Fluctuation theory of molecular association and conformational equilibria

Solvation energetics of proteins and their aggregates analyzed by all-atom molecular dynamics simulations and the energy-representation theory of solvation

Solvation is a controlling factor for the structure and function of proteins. This article addresses the effects of solvation from an energetic perspective for the fluctuations and cosolvent-induced changes in protein structures and the equilibrium of aggregate formation for a peptide. A theoretical framework to analyze the solvation effects with an explicit solvent is introduced by adopting the energy-representation theory of solvation, and the connection of the solvation free energy to the protein structure and the aggregation tendency is quantitatively described in combination with all-atom molecular dynamics simulations. The interaction components that govern the solvation effects on the structural variations of proteins are further identified through correlation analysis, and a computational scheme to assess the shift of an aggregation equilibrium due to the addition of a cosolvent is provided.

Simulated pressure denaturation thermodynamics of ubiquitin

Simulations of protein thermodynamics are generally difficult to perform and provide limited information. It is desirable to increase the degree of detail provided by simulation and thereby the potential insight into the thermodynamic properties of proteins. In this study, we outline how to analyze simulation trajectories to decompose conformation-specific, parameter free, thermodynamically defined protein volumes into residue-based contributions. The total volumes are obtained using established methods from Fluctuation Solution Theory, while the volume decomposition is new and is performed using a simple proximity method. Native and fully extended ubiquitin are used as the test conformations. Changes in the protein volumes are then followed as a function of pressure, allowing for conformation-specific protein compressibility values to also be obtained. Residue volume and compressibility values indicate significant contributions to protein denaturation thermodynamics from nonpolar and coil residues, together with a general negative compressibility exhibited by acidic residues.

The origin of cooperative solubilisation by hydrotropes

The signature of hydrotropic solubilisation is the sigmoidal solubility curve; when plotted against hydrotrope concentration, solubility increases suddenly after the minimum hydrotrope concentration (MHC), and reaches a plateau at higher hydrotrope concentrations. Here we explain the origin of hydrotropic cooperativity based on statistical thermodynamics.

Salting-Out of Methane in the Aqueous Solutions of Urea and Glycine-Betaine

We have studied the hydrophobic association and solvation of methane molecules in aqueous solutions of urea and glycine betaine (GB). We have calculated the potentials of mean force (PMFs) between methane molecules in water, aqueous GB, aqueous urea and aqueous urea-GB mixtures. The PMFs and equilibrium constants indicate that both urea and GB increase the hydrophobic association of methane. Calculation of thermodynamic parameters shows that the association of methane is stabilized by entropy whereas solvation is favored by enthalpy. In the case of the water-urea-GB mixture, both hydrophobic association and solvation are stabilized by entropy. From the investigation of radial distribution functions, running coordination numbers and excess coordination numbers, we infer that both urea and GB are preferentially excluded from methane surface in the mixtures of osmolytes and methane is preferentially solvated by water molecules in all the mixtures. The favorable exclusion of both urea and GB from the methane surface suggests that both urea and GB increase the interaction between methane molecules, i.e., salting-out of methane. We observe that addition of both urea and GB to water enhances local water structure. The calculated values of diffusion constants of water also suggest enhanced water-water interactions in the presence of urea and GB. The calculated free energies of methane in these mixtures show that methane is less soluble in the mixtures of urea and GB than in water. The data on solvation free energies support the observations obtained from the PMFs of methane molecules.

Experimental triplet and quadruplet fluctuation densities and spatial distribution function integrals for liquid mixtures

Kirkwood-Buff or Fluctuation Solution Theory can be used to provide experimental pair fluctuations, and/or integrals over the pair distribution functions, from experimental thermodynamic data on liquid mixtures. Here, this type of approach is used to provide triplet and quadruplet fluctuations, and the corresponding integrals over the triplet and quadruplet distribution functions, in a purely thermodynamic manner that avoids the use of structure factors. The approach is then applied to binary mixtures of water + methanol and benzene + methanol over the full composition range under ambient conditions. The observed correlations between the different species vary significantly with composition. The magnitude of the fluctuations and integrals appears to increase as the number of the most polar molecule involved in the fluctuation or integral also increases. A simple physical picture of the fluctuations is provided to help rationalize some of these variations.

Experimental triplet and quadruplet fluctuation densities and spatial distribution function integrals for pure liquids

Fluctuation solution theory has provided an alternative view of many liquid mixture properties in terms of particle number fluctuations. The particle number fluctuations can also be related to integrals of the corresponding two body distribution functions between molecular pairs in order to provide a more physical picture of solution behavior and molecule affinities. Here, we extend this type of approach to provide expressions for higher order triplet and quadruplet fluctuations, and thereby integrals over the corresponding distribution functions, all of which can be obtained from available experimental thermodynamic data. The fluctuations and integrals are then determined using the International Association for the Properties of Water and Steam Formulation 1995 (IAPWS-95) equation of state for the liquid phase of pure water. The results indicate small, but significant, deviations from a Gaussian distribution for the molecules in this system. The pressure and temperature dependence of the fluctuations and integrals, as well as the limiting behavior as one approaches both the triple point and the critical point, are also examined.

