Abstract
Estimation of solvent entropy from equilibrium molecular dynamics simulations is a long-standing problem in statistical mechanics. In recent years, methods that estimate entropy using k-th nearest neighbours (kNN) have been applied to internal degrees of freedom in biomolecular simulations, and for the rigorous computation of positional-orientational entropy of one and two molecules. The mutual information expansion (MIE) and the maximum information spanning tree (MIST) methods were proposed and used to deal with a large number of non-independent degrees of freedom, providing estimates or bounds on the global entropy, thus complementing the kNN method. The application of the combination of such methods to solvent molecules appears problematic because of the indistinguishability of molecules and of their symmetric parts. All indistiguishable molecules span the same global conformational volume, making application of MIE and MIST methods difficult. Here, we address the problem of indistinguishability by relabeling water molecules in such a way that each water molecule spans only a local region throughout the simulation. Then, we work out approximations and show how to compute the single-molecule entropy for the system of relabeled molecules. The results suggest that relabeling water molecules is promising for computation of solvation entropy.
Highlights
Pathway methods [9] based on free-energy perturbation [10] or thermodynamic integration [11] are accurate but difficult to apply for large systems, linking the results of the calculation to single molecular components is difficult
We focus on mapping the problem involving indistinguishable solvent molecules into a problem where solvent molecules retain their identity, which is done here via a relabeling of water molecules and hydrogen atoms
The indistinguishability of molecules results in theoretical and practical approaches mostly based on distribution functions, which form the standard basis to analyse molecular dynamics simulations of liquids
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. The estimation of free energy and entropy from molecular dynamics calculations is a long-standing problem in biomolecular simulations [1,2,3,4,5,6,7,8]. Pathway methods [9] based on free-energy perturbation [10] or thermodynamic integration [11] are accurate but difficult to apply for large systems, linking the results of the calculation to single molecular components is difficult. Entropy can be computed from the dependence of the computed solvation free energy, or using pathway methods using the proper integrand [12]
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