ArticleProceedings. Mathematical, physical, and engineering sciences2015
Closed-form stochastic solutions for non-equilibrium dynamics and inheritance of cellular components over many cell divisions.
Article in Proceedings. Mathematical, physical, and engineering sciences, 2015. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 22 papers.
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Who cites it
22 citing papers in PubMed.
- Stochasticity in mammalian cell growth rates drives cell-to-cell variability independently of cell size and divisions.Proceedings of the National Academy of Sciences of the United States of America · 2026Article
- Cyclo-stationary distributions of mRNA and Protein counts for random cell division times.bioRxiv : the preprint server for biology · 2025Article
- Mitochondrial protein heterogeneity stems from the stochastic nature of co-translational protein targeting in cell senescence.Nature communications · 2024Article
- Evolution and maintenance of mtDNA gene content across eukaryotes.The Biochemical journal · 2024Review
- Feedback between stochastic gene networks and population dynamics enables cellular decision-making.Science advances · 2024Article
- Mitochondrial network structure controls cell-to-cell mtDNA variability generated by cell divisions.PLoS computational biology · 2023Article
- Concentration fluctuations in growing and dividing cells: Insights into the emergence of concentration homeostasis.PLoS computational biology · 2022Article
- Coordination of gene expression noise with cell size: analytical results for agent-based models of growing cell populations.Journal of the Royal Society, Interface · 2021Article
- Avoiding organelle mutational meltdown across eukaryotes with or without a germline bottleneck.PLoS biology · 2021Article
- Eco-evolutionary dynamics of nested Darwinian populations and the emergence of community-level heredity.eLife · 2020Article
- Effects of cell cycle variability on lineage and population measurements of messenger RNA abundance.Journal of the Royal Society, Interface · 2020Article
- Evolving mtDNA populations within cells.Biochemical Society transactions · 2019Review
- Inheritance and variability of kinetic gene expression parameters in microbial cells: modeling and inference from lineage tree data.Bioinformatics (Oxford, England) · 2019Article
- Energetic costs of cellular and therapeutic control of stochastic mitochondrial DNA populations.PLoS computational biology · 2019Article
- Matching Mitochondrial DNA Haplotypes for Circumventing Tissue-Specific Segregation Bias.iScience · 2019Article
- Intrinsic and extrinsic noise of gene expression in lineage trees.Scientific reports · 2019Article
- Varied Mechanisms and Models for the Varying Mitochondrial Bottleneck.Frontiers in cell and developmental biology · 2019Article
- Identification of a bet-hedging network motif generating noise in hormone concentrations and germination propensity inJournal of the Royal Society, Interface · 2018Article
- Mitochondrial Heterogeneity.Frontiers in genetics · 2018Review
- Making sense of snapshot data: ergodic principle for clonal cell populations.Journal of the Royal Society, Interface · 2017Article
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2 authors.
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Abstract
Stochastic dynamics govern many important processes in cellular biology, and an underlying theoretical approach describing these dynamics is desirable to address a wealth of questions in biology and medicine. Mathematical tools exist for treating several important examples of these stochastic processes, most notably gene expression and random partitioning at single-cell divisions or after a steady state has been reached. Comparatively little work exists exploring different and specific ways that repeated cell divisions can lead to stochastic inheritance of unequilibrated cellular populations. Here we introduce a mathematical formalism to describe cellular agents that are subject to random creation, replication and/or degradation, and are inherited according to a range of random dynamics at cell divisions. We obtain closed-form generating functions describing systems at any time after any number of cell divisions for binomial partitioning and divisions provoking a deterministic or random, subtractive or additive change in copy number, and show that these solutions agree exactly with stochastic simulation. We apply this general formalism to several example problems involving the dynamics of mitochondrial DNA during development and organismal lifetimes.
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