{"year":"2014","main_file_link":[{"url":"http://arxiv.org/abs/1303.4532","open_access":"1"}],"acknowledgement":"T. Petrov is supported by SystemsX.ch—the Swiss Inititative for Systems Biology.","oa_version":"Submitted Version","month":"11","publication_status":"published","title":"Markov chain aggregation and its applications to combinatorial reaction networks","intvolume":"        69","publisher":"Springer","abstract":[{"lang":"eng","text":"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."}],"quality_controlled":"1","date_updated":"2021-01-12T06:55:01Z","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","date_created":"2018-12-11T11:55:28Z","issue":"3","date_published":"2014-11-20T00:00:00Z","language":[{"iso":"eng"}],"publication":"Journal of Mathematical Biology","scopus_import":1,"volume":69,"citation":{"chicago":"Ganguly, Arnab, Tatjana Petrov, and Heinz Koeppl. “Markov Chain Aggregation and Its Applications to Combinatorial Reaction Networks.” <i>Journal of Mathematical Biology</i>. Springer, 2014. <a href=\"https://doi.org/10.1007/s00285-013-0738-7\">https://doi.org/10.1007/s00285-013-0738-7</a>.","short":"A. Ganguly, T. Petrov, H. Koeppl, Journal of Mathematical Biology 69 (2014) 767–797.","apa":"Ganguly, A., Petrov, T., &#38; Koeppl, H. (2014). Markov chain aggregation and its applications to combinatorial reaction networks. <i>Journal of Mathematical Biology</i>. Springer. <a href=\"https://doi.org/10.1007/s00285-013-0738-7\">https://doi.org/10.1007/s00285-013-0738-7</a>","ista":"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.","ama":"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>","ieee":"A. Ganguly, T. Petrov, and H. Koeppl, “Markov chain aggregation and its applications to combinatorial reaction networks,” <i>Journal of Mathematical Biology</i>, vol. 69, no. 3. Springer, pp. 767–797, 2014.","mla":"Ganguly, Arnab, et al. “Markov Chain Aggregation and Its Applications to Combinatorial Reaction Networks.” <i>Journal of Mathematical Biology</i>, vol. 69, no. 3, Springer, 2014, pp. 767–97, doi:<a href=\"https://doi.org/10.1007/s00285-013-0738-7\">10.1007/s00285-013-0738-7</a>."},"page":"767 - 797","department":[{"_id":"CaGu"},{"_id":"ToHe"}],"type":"journal_article","publist_id":"4990","status":"public","day":"20","author":[{"first_name":"Arnab","full_name":"Ganguly, Arnab","last_name":"Ganguly"},{"id":"3D5811FC-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9041-0905","last_name":"Petrov","full_name":"Petrov, Tatjana","first_name":"Tatjana"},{"first_name":"Heinz","full_name":"Koeppl, Heinz","last_name":"Koeppl"}],"doi":"10.1007/s00285-013-0738-7","_id":"2056","oa":1}