Abstract
Cell populations are often characterised by phenotypic heterogeneity in the form of two distinct subpopulations. We consider a model of tumour cells consisting of two subpopulations: non-cancer promoting (NCP) and cancer-promoting (CP). Under steady state conditions, the model has similarities with a well-known model of population genetics which exhibits a purely noise-induced transition from unimodality to bimodality at a critical value of the noise intensity . The noise is associated with the parameter λ representing the system-environment coupling. In the case of the tumour model, λ has a natural interpretation in terms of the tissue microenvironment which has considerable influence on the phenotypic composition of the tumour. Oncogenic transformations give rise to considerable fluctuations in the parameter. We compute the phase diagram in a stochastic setting, drawing analogies between bifurcations and phase transitions. In the region of bimodality, a transition from a state of balance to a state of dominance, in terms of the competing subpopulations, occurs at λ = 0. Away from this point, the NCP (CP) subpopulation becomes dominant as λ changes towards positive (negative) values. The variance of the steady state probability density function as well as two entropic measures provide characteristic signatures at the transition point.
Highlights
Cell populations are often characterised by phenotypic heterogeneity in the form of two distinct subpopulations
In the state space defined by the concentrations of the key dynamical variables, the two stable steady states are separated by an unstable steady state
Bimodality is purely noise-induced with the deterministic dynamics yielding single stable steady states in the full parameter regime, even in the presence of positive feedback loops
Summary
The generation of heterogeneity in a population is often a consequence of the underlying stochastic nonlinear dynamics. A frequently observed case is that of bimodality with two distinct subpopulations defining the heterogeneity. The minima of the valleys define the stable steady states, the attractors of the dynamics, and the top of the hill the unstable steady state. The stochastic dynamics smear out the steady states in the form of a steady state probability distribution with two distinct peaks—the case of bimodality. In this case, bistable deterministic dynamics are essential for the observation of bimodality in the stochastic case. Bimodality is purely noise-induced with the deterministic dynamics yielding single stable steady states in the full parameter regime, even in the presence of positive feedback loops.
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