Modelling the consequences of interactions between tumour cells

Abstract

Summary Classical models of tumorigenesis assume that the mutations which cause tumours to grow act in a cell-autonomous fashion. This is not necessarily true. Sometimes tumour cells may adopt genetic strategies that boost their own replication and which also influence other cells in the tumour, whether directly or as a side-effect. Tumour growth as a whole might be enhanced or retarded. We have used mathematical models to study two non-autonomous strategies that tumour cells may use. First, we have considered the production by tumour cells of an angiogenesis growth factor that benefits both the cell from which it originates and neighbouring cells. Second, we have analysed a situation in which tumour cells produce autocrine-only or paracrine-only growth factors to prevent programmed cell death. In the angiogenesis model, stable genetic polymorphisms are likely to occur between cells producing and not producing the growth factor. In the programmed cell death model, cells with autocrine growth factor production can spread throughout the tumour. Production of paracrine-only growth factor is never selected because it is 'altruistic' (that is of no benefit to the cell that makes the growth factor), despite being potentially beneficial to tumour growth as a whole. No polymorphisms can occur in the programmed cell death model. Production of angiogenesis and other growth factors in tumours may be under stable genetic, rather than epigenetic, control, with implications for therapies aimed at such targets. Many of the mutations observed in tumours may have non-autonomous effects.Keywords: tumorigenesis; cellular interactions; non-autonomous behaviour; polymorphism In classical models of tumorigenesis, mutations that promote tumour growth are usually assumed to have cell-autonomous modes of action Doll, 1954, 1957; Cairns, 1975;Fisher, 1958;Loeb, 1991; Tomlinson and Bodmer, 1995). This assumption may hold for many mutations, but it may not always be valid. We suggest that some mutations might cause tumour cells to adopt strategies that involve interacting with other cells in the tumour. These interactions may take the form of a cell directly influencing another cell, or they may be side-effects of apparently cell-autonomous action. We have constructed specific but simple mathematical models to study the outcome when tumour cells interact with one another.The models below consider a small number of biologically plausible situations and possible behaviours that tumour cells can adopt in these situations. An individual cell's genotype leads inevitably to the adoption of a particular strategy. Given genotype frequencies and selective parameters, it is possible to determine the benefits accruing to each behaviour and the frequencies with which different genotypes interact. Changes in genotype frequency can thus be calculated. At equilibrium, some genotypes will be lost and others fixed in the population, or there will be an internal point of equilibrium (polymorphism).All the models make a number of assumptions. Correspondence...

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