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. 2008 in Math Methods Oper Res 67:117–132) for the reconstruction of standard place/transition Petri nets from time-series of experimental data sets. This previously reported method finds provably all networks capable to reproduce the experimental observations. In this paper we enhance this approach to generate extended Petri nets involving mechanisms formally corresponding to catalytic or inhibitory dependencies that mediate the involved reactions. The new algorithm delivers the set of all extended Petri nets being consistent with the time-series data used for reconstruction. It is illustrated using the phosphate regulatory network of enterobacteria as a case study.