### Math Biology Seminar Abstracts

Wednesday October 16, 2002

## An interacting spin flip model for one-dimensional proton conduction

Tom Chou

Department of Biomathematics, University of California at Los Angeles

Abstract: A discrete asymmetric exclusion process (ASEP) is developed to model
proton
conduction along one-dimensional water wires. Each lattice site represents a
water molecule that can be in only one of three states; protonated,
left-pointing,
and right-pointing. Only a right(left)-pointing water can accept a proton from
its
left(right). Results of asymptotic mean field analysis and Monte-Carlo
simulations for the three-species, open boundary exclusion model are presented
and compared. The mean field results for the steady-state proton current
suggest a number of regimes analogous to the low and maximal current phases
found in the single species ASEP [B. Derrida, Physics Reports, {\bf 301},
65-83,
(1998)]. We find that the mean field results are accurate (compared with
lattice
Monte-Carlo simulations) only in the certain regimes. Refinements and
extensions including more elaborate forces and pore defects are also discussed.

For more information contact J. Keener, 1-6089

E-mail:
keener@math.utah.edu