Phase Behavior Of Protein Solutions Research Articles

The ion-activated attractive patchy particle model and its application to the liquid-vapor phase transitions.

Patchy particles are an intriguing subject of study and indeed a model system in the field of soft matter physics. In recent years, patchy particle models have been applied to describe a wide variety of systems, including colloidal crystals, macromolecular interactions, liquid crystals, and nanoparticle assemblies. Given the importance of the topic, rationalizing and capturing the basic features of these models is crucial to their correct application in specific systems. In this study, we extend the ion-activated attractive patchy particles model previously employed to elucidate the phase behavior of protein solutions in the presence of trivalent salts. Our extension incorporates the effect of repulsion between unoccupied and occupied binding sites, depicted as patches. Furthermore, we examine the influence of model parameters on the liquid-vapor coexistence region within the phase diagram, employing numerical methods. A deeper understanding of this model will facilitate a better comprehension of the effects observed in experiments.

Effective interactions and phase behavior of protein solutions in the presence of hexamine cobalt(III) chloride

It is well established that deoxyribonucleic acid (DNA) and ribonucleic acid (RNA) exhibit a reentrant condensation (RC) phase behavior in the presence of the trivalent hexamine cobalt(III) cations (Hac) which can be important for their packing and folding. A similar behavior can be observed for negatively charged globular proteins in the presence of trivalent metal cations, such as Y3+ or La3+. This phase behavior is mainly driven by charge inversion upon an increasing salt concentration for a fixed protein concentration (cp). However, as Hac exhibits structural differences compared to other multivalent metal cations, with six ammonia ligands (NH3) covalently bonded to the central cobalt atom, it is not clear that Hac can induce a similar phase behavior for proteins. In this work, we systematically investigate whether negatively charged globular proteins β-lactoglobulin (BLG), bovine serum albumin (BSA), human serum albumin (HSA) and ovalbumin (OVA) feature Hac-induced RC. Effective protein–protein interactions were investigated by small-angle X-ray scattering. The reduced second virial coefficient (B2/B2HS) was obtained as a function of salt concentration. The virial coefficient analysis performed confirms the reentrant interaction (RI) behavior for BLG without actually inducing RC, given the insufficient strengths of the interactions for the latter to occur. In contrast, the strength of attraction for BSA, HSA and OVA are too weak to show RC. Model free analysis of the inverse intensity 1/Iq→0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1/I\\left( {q \ o 0} \\right)$$\\end{document} also supports this finding. Looking at different q-range by employing static (SLS) and dynamic light scattering experiments, the presence of RI behavior can be confirmed. The results are further discussed in view of metal cation binding sites in nucleic acids (DNA and RNA), where Hac induced RC phase behavior.Graphical abstract

An alternative approach to the osmotic second virial coefficient of protein solutions and its application to liquid-liquid phase separation.

The osmotic second virial coefficient B2 is an important parameter to describe the interactions and phase behavior of protein solutions, including colloidal systems and macromolecular solutions. Another key parameter to describe the driving force of the nucleation of a new phase is the supersaturation, which is used in the classical nucleation theory framework and is connected with the favorable contribution in the Gibbs free energy in the bulk solution. In this article, we establish a connection between B2 calculated from small angle x-ray scattering (SAXS) data and the values of B2 obtained from supersaturation measurements using thermodynamics considerations. The values of the second virial coefficient calculated employing this method agree with those determined via SAXS in the region near the liquid-liquid phase separation border for human serum albumin and bovine serum albumin. The general relations adopted are shown to be useful for the estimation of the second virial coefficient B2 for globular proteins, in the proximity of the binodal biphasic coexistent region.

Role of entropy in determining the phase behavior of protein solutions induced by multivalent ions.

