{"oa":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1303.4532"}],"intvolume":"        69","quality_controlled":"1","publist_id":"4990","language":[{"iso":"eng"}],"page":"767 - 797","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","date_published":"2014-11-20T00:00:00Z","publication":"Journal of Mathematical Biology","publication_status":"published","day":"20","doi":"10.1007/s00285-013-0738-7","author":[{"last_name":"Ganguly","full_name":"Ganguly, Arnab","first_name":"Arnab"},{"orcid":"0000-0002-9041-0905","id":"3D5811FC-F248-11E8-B48F-1D18A9856A87","last_name":"Petrov","full_name":"Petrov, Tatjana","first_name":"Tatjana"},{"first_name":"Heinz","last_name":"Koeppl","full_name":"Koeppl, Heinz"}],"volume":69,"_id":"2056","year":"2014","abstract":[{"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.","lang":"eng"}],"publisher":"Springer","issue":"3","status":"public","oa_version":"Submitted Version","department":[{"_id":"CaGu"},{"_id":"ToHe"}],"citation":{"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>.","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.","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>","short":"A. Ganguly, T. Petrov, H. Koeppl, Journal of Mathematical Biology 69 (2014) 767–797.","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.","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>","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>."},"type":"journal_article","date_created":"2018-12-11T11:55:28Z","scopus_import":1,"title":"Markov chain aggregation and its applications to combinatorial reaction networks","month":"11","date_updated":"2021-01-12T06:55:01Z","acknowledgement":"T. Petrov is supported by SystemsX.ch—the Swiss Inititative for Systems Biology."}