Mutation frequencies in a birth-death branching process

TL;DR

This paper revisits the classic stochastic Luria-Delbruck model, providing new limit theorems and extending it to multiple mutation sites, with predictions aligning with cancer genomic data.

Contribution

It introduces new theoretical results for mutation times and clone sizes, and extends the model to multiple mutation sites with empirical validation.

Findings

Proved limit theorems for mutation times and clone sizes.

Extended the model to multiple mutation sites.

Predictions match cancer genomic data.

Abstract

First, we revisit the stochastic Luria-Delbr\"uck model: a classic two-type branching process which describes cell proliferation and mutation. We prove limit theorems and exact results for the mutation times, clone sizes, and number of mutants. Second, we extend the framework to consider mutations at multiple sites along the genome. The number of mutants in the two-type model characterises the mean site frequency spectrum in the multiple-site model. Our predictions are consistent with previously published cancer genomic data.