From Petri Nets to differential equations: An integrative approach for biochemical network analysis

We report on the results of an investigation into the integration of Petri nets and ordinary differential equations (ODEs) for the modelling and analysis of biochemical networks, and the application of our approach to the model of the influence of the Raf Kinase Inhibitor Protein (RKIP) on the Extracellular signal Regulated Kinase (ERK) signalling pathway. We show that analysis based on a discrete Petri net model of the system can be used to derive the sets of initial concentrations required by the corresponding continuous ordinary differential equation model, and no other initial concentrations produce meaningful steady states. Altogether, this paper represents a tutorial in step-wise modelling and analysis of larger models as well as in structured design of ODEs

A structured approach for the engineering of biochemical network models, illustrated for signalling pathways

http://dx.doi.org/10.1093/bib/bbn026Quantitative models of biochemical networks (signal transduction cascades, metabolic pathways, gene regulatory circuits) are a central component of modern systems biology. Building and managing these complex models is a major challenge that can benefit from the application of formal methods adopted from theoretical computing science. Here we provide a general introduction to the field of formal modelling, which emphasizes the intuitive biochemical basis of the modelling process, but is also accessible for an audience with a background in computing science and/or model engineering. We show how signal transduction cascades can be modelled in a modular fashion, using both a qualitative approach { Qualitative Petri nets, and quantitative approaches { Continuous Petri Nets and Ordinary Differential Equations. We review the major elementary building blocks of a cellular signalling model, discuss which critical design decisions have to be made during model building, and present ..

An integrative top-down and bottom-up qualitative model construction framework for exploration of biochemical systems

The authors would like to thank the support on this research by the CRISP project (Combinatorial Responses In Stress Pathways) funded by the BBSRC (BB/F00513X/1) under the Systems Approaches to Biological Research (SABR) Initiative.Peer reviewedPublisher PD

Petri nets for systems and synthetic biology

We give a description of a Petri net-based framework for modelling and analysing biochemical pathways, which uni¯es the qualita- tive, stochastic and continuous paradigms. Each perspective adds its con- tribution to the understanding of the system, thus the three approaches do not compete, but complement each other. We illustrate our approach by applying it to an extended model of the three stage cascade, which forms the core of the ERK signal transduction pathway. Consequently our focus is on transient behaviour analysis. We demonstrate how quali- tative descriptions are abstractions over stochastic or continuous descrip- tions, and show that the stochastic and continuous models approximate each other. Although our framework is based on Petri nets, it can be applied more widely to other formalisms which are used to model and analyse biochemical networks

An Integrated Qualitative and Quantitative Biochemical Model Learning Framework Using Evolutionary Strategy and Simulated Annealing

The authors would like to thank the support on this research by the CRISP Project (Combinatorial Responses In Stress Pathways) funded by the BBSRC (BB/F00513X/1) under the Systems Approaches to Biological Research (SABR) Initiative.Peer reviewedPublisher PD

In-silico-Systemanalyse von Biopathways

Chen M. In silico systems analysis of biopathways. Bielefeld (Germany): Bielefeld University; 2004.In the past decade with the advent of high-throughput technologies, biology has migrated from a descriptive science to a predictive one. A vast amount of information on the metabolism have been produced; a number of specific genetic/metabolic databases and computational systems have been developed, which makes it possible for biologists to perform in silico analysis of metabolism. With experimental data from laboratory, biologists wish to systematically conduct their analysis with an easy-to-use computational system. One major task is to implement molecular information systems that will allow to integrate different molecular database systems, and to design analysis tools (e.g. simulators of complex metabolic reactions). Three key problems are involved: 1) Modeling and simulation of biological processes; 2) Reconstruction of metabolic pathways, leading to predictions about the integrated function of the network; and 3) Comparison of metabolism, providing an important way to reveal the functional relationship between a set of metabolic pathways. This dissertation addresses these problems of in silico systems analysis of biopathways. We developed a software system to integrate the access to different databases, and exploited the Petri net methodology to model and simulate metabolic networks in cells. It develops a computer modeling and simulation technique based on Petri net methodology; investigates metabolic networks at a system level; proposes a markup language for biological data interchange among diverse biological simulators and Petri net tools; establishes a web-based information retrieval system for metabolic pathway prediction; presents an algorithm for metabolic pathway alignment; recommends a nomenclature of cellular signal transduction; and attempts to standardize the representation of biological pathways. Hybrid Petri net methodology is exploited to model metabolic networks. Kinetic modeling strategy and Petri net modeling algorithm are applied to perform the processes of elements functioning and model analysis. The proposed methodology can be used for all other metabolic networks or the virtual cell metabolism. Moreover, perspectives of Petri net modeling and simulation of metabolic networks are outlined. A proposal for the Biology Petri Net Markup Language (BioPNML) is presented. The concepts and terminology of the interchange format, as well as its syntax (which is based on XML) are introduced. BioPNML is designed to provide a starting point for the development of a standard interchange format for Bioinformatics and Petri nets. The language makes it possible to exchange biology Petri net diagrams between all supported hardware platforms and versions. It is also designed to associate Petri net models and other known metabolic simulators. A web-based metabolic information retrieval system, PathAligner, is developed in order to predict metabolic pathways from rudimentary elements of pathways. It extracts metabolic information from biological databases via the Internet, and builds metabolic pathways with data sources of genes, sequences, enzymes, metabolites, etc. The system also provides a navigation platform to investigate metabolic related information, and transforms the output data into XML files for further modeling and simulation of the reconstructed pathway. An alignment algorithm to compare the similarity between metabolic pathways is presented. A new definition of the metabolic pathway is proposed. The pathway defined as a linear event sequence is practical for our alignment algorithm. The algorithm is based on strip scoring the similarity of 4-hierarchical EC numbers involved in the pathways. The algorithm described has been implemented and is in current use in the context of the PathAligner system. Furthermore, new methods for the classification and nomenclature of cellular signal transductions are recommended. For each type of characterized signal transduction, a unique ST number is provided. The Signal Transduction Classification Database (STCDB), based on the proposed classification and nomenclature, has been established. By merging the ST numbers with EC numbers, alignments of biopathways are possible. Finally, a detailed model of urea cycle that includes gene regulatory networks, metabolic pathways and signal transduction is demonstrated by using our approaches. A system biological interpretation of the observed behavior of the urea cycle and its related transcriptomics information is proposed to provide new insights for metabolic engineering and medical care

