Anticipating regime shifts in gene expression: The case of an autoactivating positive feedback loop

Abstract: Considerable evidence suggests that anticipating sudden shifts from one state to another in bistable dynamical systems is a challenging task, examples include ecosystems, financial markets, complex diseases, etc. In this paper, we investigate the effects of additive, multiplicative and cross correlated stochastic perturbations on determining regime shifts in a bistable gene regulatory sys- tem, which gives rise to two distinct states of low and high concentrations of protein. We obtain the stationary probability density and mean first passage time of the system. We show that increasing additive(multiplicative) noise intensity induces regime shift from a low(high) to a high(low) pro- tein concentration state. However, an increase in cross correlation intensity always induces regime shifts from high to low protein concentration state. For both bifurcation (often called tipping point) and noise induced (called stochastic switching) regime shifts, we further explore the robustness of recently developed critical slowing down based early warning signal (EWS) indicators (e.g., rising variance and lag-1 autocorrelation) on our simulated time series data. We identify that using EWS indicators, prediction of an impending bifurcation induced regime shift is relatively easier than that of a noise induced regime shift in the considered system. Moreover, the success of EWS indicators also strongly depends upon the nature of noise. Our results establish the key fact that finding more robust indicator to forewarn regime shifts for a broader class complex natural systems is still in its infancy and demands extensive research.