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