Dedifferentiation stabilizes stem cell lineages: From CTMC to diffusion theory and thresholds

TL;DR

This paper models stem cell lineage dynamics under demographic noise, deriving a diffusion approximation that reveals critical thresholds and failure modes, and clarifies how dedifferentiation can restore homeostasis.

Contribution

It introduces a diffusion approximation from a detailed CTMC model, identifying structural failure modes and rescue mechanisms in stem cell hierarchies under fluctuations.

Findings

Subcritical regimes lead to stem cell extinction.

Supercritical regimes cause exponential divergence of moments.

Dedifferentiation flux can rescue lineage stability.

Abstract

We study stem-terminally differentiated (TD) lineages in small niches where demographic noise from discrete division and death events is non-negligible. Starting from a mechanistic five-channel, density-dependent CTMC (symmetric self-renewal, symmetric differentiation, asymmetric division, dedifferentiation, TD death), we derive its mean-field limit and a functional CLT, obtaining a chemical Langevin diffusion whose explicit state-dependent covariance exactly matches the CTMC's aggregated channel-wise infinitesimal covariances. Within this diffusion approximation we remove the dedifferentiation flux and obtain a sharp dichotomy: in subcritical regimes the stem coordinate becomes extinct asymptotically almost surely, whereas in supercritical regimes polynomial moments diverge exponentially. This identifies, at the diffusion level, a structural failure mode of strictly hierarchical lineages under demographic fluctuations and clarifies how a cyclic return flux can rescue homeostasis. For interpretation we also derive an exact totals ODE backbone from a damage-structured transport model and obtain two steady-state constraints (ratio and equalization laws) linking compartment ratios to turnover and balancing dedifferentiation against fate bias. Numerical experiments corroborate the $\Omega^{-1/2}$ fluctuation scaling, illustrate the pathology, and contrast theorem-regime global convergence with threshold (Allee-type) behaviour outside the theorem hypotheses.