# A general mathematical framework for understanding the behavior of heterogeneous stem cell regeneration

## TL;DR

This paper introduces a comprehensive mathematical framework that models stem cell regeneration dynamics considering heterogeneity and epigenetic state transitions, extending classical models to include stochastic inheritance and potential tumor development insights.

## Contribution

It develops a generalized model incorporating continuous epigenetic states and stochastic inheritance, advancing understanding of stem cell behavior and tissue dynamics beyond previous models.

## Key findings

- The model captures tissue development, degeneration, and abnormal growth processes.
- It provides a basis for studying gene mutation effects on tumor development.
- The framework generalizes classical G0 cell cycle models.

## Abstract

Stem cell heterogeneity is essential for the homeostasis in tissue development. This paper established a general formulation for understanding the dynamics of stem cell regeneration with cell heterogeneity and random transitions of epigenetic states. The model generalizes the classical G0 cell cycle model, and incorporates the epigenetic states of stem cells that are represented by a continuous multidimensional variable and the kinetic rates of cell behaviors, including proliferation, differentiation, and apoptosis, that are dependent on their epigenetic states. Moreover, the random transition of epigenetic states is represented by an inheritance probability that can be described as a conditional beta distribution. This model can be extended to investigate gene mutation-induced tumor development. The proposed formula is a generalized formula that helps us to understand various dynamic processes of stem cell regeneration, including tissue development, degeneration, and abnormal growth.