Different costs of therapeutic resistance in cancer: Short- and long-term impact of population heterogeneity

Abstract

Therapeutic resistance continues to undercut long-term success of many promising cancer treatments. At times, development of therapeutic resistance can come at a fitness cost for the cancer cell population, which could potentially be leveraged to the patient’s advantage. A mathematical formulation of such a situation was proposed by Pressley et al. (2020), who discussed two scenarios, namely, when developing therapeutic resistance can come at a cost to proliferative capacity (such as when a drug targets a growth receptor), or to the total tumor carrying capacity (such as when a drug targets neovascularization). Here we expand the analysis of the two models and evaluate both short- and long-term dynamics of a population heterogeneous with respect to resistance. We analyze four initial distributions with respect to resistance at the time of treatment initiation: uniform, bell-shaped, exponential, and U-shaped. We show that final population composition is invariant to the initial distribution, with a single clone eventually dominating within the population; the value of the resistance parameter of the final clone depends on other system parameters but not on the initial distribution. Transitional behaviors, however, which may have more significant implications for immediate treatment decisions, depend critically on the initial distribution. Furthermore, we show that depending on the mechanism for the cost of resistance (i.e., proliferation vs carrying capacity), increase in natural cell death rate has opposite effects, with higher natural death rate selecting for less resistant cell clones in the long term for proliferation-dependent model, and selecting for more resistant cell clones for carrying capacity-dependent model, a prediction that may have implications for combination therapy with cytotoxic agents. We conclude with a discussion of strengths and limitations of using modeling for understanding treatment trajectory, as well as the promise of model-informed evolutionary steering for improved long-term therapeutic outcomes.