Error Analysis of the Poisson PM Force Field Scheme for Particle-Based Simulations of Biological Systems

The particle-particle-particle-mesh (PM) force field scheme [1], [2] is an efficient approach to account for both the long-range and short-range electrostatic interactions in the simulation of biological systems. Resolving the particle-mesh term in real-space [2], [3] improves the original approach of Hockney et al. [1] by allowing for the inclusion of non-periodic boundary conditions. To date, the PM method has not been fully utilized by the computational biophysics community due to a lack of rigorous analysis of the computational error associated with the PM approach [4]. Performing such an analysis is the main goal of this work. The PM approach is based on a separation of the Coulomb interaction into a long-range and short-range component by a smooth function f(r), 1 r = f(r) r + 1− f(r) r (1)