Influence of stochastic domain growth on pattern nucleation for diffusive systems with internal noise.

摘要: Numerous mathematical models exploring the emergence of complexity within developmental biology incorporate diffusion as dominant mechanism transport. However, self-organizing paradigms can exhibit biologically undesirable property extensive sensitivity, illustrated by behavior French-flag model in response to intrinsic noise and Turing’s when subjected fluctuations initial conditions. Domain growth is known be a stabilizing factor for latter, though interaction domain underexplored, even simplest biophysical settings. Previously, we developed analytical Fourier methods description that allowed us characterize effects deterministic on stochastically diffusing systems. In this paper extend our analysis encompass growing domains. This form used only link meso- macroscopic domains “box-splitting” microscopic scale has an ill-defined thermodynamic limit. The extension achieved allowing simulated particles undergo random walks discretized domain, while controlling length each compartment. Due dependence discretization, find cannot uniquely derived. We apply these two justified descriptions, where it shown that, under certain conditions, able support consistent inhomogeneous state far removed from equilibrium, without additional kinetics. Finally, logistically considered. Not does show deal with nonmonotonic descriptions stochastic growth, but also seen stationary produces different “on average.”