Identifying Controlling Nodes in Neuronal Networks in Different Scales

PLOS ONE, Dec 2019

Recent studies have detected hubs in neuronal networks using degree, betweenness centrality, motif and synchronization and revealed the importance of hubs in their structural and functional roles. In addition, the analysis of complex networks in different scales are widely used in physics community. This can provide detailed insights into the intrinsic properties of networks. In this study, we focus on the identification of controlling regions in cortical networks of cats’ brain in microscopic, mesoscopic and macroscopic scales, based on single-objective evolutionary computation methods. The problem is investigated by considering two measures of controllability separately. The impact of the number of driver nodes on controllability is revealed and the properties of controlling nodes are shown in a statistical way. Our results show that the statistical properties of the controlling nodes display a concave or convex shape with an increase of the allowed number of controlling nodes, revealing a transition in choosing driver nodes from the areas with a large degree to the areas with a low degree. Interestingly, the community Auditory in cats’ brain, which has sparse connections with other communities, plays an important role in controlling the neuronal networks.

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Identifying Controlling Nodes in Neuronal Networks in Different Scales

Citation: Tang Y, Gao H, Zou W, Kurths J ( Identifying Controlling Nodes in Neuronal Networks in Different Scales Yang Tang 0 Huijun Gao 0 Wei Zou 0 Ju rgen Kurths 0 Olaf Sporns, Indiana University, United States of America 0 1 Research Institute of Intelligent Control and Systems, Harbin Institute of Technology , Harbin , China , 2 Institute of Physics, Humboldt University Berlin , Berlin, Germany , 3 Potsdam Institute for Climate Impact Research , Telegraphenberg, Potsdam, Germany , 4 School of Mathematics and Statistics, Huazhong University of Science and Technology , Wuhan , China , 5 Institute for Complex systems and Mathematical Biology, University of Aberdeen , Aberdeen, United Kindom Recent studies have detected hubs in neuronal networks using degree, betweenness centrality, motif and synchronization and revealed the importance of hubs in their structural and functional roles. In addition, the analysis of complex networks in different scales are widely used in physics community. This can provide detailed insights into the intrinsic properties of networks. In this study, we focus on the identification of controlling regions in cortical networks of cats' brain in microscopic, mesoscopic and macroscopic scales, based on single-objective evolutionary computation methods. The problem is investigated by considering two measures of controllability separately. The impact of the number of driver nodes on controllability is revealed and the properties of controlling nodes are shown in a statistical way. Our results show that the statistical properties of the controlling nodes display a concave or convex shape with an increase of the allowed number of controlling nodes, revealing a transition in choosing driver nodes from the areas with a large degree to the areas with a low degree. Interestingly, the community Auditory in cats' brain, which has sparse connections with other communities, plays an important role in controlling the neuronal networks. - Funding: This research is supported by 973 Project (2009CB320600), the National Natural Science Foundation of China (60825303, 60834003, 61021002, 11171125) and the Key Laboratory of Integrated Automation for the Process Industry (Northeastern University), the Fundamental Research Funds for the Central Universities of China (2011QN161), SUMO (EU), grants of the German Research Foundation (DFG) in the Research Group FOR 868 Computational Modeling of Behavioral, Cognitive, and Neural Dynamics and in the IRTG 1740 (DFG) and the Alexander von Humboldt Foundation of Germany. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: Professor Ju rgen Kurths is a PLoS ONE Editorial Board member. This does not alter the authors adherence to all the PLoS ONE policies on sharing data and materials. Synchronization is widely observed in many fields such as coupled nonlinear systems and complex networks [16]. Especially, synchronization of distributed brain activity has been found to play an important role in neural information processing [711]. The experimentally observed brain activity, characterized by synchronization phenomena over a wide range of spatial and temporal scales, reflects the relevance for cognitive dysfunctions and pathophysiology [8]. Structurally, the analysis of the anatomical connectivity of the mammalian cortex has uncovered that large-scale neuronal networks display both high clustering and short pathlength [12,13]. The cortical network also shows a hierarchy of complex connectivity [12,1417]. Extensive information in mammalian cortex, such as the brains of macaque monkeys and cats, has been collected [1822]. Recently, hub regions, which are believed to play pivotal roles in the coordination of information flow in brain networks [2224], have been identified using modern tools from complex networks [20,22]. The hub regions of cortical networks are analyzed using node degree, structural motif, path length and clustering coefficient distributions [22]. The results in [20] highlight the influence of the topological connectivity in the formation of synchronization, revealing a few cortical areas forming a RichClub connectivity pattern. Control of complex networks is a hot topic, which is closely related to synchronization of complex networks [2527]. Some vertices in complex networks serve as reference sites, leaders or pacemakers [28] and drive all the other vertices toward desired targets or evolutions and thus synchronization is achieved. It is valuable to study the controllability of complex networks, especially for cortical networks due to the technical [29,30] and neuroscience backgrounds [8,16,20]. By fully utilizing the structure of the networks, Lu et al. [27] found out the minimum number of controllers for the pinning synchronization control of complex network with general topology and derived some efficient criteria to judge the success of the desi (...truncated)


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Yang Tang, Huijun Gao, Wei Zou, Jürgen Kurths. Identifying Controlling Nodes in Neuronal Networks in Different Scales, PLOS ONE, 2012, 7, DOI: 10.1371/journal.pone.0041375