A waiting time problem arising from the study of multi-stage carcinogenesis

TL;DR

This paper investigates the waiting time until a population accumulates a sequence of mutations, with implications for understanding the onset of cancers related to genetic mutations.

Contribution

It introduces models for the time until multiple mutations occur in a population, extending to larger mutation sequences relevant for various cancers.

Findings

Derived formulas for waiting times for multiple mutations

Application to cancer onset scenarios

Framework for future genetic mutation studies

Abstract

We consider the population genetics problem: how long does it take before some member of the population has $m$ specified mutations? The case $m=2$ is relevant to onset of cancer due to the inactivation of both copies of a tumor suppressor gene. Models for larger $m$ are needed for colon cancer and other diseases where a sequence of mutations leads to cells with uncontrolled growth.