Modularization of biochemical networks based on classification of Petri net t-invariants

<p>Abstract</p> <p>Background</p> <p>Structural analysis of biochemical networks is a growing field in bioinformatics and systems biology. The availability of an increasing amount of biological data from molecular biological networks promises a deeper understanding but confronts researchers with the problem of combinatorial explosion. The amount of qualitative network data is growing much faster than the amount of quantitative data, such as enzyme kinetics. In many cases it is even impossible to measure quantitative data because of limitations of experimental methods, or for ethical reasons. Thus, a huge amount of qualitative data, such as interaction data, is available, but it was not sufficiently used for modeling purposes, until now. New approaches have been developed, but the complexity of data often limits the application of many of the methods. Biochemical Petri nets make it possible to explore static and dynamic qualitative system properties. One Petri net approach is model validation based on the computation of the system's invariant properties, focusing on t-invariants. T-invariants correspond to subnetworks, which describe the basic system behavior.</p> <p>With increasing system complexity, the basic behavior can only be expressed by a huge number of t-invariants. According to our validation criteria for biochemical Petri nets, the necessary verification of the biological meaning, by interpreting each subnetwork (t-invariant) manually, is not possible anymore. Thus, an automated, biologically meaningful classification would be helpful in analyzing t-invariants, and supporting the understanding of the basic behavior of the considered biological system.</p> <p>Methods</p> <p>Here, we introduce a new approach to automatically classify t-invariants to cope with network complexity. We apply clustering techniques such as UPGMA, Complete Linkage, Single Linkage, and Neighbor Joining in combination with different distance measures to get biologically meaningful clusters (t-clusters), which can be interpreted as modules. To find the optimal number of t-clusters to consider for interpretation, the cluster validity measure, Silhouette Width, is applied.</p> <p>Results</p> <p>We considered two different case studies as examples: a small signal transduction pathway (pheromone response pathway in <it>Saccharomyces cerevisiae</it>) and a medium-sized gene regulatory network (gene regulation of Duchenne muscular dystrophy). We automatically classified the t-invariants into functionally distinct t-clusters, which could be interpreted biologically as functional modules in the network. We found differences in the suitability of the various distance measures as well as the clustering methods. In terms of a biologically meaningful classification of t-invariants, the best results are obtained using the Tanimoto distance measure. Considering clustering methods, the obtained results suggest that UPGMA and Complete Linkage are suitable for clustering t-invariants with respect to the biological interpretability.</p> <p>Conclusion</p> <p>We propose a new approach for the biological classification of Petri net t-invariants based on cluster analysis. Due to the biologically meaningful data reduction and structuring of network processes, large sets of t-invariants can be evaluated, allowing for model validation of qualitative biochemical Petri nets. This approach can also be applied to elementary mode analysis.</p

Model transformation of metabolic networks using a Petri net based framework

The different modeling approaches in Systems Biology create models with different levels of detail. The transformation techniques in Petri net theory can provide a solid framework for zooming between these different levels of abstraction and refinement. This work presents a Petri net based approach to Metabolic Engineering that implements model reduction methods to reduce the complexity of large-scale metabolic networks. These methods can be complemented with kinetics inference to build dynamic models with a smaller number of parameters. The central carbon metabolism model of E. coli is used as a test-case to illustrate the application of these concepts. Model transformation is a promising mechanism to facilitate pathway analysis and dynamic modeling at the genome-scale level.(undefined

Biomodelkit - a framework for modular biomodel-engineering

Otto-von-Guericke-Universität Magdeburg, Fakultät für Naturwissenschaften, Dissertation, 2017von Dipl.-Ing. Mary-Ann BlätkeLiteraturverzeichnis: Seite [177]-18

Modeling and analyzing the action process of monoamine hormones in depression: a Petri nets-based intelligent approach

In contemporary society, the incidence of depression is increasing significantly around the world. At present, most of the treatment methods for depression are psychological counseling and drug therapy. However, this approach does not allow patients to visualize the logic of hormones at the pathological level. In order to better apply intelligence computing methods to the medical field, and to more easily analyze the relationship between norepinephrine and dopamine in depression, it is necessary to build an interpretable graphical model to analyze this relationship which is of great significance to help discover new treatment ideas and potential drug targets. Petri net (PN) is a mathematical and graphic tool used to simulate and study complex system processes. This article utilizes PN to study the relationship between norepinephrine and dopamine in depression. We use PN to model the relationship between the norepinephrine and dopamine, and then use the invariant method of PN to verify and analyze it. The mathematical model proposed in this article can explain the complex pathogenesis of depression and visualize the process of intracellular hormone-induced state changes. Finally, the experiment result suggests that our method provides some possible research directions and approaches for the development of antidepressant drugs

