Measurement of the second osmotic virial coefficient for protein solutions exhibiting monomer-dimer equilibrium

The second osmotic virial coefficient (B) is a measure of solution nonideality that is useful for predicting conditions favorable for protein crystallization and for inhibition of aggregation. Static light scattering is the technique most commonly used to determine B values, typically using protein concentrations less than 5 mg/mL. During static light scattering experiments at low protein concentrations, frequently the protein is assumed to exist either as a single nonassociating species or as a combination of assembly states independent of protein concentration. In the work described here, we examined the limit for ignoring weak reversible dimerization (Kd > or =1 mM) by comparing B values calculated with and without accounting for self-association. Light scattering effects for equilibrium dimer systems with Kd <20 mM and Kd <1 mM will significantly affect apparent B values measured for 20 and 150-kDa proteins, respectively. To interpret correctly light scattering data for monomer-dimer equilibrium systems, we use an expanded coefficient model to account for separate monomer-monomer (B(22)), monomer-dimer (B(23)), and dimer-dimer (B(33)) interactions.     

Calculation of weak protein-protein interactions: the pH dependence of the second virial coefficient

Interactions between proteins are often sufficiently weak that their study through the use of conventional structural techniques becomes problematic. Of the few techniques capable of providing experimental measures of weak protein-protein interactions, perhaps the most useful is the second virial coefficient, B(22), which quantifies a protein solution's deviations from ideal behavior. It has long been known that B(22) can in principle be computed, but only very recently has it been demonstrated that such calculations can be performed using protein models of true atomic detail (Biophys. J. 1998, 75:2469-2477). The work reported here extends these previous efforts in an attempt to develop a transferable energetic model capable of reproducing the experimental trends obtained for two different proteins over a range of pH and ionic strengths. We describe protein-protein interaction energies by a combination of three separate terms: (i) an electrostatic interaction term based on the use of effective charges, (ii) a term describing the electrostatic desolvation that occurs when charged groups are buried by an approaching protein partner, and (iii) a solvent-accessible surface area term that is used to describe contributions from van der Waals and hydrophobic interactions. The magnitude of the third term is governed by an adjustable, empirical parameter, gamma, that is altered to optimize agreement between calculated and experimental values of B(22). The model is applied separately to the proteins lysozyme and chymotrypsinogen, yielding optimal values of gamma that are almost identical. There are, however, clear difficulties in reproducing B(22) values at the extremes of pH. Explicit calculation of the protonation states of ionizable amino acids in the 200 most energetically favorable protein-protein structures suggest that these difficulties are due to a neglect of the protonation state changes that can accompany complexation. Proper reproduction of the pH dependence of B(22) will, therefore, almost certainly require that account be taken of these protonation state changes. Despite this problem, the fact that almost identical gamma values are obtained from two different proteins suggests that the basic energetic formulation used here, which can be evaluated very rapidly, might find use in dynamical simulations of weak protein-protein interactions at intermediate pH values.     

Correlation of second virial coefficient with solubility for proteins in salt solutions

In this work, osmotic second virial coefficients (B(22)) were determined and correlated with the measured solubilities for the proteins, α-amylase, ovalbumin, and lysozyme. The B(22) values and solubilities were determined in similar solution conditions using two salts, sodium chloride and ammonium sulfate in an acidic pH range. An overall decrease in the solubility of the proteins (salting out) was observed at high concentrations of ammonium sulfate and sodium chloride solutions. However, for α-amylase, salting-in behavior was also observed in low concentration sodium chloride solutions. In ammonium sulfate solutions, the B(22) are small and close to zero below 2.4 M. As the ammonium sulfate concentrations were further increased, B(22) values decreased for all systems studied. The effect of sodium chloride on B(22) varies with concentration, solution pH, and the type of protein studied. Theoretical models show a reasonable fit to the experimental derived data of B(22) and solubility. B(22) is also directly proportional to the logarithm of the solubility values for individual proteins in salt solutions, so the log-linear empirical models developed in this work can also be used to rapidly predict solubility and B(22) values for given protein-salt systems.     

Correlation between the osmotic second virial coefficient and the solubility of proteins

A correlation between the osmotic second virial coefficient and the solubility of proteins is derived from classical thermodynamics to support an empirical relation previously found by Wilson and co-workers (1). The model is based on the equality of fugacities of the protein in the equilibrium phases, with the details of the model depending on the standard state used. The parameters in this model have been fitted to data for several systems, mainly with lysozyme as the protein. The model is found to describe experimental data, with variations in protein concentration, salt type and concentration, temperature, and pH, both qualitatively and quantitatively. Agreement between the model and the experimental data is very good for protein solubilities up to 30 mg/mL. Above this value the model underpredicts the experimental data, probably as a result of multibody interactions that are not included in the model here. Variations of the model parameters with protein type, temperature, pH, and salt type are discussed.     

