Estimation of excess solvation numbers of water and cosolvents from preferential interaction and volumetric experiments

To elucidate, at a molecular level, how cosolvents influence protein stability, it is indispensable to understand the distribution of water and cosolvent molecules around proteins. Calculation of excess solvation numbers of water and cosolvents serves this purpose, and I show that they can be extracted from preferential interaction parameter and volumeric data via the Kirkwood-Buff theory. This scheme was applied to trehalose and glycerol (stabilizers) and urea (denaturant). Important insights from the application include stabilizer-induced enhancement of protein hydration, which, together with the stabilizer's exclusion from protein surfaces, may contribute to protein stabilization at high osmolyte concentrations.     

The Kirkwood-Buff theory and the effect of cosolvents on biochemical reactions

Cosolvents added to aqueous solutions of biomolecules profoundly affect protein stability, as well as biochemical equilibria. Some cosolvents, such as urea and guanidine hydrochloride, denature proteins, whereas others, such as osmolytes and crowders, stabilize the native structures of proteins. The way cosolvents interact with biomolecules is crucial information required to understand the cosolvent effect at a molecular level. We present a statistical mechanical framework based upon Kirkwood-Buff theory, which enables one to extract this picture from experimental data. The combination of two experimental results, namely, the cosolvent-induced equilibrium shift and the partial molar volume change upon the reaction, supplimented by the structural change, is shown to yield the number of water and cosolvent molecules bound or released during a reaction. Previously, denaturation experiments (e.g., m-value analysis) were analyzed by empirical and stoichiometric solvent-binding models, while the effects of osmolytes and crowders were analyzed by the approximate molecular crowding approach for low cosolvent concentration. Here we synthesize these previous approaches in a rigorous statistical mechanical treatment, which is applicable at any cosolvent concentration. The usefulness and accuracy of previous approaches was also evaluated.     

Local composition in the vicinity of a protein molecule in an aqueous mixed solvent

This paper is focused on the composition of a cosolvent in the vicinity of a protein surface (local composition) and its dependence on various factors. First, the Kirkwood-Buff theory of solution is used to obtain analytical expressions that connect the excess or deficit number of cosolvent and water molecules in the vicinity of a protein surface with experimentally measurable quantities such as the bulk concentration of the mixed solvent, the preferential binding parameter, and the molar volumes of water and cosolvent. Using these expressions, relations between the preferential binding parameter (at a molal concentration scale) and the above excesses (or deficits) are established. In addition, the obtained expressions are used to examine the effect of the nonideality of the water + cosolvent mixtures and of the molar volume of the cosolvent on the excess (or deficit) number of cosolvent molecules in the vicinity of the protein surface. It is shown that at least for the mixed solvents considered (water + urea and water + glucose) the nonideality of the mixed solvent is not an important factor in the local compositions around a protein molecule and that the main contribution is provided by the nonidealities of the protein-water and protein-cosolvent mixtures. Special attention is paid to urea as cosolvent, because urea is one of only a few compounds with a concentration at the protein surface larger than its concentration in the bulk. The composition dependence of the excess of urea around a protein molecule is calculated for the water + lysozyme + urea mixture at pH = 7.0 and 2.0. At pH = 7.0, the excess of urea becomes almost composition independent at high urea concentrations. Such independence could be explained by assuming that urea totally replaces water in some areas of the protein surface, whereas on the remaining areas of the protein surface both water and urea are present with concentration comparable to those in the bulk. The Schellman exchange model was used to relate the preferential binding parameter in water + lysozyme + urea mixtures to the urea concentration.     

Microscopic understanding of preferential exclusion of compatible solute ectoine: direct interaction and hydration alteration

Ectoine, a zwitterionic compatible solute (CS), acts as an effective stabilizer of protein function. Using molecular dynamics simulation, solvent spatial distributions around both met-enkephalin (M-Enk) and chymotrypsin inhibitor 2 (CI2) were investigated at the molecular level in ectoine aqueous solution. An unexpected finding was that ectoine exhibits preferential binding, as an overall tendency, around both peptides. However, with the aid of the surficial Kirkwood-Buff parameter, it was clearly shown that the preferential exclusion of ectoine from the peptide surface was weaker in the smaller M-Enk than in the larger CI2. It is concluded that a denser and more structured hydration layer, such as that developed on the surface of CI2, is an important factor in the exclusion of ectoine.     

