BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Wasiur Khuda Bukhsh (University of Nottingham) DTSTART:20220127T163000Z DTEND:20220127T170000Z DTSTAMP:20260421T124057Z UID:MoRN/43 DESCRIPTION:Title: In corporating age and delay into models for biophysical systems\nby Wasi ur Khuda Bukhsh (University of Nottingham) as part of Seminar on the Mathe matics of Reaction Networks\n\n\nAbstract\nIn many biological systems\, ch emical reactions or changes in a physical state are assumed to occur insta ntaneously. For describing the dynamics of those systems\, Markov models t hat require exponentially distributed inter-event times have been used wid ely. However\, some biophysical processes such as gene transcription and t ranslation are known to have a significant gap between the initiation and the completion of the processes\, which renders the usual assumption of ex ponential distribution untenable. In this talk\, 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 abstrac t state space\, which allows us to keep track of the 'ages' of molecules p articipating in a chemical reaction. We study the large-volume limit of su ch 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 differ ential 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. To describe the ideas\, we will use a simple transcription process as a running example.\n LOCATION:https://researchseminars.org/talk/MoRN/43/ END:VEVENT END:VCALENDAR