Charge group partitioning in biomolecular simulation

Molecular simulation techniques are increasingly being used to study biomolecular systems at an atomic level. Such simulations rely on empirical force fields to represent the intermolecular interactions. There are many different force fields available|each based on a different set of assumptions and thus requiring different parametrization procedures. Recently, efforts have been made to fully automate the assignment of force-field parameters, including atomic partial charges, for novel molecules. In this work, we focus on a problem arising in the automated parametrization of molecules for use in combination with the gromos family of force fields: namely, the assignment of atoms to charge groups such that for every charge group the sum of the partial charges is ideally equal to its formal charge. In addition, charge groups are required to have size at most κ. We show NP-hardness and give an exact algorithm capable of solving practical problem instances to provable optimality in a fraction of a second.