into each lysozyme molecule. The mild reaction conditions of the Iodobead method, however, typically result in the substitution of one to two 1 2 5I atoms per protein molecule. As discussed below, the variable efficiency of the radiolabelling, combined with the natural decay of radioactivity, required daily calibration of the radioactivity of each labelled protein sample against absorbance measurements at 280 nm. A schematic of the radiolabelling procedure is shown in Figure 3.2. Iodobeads are non-porous polystyrene beads one-eighth inch in diameter with surface-immobilized chloramine-T molecules (N-chloro-benzenesulfonamide). Chloramine-T catalyzes the attachment of 1 2 5I to the protein by attacking the phenolic anion of its tyrosine residues, thereby allowing iodination to occur at positions ortho to the hydroxyl group. Mono- or di-substitutions may take place on the tyrosine, and under much harsher conditions, histidine residues may also be iodinated. A size-exclusion column was prepared as follows and incubated overnight to allow for matrix equilibration. Sephadex G-25 fine beads were boiled in water for one hour. Once cooled, the column was gravity-loaded into a 28 x 1.5 cm2 Biorad glass barrel econocolumn and equilibrated with 0.5-M KC1 (pH 7). (The column has polypropylene 55 reservoir fittings and a polyethylene bed support.) The separation column was preadsorbed with unlabelled lysozyme to avoid unnecessary loss of radiolabeled protein. Figure 3.2: Schematic diagram of the Iodobead radiolabelling mechanism. Preadsorption was accomplished by flushing a 1-mg/mL solution of lysozyme in 0.5-M KC1 through the column. When eluent protein breakthrough was detected at 280 nm, it was assumed that the packing was saturated with lysozyme. The settled column was then flushed overnight with 0.5-M KC1 (pH 7.0) pumped at an approximate flowrate of 0.77 mL/min using a Pharmacia P-3 peristaltic pump to remove all protein that was not irreversibly bound to the column. Immediately prior to the start of the radiolabelling, the bottom of the column was plugged and excess liquid at the top of the column was removed. This was done to minimize dilution of the radiolabeled protein when added to the column. 56 Prior to the radiolabelling, 5 to 6 Iodobeads were immersed in water and rotated slowly end-over-end for 1 hour to equilibrate. The protein stock solution used for the radiolabelling contained 0.25 mg/mL lysozyme in 50-mM phosphate buffer at pH 7. A buffer was required to effectively radiolabel the lysozyme. Attempts to radiolabel lysozyme in 50-mM KG1 solution did not succeed, probably due to pH variation in the reaction. The recovered beads, 1 mL of protein stock solution and 20 pL of 125I/NaOH solution were reacted in an uncovered polystyrene tube for 15 minutes. The mixture was gently and periodically agitated to resuspend the beads. The reaction was terminated by pulling the liquid away from the beads using a disposable polyethylene transfer pipette. The 1-mL sample was then deposited onto the separation column carefully, so as to not disturb the column packing. The beads and reaction tube were rinsed with 2 mL of additional unlabelled lysozyme solution (0.25 mg/mL, 50-mM phosphate buffer, pH 7) which was also deposited onto the top of the column. The column was then sealed at the top, the bottom unplugged and the pump started for the separation to begin. Fractions coming out of the column were collected using a Gilson microfractionator. Each fraction was approximately 1 mL in volume. Once collected, the fractions were counted for radioactivity using a LKB Wallac 1282 Compugamma y-counter. The measurement was done by adding 10 pL of the fraction and 990 pL of 50-mM KC1 into a 17x100 mm polypropylene tube, or gamma tube, to have an appropriate specific volume for the gamma count. The tube was sealed with a polyethylene stopper cap and counted for 1 minute. The gamma counts identified two separate peaks from the column. The 57 first peak represented I associated with the protein while the second peak represented 125 unreacted excess I. Fractions containing the highest amount of radiolabeled protein (from the first peak) were pooled and concentrated down to about 4 mL using 1 kD (average molecular weight cut-off) Filtron Microsep Centrifugal concentrators (Northborough, MA). During this time, the separation column was flushed thoroughly with KC1 solution to remove any remaining protein and free 1 2 5I. The concentrated radiolabeled protein mixture was then reloaded into the flushed column and separated a second time to final purity. The fractions were collected and the radioactivity measured using the methods mentioned previously. Determination of the incorporation of I (i.e., fraction of iodine associated with protein over the total amount of iodine in the sample) was carried out using thin-layer chromatography. Whatman Flexible plates of silica gel on polyester (250 um thick) were cut into 10 cm x 1.5 cm strips. At 1.5 cm from the bottom of each strip, 2 uL of purified radioactive sample was loaded. The loaded plates were immersed in a 1:1 acetone/methanol mixture in a covered beaker until the fluid was carried within 1 cm of the top. The strips were then removed and left to air-dry. Once dried, each strip was cut into 1 cm sections which were placed into separate gamma tubes containing 1 mL of 50-mM KC1. The samples were then measured for radioactivity in the y-counter. Only samples that had 96% or better incorporation (percentage of total iodine associated with the protein) were retained and stored at -20°C until required for use. 58 3.7 Hot adsorption and desorption isotherms Stock silica (0.12 g/mL) and base 50-mM KC1 solutions were prepared similarly to those used in the cold protein isotherm. 125I-lysozyme stock solution was made by mixing 1 2 5I-radiolabelled lysozyme (in 0.5-mM KC1, pH 7.0) with unlabelled lysozyme (in water, pH 7.0) in a 1 to 9 ratio. The resulting protein solution at pH 7 also contained 50-mM KC1. The final lysozyme concentration was measured using a Hewlett Packard 8450A UV/VIS spectrophotometer at a set wavelength of 280 nm. Adsorption isotherms were carried out in 2-mL disposable polypropylene tubes (National Scientific Supply Co., Inc.). The original caps were replaced with polyethylene stopper caps (Evergreen Scientific) which were found to be leakproof in contrast to the original ones. This arrangement was particularly suitable for radioactivity studies since the entire ensemble could be placed into a gamma tube for counting. Each sample contained 0.2 m2 of silica surface area in a maximum volume of 1.5 mL. After the silica stock (12% w/w), protein stock (« 0.65 mg/mL) and 50-mM KC1 solutions were added in specified proportions, the loaded tubes were left to turn end-over-end in an incubator for 18 hours. Experiments at 37°C were equilibrated in a Fisher Scientific Isotemp incubator, while isotherms at 22°C were equilibrated in a temperature controlled room. Protein standards made up from I-labelled lysozyme stock solution were used as radioactivity calibration standards to calculate the amount of radioactivity per amount of protein. For each calibration curve, the amount of radioactivity measured in the gamma-counter was plotted against spectrophotometer readings (280 nm) of the same sample. 59 Calibration curves were produced for each isotherm experiment to minimize the error associated with the differences in stoichiometry between the samples of radiolabeled protein used, and to eliminate the need to incorporate radioactive decay into the calculations. An example of a calibration curve is shown in Figure 3.3. 400 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 concentration (mg/mL) Figure 3.3: A typical calibration curve used to determine the specific radioactivity for a lysozyme sample. The gamma count (background subracted) is plotted against the protein concentration for a 10-pL sample. 60 Ascending and descending adsorption isotherms were measured for pure I-labelled lysozyme and for mixtures of unlabelled and 125I-labelled lysozyme by directly assaying radioactivity both in the bulk solution and on the washed sorbent surface after equilibrium. As a result, direct mass balance verification was possible and used as a check of experimental accuracy. All desorption isotherms for 125I-labelled lysozyme were constructed either by the serial-dilution method or by the replacement method from a specified departure point from the ascending isotherm. 3.8 Isothermal titration calorimetry experiments All calorimetric titrations used unlabelled lysozyme to avoid radioactive contamination of the calorimetry equipment. Two sets of isothermal titration calorimetry (ITC) experiments were performed: constant-temperature enthalpy of adsorption A^H determinations, and variable-temperature Aa^H studies to estimate differential heat capacities AacjsCp of adsorption. Both sets of ITC experiments were conducted in a Calorimetry Sciences Corp. Model 4200 Isothermal Titration Calorimeter. A schematic of the instrument is shown in Figure 3.4. ITC time constants and the proportionality constant for converting voltage output for the Thermal Electric Device to units of power (pW) were calibrated by standard electrical pulses. Ten 500-pJ pulses (250-pW pulses of 2 s each), spaced 1800 s apart, were delivered to the sample cell through a 1000-Q internal block heater. The heater current 61 Figure 3.4: A schematic diagram of the Calorimetry Sciences Corp. Model 4200 Isothermal Titration Calorimeter. [Adapted from the CSC ITC manual.] 62 and the heater voltage were 0.5 mA and 0.5 mV, respectively. Both the sample and reference cells contained 1 mL of degassed, deionized water (Nanopure). The stir speed in the sample cell was set at 100 rpm, which allowed for rapid (convective) heat transfer without introducing significant background heat. Figure 3.5 shows the power thermogram recorded for each 500-uJ pulse. Peaks pointing upwards represent exothermic processes. The area under each peak therefore gives the differential heat released from the sample cell (relative to the reference cell) following a standard 500-uJ internal pulse. The instrument is calibrated by determining the ratio of input heat (500 uJ) to the average integrated heat output, which should also equal 500 uJ. 18 time, hr Figure 3.5: An example of raw titration data taken to calibrate the ITC. This particular titration shows measurements of a series of 500-uJ electrical pulses delivered to the sample cells using a 1000-Q internal block heater. The sample and reference cells each contained 1 mL of degassed, deionized water. 