Mathematical modeling and dynamic analysis for cancer resistance incorporating persister cells

Drug resistance is a key impediment to cancer treatment, however, the resistance mechanism remains controversial. Experiment evidence indicated that persister cells, a subpopulation in a transient pseudo-dormant state, are posited to play a potential role in the emergence of resistance. In this study, we propose a novel mathematical model for describing the interactions among sensitive, persister, and resistant cells to qualitatively and quantitatively analyze how persister cells affect cancer evolution and unravel the underlying resistance mechanisms. The proposed model is validated by theoretical analysis and fitting of actual human CT scan and mice data. Theoretical analysis demonstrates the existence and stability of the multiple steady states, as well as the global asymptotical stability of a unique steady state. Furthermore, bifurcation analysis reveals that the key factors, including the apoptotic rate of sensitive cells and the transformation rate between sensitive and persister cells, induce bistable phenomenon and are characterized by double saddle–node and transcritical bifurcations. The bistable region indicates that persister cells under high stable steady state as a reservoir could promote the emergence of resistant cells conferring a proliferative advantage and conversely when they are in lower stable steady state, the source of resistant cells and resistance process will be controlled. Therefore, the first transcritical bifurcation point can be viewed as an early indicator to detect critical transitions from low resistance to high resistance. Together, the proposed model and quantitative results would provide new insights for searching for strategies in modulating and decreasing the risk of drug resistance.