Exploring a multi-scale method for molecular simulation in continuum solvent model: Explicit simulation of continuum solvent as an incompressible fluid

Abstract

We explored a multi-scale algorithm for the Poisson-Boltzmann continuum solvent model for more robust simulations of biomolecules. In this method, the continuum solvent/solute interface is explicitly simulated with a numerical fluid dynamics procedure, which is tightly coupled to the solute molecular dynamics simulation. There are multiple benefits to adopt such a strategy as presented below. At this stage of the development, only nonelectrostatic interactions, i.e., van der Waals and hydrophobic interactions, are included in the algorithm to assess the quality of the solvent-solute interface generated by the new method. Nevertheless, numerical challenges exist in accurately interpolating the highly nonlinear van der Waals term when solving the finite-difference fluid dynamics equations. We were able to bypass the challenge rigorously by merging the van der Waals potential and pressure together when solving the fluid dynamics equations and by considering its contribution in the free-boundary condition analytically. The multi-scale simulation method was first validated by reproducing the solute-solvent interface of a single atom with analytical solution. Next, we performed the relaxation simulation of a restrained symmetrical monomer and observed a symmetrical solvent interface at equilibrium with detailed surface features resembling those found on the solvent excluded surface. Four typical small molecular complexes were then tested, both volume and force balancing analyses showing that these simple complexes can reach equilibrium within the simulation time window. Finally, we studied the quality of the multi-scale solute-solvent interfaces for the four tested dimer complexes and found that they agree well with the boundaries as sampled in the explicit water simulations.

An efficient second‐order poisson–boltzmann method

“…Alternatively, instead of treating the solute-solvent interface explicitly, Alexov and co-workers proposed an approach that uses Gaussian-based smooth dielectric functions to model the implicit solvation environment in an interface-free manner. 69, 70 Some other interesting approaches have also been proposed to improve implicit solvent models, such as coupling electrostatic and nonelectrostatic interactions within the implicit solvation treatment, 71–75 explicit simulating implicit solvent as a fluid for the purpose of more physical modeling of solvation interactions, 76–78 and using the level set function to better define the solvent and solute interfaces for dielectric assignment. 79, 80 Among those methods, IIM has been a promising high-accuracy numerical scheme, and is able to achieve energy conservation in PB molecular dynamics (MD).…”

Improved Poisson–Boltzmann Methods for High-Performance Computing

“…Since then further efforts have also been reported to develop better interface schemes, such as the immersed interface method (IIM) by Li and co-workers − and the matched interface and boundary (MIB) method by Wei and co-workers. − The idea of IIM is to enforce the interface conditions into the finite-difference schemes at grid points near the interface, while that of MIB is to enforce the lowest-order jump condition repeatedly to achieve a high-order jump condition. In addition to these higher-order numerical methods, some other approaches have also been proposed to improve the implicit solvent models, such as using level set functions to define the interfaces for dielectric assignment − and coupling electrostatic and nonelectrostatic interactions within the implicit solvation treatment. − …”