Analysis and application of neuronal network controllability and observability.

Controllability and observability analyses are important prerequisite for designing suitable neural control strategy, which can help lower the efforts required to control and observe the system dynamics. First, 3-neuron motifs including the excitatory motif, the inhibitory motif, and the mixed motif are constructed to investigate the effects of single neuron and synaptic dynamics on network controllability (observability). Simulation results demonstrate that for networks with the same topological structure, the controllability (observability) of the node always changes if the properties of neurons and synaptic coupling strengths vary. Besides, the inhibitory networks are more controllable (observable) than the excitatory networks when the coupling strengths are the same. Then, the numerically determined controllability results of 3-neuron excitatory motifs are generalized to the desynchronization control of the modular motif network. The control energy and neuronal synchrony measure indexes are used to quantify the controllability of each node in the modular network. The best driver node obtained in this way is the same as the deduced one from motif analysis.

[1]  C. Hammond,et al.  Closing the loop of deep brain stimulation , 2013, Front. Syst. Neurosci..

[2]  Tao Jia,et al.  Control Capacity and A Random Sampling Method in Exploring Controllability of Complex Networks , 2013, Scientific Reports.

[3]  M P Young,et al.  Anatomical connectivity defines the organization of clusters of cortical areas in the macaque monkey and the cat. , 2000, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[4]  Nancy Kopell,et al.  Rapid synchronization through fast threshold modulation , 1993, Biological Cybernetics.

[5]  Alexandre Sedoglavic.  A Probabilistic Algorithm to Test Local Algebraic Observability in Polynomial Time , 2002, J. Symb. Comput..

[6]  Ali Nabi,et al.  Single input optimal control for globally coupled neuron networks , 2011, Journal of neural engineering.

[7]  Zhe-ming Lu,et al.  Controllability of deterministic complex networks , 2015 .

[8]  Marcus Kaiser,et al.  Clustered organization of cortical connectivity , 2007, Neuroinformatics.

[9]  Eugene M. Izhikevich,et al.  Simple model of spiking neurons , 2003, IEEE Trans. Neural Networks.

[10]  J. Kurths,et al.  Pinning controllability of complex networks with community structure. , 2013, Chaos.

[11]  John A. White,et al.  The Past, Present, and Future of Real-Time Control in Cellular Electrophysiology , 2014, IEEE Transactions on Biomedical Engineering.

[12]  Bin Deng,et al.  Intrinsic excitability state of local neuronal population modulates signal propagation in feed-forward neural networks. , 2015, Chaos.

[13]  Miguel A F Sanjuán,et al.  Bursting regimes in map-based neuron models coupled through fast threshold modulation. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Matjaz Perc,et al.  Can scale-freeness offset delayed signal detection in neuronal networks? , 2014, 1403.6663.

[15]  O. Sporns,et al.  Motifs in Brain Networks , 2004, PLoS biology.

[16]  Sen Song,et al.  Highly Nonrandom Features of Synaptic Connectivity in Local Cortical Circuits , 2005, PLoS biology.

[17]  Wen-Xu Wang,et al.  Exact controllability of complex networks , 2013, Nature Communications.

[18]  M. Belluscio,et al.  Closed-Loop Control of Epilepsy by Transcranial Electrical Stimulation , 2012, Science.

[19]  Albert-László Barabási,et al.  Constructing minimal models for complex system dynamics , 2015, Nature Communications.

[20]  Xingyuan Wang,et al.  Controllability of asynchronous Boolean multiplex control networks. , 2014, Chaos.

[21]  Jing-Sin Liu,et al.  A P-type iterative learning controller for robust output tracking of nonlinear time-varying systems , 1996 .

[22]  Luis A. Aguirre,et al.  Controllability and observability of linear systems: some noninvariant aspects , 1995 .

[23]  Matjaz Perc,et al.  Firing regulation of fast-spiking interneurons by autaptic inhibition , 2016, 1606.01358.

[24]  Andrew B. Schwartz,et al.  Brain-Controlled Interfaces: Movement Restoration with Neural Prosthetics , 2006, Neuron.

[25]  A. Aertsen,et al.  Spiking activity propagation in neuronal networks: reconciling different perspectives on neural coding , 2010, Nature Reviews Neuroscience.

[26]  Maxim Bazhenov,et al.  Feedback stabilizes propagation of synchronous spiking in cortical neural networks , 2015, Proceedings of the National Academy of Sciences.

[27]  S. Shen-Orr,et al.  Network motifs: simple building blocks of complex networks. , 2002, Science.

