Near-criticality underlies the behavior of early tumor growth

The controlling factors that underlie the growth of tumors have often been hard to identify because of the presence in this system of a large number of intracellular biochemical parameters. Here, we propose a simplifying framework to identify the key physical parameters that govern the early growth of tumors. We model growth by means of branching processes where cells of different types can divide and differentiate. First, using this process that has only one controlling parameter, we study a one cell type model and compute the probability for tumor survival and the time of tumor extinction. Second, we show that when cell death and cell division are perfectly balanced, stochastic effects dominate the growth dynamics and the system exhibits a near-critical behavior that resembles a second-order phase transition. We show, in this near-critical regime, that the time interval before tumor extinction is power-law distributed. Finally, we apply this branching formalism to infer, from experimental growth data, the number of different cell types present in the observed tumor.