Markov chain aggregation and its applications to combinatorial reaction networks

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2014
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Ganguly, Arnab
Koeppl, Heinz
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Journal of Mathematical Biology. 2014, 69(3), pp. 767-797. ISSN 0303-6812. eISSN 1432-1416. Available under: doi: 10.1007/s00285-013-0738-7
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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.

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Markov chain aggregation; Rule-based modeling of reaction networks; Site-graphs
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ISO 690GANGULY, Arnab, Tatjana PETROV, Heinz KOEPPL, 2014. Markov chain aggregation and its applications to combinatorial reaction networks. In: Journal of Mathematical Biology. 2014, 69(3), pp. 767-797. ISSN 0303-6812. eISSN 1432-1416. Available under: doi: 10.1007/s00285-013-0738-7
BibTex
@article{Ganguly2014-09Marko-42122,
  year={2014},
  doi={10.1007/s00285-013-0738-7},
  title={Markov chain aggregation and its applications to combinatorial reaction networks},
  number={3},
  volume={69},
  issn={0303-6812},
  journal={Journal of Mathematical Biology},
  pages={767--797},
  author={Ganguly, Arnab and Petrov, Tatjana and Koeppl, Heinz}
}
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