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Incorporating age and delay into models for biophysical systems.

Authors
  • KhudaBukhsh, Wasiur R1
  • Kang, Hye-Won
  • Kenah, Eben
  • Rempała, Grzegorz A
  • 1 Mathematical Biosciences Institute and the College of Public Health, The Ohio State University, 1735 Neil Avenue, Columbus OH 43210, United States of America. , (United States)
Type
Published Article
Journal
Physical Biology
Publisher
IOP Publishing
Publication Date
Feb 13, 2021
Volume
18
Issue
1
Pages
15002–15002
Identifiers
DOI: 10.1088/1478-3975/abc2ab
PMID: 33075757
Source
Medline
Language
English
License
Unknown

Abstract

In many biological systems, chemical reactions or changes in a physical state are assumed to occur instantaneously. For describing the dynamics of those systems, Markov models that require exponentially distributed inter-event times have been used widely. However, some biophysical processes such as gene transcription and translation are known to have a significant gap between the initiation and the completion of the processes, which renders the usual assumption of exponential distribution untenable. In this paper, we consider relaxing this assumption by incorporating age-dependent random time delays (distributed according to a given probability distribution) into the system dynamics. We do so by constructing a measure-valued Markov process on a more abstract state space, which allows us to keep track of the 'ages' of molecules participating in a chemical reaction. We study the large-volume limit of such age-structured systems. We show that, when appropriately scaled, the stochastic system can be approximated by a system of partial differential equations (PDEs) in the large-volume limit, as opposed to ordinary differential equations (ODEs) in the classical theory. We show how the limiting PDE system can be used for the purpose of further model reductions and for devising efficient simulation algorithms. In order to describe the ideas, we use a simple transcription process as a running example. We, however, note that the methods developed in this paper apply to a wide class of biophysical systems.

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