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Markov chain aggregation and its applications to combinatorial reaction networks

Ganguly, A. ; Petrov, T. ; Koeppl, H. (2013)
Markov chain aggregation and its applications to combinatorial reaction networks.
In: Journal of mathematical biology, 69 (3)
Artikel, Bibliographie

Kurzbeschreibung (Abstract)

We consider a continuous-time Markov chain (CTMC) whose state space is partitioned into aggregates, and each aggregate is assigned a probability measure. A sufficient condition for defining a CTMC over the aggregates is presented as a variant of weak lumpability, which also characterizes that the measure over the original process can be recovered from that of the aggregated one. We show how the applicability of de-aggregation depends on the initial distribution. The application section is devoted to illustrate how the developed theory aids in reducing CTMC models of biochemical systems particularly in connection to protein-protein interactions. We assume that the model is written by a biologist in form of site-graph-rewrite rules. Site-graph-rewrite rules compactly express that, often, only a local context of a protein (instead of a full molecular species) needs to be in a certain configuration in order to trigger a reaction event. This observation leads to suitable aggregate Markov chains with smaller state spaces, thereby providing sufficient reduction in computational complexity. This is further exemplified in two case studies: simple unbounded polymerization and early EGFR/insulin crosstalk.

Typ des Eintrags: Artikel
Erschienen: 2013
Autor(en): Ganguly, A. ; Petrov, T. ; Koeppl, H.
Art des Eintrags: Bibliographie
Titel: Markov chain aggregation and its applications to combinatorial reaction networks
Sprache: Englisch
Publikationsjahr: 20 November 2013
Titel der Zeitschrift, Zeitung oder Schriftenreihe: Journal of mathematical biology
Jahrgang/Volume einer Zeitschrift: 69
(Heft-)Nummer: 3
URL / URN: http://link.springer.com/article/10.1007/s00285-013-0738-7
Kurzbeschreibung (Abstract):

We consider a continuous-time Markov chain (CTMC) whose state space is partitioned into aggregates, and each aggregate is assigned a probability measure. A sufficient condition for defining a CTMC over the aggregates is presented as a variant of weak lumpability, which also characterizes that the measure over the original process can be recovered from that of the aggregated one. We show how the applicability of de-aggregation depends on the initial distribution. The application section is devoted to illustrate how the developed theory aids in reducing CTMC models of biochemical systems particularly in connection to protein-protein interactions. We assume that the model is written by a biologist in form of site-graph-rewrite rules. Site-graph-rewrite rules compactly express that, often, only a local context of a protein (instead of a full molecular species) needs to be in a certain configuration in order to trigger a reaction event. This observation leads to suitable aggregate Markov chains with smaller state spaces, thereby providing sufficient reduction in computational complexity. This is further exemplified in two case studies: simple unbounded polymerization and early EGFR/insulin crosstalk.

Freie Schlagworte: Markov chain aggregation; Rule-based modeling of reaction networks; Site-graphs
Fachbereich(e)/-gebiet(e): 18 Fachbereich Elektrotechnik und Informationstechnik
18 Fachbereich Elektrotechnik und Informationstechnik > Institut für Nachrichtentechnik > Bioinspirierte Kommunikationssysteme
18 Fachbereich Elektrotechnik und Informationstechnik > Institut für Nachrichtentechnik
Hinterlegungsdatum: 04 Apr 2014 14:09
Letzte Änderung: 23 Sep 2021 14:31
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