A Unique Transformation from Ordinary Differential Equations to Reaction Networks

Many models in Systems Biology are described as a system of Ordinary Differential Equations, which allows for transient, steady-state or bifurcation analysis when kinetic information is available. Complementary structure-related qualitative analysis techniques have become increasingly popular in recent years, like qualitative model checking or pathway analysis (elementary modes, invariants, flux balance analysis, graph-based analyses, chemical organization theory, etc.). They do not rely on kinetic information but require a well-defined structure as stochastic analysis techniques equally do. In this article, we look into the structure inference problem for a model described by a system of Ordinary Differential Equations and provide conditions for the uniqueness of its solution. We describe a method to extract a structured reaction network model, represented as a bipartite multigraph, for example, a continuous Petri net (CPN), from a system of Ordinary Differential Equations (ODEs). A CPN uniquely defines an ODE, and each ODE can be transformed into a CPN. However, it is not obvious under which conditions the transformation of an ODE into a CPN is unique, that is, when a given ODE defines exactly one CPN. We provide biochemically relevant sufficient conditions under which the derived structure is unique and counterexamples showing the necessity of each condition. Our method is implemented and available; we illustrate it on some signal transduction models from the BioModels database. A prototype implementation of the method is made available to modellers at http://contraintes.inria.fr/~soliman/ode2pn.html, and the data mentioned in the “Results” section at http://contraintes.inria.fr/~soliman/ode2pn_data/. Our results yield a new recommendation for the import/export feature of tools supporting the SBML exchange format

Modeling formalisms in systems biology

Systems Biology has taken advantage of computational tools and high-throughput experimental data to model several biological processes. These include signaling, gene regulatory, and metabolic networks. However, most of these models are specific to each kind of network. Their interconnection demands a whole-cell modeling framework for a complete understanding of cellular systems. We describe the features required by an integrated framework for modeling, analyzing and simulating biological processes, and review several modeling formalisms that have been used in Systems Biology including Boolean networks, Bayesian networks, Petri nets, process algebras, constraint-based models, differential equations, rule-based models, interacting state machines, cellular automata, and agent-based models. We compare the features provided by different formalisms, and discuss recent approaches in the integration of these formalisms, as well as possible directions for the future.Research supported by grants SFRH/BD/35215/2007 and SFRH/BD/25506/2005 from the Fundacao para a Ciencia e a Tecnologia (FCT) and the MIT-Portugal Program through the project "Bridging Systems and Synthetic Biology for the development of improved microbial cell factories" (MIT-Pt/BS-BB/0082/2008)

Design and Development of Software Tools for Bio-PEPA

This paper surveys the design of software tools for the Bio-PEPA process algebra. Bio-PEPA is a high-level language for modelling biological systems such as metabolic pathways and other biochemical reaction networks. Through providing tools for this modelling language we hope to allow easier use of a range of simulators and model-checkers thereby freeing the modeller from the responsibility of developing a custom simulator for the problem of interest. Further, by providing mappings to a range of different analysis tools the Bio-PEPA language allows modellers to compare analysis results which have been computed using independent numerical analysers, which enhances the reliability and robustness of the results computed.