Rapid measurement of protein osmotic second virial coefficients by self-interaction chromatography

Weak protein interactions are often characterized in terms of the osmotic second virial coefficient (B(22)), which has been shown to correlate with protein phase behavior, such as crystallization. Traditional methods for measuring B(22), such as static light scattering, are too expensive in terms of both time and protein to allow extensive exploration of the effects of solution conditions on B(22). In this work we have measured protein interactions using self-interaction chromatography, in which protein is immobilized on chromatographic particles and the retention of the same protein is measured in isocratic elution. The relative retention of the protein reflects the average protein interactions, which we have related to the second virial coefficient via statistical mechanics. We obtain quantitative agreement between virial coefficients measured by self-interaction chromatography and traditional characterization methods for both lysozyme and chymotrypsinogen over a wide range of pH and ionic strengths, yet self-interaction chromatography requires at least an order of magnitude less time and protein than other methods. The method thus holds significant promise for the characterization of protein interactions requiring only commonly available laboratory equipment, little specialized expertise, and relatively small investments of both time and protein.     

Direct measurement of protein osmotic second virial cross coefficients by cross-interaction chromatography

The importance of weak protein interactions, such as protein self-association, is widely recognized in a variety of biological and technological processes. Although protein self-association has been studied extensively, much less attention has been devoted to weak protein cross-association, mainly due to the difficulties in measuring weak interactions between different proteins in solution. Here a framework is presented for quantifying the osmotic second virial cross coefficient directly using a modified form of self-interaction chromatography called cross-interaction chromatography. A theoretical relationship is developed between the virial cross coefficient and the chromatographic retention using statistical mechanics. Measurements of bovine serum albumin (BSA)/lysozyme cross-association using cross-interaction chromatography agree well with the few osmometry measurements available in the literature. Lysozyme/alpha-chymotrypsinogen interactions were also measured over a wide range of solution conditions, and some counterintuitive trends were observed that may provide new insight into the molecular origins of weak protein interactions. The virial cross coefficients presented in this work may also provide insight into separation processes that are influenced by protein cross-interactions, such as crystallization, precipitation, and ultrafiltration.     

Measuring protein interactions by microchip self-interaction chromatography

The self-interaction of proteins is of paramount importance in aggregation and crystallization phenomena. Solution conditions leading to a change in the state of aggregation of a protein, whether amorphous or crystalline, have mainly been discovered by the use of trial and error screening of large numbers of solutions. Self-interaction chromatography has the potential to provide a quantitative method for determination of protein self-interactions amenable to high-throughput screening. This paper describes the construction and characterization of a microchip separation system for low-pressure self-interaction chromatography using lysozyme as a model protein. The retention time was analyzed as a function of mobile-phase composition, amount of protein injected, flow rate, and stationary-phase modification. The capacity factors (k') as a function of crystallizing agent concentration are compared with previously published values for the osmotic second virial coefficient (B(22)) obtained by static light scattering, showing the ability of the chip to accurately determine protein-protein interactions. A 500-fold reduction in protein consumption and the possibility of using conventional instrumentation and automation are some of the advantages over currently used methodologies for evaluating protein-protein interactions.     

Nonequivalence of second virial coefficients from sedimentation equilibrium and static light scattering studies of protein solutions

Experimental data for ovalbumin and lysozyme are presented to highlight the nonequivalence of second virial coefficients obtained for proteins by sedimentation equilibrium and light scattering. Theoretical considerations confirm that the quantity deduced from sedimentation equilibrium distributions is B(22), the osmotic second virial coefficient describing thermodynamic nonideality arising solely from protein self-interaction. On the other hand, the virial coefficient determined by light scattering is shown to reflect the combined contributions of protein-protein and protein-buffer interactions to thermodynamic nonideality of the protein solution. Misidentification of the light scattering parameter as B(22) accounts for published reports of negative osmotic second virial coefficients as indicators of conditions conducive to protein crystal growth. Finally, textbook assertions about the equivalence of second virial coefficients obtained by sedimentation equilibrium and light scattering reflect the restriction of consideration to single-solute systems. Although sedimentation equilibrium distributions for buffered protein solutions are, indeed, amenable to interpretation in such terms, the same situation does not apply to light scattering measurements because buffer constituents cannot be regarded as part of the solvent: instead they must be treated as non-scattering cosolutes.     

