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

TL;DR

This paper introduces a stochastic multi-phenotype branching model that unifies previous models of cancer cell phenotypic equilibrium and explains its emergence through path-wise convergence rooted in stochastic processes.

Contribution

It presents a novel stochastic model integrating cellular hierarchy and plasticity, unifying prior theories and providing deeper stochastic insights into phenotypic equilibrium.

Findings

Model unifies previous phenotypic equilibrium theories

Path-wise convergence explains emergence of equilibrium

Stochastic nature underpins average-level stability

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.