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.
KeywordsReverse engineering Petri nets Read arcs and inhibitory arcs Phosphate regulatory network
Mathematics Subject Classification (2000)68R05 92C42
Unable to display preview. Download preview PDF.
- Durzinsky M, Wagler A, Weismantel R (2008b) A combinatorial approach to reconstruct Petri nets from experimental data. In: Computational methods in systems biology, LNCS, vol 5307. Springer, Heidelberg, pp 328–346Google Scholar
- Durzinsky M, Marwan W, Wagler A (2011a) Reconstruction of extended Petri nets from time series data and its application to signal transduction and to gene regulatory networks. BMC Syst Biol 5:113. doi: 10.1186/1752-0509-5-113
- Heiner M, Koch I (2004) Petri net based model validation in systems biology. In: 25th International conference on application and theory of Petri nets. Springer, Heidelberg, pp 216–237Google Scholar
- Koch I, Heiner M (2008) Petri nets in biological network analysis. In: Junker BH, Schreiber F (eds) Analysis of biological networks. Wiley Book Series on Bioinformatics. Wiley, New York, pp 139–179Google Scholar
- Krishna R, Guo S (2008) A partial granger causality approach to explode causal networks derived from multi-parameter data. In: Computational methods in systems biology, LNCS, vol 5307. Springer, Heidelberg, pp 9–27Google Scholar
- Marwan W, Rohr C, Heiner M (2010) Petri nets in Snoopy: a unifying framework for the graphical display, computational modelling, simulation, and bioinformatic annotation of bacterial regulatory network. In: Helden Jv, Toussaint A, Thieffry D (eds) Bacterial molecular networks, methods in molecular biology. Humana Press, USA (in press)Google Scholar
- Matsuno H, Tanaka Y, Aoshima H, Doi A, Matsui M, Miyano S (2003) Biopathways representation and simulation on hybrid functional Petri net. In Silico Biol 3: 389–404Google Scholar
- Neidhardt FC, Ingraham JL, Schaechter M (1990) Physiology of the bacterial cell. A molecular approach. Sinauer Associates, SunderlandGoogle Scholar
- Umans C (1998) The minimum equivalent DNF problem and shortest implicants. In: FOCS’98, pp 556–563Google Scholar