Abstract
In most instances of tumour development, genetic instability plays a role in allowing cancer cell populations to respond to selection barriers, such as physical constraints or immune responses, and rapidly adapt to an always changing environment. Modelling instability is a nontrivial task, since by definition evolving instability leads to changes in the underlying landscape. In this article, we explore mathematically a simple version of unstable tumour progression using the formalism of adaptive dynamics (AD) where selection and mutation are explicitly coupled. Using a set of basic fitness landscapes, the so‐called canonical equation for the evolution of genetic instability on a minimal scenario associated with a population of unstable cells is derived. We obtain explicit expressions for the evolution of mutation probabilities, and the implications of the model on further experimental studies and potential mutagenic therapies are discussed.
Highlights
Cancer can be understood as the failure of those regulatory mechanisms that guarantee the maintenance of tissue and organ homoeostasis
For a simple but sensible fitness landscape, a general canonical equation has been derived from the Moran process scenario
A first relevant result of our model arises from evaluating the canonical equation for unstable cells in a linear landscape, to be associated with a premalignant stage
Summary
Cancer can be understood as the failure of those regulatory mechanisms that guarantee the maintenance of tissue and organ homoeostasis. That cancer cells are unstable is fairly well illustrated by the observation of their karyotypes: in sharp contrast with healthy cells, cancer chromosomal arrangements reveal a wide degree of aneuploidy (Lengauer, Kinzler, & Vogelstein, 1998). Such high levels of mutational load deploy the potential to overcome selection barriers, as well as involve a rather uncommon process from multicellularity to reduced cellular complexity (Solé et al, 2014), giving place to a highly adaptive and heterogeneous population. Genetic instability acts as a driver as well as the search engine for disease progression. An important (and not always appreciated) consequence of instability is that, once unleashed, it can grow as the lack of proper repair can damage other components of the check-and-repair cellular network
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