title: Cell population heterogeneity and evolution towards drug resistance in cancer: Biological and mathematical assessment, theoretical treatment optimisation.
abstract: Drug-induced drug resistance in cancer has been attributed to diverse biological mechanisms at the individual cell or cell population scale, relying on stochastically or epigenetically varying expression of phenotypes at the single cell level, and on the adaptability of tumours at the cell population level.
  
  
  
  We focus on intra-tumour heterogeneity, namely between-cell variability within cancer cell populations, to account for drug resistance. To shed light on such heterogeneity, we review evolutionary mechanisms that encompass the great evolution that has designed multicellular organisms, as well as smaller windows of evolution on the time scale of human disease. We also present mathematical models used to predict drug resistance in cancer and optimal control methods that can circumvent it in combined therapeutic strategies.
  
  
  
  Plasticity in cancer cells, i.e., partial reversal to a stem-like status in individual cells and resulting adaptability of cancer cell populations, may be viewed as backward evolution making cancer cell populations resistant to drug insult. This reversible plasticity is captured by mathematical models that incorporate between-cell heterogeneity through continuous phenotypic variables. Such models have the benefit of being compatible with optimal control methods for the design of optimised therapeutic protocols involving combinations of cytotoxic and cytostatic treatments with epigenetic drugs and immunotherapies.
  
  
  
  Gathering knowledge from cancer and evolutionary biology with physiologically based mathematical models of cell population dynamics should provide oncologists with a rationale to design optimised therapeutic strategies to circumvent drug resistance, that still remains a major pitfall of cancer therapeutics. This article is part of a Special Issue entitled "System Genetics" Guest Editor: Dr. Yudong Cai and Dr. Tao Huang.
authors.affiliation: School of Biotechnology and Biomolecular Sciences, University of New South Wales, Sydney, Australia.
authors.forename: Rebecca H
authors.initials: RH
authors.lastname: Chisholm
authors.affiliation: School of Mathematics and Statistics, University of St Andrews, North Haugh, KY16 9SS, St Andrews, Scotland, United Kingdom. Electronic address: http://www.tommasolorenzi.com.
authors.forename: Tommaso
authors.initials: T
authors.lastname: Lorenzi
authors.affiliation: INRIA Paris, MAMBA team, 2, rue Simone Iff, CS 42112, 75589 Paris Cedex 12, France; Sorbonne Universités, UPMC Univ. Paris 6, UMR 7598, Laboratoire Jacques-Louis Lions, Boîte courrier 187, 4 Place Jussieu, 75252 Paris Cedex 05, France. Electronic address: jean.clairambault@inria.fr.
authors.forename: Jean
authors.initials: J
authors.lastname: Clairambault
mesh_terms: D019008:Drug Resistance, Neoplasm / Q000187:drug effects*; D006801:Humans; D007167:Immunotherapy / Q000379:methods; D008954:Models, Biological; D008962:Models, Theoretical; D009369:Neoplasms / Q000188:drug therapy* / Q000473:pathology*; D010641:Phenotype
keywords: Cancer cell populations; Cancer therapeutics; Drug resistance; Evolution; Heterogeneity; Optimal control