The Hofmeister series and protein-salt interactions

In order to understand the origin of the Hofmeister series, a statistical-mechanical analysis, based upon the Kirkwood-Buff (KB) theory, has been performed to extract information regarding protein hydration and water-mediated protein-salt interactions from published experimental data-preferential hydration and volumetric data for bovine serum albumin in the presence of a wide range of salts. The analysis showed a linear correlation between the preferential hydration parameter and the protein-cosolvent KB parameter. The same linear correlation holds even when nonelectrolyte cosolvents, such as polyethelene glycol, have been incorporated. These results suggest that the Hofmeister series is due to a wide variation of the water-mediated protein-cosolvent interaction (but not the change of protein hydration) and that this mechanism is a special case of a more general scenario common even to the macromolecular crowding.     

Microcalorimetric study of thermal unfolding of lysozyme in water/glycerol mixtures: an analysis by solvent exchange model

Folded protein stabilization or destabilization induced by cosolvent in mixed aqueous solutions has been studied by differential scanning microcalorimetry and related to difference in preferential solvation of native and denatured states. In particular, the thermal denaturation of a model system formed by lysozyme dissolved in water in the presence of the stabilizing cosolvent glycerol has been considered. Transition temperatures and enthalpies, heat capacity, and standard free energy changes have been determined when applying a two-state denaturation model to microcalorimetric data. Thermodynamic parameters show an unexpected, not linear, trend as a function of solvent composition; in particular, the lysozyme thermodynamic stability shows a maximum centered at water molar fraction of about 0.6. Using a thermodynamic hydration model based on the exchange equilibrium between glycerol and water molecules from the protein solvation layer to the bulk, the contribution of protein-solvent interactions to the unfolding free energy and the changes of this contribution with solvent composition have been derived. The preferential solvation data indicate that lysozyme unfolding involves an increase in the solvation surface, with a small reduction of the protein-preferential hydration. Moreover, the derived changes in the excess solvation numbers at denaturation show that only few solvent molecules are responsible for the variation of lysozyme stability in relation to the solvent composition.     

Equilibrium dialysis data and the relationships between preferential interaction parameters for biological systems in terms of Kirkwood-Buff integrals

Equilibrium dialysis data has provided valuable information concerning the preferential interaction of a cosolvent with a biomolecule in aqueous solutions. Here, we formulate the experimental data in terms of Kirkwood-Buff (KB) theory, resulting in equations that provide a simple physical picture of the dialysis experiment and thereby the interaction of a cosolvent with a biomolecule. These results are then used to establish exact relationships between preferential interaction coefficients, defined in different ensembles and/or using different concentration scales, in terms of KB integrals. It is then argued that the molality based equilibrium dialysis data represent the situation most relevant to computer simulations performed in either open or closed systems.     

A protein molecule in an aqueous mixed solvent: fluctuation theory outlook

In the present paper a procedure to calculate the properties of proteins in aqueous mixed solvents, particularly the excesses of the constituents of the mixed solvent near the protein molecule and the preferential binding parameters, is suggested. Expressions for the Kirkwood-Buff integrals in ternary mixtures and for the preferential binding parameter were derived and used to calculate various properties of infinitely dilute proteins in aqueous mixed solvents. The derived expressions and experimental information regarding the partial molar volumes and the preferential binding parameters were used to calculate the excesses (deficits) of water and cosolvent (in comparison with the bulk concentrations of protein-free mixed solvent) in the vicinity of ribonuclease A, ribonuclease T1, and lysozyme molecules. The calculations showed that water was in excess in the vicinity of ribonuclease A for water/glycerol and water/trehalose mixtures, and the cosolvent urea was in excess in the vicinity of ribonuclease T1 and lysozyme. The derivative of the activity coefficient of the protein with respect to the mole fraction of water was also calculated. This derivative was negative for the water/glycerol and water/trehalose mixed solvents and positive for the water/urea mixture. The mixture of lysozyme in the water/urea solvent is of particular interest, because the lysozyme at pH 7.0 is in its native state up to 9.3M urea, while at pH 2.0 it is denaturated between 2.5 and 5M and higher concentrations of urea. Our results demonstrated a striking similarity in the hydration of lysozyme at both pHs. It is worthwhile to note that the excesses of urea were only weakly composition dependent on both cases.     

