Author: Community

Petri nets are directed, weighted bipartite graphs that have successfully been applied to the systems biology of metabolic
and signal transduction pathways in modeling both stochastic (discrete) and deterministic (continuous) processes. Here we
exemplify how molecular mechanisms, biochemical or genetic, can be consistently respresented in the form of place/transition
Petri nets. We then describe the application of Petri nets to the reconstruction of molecular and genetic networks from experimental
data and their power to represent biological processes with arbitrary degree of resolution of the subprocesses at the cellular
and the molecular level. Petri nets are executable formal language models that permit the unambiguous visualization of regulatory
mechanisms, and they can be used to encode the results of mathematical algorithms for the reconstruction of causal interaction
networks from experimental time series data.

Understanding the mechanisms involved in apoptosis has been an area of extensive study due to its critical role in the development
and homeostasis of multi-cellular organisms. Our special interest lies in understanding the apoptosis of tumor cells which
is mediated by novel potential drugs. Cephalostatin 1 is a marine compound that can induce apoptosis in leukemic cells in
a dose- and time-dependent manner even at nano-molar concentrations using a recently discovered pathway that excludes the
receptor-mediated pathway and which includes both the mitochondrial and endoplasmic reticulum pathways (Dirsch et al., Cancer
Res 63:8869–8876, 2003; López-Antón et al., J Biol Chem 28:33078–33086, 2006). In this paper, the methods and tools of Petri net theory are used to construct, analyze, and validate a discrete Petri
net model for cephalostatin 1-induced apoptosis. Based on experimental results and literature search, we constructed a discrete
Petri net consisting of 43 places and 59 transitions. Standard Petri net analysis techniques such as structural and invariant
analyses and a recently developed modularity analysis technique using maximal abstract dependent transition sets (ADT sets)
were employed. Results of these analyses revealed model consistency with known biological behavior. The sub-modules represented
by the ADT sets were compared with the functional modules of apoptosis identified by Alberghina and Colangelo (BMC Neurosci
7(Suppl 1):S2, 2006).

For the implementation of the virtual cell, the fundamental question is how to model and simulate complex biological networks.
During the last 15 years, Petri nets have attracted more and more attention to help to solve this key problem. Regarding the
published papers, it seems clear that hybrid functional Petri nets are the adequate method to model complex biological networks.
Today, a Petri net model of biological networks is built manually by drawing places, transitions and arcs with mouse events.
Therefore, based on relevant molecular database and information systems biological data integration is an essential step in
constructing biological networks. In this paper, we will motivate the application of Petri nets for modeling and simulation
of biological networks. Furthermore, we will present a type of access to relevant metabolic databases such as KEGG, BRENDA,
etc. Based on this integration process, the system supports semi-automatic generation of the correlated hybrid Petri net model.
A case study of the cardio-disease related gene-regulated biological network is also presented. MoVisPP is available at http://agbi.techfak.uni-bielefeld.de/movispp/.

The paper introduces error-correcting Petri nets, an algebraic methodology for designing synthetic biologic systems with monitoring
capabilities. Linear error-correcting codes are used to extend the net’s structure in a way that allows for the algebraic
detection and correction of non-reachable net markings. The presented methodology is based on modulo-p Hamming codes—which are optimal for the modulo-p correction of single errors—but also works with any other linear error-correcting code.