@article{2056,
  abstract     = {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.},
  author       = {Ganguly, Arnab and Petrov, Tatjana and Koeppl, Heinz},
  journal      = {Journal of Mathematical Biology},
  number       = {3},
  pages        = {767 -- 797},
  publisher    = {Springer},
  title        = {{Markov chain aggregation and its applications to combinatorial reaction networks}},
  doi          = {10.1007/s00285-013-0738-7},
  volume       = {69},
  year         = {2014},
}