Transient hysteresis and inherent stochasticity in gene regulatory networks

Cell fate determination, the process through which cells commit to differentiated states is commonly mediated by gene regulatory motifs with mutually exclusive expression states. The classical deterministic picture for cell fate determination includes bistability and hysteresis, which enables the persistence of the acquired cellular state after withdrawal of the stimulus, ensuring a robust cellular response. However, the stochasticity inherent to gene expression dynamics is not compatible with hysteresis, since the stationary solution of the governing Chemical Master Equation does not depend on the initial conditions. In this work, we provide a quantitative description of a transient hysteresis phenomenon that reconciles experimental evidence of hysteretic behaviour in gene regulatory networks with their inherent stochasticity. Under sufficiently slow dynamics, the dependency of the non-stationary solutions on the initial state of the cells can lead to what we denote here as transient hysteresis. To quantify this phenomenon, we provide an estimate of the convergence rate to the equilibrium. We also introduce the equation of a natural landscape capturing the evolution of the system that, unlike traditional cell fate potential landscapes, is compatible with the notion of coexistence at the microscopic level.
Comment: 35 pages, 13 figures