Markov chain aggregation and its applications to combinatorial reaction networks

A. Ganguly, T. Petrov, H. Koeppl, Journal of Mathematical Biology 69 (2014) 767–797.


Journal Article | Published | English
Author
; ;
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.
Publishing Year
Date Published
2014-11-20
Journal Title
Journal of Mathematical Biology
Acknowledgement
T. Petrov is supported by SystemsX.ch—the Swiss Inititative for Systems Biology.
Volume
69
Issue
3
Page
767 - 797
IST-REx-ID

Cite this

Ganguly A, Petrov T, Koeppl H. Markov chain aggregation and its applications to combinatorial reaction networks. Journal of Mathematical Biology. 2014;69(3):767-797. doi:10.1007/s00285-013-0738-7
Ganguly, A., Petrov, T., & Koeppl, H. (2014). Markov chain aggregation and its applications to combinatorial reaction networks. Journal of Mathematical Biology, 69(3), 767–797. https://doi.org/10.1007/s00285-013-0738-7
Ganguly, Arnab, Tatjana Petrov, and Heinz Koeppl. “Markov Chain Aggregation and Its Applications to Combinatorial Reaction Networks.” Journal of Mathematical Biology 69, no. 3 (2014): 767–97. https://doi.org/10.1007/s00285-013-0738-7.
A. Ganguly, T. Petrov, and H. Koeppl, “Markov chain aggregation and its applications to combinatorial reaction networks,” Journal of Mathematical Biology, vol. 69, no. 3, pp. 767–797, 2014.
Ganguly A, Petrov T, Koeppl H. 2014. Markov chain aggregation and its applications to combinatorial reaction networks. Journal of Mathematical Biology. 69(3), 767–797.
Ganguly, Arnab, et al. “Markov Chain Aggregation and Its Applications to Combinatorial Reaction Networks.” Journal of Mathematical Biology, vol. 69, no. 3, Springer, 2014, pp. 767–97, doi:10.1007/s00285-013-0738-7.

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