Temporal profile of gene transcription noise modulated by cross-talking signal transduction pathways.

Gene transcription is a central cellular process and is stochastic in nature. The stochasticity has been studied in real cells and in theory, but often for the transcription activated by a single signaling pathway at steady-state. As transcription of many genes is involved with multiple pathways, we investigate how the transcription efficiency and noise is modulated by cross-talking pathways. We model gene transcription as a renewal process for which the gene can be turned on by different pathways. We determine the transcription efficiency by solving a system of differential equations, and obtain the mathematical formula of the noise strength by the Laplace transform and standard techniques in renewal theory. Our numerical examples demonstrate that cross-talking pathways are capable of inducing more cells to transcribe than the steady-state level after a short time period of signal transduction, and creating exceedingly high stationary transcription noise strength. In contrast, it is shown that one signaling pathway alone is unable to do so. Very strikingly, it is observed that the noise strength varies gradually over most values of the system parameters, but changes abruptly over a narrow range in the neighborhoods of some critical parameter values.