Recent experiments have reported lower critical solution temperature (LCST) phase behavior of aqueous solutions of proteins induced by multivalent ions, where the solution phase separates upon heating. This phenomenon is linked to complex hydration effects that result in a net entropy gain upon phase separation. To decipher the underlying molecular mechanism, we use all-atom molecular dynamics simulations along with the two-phase thermodynamic method for entropy calculation. Based on simulations of a single BSA protein in various salt solutions (NaCl, CaCl2, MgCl2, and YCl3) at temperatures (T) ranging 283-323 K, we find that the cation-protein binding affinity increases with T, reflecting its thermodynamic driving force to be entropic in origin. We show that in the cation binding process, many tightly bound water molecules from the solvation shells of a cation and the protein are released to the bulk, resulting in entropy gain. To rationalize the LCST behavior, we calculate the ζ-potential that shows charge inversion of the protein for solutions containing multivalent ions. The ζ-potential increases with T. Performing simulations of two BSA proteins, we demonstrate that the protein-protein binding is mediated by multiple cation bridges and involves similar dehydration effects that cause a large entropy gain which more than compensates for rotational and translational entropy losses of the proteins. Thus, the LCST behavior is entropy-driven, but the associated solvation effects are markedly different from hydrophobic hydration. Our findings have direct implications for tuning the phase behavior of biological and soft-matter systems, e.g., protein condensation and crystallization.

Influence of structure properties on protein-protein interactions-QSAR modeling of changes in diffusion coefficients.

Information about protein-protein interactions provides valuable knowledge about the phase behavior of protein solutions during the biopharmaceutical production process. Up to date it is possible to capture their overall impact by an experimentally determined potential of mean force. For the description of this potential, the second virial coefficient B22, the diffusion interaction parameter kD, the storage modulus G', or the diffusion coefficient D is applied. In silico methods do not only have the potential to predict these parameters, but also to provide deeper understanding of the molecular origin of the protein-protein interactions by correlating the data to the protein's three-dimensional structure. This methodology furthermore allows a lower sample consumption and less experimental effort. Of all in silico methods, QSAR modeling, which correlates the properties of the molecule's structure with the experimental behavior, seems to be particularly suitable for this purpose. To verify this, the study reported here dealt with the determination of a QSAR model for the diffusion coefficient of proteins. This model consisted of diffusion coefficients for six different model proteins at various pH values and NaCl concentrations. The generated QSAR model showed a good correlation between experimental and predicted data with a coefficient of determination R2 = 0.9 and a good predictability for an external test set with R2 = 0.91. The information about the properties affecting protein-protein interactions present in solution was in agreement with experiment and theory. Furthermore, the model was able to give a more detailed picture of the protein properties influencing the diffusion coefficient and the acting protein-protein interactions. Biotechnol. Bioeng. 2017;114: 821-831. © 2016 Wiley Periodicals, Inc.

Second Virial Coefficient As Determined from Protein Phase Behavior.

We quantitatively link the macroscopic phase behavior of protein solutions to protein-protein interactions based on a coarse-grained colloidal approach. We exploit the extended law of corresponding states and apply the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory in order to infer the second virial coefficient b2, an integral measure of the interaction potential, from the phase behavior, namely, cloud-point temperature (CPT) measurements under conditions favoring protein crystallization. This determination of b2 yields values that quantitatively agree with the results of static light scattering (SLS) experiments. The strength of the attractions is quantified in terms of an effective Hamaker constant, which accounts for van der Waals attractions as well as non-DLVO forces, such as hydration and hydrophobic interactions. Our approach based on simple lab experiments to determine the CPT in combination with the DLVO theory is expected to facilitate further biophysical research on protein-protein interactions in complex solution environments.

Cation-Induced Hydration Effects Cause Lower Critical Solution Temperature Behavior in Protein Solutions.

The phase behavior of protein solutions is important for numerous phenomena in biology and soft matter. We report a lower critical solution temperature (LCST) phase behavior of aqueous solutions of a globular protein induced by multivalent metal ions around physiological temperatures. The LCST behavior manifests itself via a liquid-liquid phase separation of the protein-salt solution upon heating. Isothermal titration calorimetry and zeta-potential measurements indicate that here cation-protein binding is an endothermic, entropy-driven process. We offer a mechanistic explanation of the LCST. First, cations bind to protein surface groups driven by entropy changes of hydration water. Second, the bound cations bridge to other protein molecules, inducing an entropy-driven attraction causing the LCST. Our findings have general implications for condensation, LCST, and hydration behavior of (bio)polymer solutions as well as the understanding of biological effects of (heavy) metal ions and their hydration.

Competing salt effects on phase behavior of protein solutions: tailoring of protein interaction by the binding of multivalent ions and charge screening.

