Seishi Shimizu

Cooperativity principles in protein folding.

Knowledge of the physical driving forces in proteins is essential for understanding their structures and functions. As polymers, proteins have remarkable thermodynamic and kinetic properties. A well-known observation is that the folding and unfolding of many small single-domain proteins, of which chymotrypsin inhibitor 2 is a prime example, appear to involve only two main states—N (native) and D (denatured). These proteins’ folding/unfolding transitions are often referred to as ‘‘cooperative’’ because of their phenomenological similarity to ‘‘all-or-none’’ processes. Traditionally, only N, D, and a small number of postulated intermediate states were invoked to account for experimental protein folding data. Under such an interpretative framework, two-state folding is described by the reaction N Ð D, and different properties are ascribed to N and D to account for different proteins. Although useful, this approach does not address the microscopic origins of experimentally observed two-state–like behavior. Traditional analyses simply assume that there are a small number of conformational states. But proteins are chain molecules. Physically, it is obvious that a polymer chain can adopt many conformations, ranging from the most open to maximally compact, and all intermediate compactness in between. Thus, whether and how the multitude of conformations available to a protein may be grouped into two or more ‘‘states’’—as traditionally assumed— should be ascertained through a fundamental understanding of the effective intrachain interactions involved. In the protein literature, however, folding energetics are often discussed in terms of the sum of contactlike energies of a fully folded native structure versus that of a random-coil–like state or a certain other prespecified unfolded conformational ensemble. Such analyses have yielded important insight. But they obscure the remarkable nature of protein cooperativities. This is because cooperativity has already been presumed in these discourses by their preclusion of many a priori possible conformations—notably compact nonnative conformations—from the energetic equation. To gain a consistent understanding

Temperature dependence of hydrophobic interactions: A mean force perspective, effects of water density, and nonadditivity of thermodynamic signatures

A load distributing thrust mount arrangement is provided for imparting the propulsive thrust of a gas turbine engine to a vehicle. In the thrust mount arrangement there is provided a dowel extending from the vehicle wherein the dowel is slidably engaged by a collar. The thrust load distribution is accomplished by a thrust member extending forwardly from the collar into rotatable connection with the engine casing and by a thrust link extending rearwardly from the collar into axially spaced apart rotatable connection with the engine casing.

Preferential hydration and the exclusion of cosolvents from protein surfaces

Protein stability is enhanced by the addition of osmolytes, such as sugars and polyols and inert crowders, such as polyethylene glycols. This stability enhancement has been quantified by the preferential hydration parameter which can be determined by experiments. To understand the mechanism of protein stability enhancement, we present a statistical mechanical analysis of the preferential hydration parameter based upon Kirkwood-Buff theory. Previously, the preferential hydration parameter was interpreted in terms of the number of hydration waters, as well as the cosolvent exclusion volume. It was not clear how accurate these interpretations were, nor what the relationship is between the two. By using the Kirkwood-Buff theory and experimental data, we conclude that the contribution from the cosolvent exclusion dominantly determines the preferential hydration parameters for crowders. For osmolytes, although the cosolvent exclusion largely determines the preferential hydration parameters, the contribution from hydration may not be negligible.

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.

Anti-cooperativity and cooperativity in hydrophobic interactions: Three-body free energy landscapes and comparison with implicit-solvent potential functions for proteins

Potentials of mean force (PMFs) of three‐body hydrophobic association are investigated to gain insight into similar processes in protein folding. Free energy landscapes obtained from explicit simulations of three methanes in water are compared with that predicted by popular implicit‐solvent effective potentials for the study of proteins. Explicit‐water simulations show that for an extended range of three‐methane configurations, hydrophobic association at 25°C under atmospheric pressure is mostly anti‐cooperative, that is, less favorable than if the interaction free energies were pairwise additive. Effects of free energy nonadditivity on the kinetic path of association and the temperature dependence of additivity are explored by using a three‐methane system and simplified chain models. The prevalence of anti‐cooperativity under ambient conditions suggests that driving forces other than hydrophobicity also play critical roles in protein thermodynamic cooperativity. We evaluate the effectiveness of several implicit‐solvent potentials in mimicking explicit water simulated three‐body PMFs. The favorability of the contact free energy minimum is found to be drastically overestimated by solvent accessible surface area (SASA). Both the SASA and a volume‐based Gaussian solvent exclusion model fail to predict the desolvation barrier. However, this barrier is qualitatively captured by the molecular surface area model and a recent “hydrophobic force field.” None of the implicit‐solvent models tested are accurate for the entire range of three‐methane configurations and several other thermodynamic signatures considered. Proteins 2002;48:15–30.

