Reference interaction site model with hydrophobicity induced density inhomogeneity: An analytical theory to compute solvation properties of large hydrophobic solutes in the mixture of polyatomic solvent molecules

Abstract

Reference interaction site model (RISM) has recently become a popular approach in the study of thermodynamical and structural properties of the solvent around macromolecules. On the other hand, it was widely suggested that there exists water density depletion around large hydrophobic solutes (>1 nm), and this may pose a great challenge to the RISM theory. In this paper, we develop a new analytical theory, the Reference Interaction Site Model with Hydrophobicity induced density Inhomogeneity (RISM-HI), to compute solvent radial distribution function (RDF) around large hydrophobic solute in water as well as its mixture with other polyatomic organic solvents. To achieve this, we have explicitly considered the density inhomogeneity at the solute-solvent interface using the framework of the Yvon-Born-Green hierarchy, and the RISM theory is used to obtain the solute-solvent pair correlation. In order to efficiently solve the relevant equations while maintaining reasonable accuracy, we have also developed a new closure called the D2 closure. With this new theory, the solvent RDFs around a large hydrophobic particle in water and different water-acetonitrile mixtures could be computed, which agree well with the results of the molecular dynamics simulations. Furthermore, we show that our RISM-HI theory can also efficiently compute the solvation free energy of solute with a wide range of hydrophobicity in various water-acetonitrile solvent mixtures with a reasonable accuracy. We anticipate that our theory could be widely applied to compute the thermodynamic and structural properties for the solvation of hydrophobic solute.

Potential of Mean Force Calculations of Solute Permeation Across UT-B and AQP1: A Comparison between Molecular Dynamics and 3D-RISM

“…In both channels, the variations in the PMFs between different solutes seem to reflect mainly the size of the solute, but 3D-RISM seems to miss modulations due to different polarities of the solutes. These findings may be explained by previous observations that 3D-RISM faces limitations at hydrophobic surfaces and, possibly, due to the lack of orientation correlations …”

“…Hence, accurate calculations of the density of the permeating solute requires that the water–protein interactions are correctly balanced with respect to solute-protein interactions. In addition, if the permeating solute exposes a nonpolar surface, the calculations would require accurate treatment of the hydrophobic solute–protein interactions, which have remained challenging in the 3D-RISM context. ,, Moreover, molecules often adopt well-defined orientations inside a narrow channel, whereas the RISM method takes averages over the solvent’s orientational degrees of freedom. Whether the orientational average leads to artifacts in a narrow channel lumen has, to our knowledge, not been systematically addressed.…”

The Ion-Dipole Correction of the 3DRISM Solvation Model to Accurately Compute Water Distributions around Negatively Charged Biomolecules

“…An infinite order of the PSE- n closure is the hyper-netted-chain (or HNC) closure, which simply ignores the bridge function: h u v false( bold-italicr false) = e − β v u v false( bold-italicr false) + h u v false( bold-italicr false) − c u v false( bold-italicr false) − 1 The HNC closure was widely used in 1DRISM , but rarely in 3DRISM, as the HNC closure suffers from the convergence issue in large systems. Other closures include the Mean Spherical Approximation (MSA), the Kobryn-Gusarov-Kovalenko (KGK) closure, , the Percus–Yevick (PY) closure, the HNCB closure, the D2 and D2-MSA closure, − etc. Among these closures, KH and PSE- n are used the most for biological molecules.…”

“…IET-based solvation methods have been successfully applied to efficiently compute solvation structure and thermodynamics for a wide variety of systems . Among IETs, the reference interaction site model (RISM) is the most developed, including 1DRISM , for small liquid molecules, and the 3DRISM for large and dilute solute systems. ,− In particular, the 3DRISM simplifies the explicit all-atom description of solvation into a density-based description of solvent around solute on three-dimensional grids . It has been successfully applied to obtain solvation structures and thermodynamic properties for a wide variety of systems, such as the hydration of organic molecules − and the solvation of proteins and RNAs. − It has also been used to predict the preferred hydration sites , and ion-binding sites , in protein pockets.…”

Computational Studies of Small Molecule Permeation across Membrane Channels

“…The only variations in the profiles seem to originate from solute size but not from solute polarity, thereby missing any modulation due to hydrophobic effects. The lack of hydrophobic contributions to 3D-RISM has been noticed before, and thus several corrections that allow the calculation of more accurate solvent Radial Distribution Functions (RDFs) around a hyrophobic solute, such as the ones indicated by Cao et al, might improve the PMFs calculated from 3D-RISM [259].…”