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.

SUMMARY: Structural modeling of biochemical networks enables qualitative as well as quantitative analysis of those networks. Automated network decomposition into functional modules is a crucial point in network analysis. Although there exist approaches for the analysis of networks, there is no open source tool available that combines editing, visualization and the computation of steady-state functional modules. We introduce a new tool called MonaLisa, which combines computation and visualization of functional modules as well as an editor for biochemical Petri nets. The analysis techniques allow for network decomposition into functional modules, for example t-invariants (elementary modes), maximal common transition sets, minimal cut sets and t-clusters. The graphical user interface provides various functionalities to construct and modify networks as well as to visualize the results of the analysis. AVAILABILITY AND IMPLEMENTATION: MonaLisa is licensed under the Artistic License 2.0. It is freely available at http://www.bioinformatik.uni-frankfurt.de/software.html. MonaLisa requires at least Java 6 and runs under Linux, Microsoft Windows and Mac OS.