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.     

Static light scattering studies of OmpF porin: implications for integral membrane protein crystallization

Integral membrane proteins carry out some of the most important functions of living cells, yet relatively few details are known about their structures. This is due, in large part, to the difficulties associated with preparing membrane protein crystals suitable for X-ray diffraction analysis. Mechanistic studies of membrane protein crystallization may provide insights that will aid in determining future membrane protein structures. Accordingly, the solution behavior of the bacterial outer membrane protein OmpF porin was studied by static light scattering under conditions favorable for crystal growth. The second osmotic virial coefficient (B22) was found to be a predictor of the crystallization behavior of porin, as has previously been found for soluble proteins. Both tetragonal and trigonal porin crystals were found to form only within a narrow window of B22 values located at approximately -0.5 to -2 X 10(-4) mol mL g(-2), which is similar to the "crystallization slot" observed for soluble proteins. The B22 behavior of protein-free detergent micelles proved very similar to that of porin-detergent complexes, suggesting that the detergent's contribution dominates the behavior of protein-detergent complexes under crystallizing conditions. This observation implies that, for any given detergent, it may be possible to construct membrane protein crystallization screens of general utility by manipulating the solution properties so as to drive detergent B22 values into the crystallization slot. Such screens would limit the screening effort to the detergent systems most likely to yield crystals, thereby minimizing protein requirements and improving productivity.     

Measurements of protein self-association as a guide to crystallization

The challenge of crystallizing proteins has led to a significant amount of research in understanding protein self-association and assembly. Arguably the most influential finding in this field in the past decade has been that weakly attractive protein interactions, characterized in terms of the osmotic second virial coefficient, correlate with solution conditions that are conducive to crystallization. Recent work in this area has focused on the development of more efficient techniques for measuring the second virial coefficient, as traditional characterization methods suffer from poor efficiency in terms of time and protein consumption. The resulting measurements have provided new insights into patterns of protein interactions and their relation to protein phase behavior.     

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.     

A comparative study of monoclonal antibodies. 1. phase behavior and protein–protein interactions

Protein phase behavior is involved in numerous aspects of downstream processing, either by design as in crystallization or precipitation processes, or as an undesired effect, such as aggregation. This work explores the phase behavior of eight monoclonal antibodies (mAbs) that exhibit liquid–liquid separation, aggregation, gelation, and crystallization. The phase behavior has been studied systematically as a function of a number of factors, including solution composition and pH, in order to explore the degree of variability among different antibodies. Comparisons of the locations of phase boundaries show consistent trends as a function of solution composition; however, changing the solution pH has different effects on each of the antibodies studied. Furthermore, the types of dense phases formed varied among the antibodies. Protein–protein interactions, as reflected by values of the osmotic second virial coefficient, are used to correlate the phase behavior. The primary findings are that values of the osmotic second virial coefficient are useful for correlating phase boundary locations, though there is appreciable variability among the antibodies in the apparent strengths of the intrinsic protein–protein attraction manifested. However, the osmotic second virial coefficient does not provide a clear basis to predict the type of dense phase likely to result under a given set of solution conditions. © 2014 American Institute of Chemical Engineers Biotechnol. Prog., 31:268–276, 2015     

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.     

Effects of pH on protein-protein interactions and implications for protein phase behavior

The effects of pH on protein interactions and protein phase behavior were investigated by measuring the reduced second osmotic virial coefficient (b2) for ovalbumin and catalase, and the aggregate and crystal solubilities for ovalbumin, beta-lactoglobulin A and B, ribonuclease A and lysozyme. The b2 trends observed for ovalbumin and catalase show that protein interactions become increasingly attractive with decreasing pH. This trend is in good agreement with ovalbumin phase behavior, which was observed to evolve progressively with decreasing pH, leading to formation of amorphous aggregates instead of gel bead-like aggregates, and spherulites instead of needle-like crystals. For both acidic and basic proteins, the aggregate solubility during protein salting-out decreased with decreasing pH, and contrary to what is commonly believed, neither aggregate nor crystal solubility had a minimum at the isoelectric point. beta-Lactoglobulin B was the only protein investigated to show salting-in behavior, and crystals were obtained at low salt concentrations in the vicinity of its isoelectric point. The physical origin of the different trends observed during protein salting-in and salting-out is discussed, and the implications for protein crystallization are emphasized.     

