Manatee invariants reveal functional pathways in signaling networks

  • Background: Signal transduction pathways are important cellular processes to maintain the cell’s integrity. Their imbalance can cause severe pathologies. As signal transduction pathways feature complex regulations, they form intertwined networks. Mathematical models aim to capture their regulatory logic and allow an unbiased analysis of robustness and vulnerability of the signaling network. Pathway detection is yet a challenge for the analysis of signaling networks in the field of systems biology. A rigorous mathematical formalism is lacking to identify all possible signal flows in a network model. Results: In this paper, we introduce the concept of Manatee invariants for the analysis of signal transduction networks. We present an algorithm for the characterization of the combinatorial diversity of signal flows, e.g., from signal reception to cellular response. We demonstrate the concept for a small model of the TNFR1-mediated NF- κB signaling pathway. Manatee invariants reveal all possible signal flows in the network. Further, we show the application of Manatee invariants for in silico knockout experiments. Here, we illustrate the biological relevance of the concept. Conclusions: The proposed mathematical framework reveals the entire variety of signal flows in models of signaling systems, including cyclic regulations. Thereby, Manatee invariants allow for the analysis of robustness and vulnerability of signaling networks. The application to further analyses such as for in silico knockout was shown. The new framework of Manatee invariants contributes to an advanced examination of signaling systems.
Author:Leonie Amstein, Jörg Ackermann, Jennifer Scheidel, Simone FuldaORCiDGND, Ivan ĐikićORCiDGND, Ina KochORCiD
Pubmed Id:
Parent Title (English):BMC systems biology
Publisher:BioMed Central
Place of publication:London
Document Type:Article
Year of Completion:2017
Date of first Publication:2017/07/28
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2018/03/05
Tag:Feasibility; Manatee invariant; Mathematical model; NF-κB pathway; Petri net; Signaling pathway; Transition invariant
Issue:1, Art. 72
Page Number:11
First Page:1
Last Page:11
Open Access: This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver ( applies to the data made available in this article, unless otherwise stated.
Institutes:Informatik und Mathematik / Informatik
Medizin / Medizin
Exzellenzcluster / Exzellenzcluster Makromolekulare Komplexe
Dewey Decimal Classification:6 Technik, Medizin, angewandte Wissenschaften / 61 Medizin und Gesundheit / 610 Medizin und Gesundheit
Licence (German):License LogoCreative Commons - Namensnennung 4.0