63 Proper calibration of the instrument was then confirmed by measuring standard heats of mixing (protonation reaction) for titrating 250-mM Tris buffer (pH 7) with 10-uL injections of 1.0-mM HC1 standard. The enthalpy of mixing (J/mol) for this reaction is known to depend on temperature according to the equation A/T = -49659 + 102.287- 0.592757/2 where T is in °C (3.3) [Christensen, 1976]. The experiment was performed as follows: 250-mM Tris (Tris(hydroxymethyl) aminomethane) base was prepared by dissolving 3 g of Tris in 100 mL deionized water and thoroughly degassed. The 3 mL reference and sample cells of the calorimeter were cleaned, triple-rinsed with the 250-mM Tris base solution, and then loaded with 1 mL of 250-mM Tris base. The loaded cells were connected to their equilibrium casings and inserted into the calorimeter. The 250-mL burette was then loaded with degassed 1.0-mM HC1 standard and inserted into the sample cell. The instrument was then allowed to thermally equilibrate, a process which generally took between 1 to 2 hours. The time between each 10-uL injection was set at 2400 s to allow the thermal response to return to baseline. 3.8.1 AadsH measurements for lysozyme on silica In all protein titration experiments, lysozyme solution (3.5 mg/mL) was titrated into a 1 mL of silica suspension (0.005 g/mL), with a thermally equilibrated silica suspension of identical volume and composition serving as reference. The titrations were carried out so that 95% of the adsorption plateau was reached about two-thirds of the way through the 64 run. All samples were continuously mixed with an internal turbine-type blade rotating at 100 rpm, which was sufficient to fully suspend the silica and eliminate mass-transfer effects which might broaden the thermal peak. Lysozyme, silica and background-salt stock solutions, all at pH 7, were prepared as described above. were thoroughly degassed prior to loading to avoid air bubbles forming on the cell walls which can decrease both heat transfer and heat capacities. Once the system reached thermal equilibrium (ca. two hours), twenty-five 10-pL aliquots of protein solution were injected into the sample cell. The time between injections was set at 2400 s to allow establishment of a constant baseline signal before and after each thermal peak. Each titration experiment lasted about 17 hours. 3.8.2 AadsCp measurements Differential heat capacities at ca. 30°C were determined by measuring A^T/data at 22°C and 37°C. AadsCp values were then calculated using the differential form of the thermal gradient in Aa^//at constant pressure: The two temperatures, 22°C and 37°C, were chosen to allow for determination of a statistically meaningful difference in AadsH. The sample and reference solutions, and the protein solution to be injected by syringe (3.4) 65 3.9 DSC (lysozyme on silica) Differential scanning calorimetry experiments were performed in a Calorimetry Sciences Corp. Model 7707 DSC. Solutions of 0.8 mg/mL hen egg-white lysozyme in 50-mM phosphate buffer (pH 7) and 0.15 g/mL silica in 50-mM phosphate buffer (pH 7) were prepared as stock solutions. Protein concentrations were determined by spectrophotometry at 280 nm. For experiments conducted at surface saturation, 600 uL of silica stock solution was mixed with 2 mL of stock protein solution and incubated at 37°C for one hour. The mixture was then centrifuged and the supernatant extracted in order to remove all excess free protein in solution. The adsorbed protein and silica were rinsed once with phosphate buffer then resuspended in 600 uL buffer. Approximately 0.5 g of the suspension was weighed into the sample cell for each run. In preparing samples for experiments conducted at protein concentrations less than saturation, the appropriate amount of protein stock solution corresponding to the desired surface concentration was added to 600 uL of silica stock solution. After incubation, the mixture was resuspended in 600 uL of buffer and then loaded into the sample cell. Runs at 0.46, 0.74 and 1.0 of saturation level were carried out. Background excess thermal power scans with the silica solution were conducted and subtracted from the adsorbed protein scans. A solid nickel-plated aluminium cell with a heat capacity corresponding to that of 0.5 g of water was utilized as a reference cell for all DSC runs. The scan rate was 1 °C/min. Data analysis was performed using software provided with the calorimeter. 66 3.10 DSC (lysozyme on PSS-HC) Differential scanning calorimetry experiments for hen egg-white lysozyme on highly charged polystyrene sulphonate were also performed on a Calorimetry Sciences Corporation Model 7707 DSC. The highly charged polystyrene sulfonate (PSS-HC) colloidal dispersion was kindly provided by Prof. Willem Norde (Department of Physical and Colloidal Chemistry, Wageningen Agricultural University). The particles were 175 nm in diameter with a specific surface area of 32.5 m /g and a specific charge of 31.4 pC/cm . The PSS-HC was stored in water in a 20% w/w solution which was flushed with N2 gas to minimize oxidation of the sorbent surface during storage. Prior to each experiment, the PSS-HC was diluted in a solution of KC1, resulting in a 10% w/w stock solution of PSS-HC in 50-mM KC1. The pH of the solution was adjusted to 7.0. Stock solutions of lysozyme in 50-mM KC1 (~5 to 10 mg protein per g of solution, depending on the surface coverage studied for the experiment) were made. The PSS-HC and lysozyme stock solutions were then combined and rotated for 1 hour. At this point, the pH of the solution was measured and adjusted to 6.0 with either 50-mM HC1 or KOH, and the solution was left to rotate for an additional 15 minutes. One-half gram of sample was weighed into each of the DSC ampules for scanning. The adsorbed protein samples were scanned from 10°C to 90°C at an ascending scanning rate of l°C/min. Background scans of PSS-HC solutions (pH 6.0) were carried out and 67 subtracted from the adsorbed protein runs. One-half gram of water was used as the reference. As well, DSC experiments on lysozyme in 50-mM KC1 (~5 to 10 mg protein per g of solution, pH 6.0) were carried out for comparison to the adsorbed protein runs. The protein solutions were also scanned from 10 to 90°C and under the same conditions as the previous experiments involving adsorbed protein. 68 4. Results and Discussion We developed a model in Chapter 2 for describing changes in thermodynamic state functions resulting from the nonspecific adsorption of globular proteins to solid planar surfaces. Testing of this new model requires a consistent and complete set of thermodynamic and adsorption isotherm data for a well-defined protein adsorption system. Regrettably, such data are not available. The primary experimental objective of this thesis is therefore to define a suitable model adsorption system and to obtain a complete set of adsorption and thermodynamic data required for model analysis. The required data includes (1) the ascending isotherm and a set of descending isotherms for adsorption at a fixed pH, ionic strength, and temperature which extend to vanishingly small concentrations of free protein, (2) the dependence of the ascending isotherm on adsorption temperature (at otherwise constant conditions), (3) the standard-state heat of adsorption at the adsorption pH and temperature, (4) the degree of protein denaturation resulting from the adsorption process, and (5) the standard heat-capacity change resulting from the adsorption process. 4.1 Selection and properties of the model system 4.1.1 Selection of the model system The complex nature of nonspecific protein adsorption requires that a relatively simple and well-understood protein/surface model system be utilized to carry out the thermodynamic 69 analysis. We chose the adsorption of hen egg-white lysozyme (E.C.3.2.1.17) on microcrystalline silica in 50-mM KC1 at 37°C and pH 7. Hen egg-white lysozyme, a globular protein with a molecular weight of 14388 Da, has a relatively stable native state whose physical properties and chemical behaviour have been established in previous studies [Osserman et al., 1974; Pfeil and Privalov, 1976a,b,c]. Some of its properties are outlined in Table 3.1. Microcrystalline silica is a well-characterized solid sorbent [Bergna, 1994]. The silica particles used are approximately 1 to 5 microns in size, with a specific surface area A s of 5.6 m /g as determined by multipoint BET adsorption isotherms discussed in Chapter 3. Lysozyme (pi of 11.1) is positively charged at pH 7 while silica (point of zero charge of approximately pH 3) is negatively charged. Therefore, in the absence of other forces, a large affinity between lysozyme and silica would be expected because of the ionic attraction between the two at neutral pH. Hen egg-white lysozyme has been reported to be a stable, or "rigid" protein. Such proteins traditionally do not show a high affinity for surfaces. The stability of lysozyme has been determined by Privalov and Khechinashvili [1974] through DSC experiments. The Gibbs energy of stabilization for lysozyme (60 kJ/mol) is significantly higher than similarly sized proteins such as bovine pancreatic ribonuclease A (44 kJ/mol), bovine pancreatic a-chymotrypsin (49 kJ/mol), bovine heart ferricytochrome c (9.0 kcal/mol) and sperm whale ferrimyoglobin (50 kJ/mol). A background solution of 50-mM KC1 was used for a number of reasons. The presence of low molecular-weight ions such as potassium and chlorine has a tendency to stabilize a 70 protein adsorption system by partially screening long-range electrostatic forces. The ions may coadsorb to neutralize same-charge interactions within the adsorbing layer. A low ionic strength background allows for these advantages without eliminating the influence of electrostatic forces between the protein and sorbent surface. For our experimental system, an unbuffered background solution was chosen so that pH changes due to proton incorporation could be detected. However, under these conditions, the pH did not appear to change upon adsorption, indicating that relatively few protons were incorporated during the process. 