Mathematical Approach to Differentiate Spontaneous and Induced Evolution to Drug Resistance During Cancer Treatment

Abstract

PurposeDrug resistance is a major impediment to the success of cancer treatment. Resistance is typically thought to arise from random genetic mutations, after which mutated cells expand via Darwinian selection. However, recent experimental evidence suggests that progression to drug resistance need not occur randomly, but instead may be induced by the treatment itself via either genetic changes or epigenetic alterations. This relatively novel notion of resistance complicates the already challenging task of designing effective treatment protocols.Materials and MethodsTo better understand resistance, we have developed a mathematical modeling framework that incorporates both spontaneous and drug-induced resistance.ResultsOur model demonstrates that the ability of a drug to induce resistance can result in qualitatively different responses to the same drug dose and delivery schedule. We have also proven that the induction parameter in our model is theoretically identifiable and propose an in vitro protocol that could be used to determine a treatment’s propensity to induce resistance.

Molecular Mechanisms Underlying Autophagy-Mediated Treatment Resistance in Cancer

“…The ability of cancers to adapt to and survive the effects of cancer therapies remains one of the greatest impediments in medical and clinical oncology. Treatment resistance directly translates to the ineffectiveness and eventual failures of cancer therapies [31,32,33,34,35,36]. Innate treatment resistance predates therapeutic intervention, whereas acquired treatment resistance is a refractory outcome of cancer therapy that occurs when subpopulations of cancer cells within tumors acquire mutations and adaptations that desensitize them to ongoing treatment [37,38,39,40,41].…”

Drug-Induced Resistance in Micrometastases: Analysis of Spatio-Temporal Cell Lineages

“…here, ν is the damping coefficient, F rep is the repulsive spring stiffness, and 2R is the spring resting length; M denotes the number of cells that overlap with X i . Upon division, both daughter cells inherit mothers' damage level and tolerance level, while the drug absorbed by the mother cell is split into half between both daughter cells (Schmidt and Wittrup, 2009;Greene et al, 2019).…”

“…Feizabadi (2017) used mathematical modeling to show that certain chemotherapy strategies are highly unsuccessful, and even damaging to the patient, under the assumption that the drug can induce resistance during the treatment period. Greene et al (2018Greene et al ( , 2019 developed mathematical approach to differentiate between spontaneous and induced resistance to drugs and proposed in vitro experiments that can determine whether treatment can induce resistance. The authors also designed optimized treatment protocols that can prolong the time before resistance develops.…”

Delicate Balances in Cancer Chemotherapy: Modeling Immune Recruitment and Emergence of Systemic Drug Resistance

“…Numerous cancer models have been proposed to account for the emergence of therapeutic resistance due to cancer cell heterogeneity. See, for example, the extensive references in Greene et al (68). However, to our knowledge, no previous work has systematically and theoretically modeled what we call "systemic drug resistance, " by which we mean resistance as an immune-mediated dynamical phenomenon.…”