Modeling salt-mediated electrostatics of macromolecules: The discrete surface charge optimization algorithm and its application to the nucleosome

Much progress has been achieved on quantitative assessment of electrostatic interactions on the all-atom level by molecular mechanics and dynamics, as well as on the macroscopic level by models of continuum solvation. Bridging of the two representations - an area of active research - is necessary for studying integrated functions of large systems of biological importance. Following perspectives of both discrete (N-body) interaction and continuum solvation, we present a new algorithm, DiSCO (Discrete Surface Charge Optimization), for economically describing the electrostatic field predicted by Poisson-Boltzmann theory using a discrete set of Debye-Huckel charges distributed on a virtual surface enclosing the macromolecule. The procedure in DiSCO relies on the linear behavior of the Poisson-Boltzmann equation in the far zone; thus contributions from a number of molecules may be superimposed, and the electrostatic potential, or equivalently the electrostatic field, may be quickly and efficiently approximated by the summation of contributions from the set of charges. The desired accuracy of this approximation is achieved by minimizing the difference between the Poisson-Boltzmann electrostatic field and that produced by the linearized Debye-Huckel approximation using our truncated Newton optimization package. DiSCO is applied here to describe the salt-dependent electrostatic environment of the nucleosome core particle in terms of several hundred surface charges. This representation forms the basis for modeling - by dynamic simulations (or Monte Carlo) - the folding of chromatin. DiSCO can be applied more generally to many macromolecular systems whose size and complexity warrant a model resolution between the all-atom and macroscopic levels.