Boundary-Integral Methods for Fast Continuum-Model Biomolecule Electrostatics
Professor Jaydeep Bardhan
Department of Molecular Biophysics & Physiology,
Rush University
ABSTRACT
For many reasons, there exists an ongoing, healthy tension and
competition (usually friendly!) between research communities that
develop partial-differential equation (PDE) and boundary-integral
equation (BIE) models and implementations. In this talk, I will
describe two of my recent research efforts employing BIE to model the
electrostatic component of biomolecule solvation, emphasizing the
connections between PDE and BIE approaches in the hopes of encouraging
deeper and more substantive communication and collaboration towards
our shared goals: understanding experiments and the underlying
mathematics. The first project addresses an electrostatic model I
call BIBEE (boundary-integral based electrostatics estimation), which
relies on a rigorous operator approximation of the boundary-integral
formulation for the common mixed-dielectric Poisson PDE. BIBEE
represents the BIE formulation of an earlier approximation by the
Borgis group, and here BIE offers novel insights such as the fact that
the approximation gives a provable upper bound to the true answer. In
the second project, we explore the implications of nonlocal dielectric
response by the solvent. This more sophisticated solvation model and
its BIE formulation are relatively recent, and a combination of PDE
and BIE approaches will undoubtedly offer a much more efficient route
to identify and understand the limitations and strengths of this class
of solvation models, as well as its connections to other theories of
solvation.
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