Optimal path to fluctuation-driven extinction of tumors with phenotypic switching in temporally varying environment

Phenotypic plasticity/switching, in contrast to irreversible genetic intratumor variation, allows cancer cells to engage adaptive responses to the changed tumor microenvironment in a reversible fashion and begins to emerge as the explanatory mechanisms for therapy resistance. We consider a simple stochastic model of reversible phenotypic switching between two phenotypic states, a growing yet sensitive state and a quiescent yet tolerant state, in response to a time-varying tumor microenvironmental cue. An environmental stress induces the switching to a quiescent state and the absence of stress reverses its state back to a growing state. We utilized the WKB theory of large deviations, i.e., the eikonal approximation to the master equation, to find the optimal path to fluctuation-induced tumor extinction. This path to tumor extinction is forbidden in a deterministic model, but a rare event with large fluctuations brings the system from its long-lived quasi-stationary state to extinction. We also presented the necessary conditions for the temporal modulation of the environmental stress that could reduce the mean time to extinction exponentially.