On the analysis of noise in gene regulatory networks

Life processes in single cells and at the molecular level are inherently stochastic. Quantifying the noise is, however, far from trivial, as a major contribution comes from intrinsic fluctuations, arising from the randomness in the times between discrete jumps. It is discussed in the paper how an operator theoretic interpretation can be relevant for analyzing the intrinsic stochasticity in jump processes described by master equations. Such interpretation naturally exists in linear noise approximations, but it also provides an exact description of the jump process when the transition rates are linear. As an important example, it is shown in the paper how by addressing the proximity of the underlying dynamics in an appropriate topology, a sequence of coupled birth death processes, which can be relevant in gene expression, tends to a pure delay, thus implying important limitations in noise suppression capabilities. We finally consider the effects of noise in the case of nonlinear macroscopic models leading to bistabilities. It is discussed that bistability in the deterministic mass action kinetics and bimodality in the steady state solution of the master equation, neither always imply one another, nor do they necessarily lead to efficient switching behaviours: the underlying dynamics need to be taken into account in a correct context.