Self-interaction of native and denatured lysozyme in the presence of osmolytes,l-arginine and guanidine hydrochloride

Osmolyte molecules such as betaine and trehalose are protein stabilizers while l-arginine (Arg) and guanidine hydrochloride (GdnHCl) are the most widely used aggregation suppressor in protein refolding. We have herein studied the effects of the osmolyte molecules and l-arginine together with GdnHCl (0–6 mol/L) on the intermolecular interaction of native and denatured lysozyme by self-interaction chromatography. The self-interaction is characterized in terms of the osmotic second virial coefficient (B) of the protein, the increase of which represents the decrease of intermolecular attraction of the protein. It is found that the effect of Arg on the self-interaction of lysozyme is similar with GdnHCl, but its competence is much weaker than the denaturant. At higher GdnHCl concentrations (>0.5 mol/L), Arg can be used to suppress the self-association of lysozyme. In contrast to Arg, B increases with increasing betaine or trehalose concentration at the GdnHCl concentration range studied. The results indicate the cooperativity of each osmolyte with GdnHCl, and the different mechanisms of their effects from Arg on the B values. The work confirms that the osmolytes are not only protein stabilizers, but also protein aggregation suppressors for both native and denatured protein molecules.     

A simpler analysis for the measurement of second virial coefficients by self-interaction chromatography

We describe a thermodynamic approach that supports the adoption of a simplified procedure for the determination of protein second virial coefficients (B(2)) by self-interaction chromatography. Its major advantage over the original method is a decrease in the number of parameters to which magnitudes must be assigned for the determination of B(2). Improved correlation of virial coefficients obtained by the chromatographic procedure with those obtained by light scattering is achieved by taking into account the twofold larger magnitudes of the former because of the experimental distinction between free and immobilized protein molecules in self-interaction chromatography.     

Second virial coefficient determination of a therapeutic peptide by self-interaction chromatography

Self-interaction of macromolecules has been shown to play an important role in a number of physical processes, including crystallization, solubility, viscosity, and aggregation. Peptide self-interaction is not as well studied as for larger proteins, but should play an equally important role. The osmotic second virial coefficient, B, can be used to quantify peptide and protein self-interaction. B values are typically measured using static light scattering (SLS). Peptides, however, do not scatter enough light to allow such measurements. This study describes the first use of self-interaction chromatography (SIC) for the measurement of peptide B values because SIC does not have the molecular size limitations of SLS. In the present work, SIC was used to measure B for enfuvirtide, a 36-amino acid therapeutic peptide, as a function of salt concentration, salt type, and pH. B was found to correlate strongly with solubility and apparent molecular weight. In general, the solubility of enfuvirtide increases with pH from 6 to 10 and decreases as the salt concentration increases from 0 to 0.5M for three different salts. The effect of peptide concentration on B was also investigated and shown to have a significant effect, but only at high concentrations (>80 mg/mL).     

Measurements of protein-protein interactions by size exclusion chromatography

A method is presented for determining second virial coefficients (B(2)) of protein solutions from retention time measurements in size exclusion chromatography. We determine B(2) by analyzing the concentration dependence of the chromatographic partition coefficient. We show the ability of this method to track the evolution of B(2) from positive to negative values in lysozyme and bovine serum albumin solutions. Our size exclusion chromatography results agree quantitatively with data obtained by light scattering.     

Correlation of diafiltration sieving behavior of lysozyme-BSA mixtures with osmotic second virial cross-coefficients

The role of protein-protein interactions in membrane separations of protein mixtures remains incompletely understood, largely due to the difficulty of characterizing protein self- and, especially, cross-association. Recently, a novel technique, cross-interaction chromatography, has been developed to measure weak protein cross-association in terms of the osmotic second virial cross-coefficient. In this work the relationship between protein cross-association and the sieving behavior of lysozyme in the presence of BSA has been investigated. Sieving coefficients were measured using a stirred diafiltration cell over a range of pH and ionic strength, and a striking correlation between the lysozyme sieving and second virial cross-coefficients for BSA/lysozyme mixtures has been found: when the protein cross-interactions are most attractive (negative second virial cross-coefficient), the lysozyme sieving coefficients are lowest, and vice versa. The correlation between the sieving and second virial cross-coefficients may be due to the physically similar environments in the chromatography and filtration experiments since one protein is passed through a concentrated region of the second protein either immobilized on the column or accumulated at the membrane surface, and the migration rate of the mobile protein in both cases is influenced by protein cross-association. This study represents the first time that molecular interactions in binary mixtures have been related directly to filtration behavior, and may provide a useful approach to optimize the separation of other binary protein mixtures.     

