Resistance to chemotherapy is a major impediment to the successful treatment of cancer. Classically, resistance has been thought to arise primarily through random genetic mutations, after which mutated cells expand via Darwinian selection. However, recent experimental evidence suggests that the progression to resistance need not occur randomly, but instead may be induced by the therapeutic agent itself. This process of resistance induction can be a result of genetic changes, or can occur through epigenetic alterations that cause otherwise drug-sensitive cancer cells to undergo "phenotype switching". This relatively novel notion of resistance further complicates the already challenging task of designing treatment protocols that minimize the risk of evolving resistance.
In an effort to better understand treatment resistance, we developed in [1] a mathematical modeling framework that incorporates both spontaneous and drug-induced resistance. Our model demonstrates that the ability (or lack thereof) of a drug to induce resistance can result in qualitatively different responses to the same drug dose and delivery schedule. The importance of induced resistance in treatment response led us to ask if, in our model, one can determine the resistance induction rate of a drug for a given treatment protocol, and this led to a structural identifiability theorem. In [2], we worked out an optimal control problem related to the model in [1]. The control structure is precisely characterized as a concatenation of bang-bang and path-constrained arcs via the Pontryagin Maximum Principle and differential Lie algebraic techniques. A structural identifiability analysis is also presented, demonstrating that patient-specific parameters may be measured and thus utilized in the design of optimal therapies prior to the commencement of therapy.
In the recent paper [3], and for a slight modification of the model in [2] and were able to obtains excellent fits to time-resolved in-vitro experimental data. From observational data of total numbers of cells, the model unravels the relative proportions of sensitive and resistance subpopulations, and quantifies their dynamics as a function of drug dose. The predictions are then validated on data on drug doses which were not used when fitting parameters. The model is then used, in conjunction with optimal control techniques, in order to discover dosing strategies that might lead to better outcomes as quantified by lower total cell volume.
This is joint work with Jana Gevertz, Jim Green, Samantha Propsperi, Cynthia Sanchez Tapia, and Natacha Comandante-Lou
References:
[1] J.M. Greene, J.L. Gevertz, and E. D. Sontag. A mathematical approach to distinguish spontaneous from induced evolution of drug resistance during cancer treatment. JCO Clinical Cancer Informatics, 2019.
[2] J. M. Greene, C. Sanchez-Tapia, and E.D. Sontag. Mathematical details on a cancer resistance model. Frontiers in Bioengineering and Biotechnology, 2020.
[3] J.L. Gevertz, J.M. Greene, Samantha Propsperi, Natacha Comandante-Lou, and E. D. Sontag. Understanding therapeutic tolerance through a mathematical model of drug-induced resistance, npj Systems Biology and Applications, 2025.
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