Nonequilibrium population dynamics of phenotype conversion of cancer cells

Tumorigenesis is a dynamic biological process that involves distinct cancer cell subpopulations proliferating at different rates and interconverting between them. In this paper we proposed a mathematical framework of population dynamics that considers both distinctive growth rates and intercellular transitions between cancer cell populations. Our mathematical framework showed that both growth and transition influence the ratio of cancer cell subpopulations but the latter is more significant. We derived the condition that different cancer cell types can maintain distinctive subpopulations and we also explain why there always exists a stable fixed ratio after cell sorting based on putative surface markers. The cell fraction ratio can be shifted by changing either the growth rates of the subpopulations (Darwinism selection) or by environment-instructed transitions (Lamarckism induction). This insight can help us to understand the dynamics of the heterogeneity of cancer cells and lead us to new strategies to overcome cancer drug resistance.