Diffusion and sedimentation interaction parameters for measuring the second virial coefficient and their utility as predictors of protein aggregation

The concentration-dependence of the diffusion and sedimentation coefficients (k_D and k_s, respectively) of a protein can be used to determine the second virial coefficient (B₂), a parameter valuable in predicting protein-protein interactions. Accurate measurement of B₂ under physiologically and pharmaceutically relevant conditions, however, requires independent measurement of k_D and k_s via orthogonal techniques. We demonstrate this by utilizing sedimentation velocity (SV) and dynamic light scattering (DLS) to analyze solutions of hen-egg white lysozyme (HEWL) and a monoclonal antibody (mAb1) in different salt solutions. The accuracy of the SV-DLS method was established by comparing measured and literature B₂ values for HEWL. In contrast to the assumptions necessary for determining k_D and k_s via SV alone, k_D and ks were of comparable magnitudes, and solution conditions were noted for both HEWL and mAb1 under which 1), k_D and k_s assumed opposite signs; and 2), k_D ≥ k_s. Further, we demonstrate the utility of k_D and k_s as qualitative predictors of protein aggregation through agitation and accelerated stability studies. Aggregation of mAb1 correlated well with B₂, k_D, and k_s, thus establishing the potential for k_D to serve as a high-throughput predictor of protein aggregation.     

Second virial coefficient studies of cosolvent-induced protein self-interaction

Protein self-interaction is important in protein crystal growth, solubilization, and aggregation, both in vitro and in vivo, as with protein misfolding diseases, such as Alzheimer's. Although second virial coefficient studies can supply invaluable quantitative information, their emergence as a systematic approach to evaluating protein self-interaction has been slowed by the limitations of traditional measurement methods, such as static light scattering. Comparatively, self-interaction chromatography is an inexpensive, high-throughput method of evaluating the osmotic second virial coefficient (B) of proteins in solution. In this work, we used self-interaction chromatography to measure B of lysozyme in the presence of various cosolvents, including sucrose, trehalose, mannitol, glycine, arginine, and combinations of arginine and glutamic acid and arginine and sucrose in an effort to develop a better fundamental understanding of protein self-interaction in complex cosolvent systems. All of these cosolvents, alone or in combination, increased B, indicating a reduction in intermolecular attraction. However, the magnitude of cosolvent-induced changes in B was found to be largely dependent on the ability to control long-range electrostatic repulsion. To the best of our knowledge, this work represents the most comprehensive virial coefficient study to date focusing on complex cosolvent-induced effects on the self-interaction of lysozyme.     

Beyond the second virial coefficient: Sedimentation equilibrium in highly non-ideal solutions

The general theory of sedimentation equilibrium (SE), applicable to mixtures of interacting sedimentable solutes at arbitrary concentration, is summarized. Practical techniques for the acquisition of SE data suitable for analysis are described. Experimental measurements and analyses of SE in concentrated protein solutions are reviewed. The method of non-ideal tracer sedimentation equilibrium (NITSE) is described. Experimental studies using NITSE to detect and quantitatively characterize intermolecular interactions in mixtures of dilute tracer species and concentrated proteins or polymers are reviewed.     

A rational design for hepatitis B virus X protein refolding and bioprocess development guided by second virial coefficient studies

The hepatitis B virus X (HBx) protein is well known for its role in hepatitis B virus infection that often leads to hepatocellular carcinoma. Despite the clinical importance of HBx, there is little progress in anti-HBx drug development strategies due to shortage of HBx from native sources. Consistent expression of HBx as insoluble inclusion bodies within various expression systems has largely hindered HBx manufacturing via economical biosynthesis routes. Confronted by this roadblock, this study aims to quantitatively understand HBx protein behaviour in solution that will guide the rational development of a refolding-based bioprocess for HBx production. Second virial coefficient (SVC) measurements were employed to study the effects of varying physicochemical parameters on HBx intermolecular protein interaction. The SVC results suggest that covalent HBx aggregates play a key role in protein destabilisation during refolding. The use of an SVC-optimised refolding environment yielded bioactive and soluble HBx proteins from the denatured–reduced inclusion body state. This study provides new knowledge on HBx solubility behaviour in vitro, which is important in structure–function elucidation behaviour of this hydrophobic protein. Importantly, a rational refolding-based Escherichia coli bioprocess that can deliver purified and soluble HBx at large scale is successfully developed, which opens the way for rapid preparation of soluble HBx for further clinical and characterisation studies.     

Determination of second virial coefficient of proteins using a dual-detector cell for simultaneous measurement of scattered light intensity and concentration in SEC-HPLC

A method is proposed for the measurement of the B22 value of proteins in aqueous solutions in flow-mode that utilizes a novel fabricated dual-detector cell, which simultaneously measures protein concentration and the corresponding scattered light intensity at 90 degrees , after the protein elutes from a size-exclusion column. Each data point on the chromatograms obtained from the light scattering detector and the concentration (ultraviolet) detector is converted to Rayleigh's ratio, Rtheta, and concentration, c, respectively. The B22 value is calculated from the slope of the Debye plot (Kc/Rtheta versus c) generated from a range of concentrations obtained from these chromatograms for a single protein injection. It is shown that this method provides reliable determination of the B22 values for such proteins as lysozyme, chymotrypsinogen, and chymotrypsin in various solution conditions that agree well with those reported in literature.     

