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Diseases, Population dynamics and ecological pattern formation, Dynamics of evolution, Growth and division,
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.
(Part of "Focus on the Physics of Cancer")
GENERAL SCIENTIFIC SUMMARY
Introduction and background. Cancer develops over decades of Darwinian evolution in cell populations. Tissues with rapid cell turnover, such as in the intestines, exhibit distinct spatial structure: cell populations are subdivided into proliferative units called crypts. Crypt-structured tissue is native to many pre-malignant conditions (e.g. ulcerative colitis or Barrett's esophagus) that may progress to cancer. Inside crypts, stem cells acquire mutations that may expand via crypt fission. Currently, models utilize cancer incidence and molecular information to estimate the waiting time for acquiring a certain number of necessary and sufficient (driver) mutations for developing cancer in pre-malignant tissues (neoplasms).
Main results. We show that modeling crypt-structured tissues as spatially-structured populations, rather than as frequently assumed well-mixed populations, significantly increases the waiting time to cancer. We provide analytical results for a characteristic interference length which determines whether mutant stem cell clones fixate sequentially in the population, (periodic selection) or interfere with another while expanding (clonal interference). We investigate the distribution of waiting times of driver mutations, distribution of clonal patch sizes, expectation for spatial versus genetic distance, distribution of the selective advantages of fixed driver mutations, and discuss how they depend on periodic selection and clonal interference.
Wider implications. Our results for the evolution of spatially structured neoplasms may be used for predicting the waiting time to cancer in pre-malignant conditions when more accurate experimental molecular information, paired with clinical outcomes, becomes available. Understanding spatial evolution in crypt-structured neoplasms could provide better diagnosis to help prevent cancers in pre-malignant conditions.
