# A mathematical model assuming frequency-dependent cost for analyzing the influence of cell competition on radiation effects

## TL;DR

This paper presents a mathematical model to study how stem cell competition affects radiation damage accumulation, especially under low dose-rate conditions.

## Contribution

The study introduces a frequency-dependent cost model to analyze how cell competition influences radiation damage in stem cells.

## Key findings

- Under low dose-rate irradiation, stem cell competition can either promote or suppress damage accumulation depending on the cell pool size.
- Spatial structure significantly alters the effect of competition on radiation-induced damage accumulation.
- Higher interaction costs between different cell types lead to qualitatively different outcomes compared to no spatial structure.

## Abstract

High dose-rate ionizing radiation exposure increases the risk of cancer; however, the health effects of low dose-rate exposure remain controversial. Stem cell competition entails stem cells with lower fitness being eliminated from the stem cell pool when interacting with neighboring stem cells with higher fitness. It is hypothesized that this phenomenon reduces radiation damage under very low dose-rate conditions rather than high dose-rate irradiation conditions. If cell-cell interactions exist, the frequency of cells in a population affects the fitness of cells. However, they have not been adequately considered in discussions of radiation damage accumulation. We developed a mathematical model to analyze the influence of radiation-induced stem cell competition on the accumulation of radiation damages. Two cell types were assumed: intact and damaged. An intact cell can be damaged by a hit of radiation track. Cell division and elimination follow the Moran process, wherein the probability of cell elimination depends on the frequency-dependent cost. Under low dose-rate irradiation conditions, the size of the cell pool can determine whether competition promotes or suppresses the accumulation of damaged cells, even when the cost parameters are the same. In addition, the presence or absence of spatial structure can qualitatively alter the effect of competition on damage accumulation. If cells had a higher cost when interacting with different cell types, the results were qualitatively different compared to scenarios with no spatial structure. Thus, considering the spatial structure is essential for an in-depth understanding of the effects of stem cell competition.