A stochastic spatial model for heterogeneity in cancer growth

Establishing a quantitative understanding of tumor heterogeneity, a major feature arising from the evolutionary processes taking place within the tumor microenvironment is an important challenge for cancer biologists. Recently established experimental techniques enabled summarizing the variety of tumor cell phenotypes in proliferative or migratory. In the former, cells mostly proliferate and rarely migrate, while the opposite happens with cells having the latter phenotype, a go-and-grow description of heterogeneity. In this manuscript we present a discrete time Markov chain to simulate the spatial evolution of a tumor which heterogeneity is described by cells having those two phenotypes. The cell density curves have two qualitatively distinct temporal regimes, as they recover the Gompertz curve widely used for tumor growth description, and a bi-phasic growth which temporal shape resembles the tumor growth dynamics under influence of immunoediting. We also show how our representation of heterogeneity gives rise to variable spatial patterning even when the tumors have similar size and dynamics.