Stochastic phenotype transition of a single cell in an intermediate region of gene-state switching

摘要

Multiple phenotypic states often arise in a single cell with differentgene-expression states that undergo transcription regulation with positivefeedback. Recent experiments have shown that at least in E. coli, the genestate switching can be neither extremely slow nor exceedingly rapid as manyprevious theoretical treatments assumed. Rather it is in the intermediateregion which is difficult to handle mathematically.Under this condition, from afull chemical-master-equation description we derive a model in which theprotein copy-number, for a given gene state, follow a deterministic mean-fielddescription while the protein synthesis rates fluctuate due to stochasticgene-state switching. The simplified kinetics yields a nonequilibrium landscapefunction, which, similar to the energy function for equilibrium fluctuation,provides the leading orders of fluctuations around each phenotypic state, aswell as the transition rates between the two phenotypic states. This rateformula is analogous to Kramers theory for chemical reactions. The resultingbehaviors are significantly different from the two limiting cases studiedpreviously.