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Constructing Irregular Surfaces to Enclose Macromolecular Complexes for
Mesoscale Modeling Using the Discrete Surface Charge Optimization (DiSCO)
Algorithm

Salt-mediated electrostatics interactions play an essential role in biomolecular
structures and dynamics. Since macromolecular systems modeled at atomic resolution
contain thousands of solute atoms, the electrostatic computations constitute
an expensive part of the force and energy calculations. Implicit solvent models are
one way to simplify the model and associated calculations, but they are generally
used in combination with standard atomic models for the solute. To approximate
electrostatics interactions in models on the polymer level (e.g., supercoiled DNA)
that are simulated over long times (e.g., milliseconds), Beard and Schlick have developed
the DiSCO (Discrete Surface Charge Optimization) algorithm. DiSCO
represents a macromolecular complex by a few hundred discrete charges on a
surface enclosing the system modeled by the Debye-Huckel (screened Coulombic)
approximation to the Poisson-Boltzmann equation, and treats the salt solution
as continuum solvation. DiSCO can represent the nucleosome core particle
( > 12,000 atoms), for example, by 353 discrete surface charges distributed on the
surfaces of a large disk for the nucleosome core particle and a slender cylinder for
the histone tail; the charges are optimized with respect to the PoissonBoltzmann
solution for the electric field, yielding a ~5.5%
residual. Since regular surfaces enclosing macromolecules are not sufficiently general and may be suboptimal for
certain systems, we develop a general method to construct irregular models tailored
to the geometry of macromolecules. We also compare charge optimization
based on both the electric field and electrostatic potential refinement. Results indicate
that irregular surfaces can lead to a more accurate approximation (lower residuals),
and the refinement in terms of the electric field is more robust. We also show
that surface smoothing for irregular models is important, that the charge optimization
(by the TNPACK minimizer) is efficient and does not depend on the initial
assigned values, and that the residual is acceptable when the distance to the model
surface is close to, or larger than, the Debye length. We illustrate applications of
DiSCO to two complex macromolecular problems studied by Brownian dynamics
over milliseconds: chromatin folding and *Hin*-mediated and *Fis*-enhanced DNA
inversion. DiSCO is generally applicable to other interesting macromolecular systems
for which mesoscale models are appropriate, to yield a resolution between
the all-atom representative and the polymer level.

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