Representability and Transferability of Kirkwood–Buff Iterative Boltzmann Inversion Models for Multicomponent Aqueous Systems

We discuss the application of the Kirkwood–Buff iterative Boltzmann inversion (KB-IBI) method for molecular coarse-graining (Ganguly et al.<i> J. Chem. Theory Comput.</i> <b>2012</b>, <i>8</i>, 1802) to multicomponent aqueous mixtures. Using a fixed set of effective single-site solvent–solvent potentials previously derived for binary urea–water systems, solute–solvent and solute–solute KB-IBI coarse-grained (CG) potentials have been derived for benzene in urea–water mixtures. Preferential solvation and salting-in coefficients of benzene are reproduced in quantitative agreement with the atomistic force field model. The transferability of the CG models is discussed, and it is shown that free energies of formation of hydrophobic benzene clusters obtained from simulations with the CG model are in good agreement with results obtained from all-atom simulations. The state-point representability of the CG models is discussed with respect to reproducing thermodynamic quantities such as pressure, isothermal compressibility, and preferential solvation. Combined use of KB-IBI and pressure corrections in deriving single-site CG models for pure-water, binary mixtures of urea and water, and ternary mixtures of benzene in urea–water at infinite benzene dilution provides an improved scheme to representing the atomistic pressure and the preferential solvation between the solution components. It is also found that the application of KB-IBI leads to a faster and improved convergence of the pressure and potential energy compared to the IBI method

Peptide Backbone Effect on Hydration Free Energies of Amino Acid Side Chains

We have studied the hydrophobicity of amino acid side chains by computing conditional solvation free energies that account for effects of the peptide backbone on the side chains’ solvent environment. The free energies reported herein correspond to a gas–liquid transfer process, which mimics solvation of the side chain under the condition that the backbone has been solvated already, and have been obtained on the basis of free energy calculations with empirical force field models. We find that the peptide backbone strongly impacts the solvation of nonpolar side chains, while its effect on the polar side chains is less pronounced. The results indicate that, in the presence of the short peptide backbone, nonpolar amino acid side chains are less hydrophobic than what is expected based on small molecule (analogue) solvation data

Direct Osmolyte–Macromolecule Interactions Confer Entropic Stability to Folded States

Protective osmolytes are chemical compounds that shift the protein folding/unfolding equilibrium toward the folded state under osmotic stresses. The most widely considered protection mechanism assumes that osmolytes are depleted from the protein’s first solvation shell, leading to entropic stabilization of the folded state. However, recent theoretical and experimental studies suggest that protective osmolytes may directly interact with the macromolecule. As an exemplary and experimentally well-characterized system, we herein discuss poly­(<i>N</i>-isopropylacrylamide) (PNiPAM) in water whose folding/unfolding equilibrium shifts toward the folded state in the presence of urea. On the basis of molecular dynamics simulations of this specific system, we propose a new microscopic mechanism that explains how direct osmolyte–macromolecule interactions confer stability to folded states. We show that urea molecules preferentially accumulate in the first solvation shell of PNiPAM driven by attractive van der Waals dispersion forces with the hydrophobic isopropyl groups, leading to the formation of low entropy urea clouds. These clouds provide an entropic driving force for folding, resulting in preferential urea binding to the folded state and a decrease of the lower folding temperature in agreement with experiment. The simulations further indicate that thermodynamic nonideality of the bulk solvent opposes this driving force and may lead to denaturation, as illustrated by simulations of PNiPAM in aqueous solutions with dimethylurea. The proposed mechanism provides a new angle on relations between the properties of protecting and denaturing osmolytes, salting-in or salting-out effects, and solvent nonidealities

Convergence of Kirkwood–Buff Integrals of Ideal and Nonideal Aqueous Solutions Using Molecular Dynamics Simulations

