Markov chain aggregation and its applications to combinatorial reaction networks
Ganguly, Arnab
Petrov, Tatjana
Koeppl, Heinz
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.
Springer
2014
info:eu-repo/semantics/article
doc-type:article
text
https://research-explorer.app.ist.ac.at/record/2056
Ganguly A, Petrov T, Koeppl H. Markov chain aggregation and its applications to combinatorial reaction networks. <i>Journal of Mathematical Biology</i>. 2014;69(3):767-797. doi:<a href="https://doi.org/10.1007/s00285-013-0738-7">10.1007/s00285-013-0738-7</a>
eng
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00285-013-0738-7
info:eu-repo/semantics/openAccess