Closed-form stochastic solutions for non-equilibrium dynamics and inheritance of cellular components over many cell divisions
File(s)
Published version
OA Location
Author(s)
Johnston, IG
Jones, NS
Type
Journal Article
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.
Date Issued
2015-07-15
Date Acceptance
2015-06-05
Citation
Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences, 2015, 471 (2180)
ISSN
1364-5021
Publisher
The Royal Society
Journal / Book Title
Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences
Volume
471
Issue
2180
Copyright Statement
© 2015 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.
License URL
Sponsor
Medical Research Council (MRC)
Grant Number
MR/J013617/1
Subjects
Science & Technology
Multidisciplinary Sciences
Science & Technology - Other Topics
stochastic processes
stochastic biology
cellular populations
MITOCHONDRIAL-DNA MUTATIONS
RANDOM GENETIC DRIFT
CLONAL EXPANSION
MODEL
EXPRESSION
REPLICATION
VARIABILITY
MTDNA
SIZE
DIVERSIFICATION
01 Mathematical Sciences
02 Physical Sciences
09 Engineering
Publication Status
Published
Article Number
20150050