4.1.2 Physico-chemical equivalence of radiolabeled and unlabelled lysozyme Radiolabelling is among the most sensitive general methods (fluorescent tagging and amino-acid analysis are others) for detecting dilute amounts of protein. Accurate measurements of picomolar concentrations of radiolabeled protein in solution have been reported [Feng and Andrade, 1994]. For our purposes, radiolabelling must satisfy the condition that it does not alter the adsorption properties of lysozyme. There have been reports of cases where radiolabelling affected the adsorption properties of a protein. For instance, van der Scheer et al. [1978] found that 125I-labelled human serum albumin was adsorbed preferentially to polystyrene and silicon rubber surfaces, regardless of the labelling technique used. In most cases, however, radiolabelling does not alter adsorption properties [Brash et al, 1974; Feng and Andrade, 1994; Grant et al, 1977; Horbett, 1981]. For mixtures of radiolabeled and 71 lysozyme adsorbed per m2 of surface, as a function of the fraction of radiolabeled protein. Here, surface concentrations are reported from solution-depletion measurements in which the free lysozyme concentration was determined by gamma counts. The upper data set (•) represents a solution containing 0.2 m2 of particulate silica where the surface concentration F is near (0.89Tp/) monolayer coverage, Tpl. The lower data set (•) represents a surface coverage of 0.73rp/. 1.6 CM E E 1.4-1.2-1.0-0.8-0.6-0.4-0.2-0.0 • at low surface coverage • at high surface coverage -1 1 1 1 1 1 1— 0.2 0.4 0.6 0.8 Fraction of radiolabelled protein 0.0 1.0 Figure 4.1: A comparison of binding characteristics between labelled and unlabelled lysozyme. Surface concentrations are measured by radioactivity counts. 72 Preferential binding of the labelled or non-labelled protein would result in a dependence of r on the ratio of radiolabeled to unlabelled protein in the system. This would be especially apparent at high surface coverages, where competitive adsorption for a limited number of sites on the surface takes place. The invariance of T with the fraction of radiolabeled protein at both surface coverages indicates that 1 2 5I labelling has no influence on the adsorption properties of lysozyme. 4.1.3 Detection limit It was necessary to determine the specific radioactivity of the radiolabeled lysozyme in each experiment to account for variations in radiolabelling stoichiometry and radioactive decay with time. To achieve this, calibration curves of radioactivity measured in the gamma counter versus protein concentration (as determined by spectrophotometric measurements taken at 280 nm) were taken for each adsorption isotherm carried out. From these calibration curves, the detection limit of free radiolabeled protein was calculated. Figure 3.3 shown in the previous chapter is a typical calibration curve for radiolabeled lysozyme. The detection limit, calculated as the concentration at which the ordinate value of the calibration curve equals three times the standard deviation of the measurement at zero concentration, is estimated to be 4.6 nM. This detection limit, although much better than standard methods such as absorbance, is an order of magnitude or more higher than that for some other radiolabelling studies [Feng and Andrade, 1994; Horbett, 1981]. This may be attributed to a number of factors, for example, the mild technique used to iodinate 73 the samples, and the fact that the radiolabeled protein was diluted with unlabelled lysozyme prior to experimentation, reduced the sensitivity of the measurements. Nevertheless, the detection limit achieved was sufficient for our studies and no further attempts were made to reduce the detection limit by improving the radiolabelling procedure. 4.2 Binding isotherm data The adsorption isotherm provides a quantitative description of the affinity of a protein to a surface, the capacity of the surface, and to what extent the protein remains on the surface. Protein-sorbent and protein-protein interactions on the surface can be studied from variations of the isotherm with pH and temperature. As well, the overlap of the descending binding isotherm to the ascending data reveals the degree of reversibility of the adsorption process and whether a true equilibrium state exists in the system. This section will present binding isotherm data taken for the adsorption of radiolabeled hen egg-white lysozyme on silica. The isotherm data will then be used to determine the parameters necessary for the thermodynamic model developed in Chapter 2. We will first examine ascending isotherms to determine the characteristics of the quasi-equilibrium state. Descending binding isotherms will then be studied. 74 4.2.1 Ascending isotherm at 37°C Figure 4.2 shows ascending isotherm data for radiolabeled hen egg-white lysozyme on silica in 50-mM KC1 solution at 37°C. The shape of the isotherm is typical for nonspecific protein adsorption: a relatively steep initial slope followed by the emergence 0.10 0.15 0.20 [P] ( m g / m L ) Figure 4.2: Ascending isotherm binding data for radiolabeled hen egg-white lysozyme on silica in 50-mM KC1 solution at pH 7 and 37°C. The open and closed squares show separate runs of the same experiment. 75 of a plateau (Tpl) at surface concentrations (Jf) near monolayer coverage. Assuming a projected surface area of 1260 A for lysozyme (which corresponds to an average hydrated protein diameter of 40 A), the plateau value of 9.2 x 10"2 pmol/m2 (or 1.3 mg/m ) corresponds to 0.7 times monolayer coverage based on the silica specific surface area of 5.6 m /g measured by BET analysis. Plateau values slightly below monolayer coverage are typical of nonspecific protein adsorption processes where the protein sorbent interaction is dominant and protein structural changes are known to occur. In such systems, the shape of the measured binding isotherm is therefore thought to reflect the nature of the interaction of silica with fully solvated lysozyme at the given solution conditions, and does not include contributions from undesirable events such a lysozyme aggregation or condensation (multilayering) at the silica surface. The finite initial slope of the isotherm in Figure 4.2 indicates a relatively weak attraction of lysozyme for silica compared with that for more amphipolar sorbents. For lysozyme adsorption on a negatively charged polystyrene latex at pH 7, Haynes and Norde [1995] found a near infinite initial slope for the isotherm. They argued that the high affinity is due to a combination of strong electrostatic attraction, sorbent and protein dehydration effects, and changes in protein conformation which increases the conformational entropy of the protein. Lysozyme and silica are oppositely charged at pH 7, indicating that electrostatics also contribute to the driving force for adsorption in our system. Due to the hydrophilicity of the sorbent, dehydration effects should provide a much smaller driving force for adsorption to silica (and thus a lower initial slope). The contribution of changes in protein structure will be explored by differential scanning calorimetry in a later section. 76 In accordance with our (quasi-Equilibrium adsorption theory, the shape of the ascending isotherm is time-invariant and shows that free protein can be detected in solution prior to reaching surface saturation. Moreover, the ascending isotherm does not depend on the manner in which the protein was added. For a given total protein concentration, the ascending adsorption isotherm generated when lysozyme is added in a single dose is identical to that when the lysozyme is added in two steps with an 18-hour incubation period between the additions. With these model assumptions verified (see Chapter 2), we have estimated a quasi-equilibrium association constant Ka for the ascending isotherm by fitting a Langmuir-type isotherm by nonlinear least-squares regression TplK TPl T(c) = — ( 4 . 1 ) l + Ka[P] to the data in Figure 4.2 (see curve in figure). The quasi-equilibrium adsorption constants for lysozyme binding to silica at 37°C are Tpl - 9.2 (±1.6) x 10"2 umol/m2 (= 1.3 mg/m2; MW = 14388 g/mol) and Ka = 9.8 (±3.7) x 105 M"1. This Ka is similar to those reported for weak antigen-antibody interactions and is significantly stronger than most binding events between low-molecular-weight analytes. It is useful to know how Equation 4.1 was derived. Since the adsorption process is considered to be a (quasi-)equilibrium reaction, it can be described through the equilibrium equation, 77 [P] + [S] [PS] (4.2) where [P] is the free protein concentration (M), [S] is the concentration of free binding sites on the sorbent surface (M), [PS] is the concentration of the complex (M), and Ka is the binding equilibrium constant (M"1). Traditionally, the concentration of surface-bound protein is reported as r([P]) in units of moles bound protein per m2 of surface area. The relation between T([P]) and [PS] is therefore. r ( ™ = ™ ( « ) where As is the specific surface area of the sorbent (m2/g) and cs is the sorbent concentration (g/L). Consequently, the equilibrium constant, Ka, can be written in terms ofr([P]), [PSi=r{[P]Hcs [P][S] [P][S] An overall mass balance on the concentration of surface binding sites gives [SI = [S] + [PS] = [S]+ Ka[P][S] (4.5) where [S]0 is the total molar concentration of surface binding sites on the sorbent. 78 Substituting Equation 4.5 into Equation 4.4 and solving for T([P]) then gives the appropriate form of the Langmuir adsorption isotherm for protein adsorption. The quantity ([S]JAscs) is identified as Tpl, the maximum binding capacity of the sorbent (mol/m ), to give Equation 4.1. 4.2.2 Temperature dependence of ascending isotherm and initial slopes The temperature dependence of the (quasi-)equilibrium constant found from Equation 4.1 can be used to determine the reversible enthalpy of adsorption, AadsHqe, according to the Gibbs-Helmholtz equation: Ascending isotherms were therefore measured for the adsorption of radiolabeled lysozyme to silica at 22°C as well as 37°C. The measured ascending isotherm at 22°C is shown in Figure 4.3. Similar to the isotherm at 37°C, the data resembles a typical monolayer adsorption system. When fitted to the Langmuir model described by Equation 4.1, the data in Figure 4.3 give values for Tp! and Ka of 8.7x10"8 mol/m2 and 6.9x105 M"1, respectively. (4.6) (4.7) 79 0.00 0.05 0.10 0.15 [P] (mg/mL) 0.20 0.25 Figure 4.3: Ascending isotherm binding data for radiolabeled hen egg-white lysozyme on silica in 50-mM KC1 at pH 7 and 22°C. Equation 4.7 can be approximated to T2 Tx ^ ^Hqe(T2) T2-Tx ~ T22 Application of Equation 4.8 gives a value for AadsHqe of 18(±9) kJ/mol. This positive value indicates that the quasi-equilibrium process described by the ascending isotherm is 80 endothermic. The value of AadsHqe will later be compared to enthalpy measurements for the overall process. Le Chatelier's principal applied to Equations 4.2 and 4.4 states that for an endothermic reaction to occur, dK dT ±>0 (4.9) and therefore in the context of the measured ascending isotherms, the initial slope must increase with increasing temperature. 