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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