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The Poisson-Boltzmann theory of continuum electrostatics with application to variational solvation of molecules

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Professor Bo Li

Department of Mathematics and Center for Theoretical Biological Physics

UC San Diego

## Abstract

Electrostatic interactions are crucial in determining biomoleular
structures, dynamics, and functions. The Poisson-Boltzmann (PB)
theory of continuum electrostatics has been widely used to describe
such interactions. In this talk, I will begin with a review of the PB
theory, in particular, the derivation of the PB equation by a
variational approach. I will then present two classes of new results
related to the PB theory. The first is on the calculation of effective
electrostatic surface forces which is defined as negative the
variation of the electrostatic free energy with respect to the
location change of the dielectric boundary. This force is exactly
the polar part of the normal velocity in the level-set variational
implicit solvent model of biomolecular structures. The second is
on the size-modified PB theory for multiple ionic species with different
ionic sizes. Although explicit, generalized Boltzmann distributions
can be hardly found, it is shown that a generalized PB equation is
still available.