Abstract
Cancer results from a sequence of genetic and epigenetic changes that lead to a variety of abnormal phenotypes including increased proliferation and survival of somatic cells and thus to a selective advantage of pre-cancerous cells. The notion of cancer progression as an evolutionary process has been attracting increasing interest in recent years. A great deal of effort has been made to better understand and predict the progression to cancer using mathematical models; these mostly consider the evolution of a well-mixed cell population, even though pre-cancerous cells often evolve in highly structured epithelial tissues. In this study, we propose a novel model of cancer progression that considers a spatially structured cell population where clones expand via adaptive waves. This model is used to assess two different paradigms of asexual evolution that have been suggested to delineate the process of cancer progression. The standard scenario of periodic selection assumes that driver mutations are accumulated strictly sequentially over time. However, when the mutation supply is sufficiently high, clones may arise simultaneously on distinct genetic backgrounds, and clonal adaptation waves interfere with each other. We find that in the presence of clonal interference, spatial structure increases the waiting time for cancer, leads to a patchwork structure of non-uniformly sized clones and decreases the survival probability of virtually neutral (passenger) mutations, and that genetic distance begins to increase over a characteristic length scale Lc. These characteristic features of clonal interference may help us to predict the onset of cancers with pronounced spatial structure and to interpret spatially sampled genetic data obtained from biopsies. Our estimates suggest that clonal interference likely occurs in the progression of colon cancer and possibly other cancers where spatial structure matters.
Highlights
Progression to cancer is a process of somatic evolution within the body
For large neoplasms clonal interference becomes relevant, and we observe in Fig. 5 that the waiting time for k hits is shorter for non-structured crypt populations than for spatially structured populations
Several studies have focused on the waiting time to cancer [5, 6, 37], which may be defined as the time until a critical number of hits are accumulated and initiate the growth of carcinoma
Summary
Progression to cancer is a process of somatic evolution within the body. The idea that cancer can be understood as an evolutionary process was already formulated by Nowell in 1976 [1]; still, relatively little attention has been directed on applying principles from population genetics to understand and control neoplastic progression until recently [2, 3, 4, 5, 6, 7]. Because somatic abnormalities have differing, heritable effects on the fitness of neoplastic cells, mutant clones may expand or decrease in size by the principles of Darwinian evolution, e.g. via natural selection and genetic drift (number fluctuations). New mutations survive genetic drift (stochastic number fluctuations) with a probability 2s for small selective advantages s This relation has been shown to hold for both non-structured [40, 41] and spatially structured populations [27, 42, 39, 43] under certain simplifying assumptions. To compare waiting times between spatially structured and non-structured populations, we have adjusted the algorithm to allow for simulations of an effectively well-mixed crypt population: instead of selecting the offspring (crypt) from the nearest neighbors of a crypt at site i, all neighbors are replaced with crypts chosen randomly from any crypt neoplasm. We quantify the spatial genetic (Hamming) distance as a function of spatial distance, as we explain further below
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