1.0 CM E 0.8-J 0.6 A 0.4 H 0.2-^  0.0 a-• -,0 37°C \ • - 22°C • 22°C isotherm O 37°C isotherm 1 1 1 1 1 1 1 " 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 [P] ( m g / m L ) Figure 4.4: A comparison of the initial slopes of isotherm binding data for radiolabeled hen egg-white lysozyme on silica in 50-mM KC1 solution at 37°C at 22°C. 81 A comparison of the isotherms at the two temperatures as shown in Figure 4.4 demonstrates that the initial slope at 37°C is slightly higher, confirming that the adsorption process is endothermic, and that for the quasi-equilibrium state, entropy is the leading driving force. The closeness between the slopes at the two temperatures, however, would also imply that the magnitude of AadsH is small and therefore in agreement with analysis by the Gibbs-Helmholtz equation. 4.2.3 pH dependence of ascending isotherm Experiments were conducted measuring the variation of surface concentration of lysozyme at saturation levels versus changes in pH. Figure 4.5 shows that Tpl depends on pH. A maximum in Tpl is observed between pH 9 and 10, which lies between the point of zero charge for lysozyme (p.z.c. « 11) and that for the silica sorbent (p.z.c. « 3). Through potentiometric titration experiments, Haynes and Norde [1994] argued that the adsorption pH where Ypl is a maximum corresponds to a point where the charge densities of the contacting surfaces are optimally matched. Thus, adsorption requires a minimum transfer of low-molecular-weight ions into the interfacial layer to neutralize excess charge. No residues on hen egg-white lysozyme titrate between pH 8 and pH 7 [Haynes and Norde, 1994]. Protonation of surface hydroxyls on the silica surface is also small over this region [van Wagenen et al., 1976]. Thus, as evidenced by the lack of a measured pH change accompanying the lysozyme adsorption process, ion incorporation into the contact 82 2.0 1.5 J C \ l , E I51.0 0.5 H 0.0 S a 4 B B • • • 8 PH 10 12 Figure 4.5: A plot showing saturated surface concentration (Tpl) versus pH for hen egg-white lysozyme adsorbed onto particulate silica in 50-mM KC1 at 37°. layer is likely near its minimum at the adsorption pH. As noted in Chapter 2 (see Equation 2.7 and associated discussion), the dominant contributions to Aa^H are generally made by AadsHstr.pr , AadsHion (=AadsHH++AadsHion.coad), and AadsHei- However, given that our model adsorption system is near the pH optimum, we might expect KdsHstr-pr and AadsHei to dominate, causing Aa&H to be a balance between the highly endothermic AadsHstr.pr and the exothermic A a ^i/ e / . 83 4.2.4 Descending isotherm data Figure 4.6 shows surface concentrations (O) of 125I-labelled lysozyme at steady state (18 hours equilibration) following sequential dilution (or removal) of free protein from an ascending-isotherm departure point (•) of 2.67x10"2 umol/m2, which falls near the linear region of the ascending isotherm (r = 0.29rp/). As is usually observed in nonspecific protein adsorption, dilution of free protein does not lead to measurable desorption of bound protein [Norde and Haynes, 1995; Haynes et al, 1994; Jennissen, 1995]. Dilution i i I i r. 1 1 1 1 1 1 1 r 0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 [P] ( m g / m L ) Figure 4.6: Data showing the sequential dilution of free protein starting from an ascending departure point at 0.29F/ for radiolabeled hen egg-white lysozyme adsorbed onto particulate silica in 50-mM KC1 at pH 7 and 37°C. 84 or replacement of free lysozyme down to a concentration of 4.6 nM, the detection limit of 125 our I-labelled protein, leads to no appreciable loss of adsorbed lysozyme at any departure point below Tpl (see Figure 4.6). Thus, an infinite number of desorption isotherms can be generated off the ascending isotherm for lysozyme adsorption to silica at pH 7 and 37°C. Four such desorption isotherms, measured to the detection limit of 4.6 nM free lysozyme, are shown in Figure 4.7. The departure points of the descending isotherms correspond to 0.29rp/0.46Tp/, 0.74rp/, and LOOT*'. 1.6 -i 1 0.00 0.05 0.10 0.15 0.20 0.25 [P] ( m g / m L ) Figure 4.7: Desorption isotherms of hen egg-white lysozyme adsorbed to particulate silica in 50-mM KC1 solution at pH 7 and 37°C. The departure points of the descending isotherms correspond to Q.29Tpl, 0.46Pp/, 0.74P7', and i.orp/. 85 As might be expected, construction of descending isotherms by sequential dilution leads to increasing error with degree of dilution. As a result, as shown in Figure 4.6, dilution did not allow us to reduce with accuracy free-protein concentrations down to the detection limit. However, serial dilutions experiments allowed for determination of descending isotherm data at free-protein concentrations between the departure point and the detection limit. The irreversibility of lysozyme adsorption to silica was further confirmed by the replacement method, where silica-bound 125I-labelled lysozyme is first extensively washed and then contacted with protein-free 50-mM KC1 for 18 hours at 37°C. This experiment, where the loaded silica surface is first washed with 50-mM KC1 solution to remove any unbound protein, was repeated over a range of surface concentrations up to F p / . For each surface concentration, no free 125I-labelled lysozyme could be detected in solution after the 18 hour equilibration period. Gamma counts of the centrifuged silica pellet indicated that all protein remained bound to surface. Thus, at least down to the detection limit of 125I-labelled lysozyme, desorption isotherms do not reconnect with the ascending isotherm. 4.3 Isothermal titration microcalorimetry and the enthalpy of adsorption 4.3.1 Instrument calibration and raw data Isothermal titration calorimetry (ITC) was used to measure standard enthalpies of adsorption AadsH for lysozyme on silica at pH 7 and 37°C in 50-mM KC1. ITC 86 measurements were also made at 29.5°C and 44.5°C in order to estimate the differential heat capacity change, AadsCP, for the adsorption process. The Calorimetry Sciences ITC was calibrated using both standard electrical pulses and a known chemical standard as described in Chapter 3. The electrical calibration (Figure 3.5) was used to determine the proportionality constant for converting the voltage output from the thermal electric device (TED) to power units (uW). The instrument proportionality constant was set by multiplying the previous proportionality constant by the ratio of input heat to the average integrated heat output. In all cases, the new proportionality constant differed from the old value by less than 3%. .c/5 H CD •4—« CO CD Figure 4.8: time, hr Calibration data for the ITC showing the titration of 1.0-mM KC1 standard into 250-mM Tris buffer. Both the reference cell and sample cell contained 1 mL of degassed Tris buffer. Each injection was 10 uL in volume. 87 A typical thermogram from a Tris-base chemical calibration is given in Figure 4.8. The measured enthalpy of protonation, taken as the average heat output from ten independent titrations, generally differed from the literature value (474.4 pJ at 25°C) by no more than ±4%, which therefore gives an estimate of heat errors per injection in our ITC titrations. 4.3.2 Heat of adsorption AADSH Application of isothermal titration microcalorimetry to the determination of Langmuir-type equilibrium binding constants (see Equation 4.1) for lysozyme to silica requires performing a set of two titrations at each adsorption condition. Consider the prototype association reaction given by Equation 4.2. The total calorimetric heat effect W associated with each titration is the sum of the heat associated with the binding event Q and the heat of dilution of components Qdn, which includes the heat associated with the physical mixing of the solutions using the internal impeller. Q([P]) = W([P])-Qdil (4.10) In the microcalorimetry experiment, both Qai and W must be determined separately before Equation 4.10 can be used to evaluate the variable of interest, Q, as a function of [P]. If the association reaction goes to saturation, the measured heat of reaction will be Qmax- If all protein is bound in this case, the quantity Q m a x is the enthalpy change per mole of macromolecule. If the sorbent is limited, Q m a x is the enthalpy change per mole of independent sorbent binding sites. The heat effect, Q, for the binding of macromolecule is proportional to the fractional completion of saturation: 88 Q = ^~-Qm^ (4.ii) where [S]0 is the total molar concentration of independent binding sites and Q m a x is the cumulative heat of binding. In accordance with Equation 4.1, we assume that the projected effective surface area of each bound protein defines the size of one independent binding site on the silica surface. The molar concentration of free binding sites is then given by [SI = [S]0 - [PS] = Ascs(Tpl - T([P])) (4.12) where As is the specific surface area of the silica sorbent (m2/g) and cs is the concentration of silica sorbent in the sample (g/L). Combination of Equations 4.4, 4.11, and 4.12 gives a working expression for Q in terms of the equilibrium association constant Ka and Aa&H Q = Q ^ m ( 4 1 3 ) * l + Ka[P] { ^ U ) where [P~\ = [ P \ - Q [ S \ I Q ^ where [P]0 is the total molar concentration of protein in the system. Thus, calorimetry provides a second independent method for determining the quasi-equilibrium binding 89 constant Ka describing the ascending isotherm. The standard enthalpy of adsorption, AadsH is given by the calorimetric heat Q released per mole of protein bound. A^jy=Um80 (4.14) Figures 4.9 and 4.10 show raw ITC thermograms for titrating a 50-mM KC1 solution (pH 7) and a solution of 3.5 g/L lysozyme in 50-mM KC1 (pH 7), respectively, into a 1 mL Figure 4.9: ITC thermogram for the titration of 50-mM KC1 (pH 7) into 1 mL of 50-mM KC1 solution containing 5.4 mg of particulate silica at pH 7 and 37°C. 90 32.5 30.0 1 1 ' i I 0 10000 20000 30000 40000 50000 60000 70000 time (s) Figure 4.10: ITC thermogram for the titration of hen egg-white lysozyme solution in 50-mM KC1 (3.5 g/L, pH 7) into 1 mL of 50-mM KC1 solution containing 5.4 mg of particulate silica at pH 7 and 37°C. 50-mM KC1 solution at 37°C containing 5.4 mg silica. Peaks pointing upwards in thermograms from the Calorimetry Sciences Corp. 4200 ITC indicate an overall exothermic mixing process. Thus Figure 4.9 and 4.10 indicate that Qdu and W, respectively, are exothermic. The heat of dilution Qdi\ was taken as the arithmatic average of the individual peak areas determined using Dataworks™ (Calorimetry Sciences Corp.). For the data shown in Figure 4.9, Qdu is -516 (±62) pj. Subsequent titrations under identical conditions were within ±10% of this value, so that triplicate averaging of dilution experiments gave a similar value of Qdu {ca. -500 pJ). 