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Open AccessArticle

Structure and Hierarchy of Influenza Virus Models Revealed by Reaction Network Analysis

1
Ernst-Abbe University of Applied Sciences Jena, Carl-Zeiss-Promenade 2, 07745 Jena, Germany
2
Bio Systems Analysis Group, Department of Mathematics and Computer Science, University of Jena, Ernst-Abbe-Platz 2, 07743 Jena, Germany
3
RNA Bioinformatics and High-Throughput Analysis, Friedrich Schiller University Jena, Leutragraben 1, 07743 Jena, Germany
4
European Virus Bioinformatics Center, Leutragraben 1, 07743 Jena, Germany
5
Mathematics and Computer Applications Department, Al-Nahrain University, Al-Jadriya, Baghdad 10072, Iraq
6
Chair of Bioinformatics, Matthias-Schleiden-Institute, University of Jena, Ernst-Abbe-Platz 2, 07743 Jena, Germany
*
Authors to whom correspondence should be addressed.
Viruses 2019, 11(5), 449; https://doi.org/10.3390/v11050449
Received: 26 March 2019 / Revised: 8 May 2019 / Accepted: 11 May 2019 / Published: 16 May 2019
(This article belongs to the Special Issue Virus Bioinformatics)
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Abstract

Influenza A virus is recognized today as one of the most challenging viruses that threatens both human and animal health worldwide. Understanding the control mechanisms of influenza infection and dynamics is crucial and could result in effective future treatment strategies. Many kinetic models based on differential equations have been developed in recent decades to capture viral dynamics within a host. These models differ in their complexity in terms of number of species elements and number of reactions. Here, we present a new approach to understanding the overall structure of twelve influenza A virus infection models and their relationship to each other. To this end, we apply chemical organization theory to obtain a hierarchical decomposition of the models into chemical organizations. The decomposition is based on the model structure (reaction rules) but is independent of kinetic details such as rate constants. We found different types of model structures ranging from two to eight organizations. Furthermore, the model’s organizations imply a partial order among models entailing a hierarchy of model, revealing a high model diversity with respect to their long-term behavior. Our methods and results can be helpful in model development and model integration, also beyond the influenza area. View Full-Text
Keywords: chemical organization theory; influenza A; virus dynamics modeling; complex networks analysis chemical organization theory; influenza A; virus dynamics modeling; complex networks analysis
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Peter, S.; Hölzer, M.; Lamkiewicz, K.; di Fenizio, P.S.; Al Hwaeer, H.; Marz, M.; Schuster, S.; Dittrich, P.; Ibrahim, B. Structure and Hierarchy of Influenza Virus Models Revealed by Reaction Network Analysis. Viruses 2019, 11, 449.

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