The computation of Kirkwood–Buff integrals (KBIs) using molecular simulations of closed systems is challenging due to finite system-size effects. One of the problems involves the incorrect asymptotic behavior of the radial distribution function. Corrections to rectify such effects have been proposed in the literature. This study reports a systematic comparison of the proposed corrections (as given by Ganguly et al. <i>J. Chem. Theory Comput.</i> <b>2013</b>, <i>9</i>, 1347–1355 and Krüger et al. <i>J. Phys. Chem. Lett.</i> <b>2013</b>, <i>4</i>, 4–7) to assess the asymptotic behavior of the RDFs, the KBIs, as well as the estimation of thermodynamic quantities for ideal urea–water and nonideal modified-urea–water mixtures using molecular dynamics simulations. The results show that applying the KBI correction suggested by Krüger et al. on the RDF corrected with the Ganguly et al. correction (denoted as B-KBI) yields improved KBI convergence for the ideal and nonideal aqueous mixtures. Different averaging regions in the running KBIs (correlated or long-range) are assessed, and averaging over the correlated region for large system sizes is found to be robust toward the change in the degree of solvent nonideality and concentration, providing good estimates of thermodynamic quantities. The study provides new insights into improving the KBI convergence, the suitability of different averaging regions in KBIs to estimate thermodynamic properties, as well as the applicability of correction methods to achieve KBI convergence for nonideal aqueous binary mixtures

Comparison of Different TMAO Force Fields and Their Impact on the Folding Equilibrium of a Hydrophobic Polymer

Trimethylamine <i>N</i>-oxide (TMAO) is a protective osmolyte able to preserve protein folded states in the presence of denaturants like urea and under extreme thermodynamic conditions of high pressure and temperature. The current understanding posits that TMAO exerts its stabilizing effect on proteins by preferential exclusion from the macromolecular hydration shell. Additionally, TMAO is also known to favor the folding of hydrophobic polymers. In this latter case, theoretical and experimental studies support a scenario in which TMAO directly interacts with the macromolecule. While atomistic simulations may potentially elucidate the precise TMAO-induced stabilization mechanism, the comparative accuracy of the different TMAO force field models available in the literature remains elusive. Herein, we compare four different TMAO models, study their structural hydration properties, and validate the models against experimental osmotic coefficients and air–water surface tension data over a broad range of TMAO concentrations. The models were furthermore applied to study the effect of TMAO on the folding equilibrium of a generic hydrophobic polymer in aqueous solution. Interestingly, we find that TMAO increasingly stabilizes the compact globular state of the polymer up to approximately 1 M TMAO, while in turn destabilizing it with further increase in TMAO concentration. Hence, TMAO acts as a stabilizing osmolyte or as a denaturant depending on the TMAO concentration of the solution. TMAO-induced stabilization up to 1 M is accompanied by positive preferential TMAO binding and with an increase in the chain configurational entropy, which is reduced at concentrations higher than 1 M. These results are qualitatively independent of the TMAO force field

Molecular Simulation Study on Hofmeister Cations and the Aqueous Solubility of Benzene

We study the ion-specific salting-out process of benzene in aqueous alkali chloride solutions using Kirkwood–Buff (KB) theory of solutions and molecular dynamics simulations with different empirical force field models for the ions and benzene. Despite inaccuracies in the force fields, the simulations indicate that the decrease of the Setchenow salting-out coefficient for the series NaCl > KCl > RbCl > CsCl is determined by direct benzene–cation correlations, with the larger cations showing weak interactions with benzene. Although ion-specific aqueous solubilities of benzene may be affected by indirect ion–ion, ion–water, and water–water correlations, too, these correlations are found to be unimportant, with little to no effect on the Setchenow salting-out coefficients of the various salts. We further considered LiCl, which is experimentally known to be a weaker salting-out agent than NaCl and KCl and, therefore, ranks at an unusual position within the Hofmeister cation series. The simulations indicate that hydrated Li⁺ ions can take part of the benzene hydration shell while the other cations are repelled by it. This causes weaker Li⁺ exclusion around the solute and a resulting, weaker salting-out propensity of LiCl compared to that of the other salts. Removing benzene–water and benzene–salt electrostatic interactions in the simulations does not affect this mechanism, which may therefore also explain the smaller effect of LiCl, as compared to that of NaCl or KCl, on aqueous solvation and hydrophobic interaction of nonpolar molecules