91 The area under each peak in Figure 4.10 gives the differential heat of mixing for each successive 10-uL aliquot of lysozyme-containing titrant solution added. Lysozyme titrations were performed in quadruplicate (with Figure 4.10 representing a typical titration result) and the differential heats of mixing for a given volume of titrant added were arithmatically averaged to give a set of 5JF([P]) data. Equation 4.10 written in its differential form (8Q=dW- Qdu) was then used to determine 8c2([P])-0 5 10 15 20 25 [P] (MM) Figure 4.11: The differential heat of adsorption, 5Q, plotted against the free protein concentration for the adsorption of hen egg-white lysozyme in 50-mM KC1 (pH 7) into particulate silica in 50-mM KC1 (pH 7) at 37°C. 92 Figure 4.11 plots 5Q, the differential heat of adsorption (kJ/mol) as a function of free protein concentration [P] as calculated from Figure 4.2. At low surface coverages, where virtually all protein added adsorbs, 5g([P]) is strongly endothermic, giving a value for AadsHof 34(±6) kJ/mol through application of Equation 4.14. As expected, 5g([P]) drops to (near) zero as the silica surface becomes saturated. 300 J 250 200 J 150 J 100 -J 50 -J [P] (MM) Figure 4.12: The cumulative calorimetric heat, Q, plotted against the unbound protein concentration, [P], for the adsorption of hen egg-white lysozyme adsorbed onto particulate silica in 50-mM KC1 at pH 7 and 37°C. 93 The AadsH regressed from ITC data is similar to that determined from application of the Gibbs-Helmholtz equation and quasi-equilibrium theory to adsorption isotherm data. The fact that adsorption of lysozyme to silica at pH 7 and 37°C is endothermic indicates that binding must be entropically driven such that TAadsS > 34 kJ/mol - AadsGqe ( = 34 kJ/mol + tfrin A f l = 70 kJ/mol). Figure 4.12 shows the cumulative calorimetric heat Q, where Q =25£>, as a function of unbound protein concentration [P] for binding of lysozyme to silica at pH 7 and 37°C. The shape of the cumulative calorimetric isotherm is consistent with Equation 4.13. Figure 4.13 shows a double reciprocal plot of the calorimetric heat data shown in Figure 4.12, from which a second estimate of KA can be determined from the slope according to (see Equation 4.13) ± = - L - J L + _ L (4.15) Q K&^IP] e „ „ Regression of the average calorimetric data gives a value for KA of 8.3(±5.6)xl0 5 M"1, which is within experimental error of that regressed from binding isotherm data. 94 0.2 0.4 [P]"1 (UM)-1 0.6 0.8 Figure 4.13: Double reciprocal plot of calorimetric heat data taken from ITC experiments. Plotted are the inverse cumulative heat of adsorption versus inverse protein concentration. 4.3.3 Heat capacity of adsorption Afl(fcCp The thermodynamic model developed in Chapter 2 for irreversible protein adsorption does not explicitly require a value for AactsCp at the adsorption temperature 37°C. However, through analogy with thermodynamic models for protein folding [Gomez et al., 1995] the sign and magnitude of Aa£&Cp can provide important insights into the nature of 95 \the protein sorbent interaction and the conformational state of the adsorbed protein. A loss in heat capacity occurs when hydrophobic surfaces and residues are dehydrated [Haynes and Norde, 1994]. Khechinashvili et al [1995] have shown for reversible protein folding that the associated decrease in heat capacity ACP is related to the total nonpolar atomic surface area (ANP-AS A) which becomes dehydrated during the folding Table 4.1: ACP data for various globular proteins versus their relative total nonpol atomic surface areas (ANP-ASA). ar Protein ANP-ASA ACp reference (A 2) (kJ mof1 K"1) Pancreatic trypsin inhibitor 2050 3.0 1 Erobutoxin B 2100 1.9 2 Parvalbumin 4195 4.8 1 Cytochrome c 4760 7.0 3 Ribonuclease A 4830 5.2 3 Hen egg-white lysozyme 5010 6.5 4 T4 lysozyme 7210 9.3 1 Myoglobin 7055 11.7 3 C B D N ! 7775 7.5 5 Papain 10910 13.5 6 P-Trypsin 11320 12.3 1 a-Chymotrypsin 11930 13.1 3 1: [Privalov, 1979] 2: [Khechinashvili and Tsetlin, 1984] 3: [Privalov and Khechinashvili, 1974] 4: [Khechinashvili et al, 1973] 5: [Creagh ef a/., 1997] 6: [Tiktopolo and Privalov, 1978] 96 process. Table 4.1 gives a list of literature ACp values for denaturation determined by DSC for a wide range of globular proteins against ANP-ASA values in A 2 determined by the method of Lee and Richards [1971], where the peptide backbone torsional angles § and 9 in the denatured state have been set to -140° and +140°, respectively. This gives the polypeptide chain in the denatured state an extended, hydrated conformation. Figure 4.14 gives a corresponding plot of these values. ANP-ASA (A2) Figure 4.14: Plot of ACp data for various globular proteins versus their relative total nonpolar atomic surface areas (ANP-ASA). 97 Similar to protein folding, which results in extensive dehydration of apolar groups, protein adsorption from aqueous solution results in dehydration of apolar surface residues in direct contact with the sorbent. Since the hydrophobic effect operates in both processes, a measured value for AadsCP combined with Figure 4.14 may provide a reasonable estimate of the apolar surface area of lysozyme which is dehydrated during adsorption to silica. The change in heat capacity AadsCp for the model adsorption process was determined by measuring AaasH at 29.5°C and 44.5°C. The values of AaasH at surface saturation for these two temperatures were 8.3 and -7.8 kJ/mol, respectively. The measured dependence of AadsH on temperature then gives AadsCP through the relation involving net dehydration. Haynes and Norde [1995] compiled AadsCP data for a number of protein adsorption processes involving moderately hydrophobic and hydrophilic sorbents. They concluded that although AadsCP can be increased to more positive values by interfacial ion-incorporation effects and increases in polypeptide-backbone rotational mobility, it is dominated by the hydrophobic effect. (4.16) A AadsCP of-1.1 kJmof K was obtained which is consistent with an adsorption process 98 As shown in Figure 4.14, ACp is directly proportional to ANP-ASA. A linear fit of a larger set of denaturation data resulted in the following correlation [Khechinashvili et al., 1995]: -A^Cp « +ACP = 1.2 x IO'3 ANP-ASA (4.17) where ANP-ASA is in A 2 and ACp is in kJ mol"1 K"1. Based on a AadsCp of -1.1 kJ mol"1 K" , Equation 4.17 predicts that ca. 900 A of apolar surface is dehydrated during the adsorption of lysozyme to silica at pH 7 and 37°C. The dimensions for native-state lysozyme are given in Table 3.1. From these, the projected area of lysozyme in a side-on orientation is ca. 1200 A 2, however, only ca. 60% of the surface residues of lysozyme are apolar. Moreover, given the globular structure of native lysozyme, it is not possible for the entire projected area of the protein to make sufficiently close contact with the sorbent to exclude water without undergoing a significant change in conformation. These results therefore provide our first indication that lysozyme may change conformation during adsorption, which, if true, would at least partially explain the observed hysteresis in the measured adsorption isotherms. Multiple contact formation between the adsorbed protein and sorbent surfaces may also contribute to adsorption irreversibility. Taking together the average atomic packing fraction in globular proteins of 0.7 (density of 1.33 g/cm3), and average fraction of apolar ° 9 atoms of 60%, and the estimated dehydrated surface area of 900 A , we can estimate that adsorbed lysozyme makes ca. 40 apolar atomic contacts with the silica surface. Taking 99 the size of the protein into account, this result is consistent with the FTIR studies of Morrissey and Stromberg [1974]. 4.4 Quantifying protein denaturation by differential scanning calorimetry Differential scanning calorimetry (DSC) is among the most powerful methods for quantifying the energetics of biological processes. In particular, Privalov and coworkers [Griko et al, 1995; Privalov, 1979; Privalov and Khechinashvili, 1974] have used DSC to directly measure denaturation thermodynamics for a wide range of globular proteins. The transition from the native (N) to denatured (D) state is defined by the fundamental thermodynamic difference functions AN_DH=HD-HN, AN_DS = SD-SN and AN_DG = GD — GN (4.18) The thermodynamic observables in the DSC experiment are the temperature of denaturation Td, the enthalpy of denaturation AN-DH, and the heat capacity change upon denaturation ACp. The thermodynamic difference functions given in Equation 4.18 are related to these observables by (4.19) T T (4.20) and 100 AN_DG(T) = A „ _ D t f ( 7 / d ) ^ — ^ - ]ACPdT+T]ACPd(\nT) (4.21) d j T For hen egg-white lysozyme (and most other globular proteins studied), ACp is temperature independent over the range 10°C to 80°C [Khechinashvili et al., 1973]. Thus, a single thermogram measured by DSC can provide a complete thermodynamic description of the denaturation thermodynamics of a single-domain globular protein. Our objective is to use DSC measurements, according to the previously established method of Haynes and Norde [1995], to quantify differences in denaturation thermodynamics for lysozyme adsorbed to silica relative to those for lysozyme free in aqueous solution at otherwise constant conditions. 4.4.1 Denaturation thermodynamics for hen egg-white lysozyme in solution Figure 4.15 shows the denaturation thermogram, measured by differential scanning calorimetry, for hen egg-white lysozyme in a buffered aqueous solution (50-mM phosphate) containing 50-mM KC1. The single endothermic peak centered at a denaturation temperature Td of 76(±0.2)°C indicates that unfolding of this single-domain globular protein is cooperative and characterized by a two-state transition from the native state to a thermodynamically defined denatured state (which includes a large ensemble of chain configurations). The denaturation thermogram for hen egg-white lysozyme under these conditions is reversible; cooling of the 'denatured' solution to 20°C causes complete refolding of the protein. 