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Markov Chain Aggregation and Its Application to Rule-Based Modelling

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2019

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https://doi.org/10.1007/978-1-4939-9102-0_14
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HLAVACEK, William S., ed.. Modeling Biomolecular Site Dynamics : Methods and Protocols. New York: Springer, 2019, pp. 297-313. Methods in Molecular Biology (MIMB). 1945. ISBN 978-1-4939-9100-6. Available under: doi: 10.1007/978-1-4939-9102-0_14

Zusammenfassung

Rule-based modelling allows to represent molecular interactions in a compact and natural way. The underlying molecular dynamics, by the laws of stochastic chemical kinetics, behaves as a continuous-time Markov chain. However, this Markov chain enumerates all possible reaction mixtures, rendering the analysis of the chain computationally demanding and often prohibitive in practice. We here describe how it is possible to efficiently find a smaller, aggregate chain, which preserves certain properties of the original one. Formal methods and lumpability notions are used to define algorithms for automated and efficient construction of such smaller chains (without ever constructing the original ones). We here illustrate the method on an example and we discuss the applicability of the method in the context of modelling large signaling pathways.

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570 Biowissenschaften, Biologie

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ISO 690PETROV, Tatjana, 2019. Markov Chain Aggregation and Its Application to Rule-Based Modelling. In: HLAVACEK, William S., ed.. Modeling Biomolecular Site Dynamics : Methods and Protocols. New York: Springer, 2019, pp. 297-313. Methods in Molecular Biology (MIMB). 1945. ISBN 978-1-4939-9100-6. Available under: doi: 10.1007/978-1-4939-9102-0_14
BibTex
@incollection{Petrov2019Marko-69884,
  year={2019},
  doi={10.1007/978-1-4939-9102-0_14},
  title={Markov Chain Aggregation and Its Application to Rule-Based Modelling},
  number={1945},
  isbn={978-1-4939-9100-6},
  publisher={Springer},
  address={New York},
  series={Methods in Molecular Biology (MIMB)},
  booktitle={Modeling Biomolecular Site Dynamics : Methods and Protocols},
  pages={297--313},
  editor={Hlavacek, William S.},
  author={Petrov, Tatjana}
}
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