Unraveling the stochastic transition mechanism between oscillation states by the landscape and the minimum action...

Cell fate transitions have been studied from various perspectives, such as the transition between stable states, or the transition between stable states and oscillation states. However, there is a lack of study on the stochastic transition between different oscillation states. Here, we aim to explore the stochastic transition mechanism for the switching between oscillations. By employing a landscape and flux theory for a simplified two-dimensional model, we quantify the stochastic dynamics and the global stability of the double oscillation system, and find that the system will escape the starting limit cycle at the position where the flux is large, and cross the barrier between oscillations at the position where the barrier is lower. We also calculate the transition path between limit cycle states based on the minimum action path (MAP) theory. So, the barrier height based on landscape topography and probability flux govern the stochastic transition process between limit cycles, which is further supported by the analysis of mean first passage time (MFPT). We provide a way to calculate the critical points where the switching behavior most likely occurs along a cycle. We validate these conclusions in a realistic biological system; the NF-κB gene regulatory system. The results for the potential landscape, flux and transition path further our understanding of the underlying mechanism of stochastic transitions between different oscillation states.