BACKGROUND: The concept of Petri nets (PN) is widely used in systems biology and allows modeling of complex biochemical systems like metabolic systems, signal transduction pathways, and gene expression networks. In particular, PN allows the topological analysis based on structural properties, which is important and useful when quantitative (kinetic) data are incomplete or unknown. Knowing the kinetic parameters, the simulation of time evolution of such models can help to study the dynamic behavior of the underlying system. If the number of involved entities (molecules) is low, a stochastic simulation should be preferred against the classical deterministic approach of solving ordinary differential equations. The Stochastic Simulation Algorithm (SSA) is a common method for such simulations. The combination of the qualitative and semi-quantitative PN modeling and stochastic analysis techniques provides a valuable approach in the field of systems biology. RESULTS: Here, we describe the implementation of stochastic analysis in a PN environment. We extended MONALISA - an open-source software for creation, visualization and analysis of PN - by several stochastic simulation methods. The simulation module offers four simulation modes, among them the stochastic mode with constant firing rates and Gillespie's algorithm as exact and approximate versions. The simulator is operated by a user-friendly graphical interface and accepts input data such as concentrations and reaction rate constants that are common parameters in the biological context. The key features of the simulation module are visualization of simulation, interactive plotting, export of results into a text file, mathematical expressions for describing simulation parameters, and up to 500 parallel simulations of the same parameter sets. To illustrate the method we discuss a model for insulin receptor recycling as case study. CONCLUSIONS: We present a software that combines the modeling power of Petri nets with stochastic simulation of dynamic processes in a user-friendly environment supported by an intuitive graphical interface. The program offers a valuable alternative to modeling, using ordinary differential equations, especially when simulating single-cell experiments with low molecule counts. The ability to use mathematical expressions provides an additional flexibility in describing the simulation parameters. The open-source distribution allows further extensions by third-party developers. The software is cross-platform and is licensed under the Artistic License 2.0.

Erratum After publication of the original article [1] the authors have brought to our attention that the following revisions had not been incorporated into the final published version. In Definition 1 (Petri net): “E⊆ ((P x T)∪(T x P))” is the set of directed edges not “E⊆ ((P T) ∪ (T P))”. A segment of the Legend in Figure two: “A model of insulin receptor activation and recycling.” was incorrect and has been removed. The Legend of Figure three was incorrect and the correct legend is: “The model of insulin receptor recycling according to Figure 2 is represented as a Petri net. Places are drawn as circles and transitions as black squares.” These mistakes have been updated in the original article as detailed in this erratum.

The program HBexplore is a new tool for identifying and analysing H-bonding patterns in biological macromolecules. It selects all potential H-bonds according to geometrical criteria. The H-bond table can then be subjected to further automatic or interactive analysis tools. These tools include the calculation of mean values and distributions of geometrical H-bond parameters for parts of a single structure, for complete single structures and for structure sets, the classification of each H-bond according to the participation of backbone, side chain or base, ligand and water parts of nucleic acids or proteins, identification of Watson-Crick nucleotide pairs and of H-bonded pairs of equal nucleotides, the calculation of the mean number of H-bonds per residue, and of the fraction of potential donor and acceptor atoms involved in H-bonds. HBexplore further generates automatically a H-bond residue interaction table. This table lists for all residues of the structure the other residues, ligands or water molecules directly connected via a H-bond. By means of a binary tree search algorithm, this table is then converted into a H-bond cluster table. Clusters are understood here as an uninterrupted network of H-bonded residues. For nucleic acids, secondary structures and tertiary interactions are automatically derived from the H-bonding pattern. HBexplore is applied to two example RNA structures: a pseudoknot and a hairpin. It provides a comprehensive listing of individual H-bonds and statistical information for larger structure sets. In addition, it can identify interesting new H-bond motifs. One example is a pentanucleotide base-base H-bond interaction motif in the RNA pseudoknot. HBexplore is intended to contribute both to the elucidation of general principles of the architecture of biological macromolecules, and to the prediction and refinement of single structures.