Large-scale parallelised boundary element method electrostatics for biomolecular simulation

Large-scale biomolecular simulations require a model of particle interactions capable of incorporating the behaviour of large numbers of particles over relatively long timescales. If water is modelled as a continuous medium then the most important intermolecular forces between biomolecules can be modelled as long-range electrostatics governed by the Poisson- Boltzmann Equation (PBE). We present a linearised PBE solver called the "Boundary Element Electrostatics Program"(BEEP). BEEP is based on the Boundary Element Method (BEM), in combination with a recently developed O(N) Fast Multipole Method (FMM) algorithm which approximates the far-�field integrals within the BEM, yielding a method which scales linearly with the number of particles. BEEP improves on existing methods by parallelising the underlying algorithms for use on modern cluster architectures, as well as taking advantage of recent progress in the �field of GPGPU (General Purpose GPU) Programming, to exploit the highly parallel nature of graphics cards. We found the stability and numerical accuracy of the BEM/FMM method to be highly dependent on the choice of surface representation and integration method. For real proteins we demonstrate the critical level of surface detail required to produce converged electrostatic solvation energies, and introduce a curved surface representation based on Point-Normal G1-continuous triangles which we �find generally improves numerical stability compared to a simpler surface constructed from planar triangles. Despite our improvements upon existing BEM methods, we �find that it is not possible to directly integrate BEM surface solutions to obtain intermolecular electrostatic forces. It is, however, practicable to use the total electrostatic solvation energy calculated by BEEP to drive a Monte-Carlo simulation

Domain decomposition method for Poisson--Boltzmann equations based on Solvent Excluded Surface

In this paper, we develop a domain-decomposition method for the generalized Poisson-Boltzmann equation based on a solvent-excluded surface which is widely used in computational chemistry. The solver requires to solve a generalized screened Poisson (GSP) equation defined in $\mathbb{R}^3$ with a space-dependent dielectric permittivity and an ion-exclusion function that accounts for Steric effects. Potential theory arguments transform the GSP equation into two-coupled equations defined in a bounded domain. Then, the Schwarz decomposition method is used to formulate local problems by decomposing the cavity into overlapping balls and only solving a set of coupled sub-equations in each ball in which, the spherical harmonics and the Legendre polynomials are used as basis functions in the angular and radial directions. A series of numerical experiments are presented to test the method

Tools for Biomolecular Modeling and Simulation

Electrostatic interactions play a pivotal role in understanding biomolecular systems, influencing their structural stability and functional dynamics. The Poisson-Boltzmann (PB) equation, a prevalent implicit solvent model that treats the solvent as a continuum while describes the mobile ions using the Boltzmann distribution, has become a standard tool for detailed investigations into biomolecular electrostatics. There are two primary methodologies: grid-based finite difference or finite element methods and body-fitted boundary element methods. This dissertation focuses on developing fast and accurate PB solvers, leveraging both methodologies, to meet diverse scientific needs and overcome various obstacles in the field

Parallel AFMPB solver with automatic surface meshing for calculation of molecular solvation free energy

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018) Abstract We present PAFMPB, an updated and parallel version of the AFMPB software package for fast calculation of molecular solvation-free energy. The new version has the following new features: (1) The adaptive fast multipole method and the boundary element methods are parallelized; (2) A tool is embedded for automatic molecular VDW/SAS surface mesh generation, leaving the requirement for a mesh file at input optional; (3) The package provides fast calculation of the total solvation-free energy, incl... Title of program: Parallel AFMPB Catalogue Id: AEGB_v2_0 Nature of problem Numerical solution of the linearized Poisson-Boltzmann equation that describes electrostatic interactions of molecular systems in ionic solutions. Versions of this program held in the CPC repository in Mendeley Data AEGB_v1_0; AFMPB: Adaptive Fast Multipole Poisson-Boltzmann Solver; 10.1016/j.cpc.2010.02.015 AEGB_v1_1; AFMPB; 10.1016/j.cpc.2013.05.012 AEGB_v2_0; Parallel AFMPB; 10.1016/j.cpc.2014.12.02