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. Author summary We present a spatial stochastic model to represent the growth of a tumor as a structure having cells of two phenotypes: one whose cells have division as their predominant transition, and another where cells are mostly migrating. The migratory phenotype results from a transformation of the proliferative. Our proposition is based on the assumption that a tumor grows initially within a limited region while its cells are capable of acquire nutrients. During that phase, the cancer cells start changing their phenotype because of stress in their microenvironment and exhaustion of nutrients that lead them to become more migratory and capable of generating metastasis. Our model enables us to recover the usual dynamics observed in tumor growth such as a logistic-like curve, called Gompertz model, widely observed, or the bi-phasic growth observed characterized by equilibrium phase interspersed between two growth regimes. Our approach also enable us to understand the internal spatial and temporal structure of the two sub-populations and can be useful to investigate the phenomena underpinning heterogeneous tumor growth, a feature that helps on the design of treatment strategies based on mitigating heterogeneity related drug resistance.