A mathematical approach to differentiate spontaneous and induced evolution to drug resistance during cancer treatment

Abstract

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 drug 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 developing drug resistance. In an effort to better understand resistance to treatment, we have developed a mathematical modeling framework that incorporates both random 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. Not only could we prove that the induction parameter in our model is theoretically identifiable, we have also proposed a possible in vitro protocol which could potentially be used to determine a treatment's propensity to induce resistance. (which was not peer-reviewed) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity.The copyright holder for this preprint . http://dx.doi.org/10.1101/235150 doi: bioRxiv preprint first posted online Dec. 15, 2017; Tumor resistance to chemotherapy and targeted drugs is a major cause of treatment failure. Both molecular and microenvironmental factors have been implicated in the development of drug resistance [34]. As an example of molecular resistance, the upregulation of drug efflux transporters can prevent sufficiently high intracellular drug accumulation, limiting treatment efficacy [31]. Other molecular causes of drug resistance include modification of drug targets, enhanced DNA damage repair mechanisms, dysregulation of apoptotic pathways, and the presence of cancer stem cells [31,17,34,78,81]. The irregular tumor vasculature which results in inconsistent drug distribution and hypoxia is an example of a microenvironmental factor that impacts drug resistance [76]. Other characteristics of the tumor microenvironment that influence drug resistance include regions of acidity, immune cell infiltration and activation, and the tumor stroma [27,76,56,15,34,55].Research continues to shed light on the multitude of factors that contribute to cancer drug resistance. Mathematical modeling studies in particular have been used to explore both broad and detailed aspects of cancer drug resistance, as reviewed in [43,7,25]. The fundamental ques...

Turnover modulates the need for a cost of resistance in adaptive therapy

“…This is also the most common way in which the cost is modelled (e.g. [12,13,26]). Note that the factor of 2 in the drug response accounts for the fact that if a cell dies during mitosis not only the potential daughter but also the mother are lost.…”

Integrating multimodal data sets into a mathematical framework to describe and predict therapeutic resistance in cancer

“…To describe and predict the dynamics of cancer cells in response to treatment, we use a mechanistic model that describes sensitive and resistant cell subpopulations growing, dying, and transitioning from the sensitive, S, to resistant, R, state as a direct result of treatment (17). In this model (Fig 1A), sensitive and resistant cells grow via a logistic growth hypothesis at their own intrinsic growth rates (rS and rR) and a joint carrying capacity (K), which will either take the value of KN for the carrying capacity of the cells in the longitudinal treatment experiment or Kf for the carrying capacity of the cells in the scRNA-seq experiment.…”

“…These models describe cancer cells dynamically growing and responding to drug with differential growth rates and drug sensitivities. Knowledge of these model parameters have enabled the theoretical optimization of treatment protocols (16)(17)(18), and have been applied successfully to prolong tumor control in both mice (12) and patients (14,19).…”

Drug-induced resistance in micrometastases: analysis of spatio-temporal cell lineages

“…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 (18,38).…”

“…Feizabadi (17) 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 (18,19) developed mathematical approach to differentiate between spontaneous and induced resistance to drugs and proposed in vitro experiments that can determine weather treatment can induce resistance. The authors also designed optimized treatment protocols that can prolong the time before resistance develops.…”