Interpretation of thermodynamic non-ideality in sedimentation equilibrium experiments on proteins

This investigation re-examines theoretical aspects of the allowance for effects of thermodynamic non-ideality on the sedimentation equilibrium distribution for a single macromolecular solute, and thereby resolves the question of the constraints that pertain to the definition of the activity coefficient term in the basic sedimentation equilibrium expression. Sedimentation equilibrium results for ovalbumin are then presented to illustrate a simple procedure for evaluating the net charge (valence) of a protein from the magnitude of the second virial coefficient in situations where the effective radius of the protein can be assigned. Finally, published sedimentation equilibrium results on lysozyme are reanalysed to demonstrate the feasibility of employing the dependence of the second virial coefficient upon ionic strength to evaluate both the valence and the effective radius of the non-interacting solute.     

Phase behavior of an intact monoclonal antibody

Understanding protein phase behavior is important for purification, storage, and stable formulation of protein drugs in the biopharmaceutical industry. Glycoproteins, such as monoclonal antibodies (MAbs) are the most abundant biopharmaceuticals and probably the most difficult to crystallize among water-soluble proteins. This study explores the possibility of correlating osmotic second virial coefficient (B(22)) with the phase behavior of an intact MAb, which has so far proved impossible to crystallize. The phase diagram of the MAb is presented as a function of the concentration of different classes of precipitants, i.e., NaCl, (NH4)2SO4, and polyethylene glycol. All these precipitants show a similar behavior of decreasing solubility with increasing precipitant concentration. B(22) values were also measured as a function of the concentration of the different precipitants by self-interaction chromatography and correlated with the phase diagrams. Correlating phase diagrams with B(22) data provides useful information not only for a fundamental understanding of the phase behavior of MAbs, but also for understanding the reason why certain proteins are extremely difficult to crystallize. The scaling of the phase diagram in B(22) units also supports the existence of a universal phase diagram of a complex glycoprotein when it is recast in a protein interaction parameter.     

Screening of protein-ligand interactions by affinity chromatography

This paper examines affinity chromatography (AC) as an alternative tool for the determination of protein-ligand interactions for the particular case in which the ligand is the same protein. The methodology is less labor-intensive and more sample-efficient than traditional methods used to measure the second virial coefficient (B(22)), a parameter commonly used to evaluate protein-protein interactions. The chromatographic capacity factor (k') was studied for lysozyme and equine serum albumin for a wide range of experimental solution conditions such as crystallizing agent concentration, protein concentration and pH. Parallel experiments using AC to determine k' and static light scattering (SLS) to determine B(22) showed that the two parameters were highly correlated. Two different column volumes ( approximately 1 and approximately 0.1 mL) were tested and gave essentially the same values for k', showing the feasibility of miniaturization.     

Lysozyme-lysozyme self-interactions as assessed by the osmotic second virial coefficient: Impact for physical protein stabilization

The purpose of the presented study is to understand the physicochemical properties of proteins in aqueous solutions in order to identify solution conditions with reduced attractive protein-protein interactions, to avoid the formation of protein aggregates and to increase protein solubility. This is assessed by measuring the osmotic second virial coefficient (B²²), a parameter of solution non-ideality, which is obtained using self-interaction chromatography. The model protein is lysozyme. The influence of various solution conditions on B²² was investigated: protonation degree, ionic strength, pharmaceutical relevant excipients and combinations thereof. Under acidic solution conditions B²² is positive, favoring protein repulsion. A similar trend is observed for the variation of the NaCl concentration, showing that with increasing the ionic strength protein attraction is more likely. B²² decreases and becomes negative. Thus, solution conditions are obtained favoring attractive protein-protein interactions. The B²² parameter also reflects, in general, the influence of the salts of the Hofmeister series with regard to their salting-in/salting-out effect. It is also shown that B²² correlates with protein solubility as well as physical protein stability.     

Analysis of the thermodynamic non-ideality of proteins by sedimentation equilibrium experiments

This paper presents a modified method to determine experimentally the second virial coefficient of protein solutions by sedimentation equilibrium experiments. The improvement is based on the possibility of fitting simultaneously up to seven radial concentration distribution curves of solutions with different loading concentrations. The possibility of precise determination of the second virial coefficient allows estimation of the net charge and the excluded volume of a monomeric protein. Application of the method is demonstrated for lysozyme and ovalbumin. In 0.1 M sodium acetate buffer, pH 4.5, the second virial coefficient of hen egg white lysozyme amounts to 24 +/- 1 ml/g. Analysis based on spherical particle theory yield an excluded volume of 3.5 ml/g and a charge dependent value of 20.5 ml/g which is induced by a net charge number of 14.1 +/- 1. Under low salt conditions self-association processes on lysozyme are unfavorable due to electrostatic repulsion. To overcome these repulsive contributions, either a shift to neutral pH or addition of at least 2% NaCl is necessary. In this way the charge dependent contribution decreases below the value responsible for the excluded volume and allows crystallization of the protein. Similar effects can be observed with ovalbumin. The high virial coefficient observed at pH 8.5 is induced by the high net charge number of 27 +/- 1.     

