Reconstruction of extended Petri nets from time-series data by using logical control functions.

The aim of this work is to extend a previously presented algorithm (Durzinsky et al. 2008b in Computational methods in systems biology, LNCS, vol 5307. Springer, Heidelberg, pp 328–346; Marwan et al.

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

Background: 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 deliveries all possible alternative minimal networks in terms of simple place/transition Petri nets that are consistent with a given discrete time series data set.

Results: We fundamentally extended the previously published algorithm to consider catalysis and inhibition of the reactions that occur in the underlying network.

Automatic reconstruction of molecular and genetic networks from discrete time series data.

We apply a mathematical algorithm which processes discrete time series data to generate a complete list of Petri net structures containing the minimal number of nodes required to reproduce the data set. The completeness of the list as guaranteed by a mathematical proof allows to define a minimal set of experiments required to discriminate between alternative network structures. This in principle allows to prove all possible minimal network structures by disproving all alternative candidate structures.