Mechanisms of How Random Input Controls Bursting Gene Expression

The process of gene expression is affected by many extracellular stimulus signals, and the stochasticity of these signals reshapes gene expression. To adapt the fluctuation of the extracellular environment, genes have many strategies for augmenting their survival probability, frequency modulation, and amplitude modulation. However, it is unclear how genes utilize the stochasticity of signals to regulate gene expression and which strategy will be chosen to maximize cellular function. Here, we analyze a simple mechanistic model to clarify the effect of extracellular random input on gene expression and burst kinetics at different timescales. We can see that in different contexts, extracellular noise has different effects on downstream gene expression, effects which include the following: (1) extracellular noise will make the ON-OFF-state dwell time drift, which will influence the burst frequency and burst size of downstream gene expression under different modulation paradigms; (2) comparing the burst parameter or gene expression products under different modulation paradigms, we can see that the amplitude signal is more sensitive in the case of extracellular noise input, whereas the signal in noiseless conditions is more sensitive when the random input is a fast process, which indicates that the amplitude signal is a superior and common signal in gene expression; and (3) extracellular random input will change the bimodality for gene expression, but its influence is different for gene expression products under different modulation paradigms. These qualitative results reveal that extracellular random input can prompt the gene to achieve its function quickly under different modulation paradigms.