Hydrophobic interactions in presence of osmolytes urea and trimethylamine-N-oxide

Molecular dynamics simulations were carried out to study the influences of two naturally occurring osmolytes, urea, and trimethylamine-N-oxide (TMAO) on the hydrophobic interactions between neopentane molecules. In this study, we used two different models of neopentane: One is of single united site (UA) and another contains five-sites. We observe that, these two neopentane models behave differently in pure water as well as solutions containing osmolytes. Presence of urea molecules increases the stability of solvent-separated state for five-site model, whereas osmolytes have negligible effect in regard to clustering of UA model of neopentane. For both models, dehydration of neopentane and preferential solvation of it by urea and TMAO over water molecules are also observed. We also find the collapse of the second-shell of water by urea and water structure enhancement by TMAO. The orientational distributions of water molecules around different layers of neopentane were also calculated and we find that orientation of water molecules near to hydrophobic moiety is anisotropic and osmolytes have negligible effect on it. We also observe osmolyte-induced water-water hydrogen bond life time increase in the hydration shell of neopentane as well as in the subsequent water layers.     

Various contributions to the osmotic second virial coefficient in protein-water-cosolvent solutions

An analysis of the cosolvent concentration dependence of the osmotic second virial coefficient (OSVC) in water-protein-cosolvent mixtures is developed. The Kirkwood-Buff fluctuation theory for ternary mixtures is used as the main theoretical tool. On its basis, the OSVC is expressed in terms of the thermodynamic properties of infinitely dilute (with respect to the protein) water-protein-cosolvent mixtures. These properties can be divided into two groups: (1) those of infinitely dilute protein solutions (such as the partial molar volume of a protein at infinite dilution and the derivatives of the protein activity coefficient with respect to the protein and water molar fractions) and (2) those of the protein-free water-cosolvent mixture (such as its concentrations, the isothermal compressibility, the partial molar volumes, and the derivative of the water activity coefficient with respect to the water molar fraction). Expressions are derived for the OSVC of ideal mixtures and for a mixture in which only the binary mixed solvent is ideal. The latter expression contains three contributions: (1) one due to the protein-solvent interactions B2(p-s), which is connected to the preferential binding parameter, (2) another one due to protein/protein interactions (B2(p-p)), and (3) a third one representing an ideal mixture contribution (B2(id)). The cosolvent composition dependencies of these three contributions were examined for several water-protein-cosolvent mixtures using experimental data regarding the OSVC and the preferential binding parameter. For the water-lysozyme-arginine mixture, it was found that OSVC exhibits the behavior of an ideal mixture and that B2(id) provides the main contribution to the OSVC. For the other mixtures considered (water-Hm MalDH-NaCl, water-Hm MalDH-(NH4)2SO4, and water-lysozyme-NaCl mixtures), it was found that the contribution of the protein-solvent interactions B2(p-s) is responsible for the composition dependence of the OSVC on the cosolvent concentration, whereas the two remaining contributions (B2(p-p)) and B2(id)) are almost composition independent.     

Structure of aqueous sodium perchlorate solutions

Salt solutions have been the object of study of many scientists through history, but one of the most important findings came along when the Hofmeister series were discovered. Their importance arises from the fact that they influence the relative solubility of proteins, and solubility is directly related to one of today's holy grails: protein folding. In this work we characterize one of the more-destabilizing salts in the series, sodium perchlorate, by studying it as an aqueous solution at various concentrations ranging from 0.08 to 1.60 mol/L. Molecular dynamics simulations at room temperature permitted a detailed study of the organization of solvent and cosolvent, in terms of its radial distribution functions, along with the study of the structure of hydrogen bonds in the ions' solvation shells. We found that the distribution functions have some variations in their shape as concentration changes, but the position of their peaks is mostly unaffected. Regarding water, the most salient fact is the noticeable (although small) change in the second hydration shell and even beyond, especially for g(O(w)***O(w)), showing that the locality of salt effects should not be restricted to considerations of only the first solvation shell. The perturbation of the second shell also appears in the study of the HB network, where the difference between the number of HBs around a water molecule and around the Na(+) cation gets much smaller as one goes from the first to the second solvation shell, yet the difference is not negligible. Nevertheless, the effect of the ions past their first hydration shell is not enough to make a noticeable change in the global HB network. The Kirkwood-Buff theory of liquids was applied to our system, in order to calculate the activity derivative of the cosolvent. This coefficient, along with a previously calculated preferential binding, allowed us to establish that if a folded AP peptide is immersed in the studied solution, becoming the solute, then increasing the salt concentration will make the helix more stable.     

