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Lumpability Abstractions of Rule-based Systems

Jérôme Feret 1, * Thomas Henzinger 2 Heinz Koeppl 3 Tatjana Petrov 3 
* Corresponding author
1 ABSTRACTION - Abstract Interpretation and Static Analysis
DI-ENS - Département d'informatique - ENS Paris, Inria Paris-Rocquencourt, CNRS - Centre National de la Recherche Scientifique : UMR 8548
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 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.
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https://hal.inria.fr/inria-00527971
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Submitted on : Wednesday, October 20, 2010 - 4:56:20 PM
Last modification on : Thursday, March 17, 2022 - 10:08:35 AM

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  • HAL Id : inria-00527971, version 1

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Jérôme Feret, Thomas Henzinger, Heinz Koeppl, Tatjana Petrov. Lumpability Abstractions of Rule-based Systems. The 4th Workshop on Membrane Computing and Biologically Inspired Process Calculi - MeCBIC 2010, Ciobanu, G. and Koutny, M., Aug 2010, Jena, Germany. ⟨inria-00527971⟩

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