[28]  Sean N. Brennan,et al.  Observability and Controllability of Nonlinear Networks: The Role of Symmetry , 2013, Physical review. X.

[29]  Olaf Sporns,et al.  Mechanisms of Zero-Lag Synchronization in Cortical Motifs , 2013, PLoS Comput. Biol..

[30]  Jinzhi Lei,et al.  Burst synchronization transitions in a neuronal network of subnetworks. , 2011, Chaos.

[31]  L. Bunimovich,et al.  Dynamical networks: interplay of topology, interactions and local dynamics , 2007 .

[32]  Matjaž Perc,et al.  Effects of small-world connectivity on noise-induced temporal and spatial order in neural media , 2007 .

[33]  Andre Levchenko,et al.  Dynamic Properties of Network Motifs Contribute to Biological Network Organization , 2005, PLoS biology.

[34]  M. Perc,et al.  Regulation of Irregular Neuronal Firing by Autaptic Transmission , 2016, Scientific Reports.

[35]  Bin Deng,et al.  Delay-induced synchronization transitions in modular scale-free neuronal networks with hybrid electrical and chemical synapses , 2014 .

[36]  Albert-László Barabási,et al.  Observability of complex systems , 2013, Proceedings of the National Academy of Sciences.

[37]  P. Tass,et al.  Control of Abnormal Synchronization in Neurological Disorders , 2014, Front. Neurol..

[38]  Bernard Friedland,et al.  Controllability Index Based on Conditioning Number , 1975 .

[39]  Kevin L. Moore,et al.  Iterative Learning Control: Brief Survey and Categorization , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[40]  Leonardo Dueñas-Osorio,et al.  Characterizing the topological and controllability features of U.S. power transmission networks , 2016 .

[41]  Wen-Xu Wang,et al.  Intrinsic dynamics induce global symmetry in network controllability , 2015, Scientific Reports.

[42]  Yang-Yu Liu,et al.  Inducing effect on the percolation transition in complex networks , 2013, Nature Communications.

[43]  David Golomb,et al.  Neuronal synchrony measures , 2007, Scholarpedia.

[44]  Cunlai Pu,et al.  Robustness analysis of network controllability , 2012 .

[45]  D. McCormick,et al.  Neocortical Network Activity In Vivo Is Generated through a Dynamic Balance of Excitation and Inhibition , 2006, The Journal of Neuroscience.

[46]  Luis A. Aguirre,et al.  On the non-equivalence of observables in phase-space reconstructions from recorded time series , 1998 .

[47]  Daqing Guo,et al.  Stochastic and coherence resonance in feed-forward-loop neuronal network motifs. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[48]  W. Lytton.  Computer modelling of epilepsy , 2008, Nature Reviews Neuroscience.

[49]  Michele Giugliano,et al.  Command-line cellular electrophysiology for conventional and real-time closed-loop experiments , 2014, Journal of Neuroscience Methods.

[50]  Guanrong Chen,et al.  Synaptic plasticity induced transition of spike propagation in neuronal networks , 2013, Commun. Nonlinear Sci. Numer. Simul..

[51]  Matjaz Perc,et al.  Delay-induced multiple stochastic resonances on scale-free neuronal networks. , 2009, Chaos.

[52]  Stefan Rotter,et al.  The Role of Inhibition in Generating and Controlling Parkinson’s Disease Oscillations in the Basal Ganglia , 2011, Front. Syst. Neurosci..

[53]  John Rinzel,et al.  Dynamics of Spiking Neurons Connected by Both Inhibitory and Electrical Coupling , 2003, Journal of Computational Neuroscience.

[54]  Albert-László Barabási,et al.  Controllability of complex networks , 2011, Nature.

[55]  J. Danckaert,et al.  Synchronization properties of network motifs: influence of coupling delay and symmetry. , 2008, Chaos.

[56]  Viktor K. Jirsa,et al.  A Low Dimensional Description of Globally Coupled Heterogeneous Neural Networks of Excitatory and Inhibitory Neurons , 2008, PLoS Comput. Biol..

[57]  Albert-László Barabási,et al.  Control Principles of Complex Networks , 2015, ArXiv.

[58]  Andrey Shilnikov,et al.  Spikes matter for phase-locked bursting in inhibitory neurons. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[59]  Tatsuya Akutsu,et al.  Structural controllability of unidirectional bipartite networks , 2013, Scientific Reports.

[60]  Bin Deng,et al.  Chaotic phase synchronization in small-world networks of bursting neurons. , 2011, Chaos.