Predictive crystallization of ribonuclease A via rapid screening of osmotic second virial coefficients

Important progress has been made in recent years toward developing a molecular-level understanding of protein phase behavior in terms of the osmotic second virial coefficient, a thermodynamic parameter that characterizes pairwise protein interactions. Yet there has been little practical application of this knowledge to the field of protein crystallization, largely because of the difficult and time-consuming nature of traditional techniques for characterizing protein interactions. Self-interaction chromatography has recently been proposed as a highly efficient method for measuring the osmotic second virial coefficient. The utility of the technique is examined in this work by characterizing virial coefficients for ribonuclease A under 59 solution conditions using several crystallization additives, including PEG, sodium chloride, ammonium sulfate, and propanol. The virial coefficient measurements show some counterintuitive trends and shed light on the previous difficulties in crystallizing ribonuclease A. Crystallization experiments at the corresponding solution conditions were conducted by using ultracentrifugal crystallization. Using this methodology, ribonuclease A crystals were obtained under conditions for which the virial coefficients fell within the "crystallization slot." Crystallographic characterization showed that the crystals diffract to high resolution. Metastable crystals were also obtained for conditions outside, but near, the "crystallization slot," and they could also be frozen and used to collect structural information.     

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.     

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.     

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.     

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.     

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     

Protein interactions in solution characterized by light and neutron scattering: comparison of lysozyme and chymotrypsinogen.

The effects of pH and electrolyte concentration on protein-protein interactions in lysozyme and chymotrypsinogen solutions were investigated by static light scattering (SLS) and small-angle neutron scattering (SANS). Very good agreement between the values of the virial coefficients measured by SLS and SANS was obtained without use of adjustable parameters. At low electrolyte concentration, the virial coefficients depend strongly on pH and change from positive to negative as the pH increases. All coefficients at high salt concentration are slightly negative and depend weakly on pH. For lysozyme, the coefficients always decrease with increasing electrolyte concentration. However, for chymotrypsinogen there is a cross-over point around pH 5.2, above which the virial coefficients decrease with increasing ionic strength, indicating the presence of attractive electrostatic interactions. The data are in agreement with Derjaguin-Landau-Verwey-Overbeek (DLVO)-type modeling, accounting for the repulsive and attractive electrostatic, van der Waals, and excluded volume interactions of equivalent colloid spheres. This model, however, is unable to resolve the complex short-ranged orientational interactions. The results of protein precipitation and crystallization experiments are in qualitative correlation with the patterns of the virial coefficients and demonstrate that interaction mapping could help outline new crystallization regions.     

Description of the thermodynamic incompatibility of the guar–dextran aqueous two-phase system by light scattering

The phase diagram of the guar–dextran aqueous two-phase system has been described on the basis of static light scattering measurements in the dilute regime. By determining the molar weight and second virial coefficient from the two single polymers and the second virial cross coefficient from mixtures at constant guar/dextran ratio (either 17/83 or 28/72), the thermodynamic models based on the virial expansion or the Flory–Huggins theory were successfully applied. The second virial coefficient of guar was difficult to estimate with enough accuracy by light scattering and therefore was obtained by adjustment using a simple criterion stating that the calculated spinodal passes through the experimental critical point. The obtained value was within the confidence interval given by light scattering. Virial expansion and Flory–Huggins approaches yielded quite similar theoretical phase diagrams that satisfactorily fitted the experimental one. The slight discrepancies observed on the position of binodals and critical points has been attributed to the polydispersity of guar or the difficulty in extrapolating from the dilute regime to the semidilute one. The slope of the tie-lines was predicted with a good accuracy, especially with the virial expansion model. The fact that both approaches gave such similar results is probably related to the fact that the expressions of chemical potentials are equivalent if the polymer concentrations are low enough. In this particular case, both models are based on excluded volume interactions and equally describe the phase behavior of the guar–dextran aqueous system.     

Second virial coefficients as a measure of protein--osmolyte interactions

The cytoplasm contains high concentrations of cosolutes. These cosolutes include macromolecules and small organic molecules called osmolytes. However, most biophysical studies of proteins are conducted in dilute solutions. Two broad classes of models have been used to describe the interaction between osmolytes and proteins. One class focuses on excluded volume effects, while the other focuses on binding between the protein and the osmolyte. To better understand protein--smolyte interactions, we have conducted sedimentation equilibrium analytical ultracentrifugation experiments using ferricytochrome c as a model protein. From these experiments, we determined the second virial coefficients for a series of osmolytes. We have interpreted the second virial coefficient as a measure of both excluded volume and protein--osmolyte binding. We conclude that simple models are not sufficient to understand the interactions between osmolytes and proteins.     

