title: Dynamics of a stochastic spatially extended system predicted by comparing deterministic and stochastic attractors of the corresponding birth-death process.
abstract: Living cells may be considered as biochemical reactors of multiple steady states. Transitions between these states are enabled by noise, or, in spatially extended systems, may occur due to the traveling wave propagation. We analyze a one-dimensional bistable stochastic birth-death process by means of potential and temperature fields. The potential is defined by the deterministic limit of the process, while the temperature field is governed by noise. The stable steady state in which the potential has its global minimum defines the global deterministic attractor. For the stochastic system, in the low noise limit, the stationary probability distribution becomes unimodal, concentrated in one of two stable steady states, defined in this study as the global stochastic attractor. Interestingly, these two attractors may be located in different steady states. This observation suggests that the asymptotic behavior of spatially extended stochastic systems depends on the substrate diffusivity and size of the reactor. We confirmed this hypothesis within kinetic Monte Carlo simulations of a bistable reaction- diffusion model on the hexagonal lattice. In particular, we found that although the kinase-phosphatase system remains inactive in a small domain, the activatory traveling wave may propagate when a larger domain is considered.
authors.affiliation: Institute of Fundamental Technological Research, Warsaw 02-106, Poland.
authors.forename: Pawel J
authors.initials: PJ
authors.lastname: Zuk
authors.forename: Marek
authors.initials: M
authors.lastname: Kochańczyk
authors.forename: Joanna
authors.initials: J
authors.lastname: Jaruszewicz
authors.forename: Witold
authors.initials: W
authors.lastname: Bednorz
authors.forename: Tomasz
authors.initials: T
authors.lastname: Lipniacki
mesh_terms: D004789:Enzyme Activation; D008390:Markov Chains; D008954:Models, Biological; D009010:Monte Carlo Method; D010744:Phosphoric Monoester Hydrolases / Q000378:metabolism*; D010770:Phosphotransferases / Q000378:metabolism*; D013269:Stochastic Processes; D013696:Temperature; D013816:Thermodynamics
chemical_list: D010770:Phosphotransferases; D010744:Phosphoric Monoester Hydrolases