| Ամփոփում: | <p>Solid tumours have highly irregular vasculatures that are constantly re-modelled, giving rise to spatio-temporal heterogeneity in the level of nutrients, metabolites, and drugs. Such variability requires cells to adapt, and is hypothesised to select for more aggressive cancer phenotypes. Risk spreading through spontaneous phenotypic variations is an ecological concept which is used to explain how species may survive in temporally varying environments. It allows individuals within a species to diversify their phenotypes ensuring that at least some of them can survive in the face of sudden environmental change. In this thesis, we aim to investigate whether cancer cells may adopt this strategy when dealing with rapidly changing levels of nutrient due to temporally-varying blood flow. </p>
<p>Accordingly, we develop and analyse a series of mathematical models of increasing biological complexity in order to investigate, in a systematic way, the impact that temporal variations in the nutrient supply might have on cancer cell populations. First, we present a mathematical model consisting of a system of non-local partial differential equations modelling the evolutionary dynamics of two competing phenotypically-structured populations in the presence of periodically oscillating nutrient levels. The two populations undergo heritable, spontaneous phenotypic variations at different rates. The phenotypic state of each individual is represented by a continuous variable, and the phenotypic landscape of the populations evolves in time due to variations in the nutrient level. We then extend the model by modelling nutrient dynamics explicitly and evaluate the effects of cellular feedback on the environment. Moreover, we develop corresponding individual-based models and study the differences that arise between continuum and discrete approaches at low population sizes.</p>
<p>Exploiting the analytical tractability of our models, coupled with numerical simulations, we identify environmental regimes that select the population with higher rate of spontaneous phenotypic variation. In particular, we expect environmental conditions where cells experience periods of starvation followed by re-oxygenation to promote phenotypic heterogeneity, which is consistent with experimental observations. This allows us to predict how certain interventions, for example, the vascular normalisation strategy that aims at stabilising the blood flow within tumours, could reduce phenotypic heterogeneity and drive the tumour to a treatable phenotype. Furthermore, we apply our discrete model to study adaptive strategies during the metastatic colonisation of distant organs.</p>
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