Petri nets for modelling metabolic pathways: a survey

In the last 15 years, several research efforts have been directed towards the representation and the analysis of metabolic pathways by using Petri nets. The goal of this paper is twofold. First, we discuss how the knowledge about metabolic pathways can be represented with Petri nets. We point out the main problems that arise in the construction of a Petri net model of a metabolic pathway and we outline some solutions proposed in the literature. Second, we present a comprehensive review of recent research on this topic, in order to assess the maturity of the field and the availability of a methodology for modelling a metabolic pathway by a corresponding Petri net

Automatic Curation of SBML Models based on their ODE Semantics

Many models in Systems Biology are described as a system of Ordinary Differential Equations. The fact that the Systems Biology Markup Language SBML has become a standard for sharing and publishing models, has helped in making modelers formalize the structure of the reactions and use structure-related methods for reasoning about models. Unfortunately, SBML does not enforce any coherence between the structure and the kinetics of a reaction. Therefore the structural interpretation of models transcribed in SBML may vary according to different choices of representation of the original model and may be incorrect for some analyses. The first contribution of this paper is to propose a general compatibility condition between the kinetic expression and the structure of a reaction. We show that these well-formedness conditions are satisfied by standard kinetics and that they entail a property of independence from the kinetic expressions for the influence graph associated to the ODEs. We present a heuristic algorithm of low computational complexity for, given an ODE system, inferring a reaction model that preserves the ODE semantics and infers well-formed reactions whenever possible. This algorithm can be used for not only checking whether the network and ODE structures of an SBML model are consistent but also automatically curating SBML models by exporting them as ODE systems and then importing them as well-formed reaction models. We show how this strategy is capable of automatically curating SBML models on a large scale and provide some statistics figures obtained on the whole biomodels.net repository. The algorithms described in this paper are implemented in the open-source software modeling platform BIOCHAM [Fages and Soliman, 2008a, Calzone et al., 2006] available at http://contraintes.inria.fr/biocham The models used in the experiments are available from http://www.biomodels.net

Computational analysis of alternative splicing in human and mice

Im ersten Teil wurden Transkript-Spleißstellen untersucht, mit dem Ziel, alternative und Referenzspleißstellen zu unterscheiden. Die Ergebnisse belegen, dass sich beide Klassen von Spleißstellen durch einen Spleißstellen-Score und vermehrtes Auftreten von Spleißfaktor-Bindemotiven in Umgebung der Spleißstellen abgrenzen lassen. Zusätzlich konnte eine positive Korrelation zwischen der Häufigkeit der Nutzung bestimmter Spleißstellen und dem Spleißstellen-Score in beiden Vergleichsklassen nachgewiesen werden. Diese Abhängigkeit impliziert, dass die Genauigkeit der Annotation alternativer Spleißvarianten mit der Anzahl beobachteter Transkripte steigt. Im zweiten Teil wurde das Spleißsignalmotiv GYNNGY untersucht, welches mehr als 40% aller überlappenden Donor-Spleißsignale ausmacht. Mittels in silico Analysen und experimenteller Validierung wurde die Plausibilität dieses subtilen Spleißmusters bestätigt. Der Vergleich mit anderen humanen Spleißvarianten sowie mit Tandem Donoren in Maus-Transkripten zeigte zudem ausgeprägte Unterschiede bezüglich des Spleißstellen-Scores, der Konservierung, sowie dem Vorkommen von Spleißfaktoren-Bindemotiven. Die Verschiebung des Leserasters durch alternatives Spleißen an GYNNGY-Donoren lässt auf eine komplexe Rolle im RNA-Reifungsprozess schließen. Im dritten Teil wurden Reaktionen des spleißosomalen Makrokomples aus publizierten, experimentellen Daten zusammengestellt und mit Hilfe der Petri-Netz-Theorie in einem qualitativen Modell dargestellt. Unter Annahme eines Steady-State Systems wurden minimale, semipositive T-Invarianten berechnet und zur Validierung des Modells herangezogen. Auf Grundlage der vollständigen Abdeckung des Reaktionsnetzwerks mit T-Invarianten konnten weitere Strukturmerkmale, wie Maximal-Gemeinsame Transitions.Mengen und T-Cluster berechnet werden, welche wichtige Stadien des Spleißosomaufbaus widerspiegeln