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Disassembling solvation free energies into local contributions—Toward a microscopic understanding of solvation processes

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Solvation free energies contribute to the driving force of molecular processes in solution and play a significant role for the relative stability of biomolecular conformations or the formation of complexes. Changes in solvation free energy are the origin of solvent‐mediated interactions such as the hydrophobic effect in water. However, an accurate description of solvation free energies, specifically in aqueous solution, without explicit representation of the solvent is a challenging task in computer simulations. To improve existing models detailed microscopic information on solute–solvent interactions is required, which is not directly accessible from experiments. Explicit solvent simulations include solvent‐mediated effects, however, at a considerable computational cost. Computational tools have been proposed in recent years to extract information on solvation free energies and solute–solvent interactions from explicit solvent simulations. The latter includes spatial decompositions of the solvation enthalpy and entropy, which may eventually lead to an improved theoretical understanding of solvation thermodynamics. This article is categorized under: Molecular and Statistical Mechanics> Free Energy Methods Theoretical and Physical Chemistry > Statistical Mechanics Structure and Mechanism > Computational Biochemistry and Biophysics
Spatial distribution of local solvation entropy contributions in the environment of the receptor molecule cucurbit[7]uril. The top panels displays the density of solvation entropy contributions from translational degrees of freedom of water using two distinct perspectives: tan‐colored isosurfaces represent bulk‐like translational entropies of hydration water and the red isosurface encloses a volume with negative solvation entropy densities of at least −1.4 J/(K mol Å3). The lower panels display similar information for the orientational solvation entropy. The lower left panel describes orientational solvation entropy contributions per water molecule. Yellow and violet isosurfaces indicate negative solvation entropy contributions of −7 and −21 J/(K mol) per water molecule, respectively. The lower right panel displays the orientational solvation entropy density with yellow and violet isosurfaces at −0.7 and −2.1 J/(K mol Å3), respectively. (Reprinted with permission from Ref (). Copyright 2012 AIP Publishing)
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Spatial distribution of local solvation enthalpy contributions for N‐methylacetamide in water. Shown are 0.125 Å3 voxels in the first hydration shell with a local water number density ρ(r) that is increased by 20% relative to bulk water. The left panel shows local contributions from direct solute–water interactions ΔUsw(r) per water molecule. Negative values indicate favorable interactions between water and the solute, for example, via formation of hydrogen bonds. The right panel shows contributions from the local solvent reorganization energy ΔUww(r), which describes solute‐induced changes of interactions between hydration water molecules. Positive values indicate the loss of favorable water–water interactions, most prominently due to the replacement of water–water hydrogen bonds by a solute–water hydrogen bond. (Reprinted with permission from Ref (). Copyright 2017 American Chemical Society)
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The total free energy change that drives the complex formation of biomolecules can be conceptually described in terms of separate contributions from direct interactions and solvent‐mediated interactions. The latter include hydrophobic forces as well water‐mediated hydrogen bonds in aqueous solution
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Local contributions to the solvation entropy of three small solutes in water: methanol (left), benzene (middle), and N‐methylacetamide (right). Solvation entropy contributions are shown as isosurfaces of the solvation entropy contribution density. For methanol, the individual numerical values for the isosurfaces are +0.028 J/(K mol Å3) (red), −0.084 J/(K mol Å3) (transparent blue) and −0.70 J/(K mol Å3) (blue); for benzene +0.038 J/(K mol Å3) (red), −0.21 J/(K mol Å3) (transparent blue) and −0.28 J/(K mol Å3) (blue); and for N‐methylacetamide +0.042 J/(K mol Å3) (red), −0.14 J/(K mol Å3) (transparent blue) and −0.28 J/(K mol Å3) (blue). (Reprinted with permission from Ref (). Copyright 2013 American Chemical Society)
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Local translational and rotational vibrational density of states (VDOS) and spatial distribution of solvation entropy contributions for N‐methylacetamide in water. On the left side, the separated VDOS for translational and rotational degrees of freedom are shown for a voxel of the analysis grid, as well as the partitioning into hard sphere/rigid rotor and harmonic oscillator contributions via the 2PT formalism. On the right, local solvation entropy contributions per water molecule are shown, which describe the strongest decrease in entropy relative to bulk water in the solute‐water hydrogen bond binding sites and a less pronounced decrease next to nonpolar methyl groups. Shown are 0.125 Å3 voxels in the first hydration shell as described for Figure . (Reprinted with permission from Ref (). Copyright 2017 American Chemical Society)
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Vibrational density of states of water with graphical representations of typical intermolecular vibrations at frequencies below 1,000 cm−1. The contribution of the vibrational density of states (VDOS) as a function of frequency to the total liquid entropy is described by the color code and highlights the dominant role of low‐frequency vibrations. (Reprinted with permission from Ref (). Copyright 2017 American Chemical Society)
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Effect of the permutation operation on a molecular dynamics simulation trajectory of 216 water molecules. The left panel shows the positions of water oxygen atoms as a function of simulation time. The trajectories of each water molecule are shown in a different color. Notably, the trajectories include sudden jumps across the simulation box due to the periodic boundary conditions employed in the simulation. The right panel shows the same trajectories after the permutation operation has been applied, indicating localized fluctuations of individual water molecules. (Reprinted with permission from Ref (). Copyright 2007 AIP Publishing)
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Structure and Mechanism > Computational Biochemistry and Biophysics
Theoretical and Physical Chemistry > Statistical Mechanics
Molecular and Statistical Mechanics > Free Energy Methods

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