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.
Theoretical Computer Science
We would like to thank the anonymous reviewers for their comments on the different versions of the paper. We would also like to thank Ferdinanda Camporesi for her careful reading and the useful insights that she gave us about the paper. Jérôme Feret’s contribution was partially supported by the AbstractCell ANR-Chair of Excellence. Heinz Koeppl’s research is supported by the Swiss National Science Foundation, grant no. 200020-117975/1. Tatjana Petrov’s research is supported by SystemsX.ch (the Swiss Initiative in Systems Biology).
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Feret J, Henzinger TA, Koeppl H, Petrov T. Lumpability abstractions of rule based systems. Theoretical Computer Science. 2012;431:137-164. doi:10.1016/j.tcs.2011.12.059
Feret, J., Henzinger, T. A., Koeppl, H., & Petrov, T. (2012). Lumpability abstractions of rule based systems. Theoretical Computer Science. Elsevier. https://doi.org/10.1016/j.tcs.2011.12.059
Feret, Jérôme, Thomas A Henzinger, Heinz Koeppl, and Tatjana Petrov. “Lumpability Abstractions of Rule Based Systems.” Theoretical Computer Science. Elsevier, 2012. https://doi.org/10.1016/j.tcs.2011.12.059.
J. Feret, T. A. Henzinger, H. Koeppl, and T. Petrov, “Lumpability abstractions of rule based systems,” Theoretical Computer Science, vol. 431. Elsevier, pp. 137–164, 2012.
Feret J, Henzinger TA, Koeppl H, Petrov T. 2012. Lumpability abstractions of rule based systems. Theoretical Computer Science. 431, 137–164.
Feret, Jérôme, et al. “Lumpability Abstractions of Rule Based Systems.” Theoretical Computer Science, vol. 431, Elsevier, 2012, pp. 137–64, doi:10.1016/j.tcs.2011.12.059.
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