# Genetic composition of an exponentially growing cell population

## TL;DR

This paper analyzes a DNA evolution model in growing cell populations, revealing that most sites mutate finitely many times and independence across sites generally holds, with some rare sites showing correlated mutations, challenging the infinite sites assumption.

## Contribution

It introduces a model that relaxes the infinite sites assumption and provides insights into mutation independence and frequency in expanding cell populations.

## Key findings

- Most sites mutate finitely many times in large populations.
- Independence across sites generally holds except for rare highly mutated sites.
- The model's predictions are applied to estimate mutation rates in lung cancer.

## Abstract

We study a simple model of DNA evolution in a growing population of cells. Each cell contains a nucleotide sequence which randomly mutates at cell division. Cells divide according to a branching process. Following typical parameter values in bacteria and cancer cell populations, we take the mutation rate to zero and the final number of cells to infinity. We prove that almost every site (entry of the nucleotide sequence) is mutated in only a finite number of cells, and these numbers are independent across sites. However independence breaks down for the rare sites which are mutated in a positive fraction of the population. The model is free from the popular but disputed infinite sites assumption. Violations of the infinite sites assumption are widespread while their impact on mutation frequencies is negligible at the scale of population fractions. Some results are generalised to allow for cell death, selection, and site-specific mutation rates. For illustration we estimate mutation rates in a lung adenocarcinoma.