Lumpability abstractions of rule-based systems

Feret, Jerome; Henzinger, Thomas; Koeppl, Heinz; Petrov, Tatjana

Lumpability abstractions of rule-based systems

Dateien

Feret_2-wh1932hvqp1w4.pdfGröße: 935.4 KBDownloads: 244

Datum

2012

Autor:innen

Feret, Jerome

Henzinger, Thomas

Koeppl, Heinz

Petrov, Tatjana

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

Theoretical Computer Science. 2012, 431, pp. 137-164. ISSN 0304-3975. eISSN 1879-2294. Available under: doi: 10.1016/j.tcs.2011.12.059

Zusammenfassung

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 (that is to say that the quotient system is still Markovian for a given set of initial distributions) and that it gives rise to a backward Markov bisimulation between the original and aggregated transition system (which means that the conditional probability of being in a given state in the original system knowing that we are in its equivalence class is an invariant of the system). We illustrate the framework on a case study of the epidermal growth factor (EGF)/insulin receptor crosstalk.

Fachgebiet (DDC)

004 Informatik

Schlagwörter

Markov chains; Abstraction; Lumpability; Bisimulation

Zitieren

ISO 690

FERET, Jerome, Thomas HENZINGER, Heinz KOEPPL, Tatjana PETROV, 2012. Lumpability abstractions of rule-based systems. In: Theoretical Computer Science. 2012, 431, pp. 137-164. ISSN 0304-3975. eISSN 1879-2294. Available under: doi: 10.1016/j.tcs.2011.12.059

BibTex

@article{Feret2012-05Lumpa-42137,
  year={2012},
  doi={10.1016/j.tcs.2011.12.059},
  title={Lumpability abstractions of rule-based systems},
  volume={431},
  issn={0304-3975},
  journal={Theoretical Computer Science},
  pages={137--164},
  author={Feret, Jerome and Henzinger, Thomas and Koeppl, Heinz and Petrov, Tatjana}
}

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