The phase behavior of protein solutions is affected by additives such as crowder molecules or salts. In particular, upon addition of multivalent counterions, a reentrant condensation can occur; i.e., protein solutions are stable for low and high multivalent ion concentrations but aggregating at intermediate salt concentrations. The addition of monovalent ions shifts the phase boundaries to higher multivalent ion concentrations. This effect is found to be reflected in the protein interactions, as accessed via small-angle X-ray scattering. Two simulation schemes (a Monte Carlo sampling of the counterion binding configurations using the detailed protein structure and an analytical coarse-grained binding model) reproduce the shifts of the experimental phase boundaries. The results support a consistent picture of the protein interactions responsible for the phase behavior. The repulsive Coulomb interaction is varied by the binding of multivalent counterions and additionally screened by any increase of the ionic strength. The attractive interaction is induced by the binding of multivalent ions, most likely due to ion bridging between protein molecules. The overall picture of these competing interactions provides interesting insight into possible mechanisms for tailoring interactions in solutions via salt effects.

Specific anion effects on the pressure dependence of the protein–protein interaction potential

We present a study on ion specific effects on the intermolecular interaction potential V(r) of dense protein solutions under high hydrostatic pressure conditions. Small-angle X-ray scattering in combination with a liquid-state theoretical approach was used to determine the effect of structure breaking/making salt anions (Cl(-), SO4(2-), PO4(3-)) on the intermolecular interaction of lysozyme molecules. It was found that besides the Debye-Hückel charge screening effect, reducing the repulsiveness of the interaction potential V(r) at low salt concentrations, a specific ion effect is observed at high salt concentrations for the multivalent kosmotropic anions, which modulates also the pressure dependence of the protein-protein interaction potential. Whereas sulfate and phosphate strongly influence the pressure dependence of V(r), chloride anions do not. The strong structure-making effect of the multivalent anions, dominating for the triply charged PO4(3-), renders the solution structure less bulk-water-like at high salt concentrations, which leads to an altered behavior of the pressure dependence of V(r). Hence, the particular structural properties of the salt solutions are able to influence the spatial organization and the intermolecular interactions of the proteins, in particular upon compression. These results are of interest for exploring the combined effects of ionic strength, temperature and pressure on the phase behavior of protein solutions, but may also be of relevance for understanding pressure effects on the hydration behavior of biological matter under extreme environmental conditions.

Universality of protein reentrant condensation in solution induced by multivalent metal ions

The effective interactions and phase behavior of protein solutions under strong electrostatic coupling conditions are difficult to understand due to the complex charge pattern and irregular geometry of protein surfaces. This distinguishes them from related systems such as DNA or conventional colloids. In this work, we discuss the question of universality of the reentrant condensation (RC) of proteins in solution induced by multivalent counterions, i.e., redissolution on adding further salts after phase separation, as recently discovered (Zhang et al., Phys Rev Lett 2008; 101:148101). The discussion is based on a systematic investigation of five different proteins with different charge patterns and five different multivalent counterions. Zeta potential measurements confirm the effective charge inversion of proteins in the reentrant regime via binding of multivalent counterions, which is supported by Monte Carlo simulations. Charge inversion by trivalent cations requires an overall negative net charge of the protein. Statistical analysis of a representative set of protein sequences reveals that, in theory, this effect could be possible for about half of all proteins. Our results can be exploited for the control of the phase behavior of proteins, in particular facilitating protein crystallization.

Square-well fluid modelling of protein liquid-vapor coexistence

The liquid-vapor phase diagrams for square-well fluid with extremely short attractive well, lambda=1.05 and 1.1, are obtained by means of canonical Monte Carlo simulations. These new results show that the coexistence curves obey the law of corresponding states in the similar form as several proteins do. Besides, the critical packing fraction of gamma-crystalline obtained experimentally is surprisingly close to the critical value of the model fluid with lambda=1.1. Thus, we demonstrate that the phase behavior of protein solutions may be modeled without taking into account an implicit anisotropic patchy character of the interprotein interaction.

Salting-Out of Lysozyme and Ovalbumin from Mixtures: Predicting Precipitation Performance from Protein−Protein Interactions

Protein−protein interactions, whether desirable or not, can have direct effects on protein separations. The most obvious of these are interactions between similar molecules, which determine the thermodynamic properties and phase behavior of protein solutions. Interactions between dissimilar molecules also affect the properties and phase behavior of protein mixtures and, therefore, protein separations. Here, we seek to quantify these effects by comparing precipitation behavior from binary solutions with direct measurements of protein−protein interactions using cross-interaction chromatography, which is a variant of affinity chromatography that provides data that can be interpreted in terms of the virial cross-coefficient. First, the effects of pH, ionic strength, different precipitants and the initial protein concentrations and their ratio on the binary precipitation of lysozyme and ovalbumin were investigated. Next, self- and cross-interaction measurements were used to suggest the optimal precipitation conditions for separating lysozyme from ovalbumin. The results show that protein interactions can explain anomalies and inconsistencies that frequently confound the extraction of meaningful general trends in separations analyses.

