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# Impact of modular organization on dynamical richness in cortical networks

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### Abstract

Balance of functional integrability and spatial segregation mediates dynamical richness in modular cortical networks.

### Abstract

As in many naturally formed networks, the brain exhibits an inherent modular architecture that is the basis of its rich operability, robustness, and integration-segregation capacity. However, the mechanisms that allow spatially segregated neuronal assemblies to swiftly change from localized to global activity remain unclear. Here, we integrate microfabrication technology with in vitro cortical networks to investigate the dynamical repertoire and functional traits of four interconnected neuronal modules. We show that the coupling among modules is central. The highest dynamical richness of the network emerges at a critical connectivity at the verge of physical disconnection. Stronger coupling leads to a persistently coherent activity among the modules, while weaker coupling precipitates the activity to be localized solely within the modules. An in silico modeling of the experiments reveals that the advent of coherence is mediated by a trade-off between connectivity and subquorum firing, a mechanism flexible enough to allow for the coexistence of both segregated and integrated activities. Our results unveil a new functional advantage of modular organization in complex networks of nonlinear units.

### Most cited references41

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### Community detection in graphs

(2009)
The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such clusters, or communities, can be considered as fairly independent compartments of a graph, playing a similar role like, e. g., the tissues or the organs in the human body. Detecting communities is of great importance in sociology, biology and computer science, disciplines where systems are often represented as graphs. This problem is very hard and not yet satisfactorily solved, despite the huge effort of a large interdisciplinary community of scientists working on it over the past few years. We will attempt a thorough exposition of the topic, from the definition of the main elements of the problem, to the presentation of most methods developed, with a special focus on techniques designed by statistical physicists, from the discussion of crucial issues like the significance of clustering and how methods should be tested and compared against each other, to the description of applications to real networks.
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### Efficient Behavior of Small-World Networks

(2001)
We introduce the concept of efficiency of a network, measuring how efficiently it exchanges information. By using this simple measure small-world networks are seen as systems that are both globally and locally efficient. This allows to give a clear physical meaning to the concept of small-world, and also to perform a precise quantitative a nalysis of both weighted and unweighted networks. We study neural networks and man-made communication and transportation systems and we show that the underlying general principle of their construction is in fact a small-world principle of high efficiency.
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### Functional cartography of complex metabolic networks

,   (2005)
High-throughput techniques are leading to an explosive growth in the size of biological databases and creating the opportunity to revolutionize our understanding of life and disease. Interpretation of these data remains, however, a major scientific challenge. Here, we propose a methodology that enables us to extract and display information contained in complex networks. Specifically, we demonstrate that one can (i) find functional modules in complex networks, and (ii) classify nodes into universal roles according to their pattern of intra- and inter-module connections. The method thus yields a cartographic representation'' of complex networks. Metabolic networks are among the most challenging biological networks and, arguably, the ones with more potential for immediate applicability. We use our method to analyze the metabolic networks of twelve organisms from three different super-kingdoms. We find that, typically, 80% of the nodes are only connected to other nodes within their respective modules, and that nodes with different roles are affected by different evolutionary constraints and pressures. Remarkably, we find that low-degree metabolites that connect different modules are more conserved than hubs whose links are mostly within a single module.
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### Author and article information

###### Journal
American Association for the Advancement of Science
2375-2548
November 2018
14 November 2018
: 4
: 11
###### Affiliations
[1 ]WPI–Advanced Institute for Materials Research (WPI-AIMR), Tohoku University, Sendai 980-8577, Japan.
[2 ]Research Institute for Electrical Communication, Tohoku University, Sendai 980-8577, Japan.
[3 ]Graduate School of Science and Engineering, Yamagata University, Yamagata 992-8510, Japan.
[4 ]Faculty of Science and Engineering, Waseda University, Tokyo 169-8555, Japan.
[5 ]Departament de Física de la Matèria Condensada, Universitat de Barcelona, Barcelona 08028, Catalonia, Spain.
[6 ]Universitat de Barcelona Institute of Complex Systems (UBICS), Barcelona 08028, Catalonia, Spain.
###### Author notes
[* ]Corresponding author. Email: hideaki.yamamoto.e3@ 123456tohoku.ac.jp (H.Y.); jordi.soriano@ 123456ub.edu (J.S.)
[†]

Present address: Kansei Fukushi Research Institute, Tohoku Fukushi University, Sendai 989-3201, Japan.

###### Article
aau4914
6235526
30443598

This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial license, which permits use, distribution, and reproduction in any medium, so long as the resultant use is not for commercial advantage and provided the original work is properly cited.

###### Funding
Funded by: doi http://dx.doi.org/10.13039/100010664, H2020 Future and Emerging Technologies;
Award ID: 713140 MESOBRAIN
Funded by: doi http://dx.doi.org/10.13039/501100001691, Japan Society for the Promotion of Science;
Award ID: 15K17449, 18H03325
Funded by: doi http://dx.doi.org/10.13039/501100002809, Generalitat de Catalunya;
Award ID: 2014-SGR-878
Funded by: doi http://dx.doi.org/10.13039/501100003329, Ministerio de Economía y Competitividad;
Award ID: FIS2016-78507-C2-2-P
Funded by: doi http://dx.doi.org/10.13039/501100006467, Research Institute of Electrical Communication, Tohoku University;
###### Categories
Research Article
Research Articles