Origins of protein denatured state compactness and hydrophobic clustering in aqueous urea: Inferences from nonpolar potentials of mean force

Free energies of pairwise hydrophobic association are simulated in aqueous solutions of urea at concentrations ranging from 0–8 M. Consistent with the expectation that hydrophobic interactions are weakened by urea, the association of relatively large nonpolar solutes is destabilized by urea. However, the association of two small methane‐sized nonpolar solutes in water has the opposite tendency of being slightly strengthened by the addition of urea. Such size effects and the dependence of urea‐induced stability changes on the configuration of nonpolar solutes are not predicted by solvent accessible surface area approaches based on energetic parameters derived from bulk‐phase solubilities of model compounds. Thus, to understand hydrophobic interactions in proteins, it is not sufficient to rely solely on transfer experiment data that effectively characterize a single nonpolar solute in an aqueous environment but not the solvent‐mediated interactions among two or more nonpolar solutes. We find that the m‐values for the rate of change of two‐methane association free energy with respect to urea concentration is a dramatically nonmonotonic function of the spatial separation between the two methanes, with a distance‐dependent profile similar to the corresponding two‐methane heat capacity of association in pure water. Our results rationalize the persistence of residual hydrophobic contacts in some proteins at high urea concentrations and explain why the heat capacity signature (ΔCP) of a compact denatured state can be similar to ΔCP values calculated by assuming an open random‐coil‐like unfolded state. Proteins 2002;49:560–566.

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.

Mechanism of hydrophobic drug solubilization by small molecule hydrotropes.

Drugs that are poorly soluble in water can be solubilized by the addition of hydrotropes. Albeit known for almost a century, how they work at a molecular basis is still controversial due to the lack of a rigorous theoretical basis. To clear up this situation, a combination of experimental data and Fluctuation Theory of Solutions (FTS) has been employed; information on the interactions between all the molecular species present in the solution has been evaluated directly. FTS has identified two major factors of hydrotrope-induced solubilization: preferential hydrotrope-solute interaction and water activity depression. The former is dominated by hydrotrope-solute association, and the latter is enhanced by ionic dissociation and hindered by the self-aggregation of the hydrotropes. Moreover, in stark contrast to previous hypotheses, neither the change of solute hydration nor the water structure accounts for hydrotropy. Indeed, the rigorous FTS poses serious doubts over the other common hypothesis: self-aggregation of the hydrotrope hinders, rather than promotes, solubilization.

Preferential Solvation: Dividing Surface vs Excess Numbers

How do osmolytes affect the conformation and configuration of supramolecular assembly, such as ion channel opening and actin polymerization? The key to the answer lies in the excess solvation numbers of water and osmolyte molecules; these numbers are determinable solely from experimental data, as guaranteed by the phase rule, as we show through the exact solution theory of Kirkwood and Buff (KB). The osmotic stress technique (OST), in contrast, purposes to yield alternative hydration numbers through the use of the dividing surface borrowed from the adsorption theory. However, we show (i) OST is equivalent, when it becomes exact, to the crowding effect in which the osmolyte exclusion dominates over hydration; (ii) crowding is not the universal driving force of the osmolyte effect (e.g., actin polymerization); (iii) the dividing surface for solvation is useful only for crowding, unlike in the adsorption theory which necessitates its use due to the phase rule. KB thus clarifies the true meaning and limitations of the older perspectives on preferential solvation (such as solvent binding models, crowding, and OST), and enables excess number determination without any further assumptions.

Anti-cooperativity in hydrophobic interactions: A simulation study of spatial dependence of three-body effects and beyond

To better understand the energetics of hydrophobic core formation in protein folding under ambient conditions, the potential of mean force (PMF) for different three-methane configurations in an aqueous environment is computed by constant-pressure Monte Carlo sampling using the TIP4P model of water at 25 °C under atmospheric pressure. Whether the hydrophobic interaction is additive, cooperative or anti-cooperative is determined by whether the directly simulated three-methane PMF is equal to, more favorable, or less favorable than the sum of two-methane PMFs. To ensure that comparisons between PMFs are physically meaningful, a test-particle insertion technique is employed to provide unequivocal correspondence between zero PMF value and the nonexistent inter-methane interaction (zero reference-state free energy) experienced by a pair of methanes infinitely far apart. Substantial deviations from pairwise additivity are observed. Significantly, a majority of the three-methane configurations investigated exhibi...