Stochastic competitive release and adaptive chemotherapy

Abstract

We develop a finite-cell model of tumor natural selection dynamics to investigate the stochastic fluctuations associated with multiple rounds of adaptive chemotherapy. The adaptive cycles are designed to avoid chemo-resistance in the tumor by managing the ecological mechanism of competitive release of a resistant sub-population. Our model is based on a three-component evolutionary game played among healthy (H), sensitive (S), and resistant (R) populations of N cells, with a chemotherapy control parameter, C(t), used to dynamically impose selection pressure on the sensitive sub-population to slow tumor growth but manage competitive release of the resistant population. The adaptive chemo-schedule is designed based on the deterministic (N → ∞) adjusted replicator dynamical system, then implemented using the finite-cell stochastic frequency dependent Moran process model (N = 10K – 50K) to ascertain the size and variations of the stochastic fluctuations associated with the adaptive schedules. We quantify the stochastic fixation probability regions of the R and S populations in the HSR tri-linear phase plane as a function of the control parameter C ∈ [0, 1], showing that the size of the R region increases with increasing C. We then implement an adaptive time-dependent schedule C(t) for the stochastic model and quantify the variances (using principal component coordinates) associated with the evolutionary cycles for multiple rounds of adaptive therapy, showing they grow according to power-law scaling. The simplified low-dimensional model provides some insights on how well multiple rounds of adaptive therapies are likely to perform over a range of tumor sizes if the goal is to maintain a sustained balance among competing sub-populations of cells so as to avoid chemo-resistance via competitive release in a stochastic environment.