Computational Calorimetry of PNIPAM Cononsolvency in Water/Methanol Mixtures

We revisit the mechanism for cononsolvency of PNIPAM in water/methanol mixtures. Using extensive molecular dynamics simulations, we calculate the calorimetric enthalpy of the PNIPAM collapse transition and observe a unique fingerprint of PNIPAM cononsolvency which is analyzed in terms of microscopic interactions. We find that polymer hydration is the determining factor for PNIPAM collapse in the cononsolvency regime. In particular, it is shown that methanol frustrates the ability of water to form hydrogen bonds with the amide proton and therefore causes polymer collapse

Kirkwood–Buff Coarse-Grained Force Fields for Aqueous Solutions

We present an approach to systematically coarse-grain liquid mixtures using the fluctuation solution theory of Kirkwood and Buff in conjunction with the iterative Boltzmann inversion method. The approach preserves both the liquid structure at pair level and the dependence of solvation free energies on solvent composition within a unified coarse-graining framework. To test the robustness of our approach, we simulated urea–water and benzene–water systems at different concentrations. For urea–water, three different coarse-grained potentials were developed at different urea concentrations, in order to extend the simulations of urea–water mixtures up to 8 molar urea concentration. In spite of their inherent state point dependence, we find that the single-site models for urea and water are transferable in concentration windows of approximately 2 M. We discuss the development and application of these solvent models in coarse-grained biomolecular simulations

A Chemically Accurate Implicit-Solvent Coarse-Grained Model for Polystyrenesulfonate Solutions

A systematic molecular coarse-graining (CG) approach for aqueous polyelectrolyte solutions is presented with sodium polystyrenesulfonate (NaPSS) with different chain tacticities as example systems. The styrenesulfonate repeat unit is mapped on a three-site CG representation with the counterion being modeled explicitly while the solvent is modeled implicitly. The CG force field discriminates between bonded and nonbonded forces, which have been developed independently. The bonded interactions correspond to the potentials of mean force of CG bond, angle, and torsion degrees of freedom obtained from sampling isolated chains with an atomistic force field that includes only the local interactions along the chain. The nonbonded interactions correspond to bead–bead potentials of mean force, obtained from simulations of small molecule or ion pairs in explicit water. The CG model reproduces the local and global conformations of polyelectrolyte chains in good agreement with the parent atomistic chains in aqueous solution. By using a relative dielectric permittivity based on the local concentration of counterions around the polyelectrolyte chain, the quality of our CG models can be further improved substantially. The effect of added salt (NaCl) on the radius of gyration of PSS chains with different tacticities has also been studied and results show the transferability of the CG NaPSS model to regimes with different electrostatic conditions. We furthermore show that the CG procedure presented here can easily be extended to CG models for partially sulfonated polystyrene systems

Trimethylamine <i>N</i>‑oxide Counteracts Urea Denaturation by Inhibiting Protein–Urea Preferential Interaction

Osmolytes are small organic molecules that can modulate the stability and function of cellular proteins by altering the chemical environment of the cell. Some of these osmolytes work in conjunction, via mechanisms that are poorly understood. An example is the naturally occurring protein-protective osmolyte trimethylamine <i>N</i>-oxide (TMAO) that stabilizes cellular proteins in marine organisms against the detrimental denaturing effects of another naturally occurring osmolyte, urea. From a computational standpoint, our understanding of this counteraction mechanism is hampered by the fact that existing force fields fail to capture the correct balance of TMAO and urea interactions in ternary solutions. Using molecular dynamics simulations and Kirkwood–Buff theory of solutions, we have developed an optimized force field that reproduces experimental Kirkwood–Buff integrals. We show through the study of two model systems, a 15-residue polyalanine chain and the R2-fragment (²⁷³GKVQIINKKLDL²⁸⁴) of the Tau protein, that TMAO can counteract the denaturing effects of urea by inhibiting protein–urea preferential interaction. The extent to which counteraction can occur is seen to depend heavily on the amino acid composition of the peptide