Molecular Renormalization Group Coarse-Graining of Electrolyte Solutions: Application to Aqueous NaCl and KCl

Abstract

Simplified, yet accurate, coarse-grained models are needed to explore the behavior of complex biological systems by means of Molecular Dynamics (MD) simulations, because many interesting processes occur at long time scales and large length scales that are not amenable to studies by atomistic simulations. The aqueous salt buffer provides an important contribution to the structure and function of biological molecules. While in many simplified models both water and salt are treated as a continuous medium, it is often desirable to describe mobile ions in an explicit manner. For example, the discrete nature of ions was shown to play a very important role in their interaction with highly charged biomolecules, such as DNA. In this work, we have derived an effective interaction potential for monovalent ions by systematically coarse-graining the all-atom NaCl and KCl aqueous solutions at several different ionic concentrations. Our approach is based on explicitly accounting for cross-correlations among various observables that constitute the compact basis set of the coarse-grained Hamiltonian. Compactness of the Hamiltonian ensures computational efficiency of the optimization procedure. In addition, it allows us to accurately reproduce many-body effects, in contrast with many existing algorithms. The resulting Hamiltonian produced ionic distributions that are virtually identical to those obtained in atomistic simulations with explicit water, capturing short-range hydration effects. Our coarse-grained model of monovalent electrolyte solutions allows the incorporation of ions into complex coarse-grained biomolecular simulations, where both electrostatic and short-range hydration effects must be taken into account.

Effective solvent mediated potentials of Na+ and Cl− ions in aqueous solution: temperature dependence

“…Solvent-mediated interionic effective potentials, taking into account the molecular structure of the solvent and specific short-range interactions, can be built from atomistic molecular dynamics simulations as it was done in a number of previous studies. 1,5,8,29 Hess et al 9 investigated concentration dependence of NaCl ion-ion effective potentials constructed from atomistic simulations. It was shown that the main part of this dependence can be attributed to the change of the effective dielectric permittivity, which decreases with the ion concentration, affecting the long-range behaviour of the effective potentials.…”

Computer Simulations of Soft Matter: Linking the Scales

“…In contrast to the Force Matching or Multi-scale coarse graining scheme, other structure-based methods provide CG interactions that reproduce pre-defined target structure properties-often a set of radial distribution functions [77][78][79][80][81][82][83][84][85][86][87][88][89]. This means that the many-body PMF (Equations (6) and (7)) is replaced as a target by a set of simpler structural correlation functions.…”

“…The disadvantage of IMC on the other hand is a high computational cost and problems with numerical stability; for a detailed comparison see Reference [116]. Related to IMC, there are several other recent developments, e.g., a molecular renormalization group approach [85][86][87] or an approach that relies on relative entropies [96][97][98] (which will be discussed in more detail below). While the above structure-based methods by construction reproduce exactly, within the error of the numerical procedure, the local pair structures and thus are well-suited to the reinsertion of atomistic coordinates, it can be expected a priori that they will not be equally well suited to the reproduction of thermodynamic properties (pressure, phase behavior, etc.)…”

“…In another group of approaches, one numerically generates CG interaction functions with the aim of reproducing the configurational phase space sampled in an atomistic reference simulation. These approaches may rely on different types of reference properties such as structure functions [77][78][79][80][81][82][83][84][85][86][87][88][89], mean forces [90][91][92][93][94][95] or relative entropies [96][97][98]. In the following subsection, a few basic notions of coarse-graining theory will be introduced, together with examples of the strategies that can be employed to perform the coarse-graining in practice.…”

Response to “Comment on ‘The nonmonotonic concentration dependence of the mean activity coefficient of electrolytes is a result of a balance between solvation and ion–ion correlations’” [J. Chem. Phys. 134, 157101 (2011)]

“…Different ions have different hydration shells in thickness and stability. According to molecular dynamics (MD) simulations using explicit water models, [11][12][13][14][15] small cations cannot approach each other up to contact position: there are always water molecules between two cations (large anions do not seem to produce this effect). Cation-anion pairs, on the other hand, produce the opposite behavior: due to their strong electrostatic attraction, they can approach each other closer than the sum of the ionic radii.…”