TU Darmstadt / ULB / TUbiblio

Markov chain aggregation and its applications to combinatorial reaction networks

Ganguly, A. and Petrov, T. and Koeppl, H. (2013):
Markov chain aggregation and its applications to combinatorial reaction networks.
In: Journal of mathematical biology, pp. 767-797, 69, (3), [Online-Edition: http://link.springer.com/article/10.1007/s00285-013-0738-7],
[Article]

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.

Item Type: Article
Erschienen: 2013
Creators: Ganguly, A. and Petrov, T. and Koeppl, H.
Title: Markov chain aggregation and its applications to combinatorial reaction networks
Language: English
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.

Journal or Publication Title: Journal of mathematical biology
Volume: 69
Number: 3
Uncontrolled Keywords: Markov chain aggregation; Rule-based modeling of reaction networks; Site-graphs
Divisions: 18 Department of Electrical Engineering and Information Technology > Institute for Telecommunications > Bioinspired Communication Systems
18 Department of Electrical Engineering and Information Technology
18 Department of Electrical Engineering and Information Technology > Institute for Telecommunications
Date Deposited: 04 Apr 2014 14:09
Official URL: http://link.springer.com/article/10.1007/s00285-013-0738-7
Export:

Optionen (nur für Redakteure)

View Item View Item