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Jérôme Feret, Thomas Henzinger, Heinz Koeppl,& Tatjana Petrov.
Lumpability Abstractions of Rule-based Systems.

In Theoretical Computer Science, special issue MeCBIC 2009-2010, volume 431, pages 137--164.
© 2012 Elsevier Inc.

Abstract: The induction of a signaling pathway is characterized by transient complex formation and mutual posttranslational modification of proteins. To faithfully capture this combinatorial process in a mathematical model is an important challenge in systems biology. Exploiting the limited context on which most binding and modification events are conditioned, attempts have been made to reduce the combinatorial complexity by quotienting the reachable set of molecular species, into species aggregates while preserving the deterministic semantics of the thermodynamic limit. Recently we proposed a quotienting that also preserves the stochastic semantics and that is complete in the sense that the semantics of individual species can be recovered from the aggregate semantics.
In this paper we prove that this quotienting yields a sufficient condition for \emph{weak lumpability} and that it gives rise to a backward Markov bisimulation between the original and aggregated transition system. We illustrate the framework on a case study of the EGF/insulin receptor crosstalk.

title = "Lumpability abstractions of rule-based systems",
journal = "Theoretical Computer Science",
volume = "431",
number = "0",
pages = "137 - 164",
year = "2012",
note = "Modelling and Analysis of Biological Systems Based on papers presented at the Workshop on Membrane Computing and Bio-logically Inspired Process Calculi (MeCBIC) held in 2008 (Iasi), 2009 (Bologna) and 2010 (Jena)",
issn = "0304-3975",
doi = "10.1016/j.tcs.2011.12.059",
url = "http://www.sciencedirect.com/science/article/pii/S0304397511010255",
author = "Jerome Feret and Thomas Henzinger and Heinz Koeppl and Tatjana Petrov",
keywords = "Markov chains",
keywords = "Abstraction",
keywords = "Lumpability",
keywords = "Bisimulation"