Charge grouping approaches to calculation of electrostatic forces in molecular dynamics of macromolecules

Calculation of long-range electrostatic interactions is the most time-consuming step in theoretical simulation of the structure and dynamics of macromolecules. In practice very short cutoff distances are used, which may distort the behavior of the model system. We describe two accurate approaches to calculation of electrostatic forces based on hierarchical grouping of charges into cubes. The first is similar to the O(NlogN) algorithm developed by Barnes, J. and Hut, P., Nature (London) 324, 446-449 (1986), for simulation of a gravitational motion of N bodies. The second approach we formulate for a system with periodic boundary conditions in the nearest image approximation. The calculation of electrostatic interactions and a charge grouping procedure are faster than O(N2). The average inaccuracy in the force introduced by the grouping does not exceed 1%. We describe a small modification of the same approach which makes it suitable for long strongly charged polymers as well. This accurate approach to calculation of electrostatic interactions is illustrated with an example of the dynamics of ions near DNA. Quick equilibration of the ionic distribution is observed during molecular dynamics simulation if electrostatic forces are properly calculated, while the behavior and distribution of ions are less realistic when the conventional cutoff distances are used.