Negative second virial coefficients as predictors of protein crystal growth: evidence from sedimentation equilibrium studies that refutes the designation of those light scattering parameters as osmotic virial coefficients

The effects of ammonium sulphate concentration on the osmotic second virial coefficient (BAA/MA) for equine serum albumin (pH 5.6, 20 degrees C) have been examined by sedimentation equilibrium. After an initial steep decrease with increasing ammonium sulphate concentration, BAA/MA assumes an essentially concentration-independent magnitude of 8-9 ml/g. Such behaviour conforms with the statistical-mechanical prediction that a sufficient increase in ionic strength should effectively eliminate the contributions of charge interactions to BAA/MA but have no effect on the covolume contribution (8.4 ml/g for serum albumin). A similar situation is shown to apply to published sedimentation equilibrium data for lysozyme (pH 4.5). Although termed osmotic second virial coefficients and designated as such (B22), the negative values obtained in published light scattering studies of both systems have been described incorrectly because of the concomitant inclusion of the protein-salt contribution to thermodynamic nonideality of the protein. Those negative values are still valid predictors of conditions conducive to crystal growth inasmuch as they do reflect situations in which there is net attraction between protein molecules. However, the source of attraction responsible for the negative virial coefficient stems from the protein-salt rather than the protein-protein contribution, which is necessarily positive.     

Interactions of lysozyme in guanidinium chloride solutions from static and dynamic light-scattering measurements

The interactions of partially unfolded proteins provide insight into protein folding and protein aggregation. In this work, we studied partially unfolded hen egg lysozyme interactions in solutions containing up to 7 M guanidinium chloride (GdnHCl). The osmotic second virial coefficient (B(22)) of lysozyme was measured using static light scattering in GdnHCl aqueous solutions at 20 degrees C and pH 4.5. B(22) is positive in all solutions, indicating repulsive protein-protein interactions. At low GdnHCl concentrations, B(22) decreases with rising ionic strength: in the absence of GdnHCl, B(22) is 1.1 x 10(-3) mLmol/g(2), decreasing to 3.0 x 10(-5) mLmol/g(2) in the presence of 1 M GdnHCl. Lysozyme unfolds in solutions at GdnHCl concentrations higher than 3 M. Under such conditions, B(22) increases with ionic strength, reaching 8.0 x 10(-4) mLmol/g(2) at 6.5 M GdnHCl. Protein-protein hydrodynamic interactions were evaluated from concentration-dependent diffusivity measurements, obtained from dynamic light scattering. At moderate GdnHCl concentrations, lysozyme interparticle interactions are least repulsive and hydrodynamic interactions are least attractive. The lysozyme hydrodynamic radius was calculated from infinite-dilution diffusivity and did not change significantly during protein unfolding. Our results contribute toward better understanding of protein interactions of partially unfolded states in the presence of a denaturant; they may be helpful for the design of protein refolding processes that avoid protein aggregation.     

Protein stability in mixed solvents: a balance of contact interaction and excluded volume

Changes in excluded volume and contact interaction with the surface of a protein have been suggested as mechanisms for the changes in stability induced by cosolvents. The aim of the present paper is to present an analysis that combines both effects in a quantitative manner. The result is that both processes are present in both stabilizing and destabilizing interactions and neither can be ignored. Excluded volume was estimated using accessible surface area calculations of the kind introduced by Lee and Richards. The change in excluded volume on unfolding, deltaX, is quite large. For example, deltaX for ribonuclease is 6.7 L in urea and approximately 16 L in sucrose. The latter number is greater than the molar volume of the protein. Direct interaction with the protein is represented as the solvent exchange mechanism, which differs from ordinary association theory because of the weakness of the interaction and the high concentrations of cosolvents. The balance between the two effects and their contribution to overall stability are most simply presented as bar diagrams as in Fig. 3. Our finding for five proteins is that excluded volume contributes to the stabilization of the native structure and that contact interaction contributes to destabilization. This is true for five proteins and four cosolvents including both denaturants and osmolytes. Whether a substance stabilizes a protein or destabilizes it depends on the relative size of these two contributions. The constant for the cosolvent contact with the protein is remarkably uniform for four of the proteins, indicating a similarity of groups exposed during unfolding. One protein, staphylococcus nuclease, is anomalous in almost all respects. In general, the strength of the interaction with guanidinium is about twice that of urea, which is about twice that of trimethylamine-N-oxide and sucrose. Arguments are presented for the use of volume fractions in equilibrium equations and the ignoring of activity coefficients of the cosolvent. It is shown in the Appendix that both the excluded volume and the direct interaction can be extracted in a unified way from the McMillan-Mayer formula for the second virial coefficient.     

