### GEORGE MASON
UNIVERSITY

DEPARTMENT OF MATHEMATICAL
SCIENCES

COLLOQUIUM

SEPTEMBER 26, 2014

**Speaker: **
Michael Mascagni, Florida State University

**Title: ***
Novel Stochastic Methods in Biochemical Electrostatics
*

**Abstract:**
Electrostatic forces and the electrostatic properties of molecules
in solution are among the most important issues in understanding
the structure and function of large biomolecules. The use of
implicit-solvent models, such as the Poisson-Boltzmann equation
(PBE), have been used with great success as a way of computationally
deriving electrostatics properties such molecules. We discuss
how to solve an elliptic system of partial differential equations
(PDEs) involving the Poisson and the PBEs using path-integral
based probabilistic, Feynman-Kac, representations. This leads
to a Monte Carlo method for the solution of this system which
is specified with a stochastic process, and a score function.
We use several techniques to simplify the Monte Carlo method
and the stochastic process used in the simulation, such as the
walk-on-spheres (WOS) algorithm, and an auxiliary sphere technique
to handle internal boundary conditions. We then specify some
optimizations using the error (bias) and variance to balance
the CPU time. We show that our approach is as accurate as widely
used deterministic codes, but has many desirable properties
that these methods do not. In addition, the currently optimized
codes consume comparable CPU times to the widely used deterministic
codes. Thus, we have an very clear example where a Monte Carlo
calculation of a low-dimensional PDE is as fast or faster than
deterministic techniques at similar accuracy levels.

**Time:** Friday, September 26, 2014, 3:30-4:20 p.m.

**Place:** Exploratory Hall, room 4106

**Refreshments** will be served at 3:00 p.m.

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491