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A Kinetic Finite Volume Discretization of the Multidimensional PIDE Model for Gene Regulatory Networks.
Vághy, Mihály A; Otero-Muras, Irene; Pájaro, Manuel; Szederkényi, Gábor.
Afiliación
  • Vághy MA; Faculty of Information Technology and Bionics, Pázmány Péter Catholic University, Práter u. 50/a, Budapest, 1083, Hungary. vaghy.mihaly.andras@itk.ppke.hu.
  • Otero-Muras I; Institute for Integrative Systems Biology, Spanish Council for Scientific Research, Carrer del Catedràtic Agustín Escardino Benlloch, 46980, Valencia, Spain.
  • Pájaro M; Department of Mathematics, Escola Superior de Enxeñaría Informática, University of Vigo, Campus Ourense, 32004, Ourense, Spain.
  • Szederkényi G; Faculty of Information Technology and Bionics, Pázmány Péter Catholic University, Práter u. 50/a, Budapest, 1083, Hungary.
Bull Math Biol ; 86(2): 22, 2024 01 22.
Article en En | MEDLINE | ID: mdl-38253903
ABSTRACT
In this paper, a finite volume discretization scheme for partial integro-differential equations (PIDEs) describing the temporal evolution of protein distribution in gene regulatory networks is proposed. It is shown that the obtained set of ODEs can be formally represented as a compartmental kinetic system with a strongly connected reaction graph. This allows the application of the theory of nonnegative and compartmental systems for the qualitative analysis of the approximating dynamics. In this framework, it is straightforward to show the existence, uniqueness and stability of equilibria. Moreover, the computation of the stationary probability distribution can be traced back to the solution of linear equations. The discretization scheme is presented for one and multiple dimensional models separately. Illustrative computational examples show the precision of the approach, and good agreement with previous results in the literature.
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Texto completo: 1 Colección: 01-internacional Base de datos: MEDLINE Asunto principal: Redes Reguladoras de Genes / Conceptos Matemáticos Tipo de estudio: Qualitative_research Idioma: En Revista: Bull Math Biol Año: 2024 Tipo del documento: Article País de afiliación: Hungria Pais de publicación: Estados Unidos
Texto completo
Añadir a Mi BVS
Imprimir
XML
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Texto completo: 1 Colección: 01-internacional Base de datos: MEDLINE Asunto principal: Redes Reguladoras de Genes / Conceptos Matemáticos Tipo de estudio: Qualitative_research Idioma: En Revista: Bull Math Biol Año: 2024 Tipo del documento: Article País de afiliación: Hungria Pais de publicación: Estados Unidos