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.     

Determination of the second virial coefficient of bovine serum albumin under varying pH and ionic strength by composition-gradient multi-angle static light scattering

Composition-gradient multi-angle static light scattering (CG-MALS) is an emerging technique for the determination of intermolecular interactions via the second virial coefficient B₂₂. With CG-MALS, detailed studies of the second virial coefficient can be carried out more accurately and effectively than with traditional methods. In addition, automated mixing, delivery and measurement enable high speed, continuous, fluctuation-free sample delivery and accurate results. Using CG-MALS we measure the second virial coefficient of bovine serum albumin (BSA) in aqueous solutions at various values of pH and ionic strength of a univalent salt (NaCl). The systematic variation of the second virial coefficient as a function of pH and NaCl strength reveals the net charge change and the isoelectric point of BSA under different solution conditions. The magnitude of the second virial coefficient decreases to 1.13 x 10⁻⁵ ml*mol/g² near the isoelectric point of pH 4.6 and 25 mM NaCl. These results illuminate the role of fundamental long-range electrostatic and van der Waals forces in protein-protein interactions, specifically their dependence on pH and ionic strength. Electronic supplementary material The online version of this article (doi:10.1007/s10867-014-9367-7) contains supplementary material, which is available to authorized users.     

Sedimentation-equilibrium and other physicochemical studies on the lysine-rich fraction of calf thymus histones

1. The lysine-rich fraction (Ia+Ib, or f1) of calf thymus histones was isolated as the sulphate by acid extraction. 2. Sedimentation-equilibrium measurements with interference optics showed that this fraction was monodisperse with a molecular weight of 19500±2000. 3. The `apparent molecular weight' calculated from the sedimentation-equilibrium studies varied markedly with concentration. The large second virial coefficient implied by such variation was attributed to the very high charge/mass ratio of this relatively small protein. Estimates of the charge were made from the values of this virial coefficient. 4. The very large value of the virial coefficient explains anomalies in the earlier reports of the molecular weight of this histone and also why the z-average molecular weight can appear to be lower than the weight-average molecular weight. 5. The differences of the specific refractive increments, and the partial specific volumes, between dialysed and undialysed solutions of this histone fraction could also be attributed to its high molecular charge, which was estimated from these differences and agreed, within the expected limits, with the value deduced from the second virial coefficient. 6. Sedimentation-velocity measurements combined with the known molecular weight imply that lysine-rich histone has a high frictional ratio and an extended shape. Optical-rotatory-dispersion measurements indicated that it had a low helical content.     

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.     

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.     

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.     

Phospholipid interactions in model membrane systems. II. Theory.

We describe statistical thermodynamic theory for the lateral interactions among phospholipid head groups in monolayers and bilayers. Extensive monolayer experiments show that at low surface densities, PC head groups have strong lateral repulsions which increase considerably with temperature, whereas PE interactions are much weaker and have no significant temperature dependence (see the preceding paper). In previous work, we showed that the second virial coefficients for these interactions can be explained by: (a) steric repulsions among the head groups, and (b) a tilting of the P-N+ dipole of PC so that the N+ end enters the oil phase, to an extent that increases with temperature. It was also predicted that PE interactions should be weaker and less temperature dependent because the N+ terminal of the PE head-group is hydrophilic, hence, it is tilted into the water phase, so dipolar contributions among PE's are negligible due to the high dielectric constant of water. In the present work, we broaden the theory to treat phospholipid interactions up to higher lateral surface densities. We generalize the Hill interfacial virial expansion to account for dipoles and to include the third virial term. We show that to account for the large third virial coefficients for both PC and PE requires that the short range lateral attractions among the head groups also be taken into account. In addition, the third virial coefficient includes fluctuating head group dipoles, computed by Monte Carlo integration assuming pairwise additivity of the instantaneous pair potentials. We find that because the dipole fluctuations are correlated, the average triplet interactions do not equal the sum of the average dipole pair potentials. This is important for predicting, the magnitude and the independence of temperature of the third virial coefficients for PC. The consistency of the theory with data of both the second and the third virial coefficients extends the applicability of the head-group model to semiconcentrated monolayers, in agreement with the surface potential data in the foregoing paper.