Incorporating age and delay into models for biophysical systems

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dc.contributor.authorKhudaBukhsh, Wasiur R.
dc.contributor.authorKang, Hye-Won
dc.contributor.authorKenah, Eben
dc.contributor.authorRempala, Grzegorz A.
dc.date.accessioned2021-01-25T18:01:58Z
dc.date.available2021-01-25T18:01:58Z
dc.description.abstractIn 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 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.en_US
dc.description.sponsorshipWKB was supported by the National Institute of Allergy and Infectious Diseases (NIAID) grant R01 AI116770, the National Science Foundation (NSF) grant DMS2027001 and the Ohio State University’s President’s Postdoctoral Scholars Program (PPSP). EK was supported by NIAID grant R01 AI116770 and the NSF grants DMS2027001 and DMS-1853587. GAR was supported by the NSF grants DMS-2027001 and DMS-1853587. HWK was supported in part by the NSF under the grant DMS-1620403. The project was initiated when HWK was visiting the Mathematical Biosciences Institute (MBI) at the Ohio State University in Summer 2019. The authors acknowledge the hospitality and the support of MBI. The content of this manuscript is solely the responsibility of the authors and does not represent the official views of NSF, NIGMS, NIAID, or NIH.en_US
dc.description.urihttps://arxiv.org/abs/2007.00577en_US
dc.format.extent21 pagesen_US
dc.genrejournal articles preprintsen_US
dc.identifierdoi:10.13016/m2weau-qlts
dc.identifier.citationWasiur R. KhudaBukhsh, Hye-Won Kang, Eben Kenah and Grzegorz A. Rempala, Incorporating age and delay into models for biophysical systems, https://arxiv.org/abs/2007.00577en_US
dc.identifier.urihttp://hdl.handle.net/11603/20602
dc.language.isoen_USen_US
dc.relation.isAvailableAtThe University of Maryland, Baltimore County (UMBC)
dc.relation.ispartofUMBC Mathematics Department Collection
dc.relation.ispartofUMBC Faculty Collection
dc.rightsThis item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.
dc.subjectstochastic transcriptionen_US
dc.subjecttranslationen_US
dc.subjectrandom time delaysen_US
dc.subjectmultiscale analysisen_US
dc.subjectsurvival dynamical systemsen_US
dc.subjectage-dependent processesen_US
dc.subjectnon-Markovian systemsen_US
dc.titleIncorporating age and delay into models for biophysical systemsen_US
dc.typeTexten_US

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