Journal
JOURNAL OF THE ROYAL SOCIETY INTERFACE
Volume 5, Issue 18, Pages 105-121Publisher
ROYAL SOC
DOI: 10.1098/rsif.2007.1054
Keywords
multistage carcinogenesis; chromosomal instability; somatic evolution; telomeres; optimization; bang-bang control; nonlinear control
Categories
Funding
- NCI NIH HHS [1R01 CA118545-01A1, R01 CA118545] Funding Source: Medline
- NIAID NIH HHS [R01 AI058153, 1R01 AI058153-01A2] Funding Source: Medline
- NIGMS NIH HHS [R01 GM075309, R01GM075309, R01GM067247, R01 GM067247, R01 GM067247-07] Funding Source: Medline
- NLM NIH HHS [T15 LM007443, 5 T15 LM007443] Funding Source: Medline
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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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