Fast version of the structure adapted multipole method-efficient calculation of electrostatic forces in protein dynamics

Traditional algorithms for evaluation of electrostatic forces in molecular dynamics simulations of proteins require computational work of the order O(N-2) for a system of N atoms. Truncation methods, which try to avoid that effort, entail intolerably large errors in forces, energies and other observables. Hierarchical multipole methods allow rapid and correct evaluation of electrostatic forces. We describe an improved version of the Structure Adapted Multipole Method (SAMM) which not only scales with O(N) but also works as fast as truncation algorithms. Unlike the latter it manages to reproduce electrostatic forces with an error below 1%.