A force consistent method for electrostatic energy calculation in fluctuating charge model

A practical approach to include the polarization effect in a molecular force field is the fluctuating charge method in which atomic charges vary as the configuration of the molecular system changes. However, the use of the Coulomb formula to evaluate energy in a fluctuating charge method is theoretically inconsistent with the forces given by the fluctuating method. In this work, we propose a force-consistent method to correctly calculate electrostatic energies of molecular systems using a fluctuating charge model (Effective Polarizable Bond or EPB). In this protocol, the electrostatic energy is obtained by numerical interaction of the atomic forces along the MD trajectory, rather than using the default Coulomb formula in the EPB model. Test study on the benchmark Barnase-Barstar protein-protein interaction system demonstrates that although the total electrostatic energy of the system shows little deviation due to the averaging effect, specific residue-residue electrostatic interaction energy is affected and the level of the effect depends on the charges of the interacting residues with charged residues showing pronounced differences in calculated energies between using the current protocol and the standard Coulomb formula. It is recommended that the proposed numerical interaction method should be preferred in the calculation of electrostatic energy in fluctuating charge models used in molecular dynamics simulations.