Single-cell Mutational Burden Distributions in Birth–death Processes
Christo Morison, Dudley Stark, Weini Huang.
Abstract
Genetic mutations are footprints of cancer evolution and reveal critical dynamic parameters of tumour growth, which otherwise are hard to measure in vivo. The mutation accumulation in tumour cell populations has been described by various statistics, such as site frequency spectra (SFS), single-cell division distributions (DD) and mutational burden distributions (MBD). While DD and SFS have been intensively studied in phylogenetics especially after the development of whole genome sequencing technology of bulk samples, MBD has drawn attention more recently with the single-cell sequencing data.
Introduction
Somatic mutations are important for the evolution of biological systems with clonal reproduction, including the development from healthy tissues to cancer. While less is known about the somatic mutation rates in clonal species such as plants and corals, they have been studied extensively in human tissues. Healthy cells may accumulate in the order of 1 to 2 mutations per cell per division, which is directly observable in early development. The mutational rate of tumour cells is often thought to be higher, which can be caused for example by genomic instability.
Methods:
Besides the analysis described in the Results section, we employed a modified Gillespie algorithm to stochastically simulate our system and verify our expressions. The original Gillespie formulation is used to simulate (in a statistically exact manner) continuous-time reactions that have specified rates within one or multiple populations. Rather than independently drawing an exponentially-distributed random number for each reaction (here the reactions would be birth and death within the single population of cells), the Gillespie algorithm leverages the fact that the time until the first reaction occurs is also exponentially-distributed, with rate equal to the sum of the rates of all of the reactions.
Discussion
The distribution of genetic mutations in cell populations has been studied both in the cases of constant and growing populations. With the development of single-cell sequencing technologies, exploration of more precise information in single cells is sure to follow in the footsteps of population-level research. At the population level, both site frequency spectra (SFS) and overall tumour mutational burden (TMB) have been investigated analytically. Here we focus on the single-cell distribution of the latter (the single-cell mutational burden distribution, or MBD), and use the foundation of the SFS to better understand the MBD analytically.
Acknowledgments:
We thank Tibor Antal, Sabin Lessard, Nathaniel Mon Père and Alexander Stein for fruitful discussions and two reviewers for their suggestions that improved the text.
Citation: Morison C, Stark D, Huang W (2025) Single-cell mutational burden distributions in birth–death processes. PLoS Comput Biol 21(7): e1013241. https://doi.org/10.1371/journal.pcbi.1013241
Editor: Ivana Bozic, University of Washington, UNITED STATES OF AMERICA
Received: August 28, 2024; Accepted: June 14, 2025; Published: July 7, 2025.
Copyright: © 2025 Morison et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: Code can be found on GitHub at https://github.com/crmorison/mbds-in-bds.
Funding: This work was supported by the European Union (grant number 955708 to CM). CM is fully funded by European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie EvoGamesPlus. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing interests: The authors have declared that no competing interests exist.