Patterns of protein protein interactions in salt solutions and implications for protein crystallization

The second osmotic virial coefficients of seven proteins-ovalbumin, ribonuclease A, bovine serum albumin, alpha-lactalbumin, myoglobin, cytochrome c, and catalase-were measured in salt solutions. Comparison of the interaction trends in terms of the dimensionless second virial coefficient b(2) shows that, at low salt concentrations, protein-protein interactions can be either attractive or repulsive, possibly due to the anisotropy of the protein charge distribution. At high salt concentrations, the behavior depends on the salt: In sodium chloride, protein interactions generally show little salt dependence up to very high salt concentrations, whereas in ammonium sulfate, proteins show a sharp drop in b(2) with increasing salt concentration beyond a particular threshold. The experimental phase behavior of the proteins corroborates these observations in that precipitation always follows the drop in b(2). When the proteins crystallize, they do so at slightly lower salt concentrations than seen for precipitation. The b(2) measurements were extended to other salts for ovalbumin and catalase. The trends follow the Hofmeister series, and the effect of the salt can be interpreted as a water-mediated effect between the protein and salt molecules. The b(2) trends quantify protein-protein interactions and provide some understanding of the corresponding phase behavior. The results explain both why ammonium sulfate is among the best crystallization agents, as well as some of the difficulties that can be encountered in protein crystallization.     

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.     

Molecular origins of osmotic second virial coefficients of proteins.

The thermodynamic properties of protein solutions are determined by the molecular interactions involving both solvent and solute molecules. A quantitative understanding of the relationship would facilitate more systematic procedures for manipulating the properties in a process environment. In this work the molecular basis for the osmotic second virial coefficient, B22, is studied; osmotic effects are critical in membrane transport, and the value of B22 has also been shown to correlate with protein crystallization behavior. The calculations here account for steric, electrostatic, and short-range interactions, with the structural and functional anisotropy of the protein molecules explicitly accounted for. The orientational dependence of the protein interactions is seen to have a pronounced effect on the calculations; in particular, the relatively few protein-protein configurations in which the apposing surfaces display geometric complementarity contribute disproportionately strongly to B22. The importance of electrostatic interactions is also amplified in these high-complementarity configurations. The significance of molecular recognition in determining B22 can explain the correlation with crystallization behavior, and it suggests that alteration of local molecular geometry can help in manipulating protein solution behavior. The results also have implications for the role of protein interactions in biological self-organization.     

Interactions and phase behavior of a monoclonal antibody

Protein phase behavior is implicated in numerous aspects of downstream processing either by design, as in crystallization or precipitation processes, or as an undesired effect, such as aggregation. An improved understanding of protein phase behavior is, therefore, important for developing rational design strategies for important process steps. This work explores the phase behavior of a monoclonal antibody (mAb), IDEC-152, which exhibits liquid-liquid separation, aggregation, gelation, and crystallization. A systematic study of numerous factors, including the effects of solution composition and pH, has been conducted to explore the phase behavior of this antibody. Phenomena observed include a significant dependence of the cloud point on the cation in sulfate salts and nonmonotonic trends in pH dependence. Additionally, conditions for crystallization of this mAb are reported for the first time. Protein-protein interactions, as determined from the osmotic second virial coefficient, are used to interpret the phase behavior.     

Protein interactions in undersaturated and supersaturated solutions: a study using light and x-ray scattering

Protein interactions in undersaturated and supersaturated solutions were investigated using static and dynamic light scattering and small angle x-ray scattering. A morphodrom of lysozyme crystals determined at 35 degrees C and pH = 4.6 was used as a guideline in selecting the protein and precipitant concentrations. The osmotic second virial coefficient, B(22), was determined by static and dynamic light scattering. At low ionic strengths for which no crystals were formed, B(22) was positive indicating repulsive interactions between the protein molecules. Negative B(22) at higher ionic strengths corresponds to attractive interactions where crystallization becomes possible. At two extreme salt concentrations, small angle x-ray scattering data were collected and fitted with a statistical mechanical model based on Derjaguin-Landau-Verwey-Overbeek potential using Random Phase Approximation. This model accounted well for the small angle x-ray scattering data at undersaturated condition with constant potential parameters. At very high salt concentration corresponding to supersaturated solution this model seems to fail, possibly due to the presence of non-Derjaguin-Landau-Verwey-Overbeek hydration repulsion between the molecules.     

