Biological Networks Entropies: Examples in Neural Memory Networks, Genetic Regulation Networks and Social Epidemic Networks
by
Jacques Demongeot 1,2,*
, Mariem Jelassi 1,3,4, Hana Hazgui 1, Slimane Ben Miled 3, Narjes Bellamine Ben Saoud 4 and Carla Taramasco 2
Jacques Demongeot 1,2,*, Mariem Jelassi 1,3,4, Hana Hazgui 1, Slimane Ben Miled 3, Narjes Bellamine Ben Saoud 4 and Carla Taramasco 2
1
Team AGIM (Autonomy, Gerontechnology, Imaging, Modelling & Tools for e-Gnosis Medical), Laboratory AGEIS, University Grenoble Alpes, Faculty of Medicine, La Tronche 38700, France
2
Escuela de Ingeniería Civil en Informática, Universidad de Valparaíso, General Cruz 222, Valparaíso 2340000, Chile
3
Laboratory of Bioinformatics, Biomathematics and Biostatistics (BIMS), Institut Pasteur de Tunis, Tunis 1002, Tunisia
4
National School for Computer Studies, RIADI Laboratory, University of Manouba, Manouba 2010, Tunisia
*
Author to whom correspondence should be addressed.
Entropy 2018, 20(1), 36; https://doi.org/10.3390/e20010036
Received: 8 November 2017 / Revised: 25 December 2017 / Accepted: 4 January 2018 / Published: 13 January 2018
(This article belongs to the Section Statistical Physics)
Networks used in biological applications at different scales (molecule, cell and population) are of different types: neuronal, genetic, and social, but they share the same dynamical concepts, in their continuous differential versions (e.g., non-linear Wilson-Cowan system) as well as in their discrete Boolean versions (e.g., non-linear Hopfield system); in both cases, the notion of interaction graph G(J) associated to its Jacobian matrix J, and also the concepts of frustrated nodes, positive or negative circuits of G(J), kinetic energy, entropy, attractors, structural stability, etc., are relevant and useful for studying the dynamics and the robustness of these systems. We will give some general results available for both continuous and discrete biological networks, and then study some specific applications of three new notions of entropy: (i) attractor entropy, (ii) isochronal entropy and (iii) entropy centrality; in three domains: a neural network involved in the memory evocation, a genetic network responsible of the iron control and a social network accounting for the obesity spread in high school environment.
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Keywords:
biological networks; dynamic entropy; isochronal entropy; attractor entropy; entropy centrality; robustness
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MDPI and ACS Style
Demongeot, J.; Jelassi, M.; Hazgui, H.; Ben Miled, S.; Bellamine Ben Saoud, N.; Taramasco, C. Biological Networks Entropies: Examples in Neural Memory Networks, Genetic Regulation Networks and Social Epidemic Networks. Entropy 2018, 20, 36.
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