The phenotypic equilibrium of cancer cells: From average-level stability to path-wise convergence

Abstract

The phenotypic equilibrium, i.e. heterogeneous population of cancer cells tending to a fixed equilibrium of phenotypic proportions, has received much attention in cancer biology very recently. In previous literature, some theoretical models were used to predict the experimental phenomena of the phenotypic equilibrium, which were often explained by different concepts of stabilities of the models. Here we present a stochastic multi-phenotype branching model by integrating conventional cellular hierarchy with phenotypic plasticity mechanisms of cancer cells. Based on our model, it is shown that: (i) our model can serve as a framework to unify the previous models for the phenotypic equilibrium, and then harmonizes the different kinds of average-level stabilities proposed in these models; and (ii) path-wise convergence of our model provides a deeper understanding to the phenotypic equilibrium from stochastic point of view. That is, the emergence of the phenotypic equilibrium is rooted in the stochastic nature of (almost) every sample path, the average-level stability just follows from it by averaging stochastic samples.

27 pages, 5 figures in Journal of Theoretical Biology, 2015

References in corpus (2)

• A multi-phenotypic cancer model with cell plasticity
• Do cancer cells undergo phenotypic switching? The case for imperfect cancer stem cell markers

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• Cell Population Growth Kinetics in the Presence of Stochastic Heterogeneity of Cell Phenotype
• A Bayesian statistical analysis of stochastic phenotypic plasticity model of cancer cells
• Stochastic stem cell models with mutation: A comparison of asymmetric and symmetric divisions