# A physical mechanism of heterogeneity in stem cell, cancer and cancer stem cell

## TL;DR

This paper presents a mathematical model explaining heterogeneity in stem cells, cancer, and cancer stem cells through genetic and epigenetic effects, revealing mechanisms behind cellular diversity and implications for therapy resistance.

## Contribution

It introduces a novel mathematical framework that captures how genetic and epigenetic dynamics generate heterogeneity in tumor and stem cell populations.

## Key findings

- Seven native states emerge in the adiabatic regime.
- Multiple metastable states arise in the non-adiabatic regime.
- Slow regulatory binding, mimicking epigenetics, leads to heterogeneity.

## Abstract

Heterogeneity is ubiquitous in stem cells (SC), cancer cells (CS), and cancer stem cells (CSC). SC and CSC heterogeneity is manifested as diverse sub-populations with self-renewing and unique regeneration capacity. Moreover, the CSC progeny possesses multiple plasticity and cancerous characteristics. Many studies have demonstrated that cancer heterogeneity is one of the greatest obstacle for therapy. This leads to the incomplete anti-cancer therapies and transitory efficacy. Furthermore, numerous micro-metastasis leads to the wide spread of the tumor cells across the body which is the beginning of metastasis. The epigenetic processes (DNA methylation or histone remodification etc.) can provide a source for certain heterogeneity. In this study, we develop a mathematical model to quantify the heterogeneity of SC, CSC and cancer taking both genetic and epigenetic effects into consideration. We uncovered the roles and physical mechanisms of heterogeneity from the three aspects (SC, CSC and cancer). In the adiabatic regime (relatively fast regulatory binding and effective coupling among genes), seven native states (SC, CSC, Cancer, Premalignant, Normal, Lesion and Hyperplasia) emerge. In non-adiabatic regime (relatively slow regulatory binding and effective weak coupling among genes), multiple meta-stable SC, CS, CSC and differentiated states emerged which can explain the origin of heterogeneity. In other words, the slow regulatory binding mimicking the epigenetics can give rise to heterogeneity. Elucidating the origin of heterogeneity and dynamical interrelationship between intra-tumoral cells has clear clinical significance in helping to understand the cellular basis of treatment response, therapeutic resistance, and tumor relapse.