Resisting Resistance

Ivana Bozic; Martin A. Nowak

doi:10.1146/annurev-cancerbio-042716-094839

Annual Review of Cancer Biology

Volume 1, 2017

Review Article

Free

Resisting Resistance

Ivana Bozic^1,2,3, and Martin A. Nowak^1,2,4
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Affiliations: ¹Program for Evolutionary Dynamics and ²Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138; email: [email protected] ³Department of Applied Mathematics, University of Washington, Seattle, Washington 98195; email: [email protected] ⁴Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, Massachusetts 02138
Vol. 1:203-221 (Volume publication date March 2017) https://doi.org/10.1146/annurev-cancerbio-042716-094839
First published as a Review in Advance on September 28, 2016
© Annual Reviews

Abstract

Targeted therapies, immunotherapies, and improved chemotherapies are being developed to reduce the suffering and mortality that come from human cancer. Although these approaches, and in particular combinations of them, are expected to succeed eventually to a large degree, they all suffer one obstacle: Populations of replicating cells move away—typically in a high-dimensional space—from any opposing selection pressure they encounter. They evolve resistance. It is possible, however, to develop a precise mathematical understanding of the problem and to design treatment strategies that prevent resistance if possible or manage resistance otherwise. In this article, we present the fundamental equations that characterize the evolution of resistance. We provide formulas for the probability that resistant cells exist at the start of therapy, for the average number and sizes of resistant clones, and for the probability of successful combination treatment. We also demonstrate that developing new therapies that only maximize the killing rate of cancer cells may not be optimal, and that instead the parameters determining the fraction of resistant cells and their growth rate have a larger effect on the long-term control of cancer. These mathematical tools inform the search process for optimal therapies that aim to cure cancer.

Keyword(s): cancer treatment, combination therapy, evolution, evolutionary dynamics, mathematical biology, targeted therapy

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2017-03-06

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