101 50 60 70 80 90 r ( ° C ) Figure 4.15: DSC thermogram of the denaturation of hen egg-white lysozyme in 50-mM phosphate buffer containing 50-mM KC1. The area under the endothermic denaturation peak in Figure 4.15 gives a value for AN-DH(TJ) of 470(±20) kJ/mol, and the positive shift in baseline from the native to denatured states gives a ACP value of 6.3(±0.4) kJ mol"1 K"1. Khechinashvili et al. [1973] found that ACp for hen egg-white lysozyme remained constant at a value of 6.5 kJ mol"1 K' 1, which is within experimental error of our measured value, over the temperature range 102 20°C to 80°C. The integrals in temperature for the thermodynamic difference functions given in Equation 4.19 to 4.21 are therefore easily solved. Figure 4.16 plots AN.DG, AN-DH and TAM-DS for lysozyme as a function of temperature. AN.DH and TAN-DS are both strong functions of temperature, which is consistent with an unfolding reaction dominated by the hydrophobic effect. This strong temperature dependence, combined with the almost complete compensation of enthalpic effects by entropic effects, results in relatively small AN-DG values with a pronounced nonlinear dependence on temperature. 1000 240 260 280 300 320 340 360 380 400 420 T(K) Figure 4.16: Plot of AN.DG, AN.DH, and TAjf.cS for hen egg-white lysozyme in 50-mM KC1 (pH 3) as a function of temperature. 103 Three important conclusions can be drawn from Figure 4.16. First, the stability of the native state is a maximum at ca. 0°C. Second, even at this optimal solution condition, the native state is only marginally stable; AN-DG - 47 kJ/mol, which is roughly equivalent to 2 to 4 hydrogen bonds. Third, AN-DHis large and endothermic (ca. 260 kJ/mol) at 37°C, the temperature where all of our adsorption studies were carried out. If adsorption results in denaturation of lysozyme, AaasHstr.pr would therefore make a large endothermic contribution to A^r /as defined by Equation 2.7. 4.4.2 Conformation of lysozyme adsorbed to silica (37°C, pH 7) Haynes and Norde [1995] have recently shown for globular-protein adsorption that AN-DH can be related to AadsHstr.pr by A^DH = AadsHSTR,PR+AA_DH (4.22) where AA-DH is the enthalpy required to fully denature (D) the adsorbed (A) protein. Analogous to A^-DH, AA_DH is given by the area under the thermogram peak for lysozyme adsorbed to silica in 50-mM KC1 solution at 37°C and pH 7. Equation 4.22 can then be used to estimate AadsHstr.pr.. Figure 4.17 shows the DSC thermogram for the silica suspension containing no adsorbed protein. No transition peaks are observed, indicating that the silica and surrounding fluid are inert over the temperature range of interest. Figure 4.18 compared the (baseline-corrected) denaturation thermogram for lysozyme adsorbed on silica to monolayer 104 Figure 4.17: DSC thermogram for a silica suspension in 50-mM phosphate buffer at pH 7 containing no adsorbed protein. coverage (T=rpI) with that for lysozyme in aqueous solution (pH 7, 50-mM KC1). A very small endothermic peak is seen for the adsorbed protein at a denaturation temperature of ca. 73°C. Compared with the endotherm observed for lysozyme in solution at the same conditions, AA-DH is near zero, indicating that adsorbed lysozyme undergoes no structural transitions during the heating process. Denaturation thermograms have been measured by 105 DSC for proteins which maintain some or all of their native configuration upon adsorption [Haynes and Norde, 1995; Steadman et al, 1992]. As shown in Figure 4.19, similar results were obtained at lower surface coverages of lysozyme, indicating that the conformational state of the adsorbed protein is independent of surface concentration. Application of Equation 4.22 to the data in Figures 4.16 and 4.18 yields a value for AadsHstr-pr of ca. 260 kJ/mol. Figure 4.18: DSC (background subtracted) denaturation thermogram for hen egg-white lysozyme adsorbed to particulate silica at surface saturation (pH 7, 50-mM phosphate buffer). 106 - 5 0 9 - 6 0 Lysozyme in solution Lysozyme adsorbed at 0.46rp/ Figure 4.19: DSC (background subtracted) denaturation thermograms for hen egg-white lysozyme adsorbed on particulate silica at surface coverages of 0.46rp/ and 0.20rp/ (pH 7, 50-mM phosphate buffer). 4.4.3 Conformation of lysozyme adsorbed to a highly charged polystyrene latex Adsorption of lysozyme does not always result in AA-DH values equal to zero. Figure 4.20 shows the thermogram for lysozyme adsorbed at a surface concentration of r=0.9rp/ to negatively charged polystyrene-sulphonate latex particles (PSS-HC). A significant endothermic peak centered at a Td of 58°C is observed, giving a value for AA-DH of 107 58 kJ/mol. Thus, at least a portion of the adsorbed protein maintains secondary structure which is susceptible to thermal denaturation. O 7TC) Figure 4.20: DSC (background subtracted) denaturation thermogram for hen egg-white lysozyme adsorbed at 0.91*' to negatively-charged polystyrene-sulphonate latex particles (PSS-HC) in 50-mM phosphate buffer at pH 6. Figure 4.21 plots AA-DH as a function of surface coverage for lysozyme adsorbed to PSS-HC at pH 6 and 37°C. At lower surface coverages, AA-DH is equal to zero. In contrast to the silica system, the amount of ordered structure in the adsorbed protein increases with increasing surface concentration, suggesting that the structure of the 108 adsorbed protein is at least partially determined by the amount of free sorbent surface available. This result is supported by the DSC studies of Haynes and Norde [1994], who observed an increase in &A-DH with increasing surface concentration for a number of other adsorbed protein systems. Figure 4.21: DSC data showing AA-DH as a function of surface coverage for PSS-HC adsorbed to silica particles in 50-mM phosphate buffer at pH 6 and 37°C. 109 4.5 Model calculations and analysis In this section, we combine our experimental data with the model developed in Chapter 2 and use the results from this analysis to establish the dominant energetic contributions to the adsorption of lysozyme, a typical low molecular weight single-domain globular protein, to silica. The irreversible adsorption thermodynamic model of Everett [1967] is used in combination with calorimetry results to estimate the magnitude of KdsGir and its contributions to the overall driving force for adsorption AadsG. 4.5.1 Quasi-equilibrium Gibbs energies, enthalpies and entropies of adsorpt ion Table 4.2 reports values for Ka and AadsHqe regressed from ascending binding isotherm data and, in the latter case, applications of the Gibbs-Helmholtz equation. These data can be used to estimate AaasGqe and TAadsSqe; values for AaasGqe and TAaasSqe are also provided in Table 4.2. When expressed on a per mole basis, AaasGqe (kJ/mol) and Ka are related by Aadfiv=-RT\nKu (4.23) TAadsSqe can then be determined from the fundamental relation T&adsSqe=AadsHqe-AadsGqe (4.24) The estimated value of AadsGqe (-35.6 kJ/mol) for lysozyme adsorption to silica at pH 7 is similar to AG values reported by others assuming the entire adsorption process can be modelled as reversible and in accordance with Langmuir theory. For example, van Oss 110 [1991] reports Gibbs energy of adhesion AG values for several human proteins (serum albumin, fibrinectin and fibrinogen) on a number of sorbent surfaces (teflon, charged polypropylene, and negatively charged polystyrene) which range from -4 to -40 mJ/m2 or ca. -10 to -60 kJ/mol. Similarly, Gerstner et al. [1994] report AG values between -4 and -40 kJ/mol for low molecular-weight single-domain proteins on charged ion-exchange r e s i n s . Quasi-equilibrium parameters from ascending isotherm data for hen ej white lysozyme adsorbed onto silica in 50-mM KC1 at pH 7. Parameters Isotherm at 37°C Isotherm at 22°C Ka 9.8xl0 5(±3.7) NT1 6.9xl0 5 M" 1 18(±9)kJ/mol n/a 53 kJ/mol n/a AadsGqe -36 kJ/mol -35 kJ/mol 111 The value of AadsH (34+6 kJ/mol) measured by ITC is similar to AadsHqe (18+9 kJ/mol) regressed from adsorption isotherm data and application of the Gibbs-Helmholtz equation. Since AadsH includes the effects of protein structural change upon adsorption, we conclude that the thermodynamic state defined by the ascending isotherm corresponds to an adsorbed layer of conformationally altered lysozyme in quasi-equilibrium with free protein at a concentration specified by Ka. Thus, even at the quasi-equilibrium conditions defined by the ascending isotherm, the conformational state of the adsorbed protein differs from that in solution. In this context, it is particularly useful to interpret the value of Aa(jsSqe in terms of its dominant contributions and the state of the adsorbed protein. Current protein denaturation theories [Makhatadze and Privalov, 1996; Nichols et al, 1991] identify (1) exposed surface area hydration, which decreases the degrees of freedom of adsorbed water molecules, and (2) polypeptide backbone conformation as the dominant contributions to AadsSqe. Thus, we may at least qualitatively relate AadsSqe to the sum of AadsShyd, the entropy change for (de)hydrating apolar residues upon adsorption, and Aads^str-pr AadsSqe = A ads^ hyd + ^ads^str-pr (4-25) From our AadsCp value of-1.1 kJ mol"1 K' 1, we estimated that ca. 900 A 2 of hydrophobic protein surface area is dehydrated during adsorption of lysozyme to silica at pH 7 and 37°C. Cabani et al. [1981] have measured ACP value for dissolution of a wide range of low molecular weight apolar solutes in water. As suggested by Figure 4.14, ACp for 112 small molecule dissolution in water is directly proportional to exposed apolar surface area per molecule. Dissolution of benzene, which has an apolar surface area of 260 A 2, results in a ACp of 0.293 kJ mol'1 K"1. Dehydration of benzene (removal from water) at these same conditions would therefore result in a ACp of -0.293 kJ mol"1 K"1. Multiplying this value by the dehydrated surface area ratio of adsorbed lysozyme to benzene (900A2/260A2) gives a AadsCp value of -1.01 kJ/mol, which is essentially the same as that measured by calorimetry (-1.1 kJ/mol). As shown in Figure 1.2, dissolution of benzene in water at 37°C is also accompanied by an entropy change (expressed as TAS) of 16 kJ/mol. Scaling this value by the dehydrated surface area ratio of adsorbed lysozyme to benzene gives and estimate for TAaasShyd of 52 kJ/mol, which is close to the value of TAadsSqe determined from quasi-equilibrium analysis. Application of Equation 4.25 therefore indicates that AaasSstr-pr ~ 0. 