Vapor-liquid coexistence of patchy models: Relevance to protein phase behavior

The vapor-liquid coexistence boundaries of fluids composed of particles interacting with highly directional patchy interactions, in addition to an isotropic square well potential, are evaluated using grand canonical Monte Carlo simulations combined with the histogram reweighting and finite size scaling methods. We are motivated to study this more complicated model for two reasons. First, it is established that the reduced widths of the metastable vapor-liquid coexistence curve predicted by a model with only isotropic interparticle interactions are much too narrow when compared to the experimental phase behavior of protein solutions. Second, interprotein interactions are well known to be "patchy." Our results show that at a constant total areal density of patches, the critical temperature and the critical density increase monotonically with an increasing number of uniformly spaced patches. The vapor-liquid coexistence curves plotted in reduced coordinates (i.e., the temperature and the density scaled by their respective critical values) are found to be effectively independent of the number of patches, but are much broader than those found for the isotropic models. Our findings for the reduced width of the coexistence curve are almost in quantitative agreement with the available experimental data for protein solutions, stressing the importance of patchiness in this context.

Nucleation in a simple model for protein solutions with anisotropic interactions

A lattice analog of density functional theory is used to explore the structural and thermodynamic properties of critical nuclei in mixtures of particles with attractive anisotropic interactions. Protein molecules are assumed to occupy the sites on a regular cubic lattice, with effective directional interactions that mimic hydrogen bonding and the solvation forces induced by water. Interaction parameters are chosen to qualitatively reproduce the phase behavior of protein solutions. Our model predicts that critical nuclei of the solidlike phase have nonspherical shapes, and that their specific geometry depends on the nature of the anisotropic interactions. Molecules tend to align in distinctive ways in the core and in the interfacial region of these critical clusters, and the width and structure of the interface are highly affected by the presence of a metastable fluid-fluid critical point. Close to the critical region, the height of the barrier to nucleation is strongly reduced; this effect is enhanced by increasing the anisotropy of the intermolecular interactions. Unlike systems with short-range isotropic interactions, nucleation in our model is initiated by highly ordered clusters in which the order-disorder transition is confined to the interfacial region.

Depletion interactions and protein crystallization

Depletion interactions induced by the addition of soluble, non-adsorbing polymer significantly influence the phase behavior of protein solutions. Here we investigate the influence of polymer on the strength of interactions, phase behavior and nucleation kinetics of protein solutions. The strength of protein interactions induced by the presence of polymer is characterized through protein solution second virial coefficient measurements. Working with lysozyme and poly (ethylene glycol) (PEG), we find that the second virial coefficient, B 2 is a non-monotonic function of polymer concentration at modest ionic strengths (where the protein molecules behave essentially as hard spheres). At high ionic strengths, B 2 and solubility are independent of polymer concentration. The effect of polymer on protein solution phase behavior is studied by carrying out equilibrium or solubility measurements (fluid–crystal boundary) and cloud point measurements (liquid–liquid boundary). A scintillation cell setup is used to determine nucleation induction times with and without the presence of polymer. We present a detailed experimental investigation of the influence of PEG on protein pair interactions, phase behavior and nucleation kinetics.

Diffusive Interfacial Transport: A New Approach to Concentrated Protein Solution Studies

A spatial gradient in the concentration of binary protein−water systems is deliberately created by slow evaporation of a solution of solute. Such samples are scanned by optical interferometry to record the refractive index profile and by near-infrared microspectroscopy to determine the water composition along the spatial gradient. Combination of the two data sets allows the change in refractive index with concentration and its increment dn/dc to be determined beyond the usual report limited to low protein−solvent volume fractions. Further, phase behavior of protein solutions can be studied. To illustrate the method, cytochrome c is chosen; clean, bubble-free samples of extremely concentrated (ca. 80%) metastable solutions can be produced in this way, and in time, protein crystals separate from these solutions.