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

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.Network reconstruction methods infere mathematical models of real world networks directly from experimental data ([1-5] and references therein). We have recently described an approach to the reconstruction of causal interaction networks from time series data sets [6,7]. The original algorithm has two significant properties. (1) It delivers provenly ALL minimal networks which are able to reproduce the time series data that served as input and (2) the algorithm is exact as it does not involve any heuristic decisions by the operator so that the results are independent of any personal bias. Having a complete list of alternative networks which are compatible with experimental data shall facilitate the design of new experiments aimed at ruling out alternatives to systematically find a final, unique solution.The output of the algorithm can be encoded as simple place/transition Petri net (Figure 1; [8]) containing only the minimal number of nodes and arcs required to fit the given data set. In order to exac