Volume exclusion and H-bonding dominate the thermodynamics and solvation of trimethylamine-N-oxide in aqueous urea

Trimethylamine-N-oxide (TMAO) and urea represent the extremes among the naturally occurring organic osmolytes in terms of their ability to stabilize/destabilize proteins. Their mixtures are found in nature and have generated interest in terms of both their physiological role and their potential use as additives in various applications (crystallography, drug formulation, etc.). Here we report experimental density and activity coefficient data for aqueous mixtures of TMAO with urea. From these data we derive the thermodynamics and solvation properties of the osmolytes, using Kirkwood-Buff theory. Strong hydrogen-bonding at the TMAO oxygen, combined with volume exclusion, accounts for the thermodynamics and solvation of TMAO in aqueous urea. As a result, TMAO behaves in a manner that is surprisingly similar to that of hard-spheres. There are two mandatory solvation sites. In plain water, these sites are occupied with water molecules, which are seamlessly replaced by urea, in proportion to its volume fraction. We discuss how this result gives an explanation both for the exceptionally strong exclusion of TMAO from peptide groups and for the experimentally observed synergy between urea and TMAO.     

Effects of polydisperse crowders on aggregation reactions: a molecular thermodynamic analysis

Intracellular crowding in biological systems is usually mimicked in in vitro experiments by adding single crowders at high volume fractions, without taking into consideration the polydispersity of the crowders in the cellular environment. Here, we develop a molecular thermodynamic formalism to examine the effects of size-polydispersity of crowders on aggregation reaction equilibria. Although the predominantly common practice so far has been to appeal to the entropic (excluded-volume) effects in describing crowding effects, we show that the internal energy (hence, the enthalpy) of the system could dramatically alter the effects, even qualitatively, particularly in the case of a mixture of crowders, depending on the changes in the covolume of the products relative to that of the reactants and on the preferential binding or exclusion of the crowders by the reactants and products. We also show that in the case of polydisperse crowders the crowders with the largest size difference dominate the overall changes in the yield of the reaction, depending on the individual concentrations of the crowders.     

Preferential solvation of etoricoxib in some aqueous binary cosolvent mixtures at 298.15 K

Preferential solvation parameters of etoricoxib in several aqueous cosolvent mixtures were calculated from solubilities and other thermodynamic properties by using the IKBI method. Cosolvents studied were as follows: 1,4-dioxane, N,N-dimethylacetamide, 1,4-butanediol, N,N-dimethylformamide, ethanol and dimethyl sulfoxide. Etoricoxib exhibits solvation effects, being the preferential solvation parameter δx_1,3, negative in water-rich and cosolvent-rich mixtures but positive in mixtures with similar proportions of both solvents. It is conjecturable that the hydrophobic hydration in water-rich mixtures plays a relevant role in drug solvation. In mixtures of similar solvent proportions where etoricoxib is preferentially solvated by the cosolvents, the drug could be acting as Lewis acid with the more basic cosolvents. Finally, in cosolvent-rich mixtures the preferential solvation by water could be due to the more acidic behaviour of water. Nevertheless, the specific solute–solvent interactions in the different binary systems remain unclear because no relation between preferential solvation magnitude and cosolvent polarities has been observed.     

Solubility of phenobarbital in aqueous cosolvent mixtures revisited: IKBI preferential solvation analysis

The preferential solvation parameters of phenobarbital in aqueous binary mixtures of 1,4-dioxane, t-butanol, n-propanol, ethanol, propylene glycol and glycerol were derived from solution thermodynamic properties by using the IKBI method. This drug is sensitive to preferential solvation effects in all these mixtures. The preferential solvation parameter by the cosolvent (δx_1,3) is negative in almost all the water-rich mixtures but positive in mixtures with similar proportions of solvents and cosolvent-rich mixtures, except in 1-propanol + water mixtures, where negative values are also found in mixtures with x₁ ≥ 0.70. Hydrophobic hydration around the non-polar ethyl and phenyl groups of this drug in water-rich mixtures could play a relevant role in drug solvation. Otherwise, in mixtures of similar solvent compositions and in cosolvent-rich mixtures the preferential solvation by cosolvent could be due to the acidic behaviour of the drug.     

Structural Refolding and Thermal Stability of Myoglobin in the Presence of Mixture of Crowders: Importance of Various Interactions for Protein Stabilization in Crowded Conditions

The intracellular environment is overcrowded with a range of molecules (small and large), all of which influence protein conformation. As a result, understanding how proteins fold and stay functional in such crowded conditions is essential. Several in vitro experiments have looked into the effects of macromolecular crowding on different proteins. However, there are hardly any reports regarding small molecular crowders used alone and in mixtures to observe their effects on the structure and stability of the proteins, which mimics of the cellular conditions. Here we investigate the effect of different mixtures of crowders, ethylene glycol (EG) and its polymer polyethylene glycol (PEG 400 Da) on the structural and thermal stability of myoglobin (Mb). Our results show that monomer (EG) has no significant effect on the structure of Mb, while the polymer disrupts its structure and decreases its stability. Conversely, the additive effect of crowders showed structural refolding of the protein to some extent. Moreover, the calorimetric binding studies of the protein showed very weak interactions with the mixture of crowders. Usually, we can assume that soft interactions induce structural perturbations while exclusion volume effects stabilize the protein structure; therefore, we hypothesize that under in vivo crowded conditions, both phenomena occur and maintain the stability and function of proteins.     

