Metastable States in a Model of Cancer Initiation
Tumours initiate when a population of proliferating cells accumulates a certain number and type of genetic and/or epigenetic alterations. The population dynamics of such sequential acquisition of mutations has been the topic of much investigation. The phe
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Metastable States in a Model of Cancer Initiation
5.1 Introduction We now turn our attention to a more applied subject, the accumulation of mutations and the initiation of cancer. With an ageing population, the prevalence of this genetic disease in the UK (and across developed countries) has sky-rocketed, with one in two people expected to be diagnosed with cancer in their lifetime [1]. This issue is close to the hearts of the British population. Cancer Research UK, the UK’s leading healthcare charity, received donations in excess of £500m in the last financial year (2014–2015), 80 % of which was used to fund research [2]. Although the majority of research is clinical or experimental, theoretical approaches greatly contribute to our understanding of this malady. The initiation and progression of cancer is a result of the accumulation of genetic alterations [3]. The dynamics of mutation acquisition is governed by evolutionary parameters such as the rate at which alterations arise, the selection effect that these alterations confer to cells, and the size of the population of cells that proliferate within a tissue. Therefore these processes are amenable to mathematical investigation, and much effort has been devoted to modelling these systems and analysing the rates at which mutations arise within pre-cancerous tissues [4–16]. Models of the initiation and progression of cancer vary dramatically in their complexity and tractability. At the most complex end of the scale, mathematical models consider explicit tissue structure and mechanics [17, 18], as well as resource competition and the creation of ‘public goods’ [19]. Simpler spatial models have been designed to replicate some tissue structures, such as the linear process for describing the accumulation of mutations in a colorectal crypt [20]. In terms of the dynamics of mutation acquisition, the effects of genetic instabilities [21] or the hierarchical organisation of cells within the population [22] have been considered. At the more tractable end of the scale of cancer models are the well-mixed, birth and death representations of mutation acquisition. For tumour progression, modelling a growing population is crucial as, by definition, cancerous phenotypes
© Springer International Publishing Switzerland 2016 P. Ashcroft, The Statistical Physics of Fixation and Equilibration in Individual-Based Models, Springer Theses, DOI 10.1007/978-3-319-41213-9_5
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5 Metastable States in a Model of Cancer Initiation
in the population grow in an uncontrolled manner [16]. For this reason branching processes have been used to describe the progression of cancer [9, 23]. During the initiation of cancer, however, the number of cells in pre-cancerous tissues fluctuates by only a small amount. One can then make the simplifying assumption that the population size is constant. This is the approach often used to describe the inactivation of tumour suppressor genes (TSG) [24, 25], which directly regulate the growth and differentiation pathways of cells [3]. This simple fixed-size m
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