Discretenessinduced stochastic steady state in reaction diffusion systems: selfconsistent analysis and stochastic simulations
Abstract
A selfconsistent equation to derive a discretenessinduced stochastic steady state is presented for reactiondiffusion systems. For this formalism, we use the socalled Kuramoto length, a typical distance over which a molecule diffuses in its lifetime, as was originally introduced to determine if local fluctuations influence globally the whole system. We show that this Kuramoto length is also relevant to determine whether the discreteness of molecules is significant or not. If the number of molecules of a certain species within the Kuramoto length is small and discrete, localization of some other chemicals is brought about, which can accelerate certain reactions. When this acceleration influences the concentration of the original molecule species, it is shown that a novel, stochastic steady state is induced that does not appear in the continuum limit. A theory to obtain and characterize this state is introduced, based on the selfconsistent equation for chemical concentrations. This stochastic steady state is confirmed by numerical simulations on a certain reaction model, which agrees well with the theoretical estimation. Formation and coexistence of domains with different stochastic states are also reported, which is maintained by the discreteness. Relevance of our result to intracellular reactions is briefly discussed.
 Publication:

Physica D Nonlinear Phenomena
 Pub Date:
 June 2005
 DOI:
 10.1016/j.physd.2004.12.008
 arXiv:
 arXiv:physics/0409027
 Bibcode:
 2005PhyD..205...87T
 Keywords:

 Physics  Chemical Physics;
 Physics  Biological Physics;
 Nonlinear Sciences  Pattern Formation and Solitons;
 Quantitative Biology  Subcellular Processes
 EPrint:
 12 pages, 7 figures, latex