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**Ganguly, A. and Petrov, T. and Koeppl, H.** (2013):

*Markov chain aggregation and its applications to combinatorial reaction networks.*

In: Journal of mathematical biology, 69 (3), pp. 767-797. [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 |

Journal 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 |

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