Abstract

Malignant brain tumors consist of a number of distinct subclonal populations. Each of these subpopulations may be characterized by its own behaviors and properties. These subpopulations arise from the constant genetic and epigenetic alteration of existing cells in the rapidly growing tumor. However, since each single-cell mutation only leads to a small number of offspring initially, very few newly arisen subpopulations survive more than a short time. The present work quantifies "emergence", i.e. the likelihood of an isolated subpopulation surviving for an extended period of time. Only competition between clones is considered; there are no cooperative effects included. The probability that a subpopulation emerges under these conditions is found to be a sigmoidal function of the degree of change in cell division rates. This function has a non-zero value for mutations which confer no advantage in growth rate, which represents the emergence of a distinct subpopulation with an advantage that has yet to be selected for, such as hypoxia tolerance or treatment resistance. A logarithmic dependence on the size of the mutated population is also observed. A significant probability of emergence is observed for subpopulations with any growth advantage that comprise even 0.1% of the proliferative cells in a tumor. The impact of even two clonal populations within a tumor is shown to be sufficient such that a prognosis based on the assumption of a monoclonal tumor can be markedly inaccurate.