Novel Stochastic Methods in Biochemical Electrostatics

Name:    Prof. Michael Mascagni                 
Address: Department of Computer Science and
         Department of Mathematics and
	 Department of Scientific Computing and
         Graduate Program in Molecular Biophysics	
         Florida State University
         Tallahassee, FL  32306-4530  USA
         AND
         Information Technology Laboratory
         Applied and Computational Mathematics Division
         100 Bureau Drive M/S 8910
         National Institute of Standards and Technology (NIST)
         Gaithersburg, MD  20899-8910  USA

Offices: 498 Dirac Science Library/207A Love Building (FSU) Building 225/Room B154 (NIST)
Phone:   +1.850.644.3290 (FSU) +1.301.975.2051 (NIST)
FAX:     +1.850.644.0058 (FSU) +1.301.975.2837 (NIST)
e-mail:  mascagni@fsu.edu (FSU) mascagni@nist.gov (NIST)

Title: Novel Stochastic Methods in Biochemical Electrostatics
Subtitle: Stochastic Methods for PDEs Can Beat Deterministic Methods

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.