Abstract
The hydrophobic effect is essential for many biophysical phenomena and processes. It is governed by a fine-tuned balance between enthalpy and entropy contributions from the hydration shell. Whereas enthalpies can in principle be calculated from an atomistic simulation trajectory, calculating solvation entropies by sampling the extremely large configuration space is challenging and often impossible. Furthermore, to qualitatively understand how the balance is affected by individual side chains, chemical groups, or the protein topology, a local description of the hydration entropy is required. In this study, we present and assess the new method “Per|Mut”, which uses a permutation reduction to alleviate the sampling problem by a factor of N! and employs a mutual information expansion to the third order to obtain spatially resolved hydration entropies. We tested the method on an argon system, a series of solvated n-alkanes, and solvated octanol.
Highlights
The thermodynamics of the hydration shell plays an important role in many biophyiscal processes, such as phase separation, membrane and micelle formation,[1−3] or the function and folding of proteins.[4,5] These processes are driven by the hydrophobic effect,[6−10] which results from a delicate balance between entropic and enthalpic contributions of the first few solvent layers but is quantitatively not yet fully understood.[11]
We developed an molecular dynamics (MD)-based method to calculate the spatially resolved hydration entropy from atomistic simulations via permutation reduction and a mutual information expansion (“Per|Mut”), which calculates entropies directly by sampling the configuration space probability density ρ as S = −kB⟨log ρ⟩
Our method rests on a permutation reduction[31,32] (Section 2.2), which alleviates the sampling problem by N! and localizes the water molecules (Figure 1C), leaving the physics of the system unchanged
Summary
The thermodynamics of the hydration shell plays an important role in many biophyiscal processes, such as phase separation, membrane and micelle formation,[1−3] or the function and folding of proteins.[4,5] These processes are driven by the hydrophobic effect,[6−10] which results from a delicate balance between entropic and enthalpic contributions of the first few solvent layers but is quantitatively not yet fully understood.[11] A better understanding of the behavior of water molecules at heterogeneous surfaces is necessary. Atomistic molecular dynamics (MD) simulations have proven to reproduce the effects of hydrophobic interaction quantitatively.[2,12] the lack of a straightforward way to quantify the hydration entropy contributions of specific side chains or functional groups of atoms precludes a deeper understanding of the molecular driving forces and the energetics of solvation. The shallow energy landscape that governs the dynamics of the solvent molecules requires sampling of an extremely large configuration space and poses a severe challenge for entropy calculation
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