4.5.2 Compressed ball model for ascending isotherm conditions Table 4.3 compares denaturation thermodynamics for lysozyme in aqueous solution with adsorption thermodynamics for lysozyme on silica. In solution, denaturation is highly endothermic (AN-DH - 260 kJ/mol), indicating that intramolecular atomic contacts within the interior of the folded protein are more favourable than intermolecular contacts with water. ACp is fairly large and positive, consistent with the hydrophobic effect (i.e. highly ordered water in the first solvation shell around exposed residues). Finally TAS at 37°C is 113 large and favourable, indicating that the increase in rotational mobility of the polypeptide chain is significantly larger than the loss in translational entropy of the water. Similar to free protein denaturation, adsorption of lysozyme leads to significant disruption of favourable intramolecular contacts (i.e. AadsHstr-pr « 260 kJ/mol). However, those conformational changes do not result in a significant increase in the rotational mobility of the polypeptide backbone as would be expected from analogy with denaturation in solution. Moreover, A ^ O is negative, indicating that adsorption leads to a net increase in the translational entropy of water. This suggests that during adsorption the protein distorts its native structure sufficiently to form a dehydrated, intimate contact ° 2 layer (ca. 900 A in size) with the silica surface, but not so much as to expose internal residues to the solvent. As a result, A.adsSstr-pr is small, as was determined from DSC results, since any large change in internal atomic packing density would necessarily lead to hydration. Table 4.3: Comparison of denaturation thermodynamics for lysozyme in aqueous solution with adsorption thermodynamics for lysozyme on silica. Thermal Denaturation Adsorption AH (kJ/mol) 260 260 k-adsHs str-pr (kJ/mol) ACp (kJ mol"1 K"1) 6.3 -1.1 KdsCp (kJ mol"1 K"1) rA5(kJ/mol) 190 0 TA adsSs *str-pr 114 The picture which then emerges at ascending isotherm conditions is a dense protein "ball" compressed on the sorbent surface in a manner which minimizes losses in the cohesive internal energy of the protein while maximizing adhesive energy (i.e., intermolecular interactions) between the sorbent surface and the contacting protein surface. We therefore call this the "compressed ball model" for protein adsorption. 4.5.3 Descending isotherms: Everett analysis and irreversible entropy production The second law of thermodynamics states that a process can only occur if it leads to an increase in the total entropy of the system: dS,otal > 0 (natural process) (4.26) an where the equality only holds for a reversible process at equilibrium. Consider then open system of constant total energy (enthalpy), temperature and volume consisting of a liquid phase a containing a specific number of moles npa of protein P in contact with an adsorbed phase p containing np moles of bound protein P. This is the abstract thermodynamic formalism of our protein adsorption system. The total change in entropy dStotai for transferring an amount of protein dnp from one phase to the other is then given by d S total = drr +1 — „ dn\ > 0 (natural process) (4.27) 115 From the protein mass balance, dnpa = thermodynamic relation -dn/. Inserting this and the fundamental u - T ( 8 S ) into Equation 4.27 then gives d S total = T T dnp > 0 (natural process) (4.29) At the (quasi-)equilibrium conditions defined by the ascending isotherm, dStolarO and we recover the familiar equilibrium criteria (4.30) first derived by Gibbs [1948]. For a natural process, dSMai must be positive, and Equation 4.29 shows that the sign on the quantities (u/ - \ipa)IT and dnpa must be the same. Travelling down any descending isotherm shown in Figure 4.7 is operationally achieved by removing (or diluting) free protein from the solution phase a. The re-establishment of equilibrium as defined by the ascending isotherm then requires transfer of protein from the adsorbed phase p to phase a; any transfer would therefore result in a positive value for dnpa. This means that removal or dilution of the protein in the solution phase reduces Up" relative to u / , thereby creating a chemical potential difference of magnitude p/ 1 - p / 116 In [P] Figure 4.22: Plot of ascending and descending isotherm data at surface saturation for the adsorption of 125I-lysozyme on silica in 50-mM KC1 (pH 7, 37°C) in the form of the Everett equation. which acts in favour of desorption. If the protein remains adsorbed under this chemical potential gradient, it defines a metastable state such that there must be energy of equal amount stabilizing the adsorbed state. We wish to estimate the magnitude of this stabilizing energy as a function of concentration of free protein [P]. 117 As discussed in Chapter 2, Everett [1967] proved that the entropy created by reducing free solute concentration in a system where the solute is irreversibly adsorbed is given by AadsSir = RJ~d\n[P] (4.31) where T* is the departure point of the descending isotherm from the ascending (quasi-equilibrium) isotherm. The cyclic integral in Equation 4.31 calculates the area enclosed within the descending and ascending isotherms when plotted as T versus ln[P]. Exact solution of the closed loop integral requires the two isotherms to merge at both a low concentration limit and at a high concentration limit, thereby defining a precise area within the curves. Figure 4.22 reports in the form T versus ln[P] the data in Figure 4.7 for the ascending isotherm and the descending isotherm at a departure point (T*) of Tpl. To the detection limit of our experimental (radiolabelling) method, merging of the ascending and descending isotherms at low [P] is not observed. We can, however, use the data in Figure 4.22 to calculate a minimum value for the entropy change A^Sir stabilizing the adsorbed protein under dilute free solution conditions by truncating the closed loop integral at the detection limit (given by the dashed vertical line in Figure 4.22) and the descending and ascending isotherms. Since AaasSir > 0, the estimated value of AaasSir will be less than, possibly significantly less than, the true value. For the descending isotherm measured at a departure point of Tpl, the estimated value of AaasSir is 55 J mol"1 K"1, which equates to a minimum irreversible energy stabilizing the adsorbed state of 17 kJ/mol. 118 At the detection limit, ln[P] is equal to -19.2. Further dilution of the liquid phase to a concentration of a single lysozyme molecule per litre of solution (which should provide an accurate representation of infinite dilution) gives a ln[P] of -54.8, and a resulting value of TAadsSjr of 110 kJ/mol. This then gives us a realistic upper bound for the magnitude of the irreversible energy change which occurs in the system as a result of dilution of protein in the solution phase. For the protein to remain adsorbed in a stable state, there must then be an equivalent change in energy in the adsorbed protein (i.e. u^ must decrease by this same amount). 4.5.4 Quasi-equilibrium and irreversible contributions to AadsH and AaasS Our model assumes that Aa<&i7 is given by (see Chapter 2) AadsH = A ^ H ^ + A^H^ + (AadsHH+ + A ^ H ^ ^ + A^H^ ) (4.32) where the last three terms in parenthesis determine the total contribution of charge redistribution which we will henceforth abbreviate AadsHCharge- At the adsorption conditions (pH 7), lysozyme carries a net charge of ca. +10, while the silica surface carries a negative charge. Thus, the net coulombic force between the protein and sorbent surface will be attractive, resulting in an exothermic value for AadsHcharge (particularly AadsHei)- A crude estimate of this exothermic charge contribution can be made by recognizing that AadsHhyd is likely to be fairly small at 37°C, as evidenced by the transfer enthalpy data for benzene shown in Figure 1.2. The values for AadsH measured by ITC 119 and for AadsHstr.pr determined by the Gibbs-Helmholtz equation are 34 kJ/mol and 260 kJ/mol, respectively. Application of Equation 4.32 under the assumption that AadsHhyd K 0 then yields a value for AadsHcharge of ca. -230 kJ/mol. Two important conclusions can be drawn from this analysis. First, in the absence of structural change in the protein during adsorption, we would expect binding to be exothermic due to net coulombic attraction between the protein and the sorbent. Second, in terms of magnitude, AadsHs,r-Pr and AadsHCharge make the dominant contributions to AadsH. However, these contributions are largely compensating, so that smaller enthalpic subprocesses such as AadsHhyd may also influence the value of AadsH. Since adsorption of lysozyme is spontaneous and irreversible, AadsS must be sufficiently large and positive (favourable) to compensate the endothermic value of AadsH. At ascending isotherm conditions, as shown in Section 4.5.1, protein (and sorbent) surface dehydration appear to provide most of the entropy increase, AadsShyd, required for spontaneous protein adsorption. 