The Berry phase and the pump flux in stochastic chemical kineticsN. A. Sinitsyn1, 2 and I. Nemenman2
1 Center for Nonlinear Studies, Los Alamos National Laboratory - Los Alamos, NM 87545, USA
2 Computer, Computational and Statistical Sciences Division, Los Alamos National Laboratory - Los Alamos, NM 87545, USA
received 26 October 2006; accepted in final form 4 January 2007; published March 2007
published online 15 February 2007
We study a classical two-state stochastic system in a sea of substrates and products (absorbing states), which can be interpreted as a single Michaelis-Menten catalyzing enzyme or as a channel on a cell surface. We introduce a novel general method and use it to derive the expression for the full counting statistics of transitions among the absorbing states. For the evolution of the system under a periodic perturbation of the kinetic rates, the latter contains a term with a purely geometrical (the Berry phase) interpretation. This term gives rise to a pump current between the absorbing states, which is due entirely to the stochastic nature of the system. We calculate the first two cumulants of this current, and we argue that it is observable experimentally.
82.20.-w - Chemical kinetics and dynamics.
03.65.Vf - Phases: geometric; dynamic or topological.
05.10.Gg - Stochastic analysis methods (Fokker-Planck, Langevin, etc.).
© Europhysics Letters Association 2007