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

Abstract

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.

Stress-induced mutagenesis and complex adaptation

“…Several authors have suggested that the mutation rate must balance between adaptability and adaptedness: Kimura [6] found a mutation rate that balances between mutational and substitutional load; Johnson & Barton [80] found an optimal mutation rate that balances the generation of beneficial and deleterious mutations during adaptation; Leigh [81] found an optimal mutation rate that balances the generation of deleterious mutations and maintenance of standing variation in a fluctuating environment; Komarova & Wodarz [82] found an optimal rate of chromosome loss that balances the unmasking of recessive alleles and genetic load during carcinogenesis; Komarova et al [83] and Agur et al [84] found a time-dependent mutation rate strategy that optimizes carcinogenesis and adaptive immune response, respectively. By contrast, we find that SIM breaks, rather than balances, the trade-off between adaptability and adaptedness: it allows individuals to switch between rates optimized for stressful and benign conditions according to the circumstances.…”

Evolution of genetic instability in heterogeneous tumors

“…The simple initial model was then refined to include the possibility of the mutation rate being a function of time [29]. What is the optimal (again, from cancer’s prospective) temporal course of instability that leads to the fastest growing tumors?…”

“…All these patterns of instability are realistic; the time-dependent stable – to unstable – back to stable pattern is especially interesting, given biological evidence supporting it (see the Discussion section for more details). The ideas presented in [29] were further developed mathematically and given analytical rigor in [55, 47]. …”

“…In the approach of [30, 29, 47], the instability-induced mutation rate, p , was treated as a function of time, and the optimization procedure sought the function p ( t ) that maximized tumor growth. The colony of cells was considered homogeneous with respect to the time-dependent mutation rate, p ( t ), that is, all cells were assumed to have the same mutation rate.…”

“…It is rooted in the evolutionary nature of the process of tumorigenesis, and is especially prevalent in unstable tumors [50, 10]. In the present manuscript, we include genetic heterogeneity in the description on the tumor evolution, and investigate if the patterns of instability identified in [29] can still be discovered in this more complex and more realistic system.…”