Abstract
BackgroundNetwork 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.ResultsWe 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.ConclusionsThe 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.
Highlights
Network inference methods reconstruct mathematical models of molecular or genetic networks directly from experimental data sets
Considering catalysis and inhibition we deal with controled reactions: Each set of such transitions that connect the same places in the same way is encoded by a controled reaction Rc = (r, fr), a pair, where is the reaction vector indicating the change in the marking of places caused by firing of any of the transitions of the set and fr is a control function encoding control arcs connected to the transitions
Reaction vectors and control functions separately describe two different structural properties of one and the same extended Petri net: (1) The reaction vectors r describe how the places of a Petri net are connected by transitions through directed standard arcs, and how the marking of the places changes upon firing of the transitions
Summary
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. Network reconstruction methods infere mathematical models of real world networks directly from experimental data ([1,2,3,4,5] and references therein). If the number of components measured in the time series is not sufficiently high in order to create a Petri net which is able to reproduce the data, the algorithm adds one place and restarts the reconstruction process and continues to do so until solutions are found [6,7]
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