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 inter actions on the all-atom level by molecular mechanics and dynamics, a s well as on the macroscopic level by models of continuum solvation. Bridgi ng of the two representations-an area of active research-is necessary for s tudying integrated functions of large systems of biological importance. Fol lowing perspectives of both discrete (N-body) interaction and continuum sol vation, we present a new algorithm, DiSCO (Discrete Surface Charge Optimiza tion), for economically describing the electrostatic field predicted by Poi sson-Boltzmann theory using a discrete set of Debye-Huckel charges distribu ted on a virtual surface enclosing the maclomolecule. The procedure in DiSC O relies on the linear behavior of the Poisson-Boltzmann equation in the fa r zone; thus contributions from a number of molecules may be superimposed, and the electrostatic potential, or equivalently the electrostatic field, m ay be quickly and efficiently approximated by the summation of contribution s from the set of charges. The desired accuracy of this approximation is ac hieved by minimizing the difference between the Poisson-Boltzmann electrost atic field and that produced by the linearized Debye-Huckel approximation u sing our truncated Newton optimization package. DiSCO is applied here to de scribe the salt-dependent electrostatic environment of the nucleosome core particle in terms of several hundred surface charges. This representation f orms the basis for modeling-by dynamic simulations (or Monte Carlo)-the fol ding of chromatin. DiSCO call be applied more generally to many macromolecu lar systems whose size and complexity warrant a model resolution between th e all-atom and macroscopic levels. (C) 2000 John Wiley & Sons, Inc.