Spatial stochastic models of cancer: Fitness, migration, invasion

Cancer progression is driven by genetic and epigenetic events giving rise to heterogeneity of cellphenotypes, and by selection forces that shape the changingcomposition of tumors. The selection forces are dynamic and depend onmany factors. The cells favored by selection are said to be more``fit'' than others. They tend to leave more viable offspring andspread through the population. What cellular characteristics makecertain cells more fit than others? What combinations of the mutantcharacteristics and ``background'' characteristics make the mutantcells win the evolutionary competition? In this review we concentrateon two phenotypic characteristics of cells: their reproductivepotential and their motility. We show that migration has a directpositive impact on the ability of a single mutant cell to invade apre-existing colony. Thus, a decrease in the reproductive potentialcan be compensated by an increase in cell migration. We furtherdemonstrate that the neutral ridges (the set of all types with theinvasion probability equal to that of the host cells) remain invariantunder the increase of system size (for large system sizes), thusmaking the invasion probability a universal characteristic of thecells' selection status. We list very general conditions underwhich the optimal phenotype is just one single strategy (thus leadingto a nearly-homogeneous type invading the colony), or a large set ofstrategies that differ by their reproductive potentials and migrationcharacteristics, but have a nearly-equal fitness. In the latter casethe evolutionary competition will result in a highly heterogeneouspopulation.