A Countable-Type Branching Process Model for the Tug-of-War Cancer Cell Dynamics

TL;DR

This paper models cancer cell dynamics using a countable-type branching process inspired by Tug-of-War, revealing how driver and passenger mutations influence cell type evolution and extinction probabilities.

Contribution

It introduces a novel Markov branching process model with countable types, capturing mutation-driven cell type transitions in cancer, extending previous Tug-of-War models.

Findings

Under driver dominance, cell types tend to increase indefinitely.

Passenger dominance leads to a stable type distribution.

Extinction probability remains below one for any initial cell type.

Abstract

We consider a time-continuous Markov branching process of proliferating cells with a countable collection of types. Among-type transitions are inspired by the Tug-of-War process introduced in McFarland et al. as a mathematical model for competition of advantageous driver mutations and deleterious passenger mutations in cancer cells. We introduce a version of the model in which a driver mutation pushes the type of the cell $L$-units up, while a passenger mutation pulls it $1$-unit down. The distribution of time to divisions depends on the type (fitness) of cell, which is an integer. The extinction probability given any initial cell type is strictly less than $1$, which allows us to investigate the transition between types (type transition) in an infinitely long cell lineage of cells. The analysis leads to the result that under driver dominance, the type transition process escapes to infinity, while under passenger dominance, it leads to a limit distribution. Implications in cancer cell dynamics and population genetics are discussed.