An image-based reaction field method for electrostatic interactions in molecular dynamics simulations of aqueous solutions

Abstract

In this paper, a new solvation model is proposed for simulations of biomolecules in aqueous solutions that combines the strengths of explicit and implicit solvent representations. Solute molecules are placed in a spherical cavity filled with explicit water, thus providing microscopic detail where it is most needed. Solvent outside of the cavity is modeled as a dielectric continuum whose effect on the solute is treated through the reaction field corrections. With this explicit/implicit model, the electrostatic potential represents a solute molecule in an infinite bath of solvent, thus avoiding unphysical interactions between periodic images of the solute commonly used in the lattice-sum explicit solvent simulations. For improved computational efficiency, our model employs an accurate and efficient multiple-image charge method to compute reaction fields together with the fast multipole method for the direct Coulomb interactions. To minimize the surface effects, periodic boundary conditions are employed for nonelectrostatic interactions. The proposed model is applied to study liquid water. The effect of model parameters, which include the size of the cavity, the number of image charges used to compute reaction field, and the thickness of the buffer layer, is investigated in comparison with the particle-mesh Ewald simulations as a reference. An optimal set of parameters is obtained that allows for a faithful representation of many structural, dielectric, and dynamic properties of the simulated water, while maintaining manageable computational cost. With controlled and adjustable accuracy of the multiple-image charge representation of the reaction field, it is concluded that the employed model achieves convergence with only one image charge in the case of pure water. Future applications to pKa calculations, conformational sampling of solvated biomolecules and electrolyte solutions are briefly discussed.

A critical appraisal of the zero-multipole method: Structural, thermodynamic, dielectric, and dynamical properties of a water system

“…However, the critical issue to the short-range treatment is to improve its accuracy and remove the possible artifacts arising in it. [10][11][12][13][14] As one of the approaches to address this issue in a shortrange treatment, [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29] the zero-multipole (summation) method (ZMM) has been developed. 30 The underlying physical idea is simple, as follows.…”

Ionic solvation studied by image-charge reaction field method

“…38 Here, we provide a brief outline of its most important features, for the sake of consistency. The central component is the computation of RF , the reaction field (RF) for a single charge q placed at position r s inside a spherical cavity with radius a and dielectric permittivity ε i embedded in an infinite solvent of dielectric permittivity ε o , as shown in Fig.…”

“…This number controls the accuracy of the multipleimage approximation: the greater the N i , the higher the accuracy. In the limit of o → ∞, only one image survives, q K = q K at the location r K , which is equivalent to the classical Kelvin image for a conductor in the electrostatics theory, 38 hence the notations.…”

“…In a recent paper, 38 we introduced a hybrid solvation model that combines the strengths of the implicit and explicit solvent representations. The model contains a central spherical cavity in which a solute molecule and some solvent are treated explicitly, thus removing the continuum approximation near the solute.…”

“…The reaction fields are computed efficiently using the image-charge method and the fast multipole expansion technique, 39,40 developed by our group previously. [41][42][43] Our method, termed image-charge solvation method (ICSM), had been tested in simulations of liquid water, 38 where many structural, static, and dynamic properties were seen to be identical to those obtained by the lattice-sum methods for sufficiently large boxes.…”