Integrating Biological and Mathematical Models to Explain and Overcome Drug Resistance in Cancer. Part 1: Biological Facts and Studies in Drug Resistance

Abstract

Successful, durable cancer treatment is limited by drug resistance. Cancer stem cells (CSC) comprise (typically) a rare tumor subpopulation that contributes both intrinsic drug resistance and tumor re-initiation after therapy. Emerging evidence suggests that drug resistance is more complex than this single-cell level might suggest, and is likely governed by dynamics encompassing the entire tumor population. Here, we discuss the complexity of drug resistance by focusing on efforts that interface biology (wet lab) with mathematical modeling and simulation (dry lab) to study and explain the role of CSC and other cancer cells in the context of the entire ecosystem. Starting from biological evidence, we review the current state of cancer research from the perspective of the single-cell level, “The cancer cell,” its intrinsic physiopathology and its response to drug exposure. We discuss insufficiencies of this level of observation, in particular, the unaccounted for resistance to targeted therapies, and show why it is necessary to consider the entirety of the cell population, which is the only way to capture the role of biological heterogeneity. Importantly, we review how mathematical models have been implemented to elucidate mechanisms of drug resistance, and efforts made to validate biological experiments. Finally, we present emerging biological models, and therapeutic strategies inspired by mathematics, with the goal of improving the clinical management of cancer. Over the past century, we have learned that cancer drug resistance is extraordinarily complex and requires an interdisciplinary scientific effort to unmask. The network of communication between and among cells within the diverse tumor heterogeneity drives acquired and intrinsic mechanisms of resistance. Harnessing biology and math to simulate, study, and explain the mechanisms of resistance, by considering the whole tumor population, is providing new clues to overcome it.