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Open Access Research article

Reconstruction of extended Petri nets from time series data and its application to signal transduction and to gene regulatory networks

Markus Durzinsky1, Annegret Wagler2 and Wolfgang Marwan1*

Author Affiliations

1 Magdeburg Centre for Systems Biology, Otto-von-Guericke-Universität, Magdeburg, Germany

2 LIMOS (Laboratoire d'Informatique, Modélisation et Optimisation des Systèmes), University Blaise Pascal (Faculty of Sciences and Technologies) and CNRS, Clermont-Ferrand, France

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BMC Systems Biology 2011, 5:113  doi:10.1186/1752-0509-5-113

Published: 15 July 2011



Network inference methods reconstruct mathematical models of molecular or genetic networks directly from experimental data sets. We have previously reported a mathematical method which is exclusively data-driven, does not involve any heuristic decisions within the reconstruction process, and deliveres all possible alternative minimal networks in terms of simple place/transition Petri nets that are consistent with a given discrete time series data set.


We fundamentally extended the previously published algorithm to consider catalysis and inhibition of the reactions that occur in the underlying network. The results of the reconstruction algorithm are encoded in the form of an extended Petri net involving control arcs. This allows the consideration of processes involving mass flow and/or regulatory interactions. As a non-trivial test case, the phosphate regulatory network of enterobacteria was reconstructed using in silico-generated time-series data sets on wild-type and in silico mutants.


The new exact algorithm reconstructs extended Petri nets from time series data sets by finding all alternative minimal networks that are consistent with the data. It suggested alternative molecular mechanisms for certain reactions in the network. The algorithm is useful to combine data from wild-type and mutant cells and may potentially integrate physiological, biochemical, pharmacological, and genetic data in the form of a single model.