Infinitely dilute partial molar properties of proteins from computer simulation

A detailed understanding of temperature and pressure effects on an infinitely dilute protein's conformational equilibrium requires knowledge of the corresponding infinitely dilute partial molar properties. Established molecular dynamics methodologies generally have not provided a way to calculate these properties without either a loss of thermodynamic rigor, the introduction of nonunique parameters, or a loss of information about which solute conformations specifically contributed to the output values. Here we implement a simple method that is thermodynamically rigorous and possesses none of the above disadvantages, and we report on the method's feasibility and computational demands. We calculate infinitely dilute partial molar properties for two proteins and attempt to distinguish the thermodynamic differences between a native and a denatured conformation of a designed miniprotein. We conclude that simple ensemble average properties can be calculated with very reasonable amounts of computational power. In contrast, properties corresponding to fluctuating quantities are computationally demanding to calculate precisely, although they can be obtained more easily by following the temperature and/or pressure dependence of the corresponding ensemble averages.

Quantifying the molecular origins of opposite solvent effects on protein-protein interactions

Although the nature of solvent-protein interactions is generally weak and non-specific, addition of cosolvents such as denaturants and osmolytes strengthens protein-protein interactions for some proteins, whereas it weakens protein-protein interactions for others. This is exemplified by the puzzling observation that addition of glycerol oppositely affects the association constants of two antibodies, D1.3 and D44.1, with lysozyme. To resolve this conundrum, we develop a methodology based on the thermodynamic principles of preferential interaction theory and the quantitative characterization of local protein solvation from molecular dynamics simulations. We find that changes of preferential solvent interactions at the protein-protein interface quantitatively account for the opposite effects of glycerol on the antibody-antigen association constants. Detailed characterization of local protein solvation in the free and associated protein states reveals how opposite solvent effects on protein-protein interactions depend on the extent of dewetting of the protein-protein contact region and on structural changes that alter cooperative solvent-protein interactions at the periphery of the protein-protein interface. These results demonstrate the direct relationship between macroscopic solvent effects on protein-protein interactions and atom-scale solvent-protein interactions, and establish a general methodology for predicting and understanding solvent effects on protein-protein interactions in diverse biological environments.

Quantitative characterization of local protein solvation to predict solvent effects on protein structure

Characterization of solvent preferences of proteins is essential to the understanding of solvent effects on protein structure and stability. Although it is generally believed that solvent preferences at distinct loci of a protein surface may differ, quantitative characterization of local protein solvation has remained elusive. In this study, we show that local solvation preferences can be quantified over the entire protein surface from extended molecular dynamics simulations. By subjecting microsecond trajectories of two proteins (lysozyme and antibody fragment D1.3) in 4 M glycerol to rigorous statistical analyses, solvent preferences of individual protein residues are quantified by local preferential interaction coefficients. Local solvent preferences for glycerol vary widely from residue to residue and may change as a result of protein side-chain motions that are slower than the longest intrinsic solvation timescale of ∼10 ns. Differences of local solvent preferences between distinct protein side-chain conformations predict solvent effects on local protein structure in good agreement with experiment. This study extends the application scope of preferential interaction theory and enables molecular understanding of solvent effects on protein structure through comprehensive characterization of local protein solvation.

Theory and Simulation of Multicomponent Osmotic Systems

Most cellular processes occur in systems containing a variety of components many of which are open to material exchange. However, computer simulations of biological systems are almost exclusively performed in systems closed to material exchange. In principle, the behavior of biomolecules in open and closed systems will be different. Here, we provide a rigorous framework for the analysis of experimental and simulation data concerning open and closed multicomponent systems using the Kirkwood-Buff (KB) theory of solutions. The results are illustrated using computer simulations for various concentrations of the solutes Gly, Gly(2) and Gly(3) in both open and closed systems, and in the absence or presence of NaCl as a cosolvent. In addition, KB theory is used to help rationalize the aggregation properties of the solutes. Here one observes that the picture of solute association described by the KB integrals, which are directly related to the solution thermodynamics, and that provided by more physical clustering approaches are different. It is argued that the combination of KB theory and simulation data provides a simple and powerful tool for the analysis of complex multicomponent open and closed systems.

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.

Local fluctuations in solution mixtures

An extension of the traditional Kirkwood-Buff (KB) theory of solutions is outlined which provides additional fluctuating quantities that can be used to characterize and probe the behavior of solution mixtures. Particle-energy and energy-energy fluctuations for local regions of any multicomponent solution are expressed in terms of experimentally obtainable quantities, thereby supplementing the usual particle-particle fluctuations provided by the established KB inversion approach. The expressions are then used to analyze experimental data for pure water over a range of temperatures and pressures, a variety of pure liquids, and three binary solution mixtures - methanol and water, benzene and methanol, and aqueous sodium chloride. In addition to providing information on local properties of solutions it is argued that the particle-energy and energy-energy fluctuations can also be used to test and refine solute and solvent force fields for use in computer simulation studies.