4.5.5 Descending isotherms: defining the metastable state and AatbGir In Section 4.5.3, we determined that for true irreversible binding the chemical potential of the adsorbed protein p p p must decrease by an amount -7Aa^iS,r relative to its value at the ascending isotherm and the same surface concentration. This argument was based on two assumptions: (1) each descending isotherm defines a thermodynamically (meta)stable state, and (2) the system energy remains constant, so that AadsH = AadsHqe. The first 120 assumption was verified through time-course experiments that showed no loss of adsorbed protein. The second assumption was verified by noting that AadsH measured by calorimetry is within experimental error of AadsHqe, which describes the enthalpic energy change for adsorption at ascending isotherm (quasi-equilibrium) conditions. Equation 2.5 can therefore be simplified to A ^ G , = -TA^S.dP]) (4.33) where A ^ S ^ P ] ) is given by Equation 4.31. The total Gibbs energy change A ^ G , relative to the system prior to adsorption, for any point on any descending isotherm can then be determined by AadsG = AadsGqe + AadsGjr = -RT In Ka - TAadsSir([P]) (4.34) For example, AacjsGir for the descending isotherm at Tpl and is -17 kJ/mol at the detection limit of our I25I-labelled protein and ca. -110 kJ/mol at infinite dilution; AadsG is then -52.6 kJ/mol or -145.6 kJ/mol respectively. This latter value for A a ^G is approaching the magnitude of a covalent bond, which is consistent with the irreversible nature of the adsorption process observed. Equation 4.34 can also be applied to the ascending isotherm by noting that AadsSjr = 0 for all points on the ascending isotherm. Thus, Equation 4.34 in combination with the experimental methodology developed in this chapter provide a complete thermodynamic model for nonspecific protein adsorption 121 which includes irreversible thermodynamic effects associated with protein conformational changes during adsorption. The final question which remains unanswered concerns the nature of the transition in the adsorbed protein resulting from dilution of the solution phase which provides an irreversible energy change of up to 110 kJ/mol. Without a more detailed picture of the adsorbed protein under these dilute-solution conditions, we can only speculate. However, a reasonable picture of this transition can be drawn from what we already know about adsorption and about adsorbed and desorbed protein structures. The hysteresis loop and the resulting Aa&G values indicate a higher adsorption affinity for the descending isotherm as compared to the ascending isotherm. Assuming the sorbent surface is unchanged by the adsorption/desorption process, the following identity for the chemical potential of the protein p p pp(adsorbed) - pp(desorbed) < pp(adsorbed) - \ip(native) (4.35) must therefore hold. Thus, Hp(desorbed)> \ip(native) (4.36) indicating that the protein undergoes an irreversible physical change during adsorption such that any desorbed protein has a higher chemical potential than the native protein prior to adsorption. Although nonspecifically bound proteins cannot be desorbed by dilution, limited evidence for differences in desorbed protein structures relative to the native state has been provided by Norde and Favier [1992]. They used morpholine to 122 displace bovine serum albumin from silica and showed by transmission circular dichroism a 30 to 40% reduction in ct-helix content in the desorbed protein relative to the native state. They also showed that the denatured protein did not refold into the native state. Such a change in structure would increase the molar Gibbs energy of the desorbed protein (or decrease entropy) relative to the native state by exposing more hydrophobic surface area to the aqueous solution. Could this hydration process provide an energy increase of 110 kJ/mol? Yes. The total buried apolar surface area of native lysozyme is ° 2 ca. 5000 A . Based on the transfer energy data for benzene at 37°C given in Figure 1.2, the energy increase of 110 kJ/mol would require exposure of ca. 1300 A 2 of nonpolar surface to the solvent relative to that exposed in the native state. 123 5. Conclusion Nonspecific protein adsorption at the interface between an aqueous solution phase and a solid sorbent plays an important, often critical role in a wide variety of natural and synthetic systems, including fouling of biomedical implants and food-processing equipment. These deleterious processes are driven by the strong affinity of globular proteins for solid, planar surfaces which usually results in irreversible binding of the protein on the surface. Thus, unlike classic small solute adsorption systems, nonspecifically adsorbed proteins in general cannot be eluted from the surface by decreasing the protein concentration in the bulk solvent. The central objective of this thesis was to establish a meaningful thermodynamic model for nonspecific protein adsorption which identified and at least semi-quantified the energetic subprocesses contributing to the adsorption process and its irreversible nature. The sign and magnitude of the Gibbs energy change Aa(&G ultimately determines the fate of the system; if Aa(&G < 0, adsorption will occur. Adsorption isotherm measurements for 125I-labelled hen egg-white lysozyme on microcrystalline silica particles were used to show time-independent hysteresis in the ascending and descending branches of the isotherm, thereby establishing process irreversibility and suggesting that a change of state has occured in the adsorbed phase. To account for this irreversible effect, A ^ G was split into a quasi-equilibrium (reversible) component and an irreversible component A;G=A;G +A,G ads ads qe '-'ads^ir 124 The time-independence of the ascending isotherm allowed direct regression of A ^ G ^ , which was found to be ca. -36 kJ/mol. Isothermal titration calorimetry was combined with adsorption isotherm measurements to evaluate the dominant enthalpic and entropic contributions to the overall adsorption thermodynamics. AaasH was found to be small and endothermic (34 kJ/mol), indicating that adsorption is entropically driven. In terms of charge interactions, adsorption is enthalpically favoured (AadsHcharge w -230 kJ/mol) due to the net electrostatic attraction of the components. This large exothermic subprocess, however, is more than compensated by the endotherm which accompanies protein structural changes (AadsHslr-pr = 260 kJ/mol) upon adsorption. Two subprocesses, solvent-exposed hydrophobic residue dehydration (AadsShyd) and protein structural changes (A^S^X were shown to make large favourable contributions to AadsG. On its own, TAadsShyd (= 70 kJ/mol) provides a sufficient energy gain to drive nonspecific binding with a Ka of ca. lxlO 6 M"1, which is similar to moderate antigen-antibody interactions. The effects of changes in protein structure, which are permanent and therefore affect the potential structure of any desorbed protein, can drive irreversible binding as much or more than dehydration. Application of the irreversible thermodynamic model of Everett to the adsorption hysteresis observed in our system shows that these structural changes can provide an energy change of up to 110 kJ/mol stabilizing the adsorbed state. When all of these subprocesses are combined, A a ^G takes 125 on values between -60 and -140 kJ/mol, the latter of which is in the range of covalent-bond strengths. At ascending isotherm conditions, our thermodynamic analysis indicates that the adsorbed protein assumes a non-native "compact-ball" configuration such that a dehydrated 900 A 2 contact region is formed between the protein and the silica surface. This dehydrated layer leads to a heat capacity change of -1.1 kJ mol"1 K"1 without a significant change in the conformational freedom of the polypeptide chain (Aa&Sstr-pr« 0). Thus, the native structure is perturbed just enough to allow the protein to paste its apolar residues to the silica surface such that ca. 40 apolar contacts are formed. 126 N O M E N C L A T U R E A s = specific surface area of the sorbent (m2/g) c = concentration of free protein (M) cs - concentration of sorbent (M) ACp = change in heat capacity (kJ mol"1 K"1) AadsCp = heat capacity of adsorption (kJ mol"1 K"1) GD = Gibbs energy of the denatured state (kJ/mol) GN = ., Gibbs energy of the native state (kJ/mol) AG = change in Gibbs energy (kJ/mol) A G W = reversible work of hydration per unit surface area of solid-water interface, Young-Dupre equation (mJ/m2) AadsG = Gibbs energy of adsorption (kJ/mol) &adsG,r = irreversible Gibbs energy of adsorption (kJ/mol) AadsGqe = quasi-equilibrium Gibbs energy of adsorption (kJ/mol) AN-DG = Gibbs energy of denaturation from the native state (kJ/mol) Hi = heat of adsorption of the monolayer, BET equation (kJ/mol) H2 - heat of liquification of the gas, BET equation (kJ/mol) HD - enthalpy of the denatured state (kJ/mol) HM = enthalpy of the native state (kJ/mol) AH = change in enthalpy (kJ/mol) AadsH = enthalpy of adsorption (kJ/mol) AadsHcharge = enthalpy of adsorption due to charge interactions, including ion-coadsorption, protonation and electric double layer effects (kJ/mol) 127 AadsHei - enthalpy of adsorption due to overlap of the double layers between the protein and the sorbent surface (kJ/mol) &adsHH+ - enthalpy of adsorption due to protonation of the protein and sorbent surface (kJ/mol) AadsHhyd = enthalpy of adsorption due to hydration and dehydration effects (kJ/mol) AadsHion-coads - enthalpy of adsorption due to ion-coadsorption at the protein-sorbent interface (kJ/mol) AadsHjr = irreversible enthalpy of adsorption (kJ/mol) A-adsHqe = quasi-equilibrium enthalpy of adsorption (kJ/mol) AadsHstr-pr - enthalpy of adsorption due to structural changes of the protein upon adsorption (kJ/mol) AA-DH = enthalpy of denaturation from the adsorbed state (kJ/mol) AN-DH = enthalpy of denaturation from the native state (kJ/mol) KA = equilibrium constant for the ascending isotherm (M"1) KL = equilibrium constant for the Langmuir isotherm (M"1) npa = number of moles of protein in the liquid phase a (moles) rip1 = number of moles of protein in the adsorbed phase p (moles) ANP-ASA = change in the nonpolar atomic surface area (A2) p = partial pressure, BET equation (Pa) p0 = saturation pressure, BET equation (Pa) P = pressure (Pa) [P] = concentration of free protein (M) [P]0 = total concentration of protein in the system (M) [PS] = concentration of adsorbed protein or occupied binding sites (M) Q = heat of adsorption (kJ/mol) Qdu = heat of dilution (kJ/mol) 128 Qmax = heat of adsorption at saturation (kJ/mol) R = universal gas constant (J mol"1 K"1) [S] = concentration of unoccupied binding sites (M) [S]0 = total concentration of binding sites in the system (M) So = entropy of the denatured state (kJ mol'1 K"1) SN = entropy of the native state (kJ mol"1 K"1) Stotal total entropy (kJ mol"1 K"1) AS - change in entropy (kJ mol"1 K"1) AadsSir = irreversible entropy of adsorption (kJ mol"1 K"1) AadsSqe ~ quasi-equilibrium entropy of adsorption (kJ mol"1 K"1) AN-DS = entropy of denaturation from the native state (kJ mol"1 K"1) Td = denaturation temperature (K) Ar = change in temperature (K) W = total calorimetric heat (kJ/mol) T = surface concentration (mol/m2) T = departure point of the descending isotherm from the ascending isotherm (mol/m2) Tp = surface concentration at plateau level (mol/m ) yw = surface tension of pure water (mJ/m2) 9 = contact angle, Young-Dupre equation (degrees) p/ 1 = chemical potential of protein P in the liquid phase a (kJ/mol) u p p = chemical potential of protein P in the liquid phase p (kJ/mol) v = total volume of gas adsorbed , BET equation (cm3) vm = volume of gas adsorbed when the entire adsorbent surface is covered with a complete monolayer (cm3) 129 R E F E R E N C E S 1. 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