Selective pressures for and against genetic instability in cancer: a time-dependent problem

Department of Mathematics, University of California, Irvine, CA 92697, USA.
Journal of The Royal Society Interface (Impact Factor: 3.92). 02/2008; 5(18):105-21. DOI: 10.1098/rsif.2007.1054
Source: PubMed


Genetic instability in cancer is a two-edge sword. It can both increase the rate of cancer progression (by increasing the probability of cancerous mutations) and decrease the rate of cancer growth (by imposing a large death toll on dividing cells). Two of the many selective pressures acting upon a tumour, the need for variability and the need to minimize deleterious mutations, affect the tumour's 'choice' of a stable or unstable 'strategy'. As cancer progresses, the balance of the two pressures will change. In this paper, we examine how the optimal strategy of cancerous cells is shaped by the changing selective pressures. We consider the two most common patterns in multistage carcinogenesis: the activation of an oncogene (a one-step process) and an inactivation of a tumour-suppressor gene (a two-step process). For these, we formulate an optimal control problem for the mutation rate in cancer cells. We then develop a method to find optimal time-dependent strategies. It turns out that for a wide range of parameters, the most successful strategy is to start with a high rate of mutations and then switch to stability. This agrees with the growing biological evidence that genetic instability, prevalent in early cancers, turns into stability later on in the progression. We also identify parameter regimes where it is advantageous to keep stable (or unstable) constantly throughout the growth.

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Available from: Alexander Sadovsky, Oct 05, 2015
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    • "This theory has been extensively used in economics and engineering (Kirk, 2004; Koo, 1977). Previous applications of optimal control theory in biology included an analysis of the response of the immune system to an antigen (Perelson et al., 1976), mutation rates in cancer (Komarova et al., 2008) and reproduction strategies of social insects (Macevicz and Oster, 1976). This latter problem, which has some similarities with the crypt developmental problem, considered the optimal choice that queen wasps dynamically make throughout a reproductive season between producing workers, which increase the nest's resources but do not reproduce, and reproductive nonworking progeny, with the aim of maximizing the reproductive progeny at the end of the season (Macevicz and Oster, 1976). "
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