Hydrophobic forces between protein molecules in aqueous solutions of concentrated electrolyte

Protein-protein interactions have been measured for a mutant (D101F) lysozyme and for native lysozyme in concentrated solutions of ammonium sulfate at pH 7 and sodium chloride at pH 4.5. In the mutant lysozyme, a surface aspartate residue has been replaced with a hydrophobic phenylalanine residue. The protein-protein interactions of D101F lysozyme are more attractive than those of native lysozyme for all conditions studied. The salt-induced attraction is correlated with a solvation potential of mean force given by the work required to desolvate the part of the protein surfaces that is buried by the protein-protein interaction. This work is proportional to the aqueous surface-tension increment of the salt and the fractional non-polar surface coverage of the protein. Experimental measurements of osmotic second virial coefficients validate a proposed potential of mean force that ascribes the salt-induced attraction between protein molecules to an enhancement of the hydrophobic attraction. This model provides a first approximation for predicting the protein-protein potential of mean force in concentrated aqueous electrolyte solutions; this potential is useful for determining solution conditions favorable for protein crystallization.     

Evaluation of second osmotic virial coefficients from molecular simulation following scaled-particle theory

ABSTRACT

We report a scaled particle theory-based method for evaluation of second osmotic virial coefficients from molecular simulations of dilute species in solution. In this method, we evaluate the work associated with growing a cavity in solution that is perfectly permeable to the solvent but is completely impermeable to the solutes, thereby establishing an osmotic stress between the cavity interior and exterior. Extrapolating our results to determine the solute concentration in contact with a cavity with an infinite radius, we are able to evaluate the solute osmotic pressure and second osmotic virial coefficient. A finite size correction is introduced to account for the impact of effectively concentrating the solutes in the periphery of the simulation box with increasing cavity size. We demonstrate the utility of the proposed method by evaluating second osmotic virial coefficients for methane in water as a function of temperature. The approach proposed here provides a physically transparent route for calculation of second osmotic virial coefficients by direct interrogation of simulation configurations without having to explicitly evaluate the long-range integral over solute-solute correlations required following McMillan-Mayer theory.     

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.     

Investigation on the mechanism of crystallization of soluble protein in the presence of nonionic surfactant

The mechanism of crystallization of soluble, globular protein (lysozyme) in the presence of nonionic surfactant C8E4 (tetraoxyethylene glycol monooctyl ether) was examined using both static and dynamic light scattering. The interprotein interaction was found to be attractive in solution conditions that yielded crystals and repulsive in the noncrystallizing solution conditions. The validity of the second virial coefficient as a criterion for predicting protein crystallization could be established even in the presence of nonionic surfactants. Our experiments indicate that the origin of the change in interactions can be attributed to the adsorption of nonionic surfactant monomers on soluble proteins, which is generally assumed to be the case with only membrane proteins. This adsorption screens the hydrophobic attractive force and enhances the hydration and electrostatic repulsive forces between protein molecules. Thus at low surfactant concentration, the effective protein-protein interaction remains repulsive. Large surfactant concentrations promote protein crystallization, possibly due to the attractive depletion force caused by the intervening free surfactant micelles.     

Application of the osmotic virial equation in cryobiology

The multisolute osmotic virial equation is the only multisolute thermodynamic solution theory that has been derived from first principles and can make predictions of multisolute solution behaviour in the absence of multisolute solution data. Other solution theories either (i) include simplifying assumptions that do not take into account the interactions between different types of solute molecules or (ii) require fitting to multisolute data to obtain empirical parameters. The osmotic virial coefficients, which are obtained from single-solute data, can be used to make predictions of multisolute solution osmolality. The osmotic virial coefficients for a range of solutes of interest in cryobiology are provided in this paper, for use with concentration units of both molality and mole fraction, along with an explanation of the background and theory necessary to implement the multisolute osmotic virial equation.     

Protein crystallization by design: chymotrypsinogen without precipitants

Protein crystals are usually obtained by an empirical approach based on extensive screening to identify suitable crystallization conditions. In contrast, we have used a systematic predictive procedure to produce data-quality crystals of bovine chymotrypsinogen A and used them to obtain a refined X-ray structure to 3 A resolution. Measurements of the osmotic second virial coefficient of chymotrypsinogen solutions were used to identify suitable solvent conditions, following which crystals were grown for approximately 30 hours by ultracentrifugal crystallization, without the use of any precipitants. Existing structures of chymotrypsinogen were obtained in solutions including 10-30 % ethanol, whereas simple buffered NaCl solutions were used here. The protein crystallized in the tetragonal space group P4(1)2(1)2, with one molecule per asymmetric unit. The quality of the refined map was very high throughout, with the main-chain atoms of all but four residues clearly defined and with nearly all side-chains also defined. Although only minor differences are seen compared to the structures previously reported, they indicate the possibility of structural changes due to the crystallization conditions used in those studies. Our results show that more systematic crystallization of proteins is possible, and that the procedure can expand the range of conditions under which crystals can be grown successfully and can make new crystal forms available.     

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.