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J Math Biol. 2014 Sep;69(3):767-97. doi: 10.1007/s00285-013-0738-7. Epub 2013 Nov 20.

Markov chain aggregation and its applications to combinatorial reaction networks.

Author information

1
Department of Mathematics, University of Louisville, 231 Natural Sciences Building, Louisville, KY, USA, a0gang02@louisville.edu.

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.

PMID:
24253253
DOI:
10.1007/s00285-013-0738-7
[Indexed for MEDLINE]

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