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SUMMARY:Gábor Szederkényi (Pazmany Peter Catholic University)
DTSTART:20260423T150000Z
DTEND:20260423T153000Z
DTSTAMP:20260421T123618Z
UID:MoRN/147
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MoRN/147/">C
 ompartmental discretization and simulation of gene regulation networks (GR
 Ns)</a>\nby Gábor Szederkényi (Pazmany Peter Catholic University) as par
 t of Seminar on the Mathematics of Reaction Networks\n\n\nAbstract\nGene e
 xpression is a fundamental biological process of actually realizing DNA in
 formation in the form of proteins in living organisms. It is widely accept
 ed that the stochastic nature of gene expression has to be taken into cons
 ideration during quantitative modeling due to uncertainties coming from e.
 g.\, both translational and transcriptional bursting. In (Friedman\, 2006)
  a model in partial integro-differential equation (PIDE) form was proposed
  for the description of the temporal evolution of protein distribution. Th
 is model was generalized to multiple dimensions in (Pájaro\, 2017). To ma
 ke numerical solution and analysis easier\, a finite volume discretization
  scheme in the space of molecule numbers was proposed in (Vághy\, 2024) w
 hich gives a non-homogeneous master equation which is essentially a linear
  time-varying compartmental model. In this presentation\, I will show rece
 nt results on the simulation and control of GRNs using the discretized com
 partmental model form. Existence and uniqueness of equilibria (i.e.\, stat
 ionary distributions) and stability of solutions will be studied using the
  theory of non-autonomous master equations (see\, e.g. Diblík\, 2024).\n\
 nCoauthors: Irene Otero-Muras\, Mihály A. Vághy\, Manuel Pájaro\, Chris
 tian Fernandez Perez\, Mihály Pituk\, Josef Diblík\n\nReferences:\n\nFri
 edman\, N.\, Cai\, L.\, & Xie\, X. S. (2006). Linking stochastic dynamics 
 to population Distribution: an analytical framework of gene expression. Ph
 ysical Review Letters\, 97(16)\, 168302.\n\nPájaro\, M.\, Alonso\, A. A.\
 , Otero-Muras\, I.\, & Vázquez\, C. (2017). Stochastic modeling and numer
 ical simulation of gene regulatory networks with protein bursting. Journal
  of Theoretical Biology\, 421\, 51-70.\n\nVághy\, M. A.\, Otero-Muras\, I
 .\, Pájaro\, M.\, & Szederkényi\, G. (2024). A kinetic finite volume dis
 cretization of the multidimensional PIDE model for gene regulatory network
 s. Bulletin of Mathematical Biology\, 86(2)\, 22.\n\nDiblík\, J.\, Pituk\
 , M.\, & Szederkényi\, G. (2024). Large time behavior of nonautonomous li
 near differential equations with Kirchhoff coefficients. Automatica\, 161\
 , 111473.\n
LOCATION:https://researchseminars.org/talk/MoRN/147/
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