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Electrodiffusion: A continuum modeling framework for
biomolecular systems with realistic spatiotemporal resolution

Dr. Benzhuo Lu

Howard Hughes Medical Institute, and

Department of Chemistry and Biochemistry
and Center for Theoretical Biological Physics

UC San Diego

# Abstract

**
A computational framework is presented for the continuum modeling of
cellular biomolecular diffusion influenced by electrostatic
driving forces. This framework is developed from
a combination of numerical methods,
geometric meshing and computer visualization tools.
In particular, a hybrid of (adaptive) finite element and
boundary element methods is adopted to solve
the Smoluchowski equation (SE), the Poisson equation (PE), and
the Poisson-Nernst-Planck equation (PNPE) in order to
describe electrodiffusion processes.
The finite element method is used because of its flexibility in modeling
irregular geometries and complex boundary conditions.
The boundary element method is used due to
the convenience of treating the singularities in the source charge
distribution and its accurate solution to electrostatic problems
on molecular boundaries.
Nonsteady-state diffusion can be studied using this
framework, with the electric field computed using the
densities of charged small molecules and mobile ions in the
solvent. A solution for mesh generation for biomolecular systems is
supplied,
which is an essential component for the finite element and
boundary element computations.
The partially coupled Smoluchowski equation and Poisson-Boltzmann
equation (PBE) are considered as special cases of the PNPE in numerical
algorithm,
and therefore can be solved in this framework as well.
The possible extensions of the physical model in this frame are also
discussed.
Some example computations are reported for:
reaction-diffusion rate coefficient, ion density distribution,
time-dependent diffusion process
of the neurotransmitter consumption.
**