Regime shifts driven by dynamic correlations in gene expression noise.

Gene expression is a noisy process that leads to regime shifts between alternative steady states among individual living cells, inducing phenotypic variability. The effects of white noise on the regime shift in bistable systems have been well characterized, however little is known about such effects of colored noise (noise with nonzero correlation time). Here, we show that noise correlation time, by considering a genetic circuit of autoactivation, can have a significant effect on the regime shift between distinct phenotypic states in gene expression. We demonstrate this theoretically, using stochastic potential, stationary probability density function, and first-passage time based on the Fokker-Planck description, where the Ornstein-Uhlenbeck process is used to model colored noise. We find that an increase in noise correlation time in the degradation rate can induce a regime shift from a low to a high protein concentration state and enhance the bistable regime, while an increase in noise correlation time in the basal rate retains the bimodal distribution. We then show how cross-correlated colored noises in basal and degradation rates can induce regime shifts from a low to a high protein concentration state, but reduce the bistable regime. We also validate these results through direct numerical simulations of the stochastic differential equation. In gene expression understanding the causes of regime shift to a harmful phenotype could improve early therapeutic intervention in complex human diseases.