## 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-Hückel 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-Hückel
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.

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