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 math- ematical 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 com- binatorial 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.
Jérôme Feret’s contribution was partially supported by the ABSTRACTCELL ANR-Chair of Excellence. Heinz Koeppl acknowledges the support from the Swiss National Science Foundation, grant no. 200020-117975/1. Tatjana Petrov acknowledges the support from SystemsX.ch, the Swiss Initiative in Systems Biology.
MECBIC: Membrane Computing and Biologically Inspired Process Calculi
2010-08-23 – 2010-08-23
Feret J, Henzinger TA, Koeppl H, Petrov T. Lumpability abstractions of rule-based systems. In: Vol 40. Open Publishing Association; 2010:142-161.
Feret, J., Henzinger, T. A., Koeppl, H., & Petrov, T. (2010). Lumpability abstractions of rule-based systems (Vol. 40, pp. 142–161). Presented at the MECBIC: Membrane Computing and Biologically Inspired Process Calculi, Jena, Germany: Open Publishing Association.
Feret, Jérôme, Thomas A Henzinger, Heinz Koeppl, and Tatjana Petrov. “Lumpability Abstractions of Rule-Based Systems,” 40:142–61. Open Publishing Association, 2010.
J. Feret, T. A. Henzinger, H. Koeppl, and T. Petrov, “Lumpability abstractions of rule-based systems,” presented at the MECBIC: Membrane Computing and Biologically Inspired Process Calculi, Jena, Germany, 2010, vol. 40, pp. 142–161.
Feret J, Henzinger TA, Koeppl H, Petrov T. 2010. Lumpability abstractions of rule-based systems. MECBIC: Membrane Computing and Biologically Inspired Process Calculi, EPTCS, vol. 40. 142–161.
Feret, Jérôme, et al. Lumpability Abstractions of Rule-Based Systems. Vol. 40, Open Publishing Association, 2010, pp. 142–61.
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