Markov chain aggregation and its applications to combinatorial reaction networks Ganguly, Arnab Petrov, Tatjana ; https://orcid.org/0000-0002-9041-0905 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 Article http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.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/altIdentifier/wos/000340588700008 info:eu-repo/semantics/altIdentifier/arxiv/1303.4532 info:eu-repo/semantics/openAccess