Effects of additives on surfactant phase behavior relevant to bacteriorhodopsin crystallization

The interactions leading to crystallization of the integral membrane protein bacteriorhodopsin solubilized in n-octyl-beta-D-glucoside were investigated. Osmotic second virial coefficients (B(22)) were measured by self-interaction chromatography using a wide range of additives and precipitants, including polyethylene glycol (PEG) and heptane-1,2,3-triol (HT). In all cases, attractive protein-detergent complex (PDC) interactions were observed near the surfactant cloud point temperature, and there is a correlation between the surfactant cloud point temperatures and PDC B(22) values. Light scattering, isothermal titration calorimetry, and tensiometry reveal that although the underlying reasons for the patterns of interaction may be different for various combinations of precipitants and additives, surfactant phase behavior plays an important role in promoting crystallization. In most cases, solution conditions that led to crystallization fell within a similar range of slightly negative B(22) values, suggesting that weakly attractive interactions are important as they are for soluble proteins. However, the sensitivity of the cloud point temperatures and resultant coexistence curves varied significantly as a function of precipitant type, which suggests that different types of forces are involved in driving phase separation depending on the precipitant used.     

Sucrose and glycerol effects on photosystem II

Photosystem II catalyzes the oxidation of water and the reduction of plastoquinone. The active site cycles among five oxidation states, which are called the S(n) states. PSII purification procedures include the use of the cosolvents, sucrose and/or glycerol, to stabilize water splitting activity and for cryoprotection. In this study, the effects of sucrose and glycerol on PSII were investigated. Sucrose addition was observed to stimulate the steady-state rate of oxygen evolution in the range from 0 to 1.35 M. Glycerol addition was observed to stimulate oxygen evolution in the range from 0 to 30%. Both cosolvents were observed to be inhibitory at higher concentrations. Sucrose addition was shown to have no effect on the rate of Q(A)(-) oxidation or on the K(M) for exogenous acceptor. PSII was then treated to remove extrinsic proteins. In these samples, sucrose addition stimulated activity, but glycerol addition was inhibitory at concentrations higher than approximately 0.5 M. This inhibitory effect of glycerol at relatively low concentrations is attributed to glycerol binding to the active site, when extrinsic subunits are not present. Reaction induced FTIR spectra, associated with the S(1) to S(2) transition of the water-oxidizing complex, exhibited significant differences throughout the 1,800-1,200 cm(-1) region, when glycerol- and sucrose-containing samples were compared. These measurements suggest a cosolvent-induced shift in the pK(A) of an aspartic or glutamic acid side chain, as well as structural changes at the active site. These structural alterations are attributed to a change in preferential hydration of the oxygen-evolving complex.     

Effect of alcohols on aqueous lysozyme-lysozyme interactions from static light-scattering measurements

Alcohols have been widely used as protein denaturants, precipitants and crystallization reagents. We have studied the effect of alcohols on aqueous hen-egg lysozyme self-interactions by measuring the osmotic second virial coefficient (B22) using static light scattering. Addition of alcohols increases B22, indicating stronger protein-protein repulsion or weaker attraction. For the monohydric alcohols used in this study (methanol, ethanol, 1-propanol, n-butanol, iso-butanol and trifluoroethanol), B22 for lysozyme reaches a common plateau at approximately 5% (v/v) alcohol, while glycerol increases B22 more than monohydric alcohols. For a 0.05 M NaCl hen-egg lysozyme solution at pH 7, B22 increases from 2.4 x 10(-4) to 4.7 x 10(-4) ml mol/g2 upon addition of monohydric alcohols and to 5.8 x 10(-4) ml mol/g2 upon addition of glycerol. We describe the alcohol effect using a simple model that supplements the DLVO theory with an additional alcohol-dependent term representing orientation-averaged hydrophobic interactions. In this model, the increased lysozyme repulsive forces in the presence of monohydric alcohols are interpreted in terms of adsorption of alcohol molecules on hydrophobic sites on the protein surface. This adsorption reduces attractive hydrophobic protein-protein interactions. A thicker lysozyme hydration layer in aqueous glycerol solution can explain the glycerol-increased lysozyme-lysozyme repulsion.