dorsal/arxiv
View SchemaDedifferentiation stabilizes stem cell lineages: From CTMC to diffusion theory and thresholds
| Authors | Jiguang Yu, Louis Shuo Wang, Ye Liang |
|---|---|
| Categories | |
| ArXiv ID | 2601.09752vv1 |
| URL | https://arxiv.org/abs/2601.09752 |
| License | http://creativecommons.org/licenses/by/4.0/ |
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.
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"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\u0027s 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.",
"arxiv_id": "2601.09752",
"authors": [
"Jiguang Yu",
"Louis Shuo Wang",
"Ye Liang"
],
"categories": [
"physics.bio-ph",
"math.PR"
],
"license": "http://creativecommons.org/licenses/by/4.0/",
"title": "Dedifferentiation stabilizes stem cell lineages: From CTMC to diffusion theory and thresholds",
"url": "https://arxiv.org/abs/2601.09752",
"version": "v1"
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