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

Bull Math Biol. 2024 Jan 18;86(2):18. doi: 10.1007/s11538-023-01245-1.

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 by McFarland et al. (Proc Natl Acad Sci 111(42):15138-15143, 2014) 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.

Keywords: Cancer dynamics; Deleterious passenger mutations; Multitype branching process; Negative selection; Tug-of-War.

Publication types

  • Research Support, Non-U.S. Gov't
  • Research Support, N.I.H., Extramural

MeSH terms

  • Apoptosis
  • Cell Lineage
  • Markov Chains
  • Mathematical Concepts*
  • Models, Biological
  • Neoplasms* / genetics