Molecular solvation in water-methanol and water-sorbitol mixtures: the roles of preferential hydration, hydrophobicity, and the equation of state

Molecular dynamics simulations of aqueous mixtures of methanol and sorbitol were performed over a wide range of binary composition, density (pressure), and temperature to study the equation of state and solvation of small apolar solutes. Experimentally, methanol is a canonical solubilizing agent for apolar solutes and a protein denaturant in mixed-aqueous solvents; sorbitol represents a canonical "salting-out" or protein-stabilizing cosolvent. The results reported here show increasing sorbitol concentration under isothermal, isobaric conditions results in monotonic increases in apolar solute excess chemical potential (mu2ex) over the range of experimentally relevant temperatures. For methanol at elevated temperatures, increasing cosolvent composition results in monotonically decreasing mu2ex. However, at lower temperatures mu2ex exhibits a maximum versus cosolvent concentration, as seen experimentally for Ar in ethanol-water solutions. Both density anomalies and hydrophobic effects--characterized by temperatures of density maxima and apolar solute solubility minima, respectively--are suppressed upon addition of either sorbitol or methanol at all temperatures and compositions simulated here. Thus, the contrasting effects of sorbitol and methanol on solute chemical potential cannot be explained by qualitative differences in their ability to enhance or suppress hydrophobic effects. Rather, we find mu2ex values across a broad range of temperatures and cosolvent composition can be quantitatively explained in terms of isobaric changes in solvent density--i.e., the equation of state--along with the corresponding packing fraction of the solvent. Analysis in terms of truncated preferential interaction parameters highlights that care must be taken in interpreting cosolvent effects on solvation in terms of local preferential hydration.     

A thermodynamic analysis on the coincidence of extrema conditions in the sorption equilibrium for ternary polymer systems

Flory-Huggins theory of polymer solutions has been used to express the condition of extrema values in the total sorption, as well as the inversion point in the preferential adsorption parameters for termary polymer systems. Two approaches have been followed, the first considers the binary and ternary interaction parameters independent of polymer concentration and solvent composition. In the second one, this dependence has been introduced. Our attention is focused on the volume fraction of solvent mixture dependence of the above parameters, in order to confirm or not the coincidence between the extrema values and the inversion point. Several cosolvent and cononsolvent ternary polymer systems, have been used to test the validity of the equations obtained. Also, it has been verified, from an experimental point of view, that in cosolvent ternary polymer systems there is coincidence in both compositions while in cononsolvent ternary polymer systems, such coincidence does not appear.     

渗透剂的分子体积和极性表面积分率对胰凝乳蛋白酶抑制剂2热稳定性的影响

渗透剂对蛋白质的稳定能力不仅与其极性表面积分率(fpSA)有关,而且也与其分子体积(V)密切相关.因此对于渗透剂稳定蛋白质能力的分析,需要同时考虑渗透剂的fpSA和V.为了考察渗透剂的fpSA和V对稳定蛋白质能力的影响,本文以胰凝乳蛋白酶抑制剂2(CI2)为模型蛋白,首先利用分子动力学模拟,考察了数种典型渗透剂对CI2热稳定性的影响;并根据模拟数据计算得到了渗透剂影响蛋白质热稳定性的一维结构参数;然后利用统计学双参数拟合,同时引入渗透剂的fpSA和V,建立了用于分析渗透剂稳定蛋白质能力的模型;最后利用模型分析了渗透剂的fpSA和V与其稳定蛋白质能力的关系.研究发现:利用分子动力学模拟结果定义并计算得到的一维结构参数能够较好地描述在热变性条件下渗透剂对CI2的稳定能力;所建立的模型能够很好地分析渗透剂对蛋白质的稳定能力;并且由于V和fpSA二次项的引入,可大大提高仅以fpSA为参数的模型的精度;另外,渗透剂对蛋白质的热稳定能力与其V成正比;由于拟合公式中引入了fpSA二次项,在fpSA小于0.7时,fpSA与渗透剂的稳定能力呈现负相关,但当fpSA大于0.7时,其与渗透剂的稳定能力反而呈现正相关.