Incorporating age and delay into models for biophysical systems

KhudaBukhsh, Wasiur R.; Kang, Hye-Won; Kenah, Eben; Rempa?a, Grzegorz A.

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.

Citation

KhudaBukhsh, W. R., Kang, H., Kenah, E., & Rempa?a, G. A. (2021). Incorporating age and delay into models for biophysical systems. Physical Biology, 18(1), Article 015002. https://doi.org/10.1088/1478-3975/abc2ab

• Journal Article Type: Article
• Acceptance Date: Oct 19, 2020
• Online Publication Date: Dec 30, 2020
• Publication Date: Jan 1, 2021
• Deposit Date: Apr 9, 2022
• Publicly Available Date: Apr 21, 2022
• Journal: Physical Biology
• Electronic ISSN: 1478-3975
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 18
• Issue: 1
• Article Number: 015002
• DOI: https://doi.org/10.1088/1478-3975/abc2ab
• Keywords: Cell Biology; Molecular Biology; Structural Biology; Biophysics
• Public URL: https://nottingham-repository.worktribe.com/output/7715590
• Publisher URL: https://iopscience.iop.org/article/10.1088/1478-3975/abc2ab
• Additional Information: This is an author-created, un-copyedited version of an article accepted for publication/published in Physical Biology. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1478-3975/abc2ab