title: 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 the 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.
authors.affiliation: School of Mathematics and Statistics, Central South University, Changsha 410083, PR China.
authors.forename: Yuanling
authors.initials: Y
authors.lastname: Niu
authors.affiliation: Department of Applied Mathematics, University of Washington, Seattle, WA 98195, USA.
authors.forename: Yue
authors.initials: Y
authors.lastname: Wang
authors.affiliation: School of Mathematical Sciences, Xiamen University, Xiamen 361005, PR China. Electronic address: zhouda@xmu.edu.cn.
authors.forename: Da
authors.initials: D
authors.lastname: Zhou
mesh_terms: D000066670:Cell Plasticity / Q000502:physiology; D006801:Humans; D008390:Markov Chains; D008954:Models, Biological; D014411:Neoplastic Stem Cells / Q000473:pathology*; D010641:Phenotype; D013269:Stochastic Processes
keywords: Cancer stem cell; Multi-phenotype branching process; Phenotypic plasticity; Stochastic simulation