Participating Faculty
Mark Schumaker

Associate Professor
Mathematics
Washington State University
Pullman, WA 99164-3113

Ph.D., 1987
University of Texas, Austin

Phone: 509-335-7273
Fax: 509-335-1188
Email: schumaker@wsu.edu

 

Research Interests:
Mathematical modleing of photosynthesis. Boundary conditions for diffusion equations that incorporate occupancey constraints. Framework models of highly constrained biomolecular systems.

Research Summary:
I am working with Dr. David Kramer (IBC) and an undergraduate, Chandana Somayaji, on a mathematical model for electron transport in cytochrome b6f, an enzyme involved in photosynthesis. In addition, I am developing boundary conditions for diffusion equations that incorporate the constraint that a binding site may only be occupied by a single diffuser at a given time. The motivation is to be able to study diffusion to a binding site by solving a partial differential equation, which may involve much less computation than a Brownian dynamics simulation. In collaboration with graduate students and colleagues, much of my research for the last 10 years has involved developing "framework models", which are stochastic models of highly constrained biomolecular systems (for example, permeation through the narrow ion channel gramicidin). Framework models are designed to incorporate information from molecular dynamics simulations over short times scales and use this to calculate quantities for comparison with experiments over much longer time scales.

Representative Publications:

Mark F. Schumaker, Régis Pomès and Benoit Roux, A Combined Molecular Dynamics and Diffusion Model of Single Proton Conduction Through Gramicidin, Biophysical Journal, 79, 2840-2857, (2000).

*Mark F. Schumaker, Régis Pomès and Benoit Roux, Framework Model for Simple Proton Conduction Through Gramicidin, Biophysical Journal, 80, 12-30, (2001).

Eric J. Mapes and Mark Schumaker, Mean First Passage Times Across a Potential Barrier in the Lumped State Approximation, Journal of Chemical Physics, 114, 76-83, (2001).

J. Gowen, J. Markham, S. Morrison, T. Cross, E.J. Mapes, M.F. Schumaker and D.D. Busath, Tuning Single Proton Conduction Through Gramicidin, Biophysical Journal, 83, 880-898, (2002).

Mark F. Schumaker, Boundary Conditions and Trajectories of Diffusion Processes, Journal of Chemical Physics, 117, 2469-2473, (2002).

Mark. F. Schumaker and David. S. Watkins, A Framework Model Based on the Smoluchowski Equation in Two Reaction Coordinates. Journal of Chemical Physics, 121, 6134-6144, (2004)

Eric J. Mapes and Mark F. Schumaker, Framework Models of Ion Permeation Through Membrane Channels and the Generalized King-Altman Method. Bulletin of Mathematical Biology (in press).