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

  • Mathematical Models of Stem Cell Behavior (M Kohandel, Section Editor)
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Abstract

Purpose of Review

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.

Recent Findings

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.

Summary

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.

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Author information

Authors and Affiliations

  1. Department of Medicine, Harvard Medical School, Boston, MA, 02115, USA

    Aaron Goldman

  2. Harvard-MIT Division of Health Sciences and Technology, Cambridge, MA, 02139, USA

    Aaron Goldman

  3. Division of Engineering in Medicine, Department of Medicine, Brigham and Women’s Hospital, Boston, MA, 02115, USA

    Aaron Goldman

  4. Harvard Digestive Disease Center, Boston, MA, USA

    Aaron Goldman

  5. Integrative Immuno-Oncology Center, Mitra Biotech, Woburn, MA, 01801, USA

    Aaron Goldman

  6. Department of Applied Mathematics, University of Waterloo, Waterloo, ON, N2L 3G1, Canada

    Mohammad Kohandel

  7. Centre for Mathematical Medicine, Fields Institute for Research in Mathematical Sciences, Toronto, ON, M5T 3J1, Canada

    Mohammad Kohandel

  8. INRIA Paris Research Centre, MAMBA Team, F-75012, Paris, France

    Jean Clairambault

  9. Sorbonne Universités, UPMC University Paris 06, UMR 7598, Jacques-Louis Lions Lab, F-75005, Paris, France

    Jean Clairambault

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  1. Aaron Goldman
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  2. Mohammad Kohandel
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Correspondence to Jean Clairambault.

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Conflict of Interest

Aaron Goldman, Mohammad Kohandel, and Jean Clairambault declare that they have no conflict of interest.

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This article does not contain any studies with human or animal subjects performed by any of the authors.

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This article is part of the Topical Collection on Mathematical Models of Stem Cell Behavior

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Goldman, A., Kohandel, M. & Clairambault, J. Integrating Biological and Mathematical Models to Explain and Overcome Drug Resistance in Cancer. Part 1: Biological Facts and Studies in Drug Resistance. Curr Stem Cell Rep 3, 253–259 (2017). https://doi.org/10.1007/s40778-017-0097-1

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  • DOI: https://doi.org/10.1007/s40778-017-0097-1

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