Lumpability Abstractions of Rule-based Systems

Theoretical Computer Science (Impact Factor: 0.66). 05/2012; 431:137--164. DOI: 10.1016/j.tcs.2011.12.059
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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.

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Available from: Tatjana Petrov, Oct 10, 2015
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    • "Other reaction network model reduction methods are restricted to deterministic models [32] [33] including a reduction from 42 to 29 molecular species [34]. The most comparable method in terms of problem size may be [35] which like GCCD applies to rule-based reaction networks. We will quantitatively compare degrees of model reduction of these methods to GCCD in section 3.4. "
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    • "A simple example of a Kappa model is presented in Fig. 1. For the stochastic semantics of Kappa, that is a continuoustime Markov chain (CTMC) assigned to a rule-based model, we refer to [12] or [17]. Intuitively, any rule-based system can be expanded to an equivalent reaction system (with potentially infinitely many species and reactions). "
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    • "Reduction of stochastic rule-based models, based on a weakened version of the exact lumpability criterion, has been proposed by Feret et al. (2012) to define abstract species or stochasticfragments that can be further used in simplified calculations. More generally, rule-based models alow to overcome combinatorial complexity in stochastic simulations (Danos et al., 2007b). "
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