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.     

Use of dynamic light scattering to determine second virial coefficient in a semidilute concentration regime

The present work discusses an alternative procedure to obtain static light scattering (SLS) parameters in a dilute and semidilute concentration regime from a dynamic light scattering (DLS) instrument that uses an avalanche photodiode (APD) for recording the scattered intensity signal. An APD enables one to perform both SLS and DLS measurements by photon counting and photon correlation, respectively. However, due to the associated recovery time, the APDs are susceptible to saturation (above 1000 kcps), which may limit the measurements in systems that scatter too much light. We propose an alternative way of obtaining the SLS parameters with instruments that use APD for recording signal intensities.     

Crystallization data mining in structural genomics: using positive and negative results to optimize protein crystallization screens

Recent efforts to collect and mine crystallization data from structural genomics (SG) consortia have led to the identification of minimal screens and novel screening strategies that can be used to streamline the crystallization process. Two groups, the Joint Center for Structural Genomics and the University of Toronto, carried out large-scale crystallization trials on different sets of bacterial targets (539, JCSG and 755, Toronto), using different sample processing and crystallization methods, and then analyzed their results to identify the smallest subset of conditions that would have crystallized the maximum number of protein targets. The JCSG Core Screen contains 67 conditions (from 480) while the Toronto Minimal Screen contains 6 (from 48). While the exact conditions included in the two screens do not overlap, the major precipitants of the conditions are similar and thus both screens can be used to determine if a protein has a natural propensity to crystallize. In addition, studies from other groups including the University of Queensland, the Mycobacterium tuberculosis SG group, the Southeast Collaboratory for SG, and the York Structural Biology Laboratory indicate that alternative crystallization strategies may be more successful at identifying initial crystallization conditions than typical sparse matrix screens. These minimal screens and alternative screening strategies are already being used to optimize the crystallization processes within large SG efforts. The differences between these results, however, demonstrate that additional studies which examine the influence of protein biophysical properties and sample preparation methods on crystal formation must also be carried out before more robust screens can be identified.     

From osmotic second virial coefficient (B22) to phase behavior of a monoclonal antibody

Antibodies are complex macromolecules and their phase behavior as well as interactions within different solvents and precipitants are still not understood. To shed some light into the processes on a molecular dimension, the occurring self‐interactions between antibody molecules were analyzed by means of the osmotic second virial coefficient (B₂₂). The determined B₂₂ follows qualitatively the phenomenological Hofmeister series describing the aggregation probability of antibodies for the various solvent compositions. However, a direct correlation between crystallization probability and B₂₂ in form of a crystallization slot does not seem to be feasible for antibodies since the phase behavior is strongly dependent on their anisotropy. Kinetic parameters have to be taken into account due to the molecular size and complexity of the molecules. This is confirmed by a comparison of experimental data with a theoretical phase diagram. On the other hand the solubility is thermodynamically driven and therefore the B₂₂ could be used to establish a universal solubility line for the monoclonal antibody mAb04c and different solvent compositions by using thermodynamic models. © 2015 American Institute of Chemical Engineers Biotechnol. Prog., 31:438–451, 2015     

Advanced protein crystallization using water-soluble ionic liquids as crystallization additives

The application of five water-soluble, halogen-free, alkylammonium-based ionic liquids (ILs) as additives for advanced crystallization of lysozyme was investigated. Their biocompatibility was determined by long-term measurement of the overall mean relative enzyme activities. These were maximally reduced by about 10–15% when up to 200 g IL l⁻¹ was added. Sitting-drop vapor diffusion crystallization experiments revealed that the addition of some of the ILs led to less crystal polymorphism and precipitation was avoided reliably even at larger NaCl concentrations. The addition of ILs tended to result in larger crystals. The kinetics of lysozyme crystallization were significantly enhanced using ILs as crystallization additives, e.g. by a factor of 5.5 when 100 g ethanolammonium formate l⁻¹ was added. ILs with “soft” anions, such as formate or glycolate, were superior to ILs with “hard” anions, like nitrate.     

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.     

Selection of membrane protein targets for crystallization using PFO-PAGE electrophoresis

A method to rapidly assess the oligomeric composition of multimeric proteins is notably absent from reported schemes for high throughput production and crystallization of membrane proteins. In this report we have investigated the suitability of PFO-PAGE electrophoresis for this purpose and present examples where it proves highly informative in selecting conditions favouring the functional oligomeric state of the target protein. Features such as the ability to analyze several samples in parallel, including crude membrane extracts, suggest it will be highly adaptable to high throughput analysis of membrane proteins.