Integrating Biological and Mathematical Models to Explain and Overcome Drug Resistance in Cancer, Part 2: from Theoretical Biology to Mathematical Models

Purpose of Review: Despite the promise of targeted cancer therapy (i.e., drugs targeted towards specific signaling pathways supposed to be essential to the survival and proliferation of cancer cells), unexpected treatment failures in the clinic are common. Tumor cell heterogeneity, which can result from the plasticity of individual cancer cells and/or evolutionary dynamics, has revealed the importance to study cancer at the level of the entire cell population. Here, we explore mathematical models that describe tumor dynamics under pressure of anticancer drugs by integrating cancer cell population heterogeneity and evolutionary behavior. We further explore mathematical modeling as a theoretical tool to analyze and predict the behavior of cancer cell populations as a whole, and not only of individual cells, which may reveal new clues to therapy failure and ways to overcome it. Recent Findings: An evolutionary perspective that relies on the “atavistic theory of cancer” together with the so-called “cold genes”, and the involvement of “bet hedging” in tumors, has recently changed our vision of cell plasticity in cancer. These new perspectives provide a sound theoretical basis to the emergence of resistance in cancer cell populations and to its possible reversibility. Continuous mathematical models of the evolutionary dynamics of proliferative cell populations already exist, that take into account the heterogeneity of cancer cell populations, allowing to study the evolutionary potential of cancer cell populations and predict their behavior. Those models, in turn, can be used to probe population growth control by incorporating functions (in the mathematical model) that represent the action of drugs on the mechanisms driving proliferation, and furthermore to suggest new therapeutic strategies in the clinic of cancers. Summary: In this second part of our review, that can be taken independently of Part I, we focus on the level of cell populations, the only one amenable to completely take into account phenotype plasticity in its observable consequences on the evolution of proliferative diseases, and on heterogeneity, that makes sense only in the context of cell populations, together with the fundamental evolutionary potential of cancer cell populations (and not only of single cancer cells). These are modern views that come from the transposition from ecology of species to the biology of cancer (for further reading on evolution and cancer, the reader is referred to the recent comprehensive book on the subject Ujvari et al. 2017). Finally, we present a brief review of mathematical models, with their features and their use in cell population studies, to account for phenomena found in cancer, focusing on drug resistance. We contend that a good understanding of what mathematical models can do to tackle the question of drug resistance in cancer can shed light on the mechanisms of resistance and means to control them and help design principles for biological experiments to be performed at the lab and therapeutical strategies to be applied in the clinic of cancers. © 2017, Springer International Publishing AG.