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Petri net-based approach to modeling and analysis of selected aspects of the molecular regulation of angiogenesis.

ABSTRACT: The functioning of both normal and pathological tissues depends on an adequate supply of oxygen through the blood vessels. A process called angiogenesis, in which new endothelial cells and smooth muscles interact with each other, forming new blood vessels either from the existing ones or from a primary vascular plexus, is particularly important and interesting, due to new therapeutic possibilities it offers. This is a multi-step and very complex process, so an accurate understanding of the underlying mechanisms is a significant task, especially in recent years, with the constantly increasing amount of new data that must be taken into account. A systems approach is necessary for these studies because it is not sufficient to analyze the properties of the building blocks separately and an analysis of the whole network of interactions is essential. This approach is based on building a mathematical model of the system, while the model is expressed in the formal language of a mathematical theory. Recently, the theory of Petri nets was shown to be especially promising for the modeling and analysis of biological phenomena. This analysis, based mainly on t-invariants, has led to a particularly important finding that a direct link (close connection) exist between transforming growth factor ?1 (TGF-?1), endothelial nitric oxide synthase (eNOS), nitric oxide (NO), and hypoxia-inducible factor 1, the molecules that play a crucial roles during angiogenesis. We have shown that TGF-?1 may participate in the inhibition of angiogenesis through the upregulation of eNOS expression, which is responsible for catalyzing NO production. The results obtained in the previous studies, concerning the effects of NO on angiogenesis, have not been conclusive, and therefore, our study may contribute to a better understanding of this phenomenon.

SUBMITTER: Formanowicz D

PROVIDER: S-EPMC5333880 | biostudies-literature | 2017

REPOSITORIES: biostudies-literature

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Petri net-based approach to modeling and analysis of selected aspects of the molecular regulation of angiogenesis.

Formanowicz Dorota D Radom Marcin M Zawierucha Piotr P Formanowicz Piotr P

PloS one 20170302 3

The functioning of both normal and pathological tissues depends on an adequate supply of oxygen through the blood vessels. A process called angiogenesis, in which new endothelial cells and smooth muscles interact with each other, forming new blood vessels either from the existing ones or from a primary vascular plexus, is particularly important and interesting, due to new therapeutic possibilities it offers. This is a multi-step and very complex process, so an accurate understanding of the under ...[more]

PMID: 28253310

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Project description:BackgroundStructural 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.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.MethodsHere, 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.ResultsWe considered two different case studies as examples: a small signal transduction pathway (pheromone response pathway in Saccharomyces cerevisiae) 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.ConclusionWe 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.

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Petri net-based approach to modeling and analysis of selected aspects of the molecular regulation of angiogenesis.

Publications

Petri net-based approach to modeling and analysis of selected aspects of the molecular regulation of angiogenesis.

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