title: Markov chain aggregation and its applications to combinatorial reaction networks.
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.
authors.affiliation: Department of Mathematics, University of Louisville, 231 Natural Sciences Building, Louisville, KY, USA, a0gang02@louisville.edu.
authors.forename: Arnab
authors.initials: A
authors.lastname: Ganguly
authors.forename: Tatjana
authors.initials: T
authors.lastname: Petrov
authors.forename: Heinz
authors.initials: H
authors.lastname: Koeppl
mesh_terms: D004815:Epidermal Growth Factor / Q000502:physiology; D007328:Insulin / Q000502:physiology; D008390:Markov Chains; D008954:Models, Biological; D058105:Polymerization; D011336:Probability; D011506:Proteins / Q000378:metabolism*; D015398:Signal Transduction / Q000502:physiology*
chemical_list: D007328:Insulin; D011506:Proteins; D004815:Epidermal Growth Factor