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Metastable States in a Model of Cancer Initiation

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The Statistical Physics of Fixation and Equilibration in Individual-Based Models

Part of the book series: Springer Theses ((Springer Theses))

Abstract

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 phenomenon of stochastic tunneling has been studied using a variety of computational and mathematical methods. However, the field still lacks a comprehensive analytical description since theoretical predictions of fixation times are available only for cases in which the second mutant is advantageous. Here, we study stochastic tunnelling in a Moran model. Analysing the deterministic dynamics of large populations we systematically identify the parameter regimes captured by existing approaches. Our analysis also reveals fitness landscapes and mutation rates for which finite populations are found in long-lived metastable states. These are landscapes in which the final mutant is not the most advantageous in the sequence, and resulting metastable states are a consequence of a mutation-selection balance. The escape from these states is driven by intrinsic noise, and their location affects the probability of tunnelling. Existing methods no longer apply. In these regimes it is the escape from the metastable states that is the key bottleneck. We used the so-called Wentzel–Kramers–Brillouin method to compute fixation times in these parameter regimes, successfully validated by stochastic simulations.

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Notes

  1. 1.

    The process of repeatedly accumulating disadvantageous mutations [39], named after Hermann Joseph Muller (1890–1967).

  2. 2.

    The minimum value of N for which our analysis is valid is dependent on the remaining model parameters, but comparisons with simulation results in the next section show it is accurate for \(N\gtrsim 100\).

  3. 3.

    After William Rowan Hamilton (1805–1865) and the previously introduced Carl Gustav Jacob Jacobi.

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Authors and Affiliations

  1. Institute for Integrative Biology, ETH Zürich, Zürich, Switzerland

    Peter Ashcroft

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  1. Peter Ashcroft
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Correspondence to Peter Ashcroft .

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Ashcroft, P. (2016). Metastable States in a Model of Cancer Initiation. In: The Statistical Physics of Fixation and Equilibration in Individual-Based Models. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-41213-9_5

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