article published yes Arnab Ganguly author Tatjana Petrov author 3D5811FC-F248-11E8-B48F-1D18A9856A870000-0002-9041-0905 Heinz Koeppl author CaGu department ToHe department 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. Springer2014 eng 1303.4532 00034058870000810.1007/s00285-013-0738-7 693767 - 797 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. 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> 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.” <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>. 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>. 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> A. Ganguly, T. Petrov, H. Koeppl, Journal of Mathematical Biology 69 (2014) 767–797. 20562018-12-11T11:55:28Z2025-09-29T11:50:22Z