First passage times as a measure of hysteresis in stochastic gene regulatory circuits

In the context of phenotype switching and cell fate determination, numerousexperimental studies report hysteresis, despite the fact that the (forward) Chemical Master Equation governing the inherently stochastic underlying gene regulatory networks has a unique steady state (precluding memory effects and hysteresis). In previous works, we demonstrate thathysteresis is a transient phenomenon in systems far from the thermodynamic limit, using the convergence rates of the partial integro-differential equation associated to the forward master equation governing the stochastic process. Here, we make use of the backward master equationto quantify hysteresis and irreversibility based on First Passage Times..