title: 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, and complex diseases. In this paper, we investigate the effects of additive, multiplicative, and cross-correlated stochastic perturbations on determining the regime shifts in a bistable gene regulatory system, 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 the additive (multiplicative) noise intensity induces a regime shift from a low (high) to a high (low) protein concentration state. However, an increase in the cross-correlation intensity always induces regime shifts from a high to a low protein concentration state. For both bifurcation-induced (often called the tipping point) and noise-induced (called stochastic switching) regime shifts, we further explore the robustness of recently developed critical-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 the noise.
authors.affiliation: Department of Mathematics, Indian Institute of Technology Ropar, Punjab 140 001, India.
authors.forename: Yogita
authors.initials: Y
authors.lastname: Sharma
authors.affiliation: Department of Mathematics, Indian Institute of Technology Ropar, Punjab 140 001, India.
authors.forename: Partha Sharathi
authors.initials: PS
authors.lastname: Dutta
authors.affiliation: Department of Mathematics, Indian Institute of Technology Ropar, Punjab 140 001, India.
authors.forename: A K
authors.initials: AK
authors.lastname: Gupta
mesh_terms: D025461:Feedback, Physiological; D005786:Gene Expression Regulation; D008957:Models, Genetic; D011336:Probability; D013269:Stochastic Processes; D015533:Transcriptional Activation