Computing Spatially Resolved Rotational Hydration Entropies from Atomistic Simulations.

Leonard P Heinz,Helmut Grubmüller

doi:10.1021/acs.jctc.9b00926

Abstract

For a first-principles understanding of macromolecular processes, a quantitative understanding of the underlying free energy landscape and in particular its entropy contribution is crucial. The stability of biomolecules, such as proteins, is governed by the hydrophobic effect, which arises from competing enthalpic and entropic contributions to the free energy of the solvent shell. While the statistical mechanics of liquids, as well as molecular dynamics simulations, have provided much insight, solvation shell entropies remain notoriously difficult to calculate, especially when spatial resolution is required. Here, we present a method that allows for the computation of spatially resolved rotational solvent entropies via a nonparametric k-nearest-neighbor density estimator. We validated our method using analytic test distributions and applied it to atomistic simulations of a water box. With an accuracy of better than 9.6%, the obtained spatial resolution should shed new light on the hydrophobic effect and the thermodynamics of solvation in general.

Highlights

Competing enthalpic and entropic contributions to the solvation free energies give rise to the hydrophobic effect,[1] which is vital for protein function and folding.[2−4] Despite extensive theoretical work,[1,5] a quantitative understanding of the hydrophobic effect at heterogeneous surfaces, such as of proteins and mixed bilayers, remains elusive.Because surface water shows a significantly altered behavior compared to bulk,[6,7] it is essential for our understanding of the thermodynamics and energetics of protein solvation to better characterize, e.g., the relative contributions by different solvation shells or the effect of individual protein side chains on the solvent
The distributions depend on the localization aapnnardda,mpf3(oeμr)t,epdr2(eμμ,ct)o,erwrr,mhciioncnhets,rfotohlrsetitrhhewe uisdnttrcheo,nragrsethldaetoemfdotdhniessttrcraoibtreurdetilioantnioFs nipg.1(uμr),ep22(μA), As can be seen in Figure 2B, the kNN estimator largely agrees with the analytic results for the uncorrelated distributions p1(μ), p2(μ), and p3(μ) for μ between 0 and 50 and the tested k-values between 1 and 13
We developed an estimator for spatially resolved rotational solvent entropies based on a truncated mutual information expansion and the k-nearest-neighbor algorithm on SO(3)n

Summary

Introduction

Competing enthalpic and entropic contributions to the solvation free energies give rise to the hydrophobic effect,[1] which is vital for protein function and folding.[2−4] Despite extensive theoretical work,[1,5] a quantitative understanding of the hydrophobic effect at heterogeneous surfaces, such as of proteins and mixed bilayers, remains elusive. Because surface water shows a significantly altered behavior compared to bulk,[6,7] it is essential for our understanding of the thermodynamics and energetics of protein solvation to better characterize, e.g., the relative contributions by different solvation shells or the effect of individual protein side chains on the solvent. Molecular dynamics (MD) simulations describe the hydrophobic effect at an atomic level,[8,9] but a deeper understanding of the molecular driving forces requires a quantitative and spatially resolved picture of solvation shell thermodynamics, which poses considerable challenges

Methods

Results

Conclusion