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

From Epidemic to Pandemic Modelling

We present a methodology for systematically extending epidemic models to multilevel and multiscale spatio-temporal pandemic ones. Our approach builds on the use of coloured stochastic and continuous Petri nets facilitating the sound component-based extension of basic SIR models to include population stratification and also spatio-geographic information and travel connections, represented as graphs, resulting in robust stratified pandemic metapopulation models. This method is inherently easy to use, producing scalable and reusable models with a high degree of clarity and accessibility which can be read either in a deterministic or stochastic paradigm. Our method is supported by a publicly available platform PetriNuts; it enables the visual construction and editing of models; deterministic, stochastic and hybrid simulation as well as structural and behavioural analysis. All the models are available as supplementary material, ensuring reproducibility.Comment: 79 pages (with Appendix), 23 figures, 7 table

From Epidemic to Pandemic Modelling

We present a methodology for systematically extending epidemic models to multilevel and multiscale spatio-temporal pandemic ones. Our approach builds on the use of coloured stochastic and continuous Petri nets facilitating the sound component-based extension of basic SIR models to include population stratification and also spatio-geographic information and travel connections, represented as graphs, resulting in robust stratified pandemic metapopulation models. The epidemic components and the spatial and stratification data are combined together in these coloured models and built in to the underlying expanded models. As a consequence this method is inherently easy to use, producing scalable and reusable models with a high degree of clarity and accessibility which can be read either in a deterministic or stochastic paradigm. Our method is supported by a publicly available platform PetriNuts; it enables the visual construction and editing of models; deterministic, stochastic and hybrid simulation as well as structural and behavioural analysis. All models are available as Supplementary Material, ensuring reproducibility. All uncoloured Petri nets can be animated within a web browser at https://www-dssz.informatik.tu-cottbus.de/DSSZ/Research/ModellingEpidemics, assisting the comprehension of those models. We aim to enable modellers and planners to construct clear and robust models by themselves

Application of Petri net based analysis techniques to signal transduction pathways

BACKGROUND: Signal transduction pathways are usually modelled using classical quantitative methods, which are based on ordinary differential equations (ODEs). However, some difficulties are inherent in this approach. On the one hand, the kinetic parameters involved are often unknown and have to be estimated. With increasing size and complexity of signal transduction pathways, the estimation of missing kinetic data is not possible. On the other hand, ODEs based models do not support any explicit insights into possible (signal-) flows within the network. Moreover, a huge amount of qualitative data is available due to high-throughput techniques. In order to get information on the systems behaviour, qualitative analysis techniques have been developed. Applications of the known qualitative analysis methods concern mainly metabolic networks. Petri net theory provides a variety of established analysis techniques, which are also applicable to signal transduction models. In this context special properties have to be considered and new dedicated techniques have to be designed. METHODS: We apply Petri net theory to model and analyse signal transduction pathways first qualitatively before continuing with quantitative analyses. This paper demonstrates how to build systematically a discrete model, which reflects provably the qualitative biological behaviour without any knowledge of kinetic parameters. The mating pheromone response pathway in Saccharomyces cerevisiae serves as case study. RESULTS: We propose an approach for model validation of signal transduction pathways based on the network structure only. For this purpose, we introduce the new notion of feasible t-invariants, which represent minimal self-contained subnets being active under a given input situation. Each of these subnets stands for a signal flow in the system. We define maximal common transition sets (MCT-sets), which can be used for t-invariant examination and net decomposition into smallest biologically meaningful functional units. CONCLUSION: The paper demonstrates how Petri net analysis techniques can promote a deeper understanding of signal transduction pathways. The new concepts of feasible t-invariants and MCT-sets have been proven to be useful for model validation and the interpretation of the biological system behaviour. Whereas MCT-sets provide a decomposition of the net into disjunctive subnets, feasible t-invariants describe subnets, which generally overlap. This work contributes to qualitative modelling and to the analysis of large biological networks by their fully automatic decomposition into biologically meaningful modules

09091 Abstracts Collection -- Formal Methods in Molecular Biology

From 23. February to 27. February 2009, the Dagstuhl Seminar 09091 ``Formal Methods in Molecular Biology \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Annual Report 1999 / Department for Computer Science

Selbstdarstellung des Instituts für Informatik der BTU Cottbus und Berichte der Lehrstühle für das Jahr 1999.Presentation of the Department for Computer Science of the BTU Cottbus and reports of the chairs at the department for the year 1999

Structural Analysis to Determine the Core of Hypoxia Response Network

The advent of sophisticated molecular biology techniques allows to deduce the structure of complex biological networks. However, networks tend to be huge and impose computational challenges on traditional mathematical analysis due to their high dimension and lack of reliable kinetic data. To overcome this problem, complex biological networks are decomposed into modules that are assumed to capture essential aspects of the full network's dynamics. The question that begs for an answer is how to identify the core that is representative of a network's dynamics, its function and robustness. One of the powerful methods to probe into the structure of a network is Petri net analysis. Petri nets support network visualization and execution. They are also equipped with sound mathematical and formal reasoning based on which a network can be decomposed into modules. The structural analysis provides insight into the robustness and facilitates the identification of fragile nodes. The application of these techniques to a previously proposed hypoxia control network reveals three functional modules responsible for degrading the hypoxia-inducible factor (HIF). Interestingly, the structural analysis identifies superfluous network parts and suggests that the reversibility of the reactions are not important for the essential functionality. The core network is determined to be the union of the three reduced individual modules. The structural analysis results are confirmed by numerical integration of the differential equations induced by the individual modules as well as their composition. The structural analysis leads also to a coarse network structure highlighting the structural principles inherent in the three functional modules. Importantly, our analysis identifies the fragile node in this robust network without which the switch-like behavior is shown to be completely absent

Cross-species hybridisation of human and bovine orthologous genes on high density cDNA microarrays

BACKGROUND: Cross-species gene-expression comparison is a powerful tool for the discovery of evolutionarily conserved mechanisms and pathways of expression control. The usefulness of cDNA microarrays in this context is that broad areas of homology are compared and hybridization probes are sufficiently large that small inter-species differences in nucleotide sequence would not affect the analytical results. This comparative genomics approach would allow a common set of genes within a specific developmental, metabolic, or disease-related gene pathway to be evaluated in experimental models of human diseases. The objective of this study was to investigate the feasibility and reproducibility of cross-species analysis employing a human cDNA microarray as probe. RESULTS: As a proof of principle, total RNA derived from human and bovine fetal brains was used as a source of labelled targets for hybridisation onto a human cDNA microarray composed of 349 characterised genes. Each gene was spotted 20 times representing 6,980 data points thus enabling highly reproducible spot quantification. Employing high stringency hybridisation and washing conditions, followed by data analysis, revealed slight differences in the expression levels and reproducibility of the signals between the two species. We also assigned each of the genes into three expression level categories- i.e. high, medium and low. The correlation co-efficient of cross hybridisation between the orthologous genes was 0.94. Verification of the array data by semi-quantitative RT-PCR using common primer sequences enabled co-amplification of both human and bovine transcripts. Finally, we were able to assign gene names to previously uncharacterised bovine ESTs. CONCLUSIONS: Results of our study demonstrate the harnessing and utilisation power of comparative genomics and prove the feasibility of using human microarrays to facilitate the identification of co-expressed orthologous genes in common tissues derived from different species