Closed-form stochastic solutions for non-equilibrium dynamics and inheritance of cellular components over many cell divisions

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 proces...

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Bibliographic Details
Published in:arXiv.org
Main Authors: Johnston, Iain G, Jones, Nick S
Format: Paper
Language:English
Published: Ithaca Cornell University Library, arXiv.org 25.01.2015
Subjects:
Biology
Chemical partition
Closed form solutions
Computer simulation
Deoxyribonucleic acid
DNA
Dynamics
Exact solutions
Formalism
Gene expression
Mathematical analysis
Mitochondrial DNA
Partitioning
Stochastic processes
ISSN:2331-8422
Online Access:Get full text
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Summary: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 (mtDNA) during development and organismal lifetimes.
Bibliography:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
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ISSN:2331-8422
DOI:10.48550/arxiv.1501.06149