1、9:37:271Some Recent Study in Biological Neuronal Oscillatory NetworksQingyun Wang(王青云)Department of Dynamics and Control, Beihang University, Beijing 100191Email: 9:37:272 With complimentsa Prof. Lu Qishao(Beihang University)a Prof. Duan ZhiSheng (Peking University)a Prof. Chen GuanRong (City Univer
2、sity of HongKong)a Dr. Matjaz Perc (University of Maribor, Koroska cesta 160, SI-2000 Maribor, Slovenia)9:37:273ContentsFMotivationFNeuronal structure and networkFDynamics of a single neuronFSynchronization transition and Rhythm dynamics on networksFBursting Dynamics on Realistic Neuronal Networks F
3、Spatial Resonance in Neuronal NetworksFOpen problems 9:37:274The single neuron in the vertebrate cortex connects to more than 10,000 postsynaptic neurons via synapses forming complex networks.The biological nervous system can communicate and transform information through interaction of networks.Neur
4、onal information encoding and processing are reflected by oscillation patterns of electrical impulse sequences in neurons.Motivation9:37:275Neurodynamics deals with the dynamics and control problems of electrical activities and information processes in nervous systems and is important in the researc
5、h of biological motions and intelligent behavior. Neurodynamics is a multi-disciplinary research area in nonlinear dynamics, network science and neuroscience.Synchronization is of great importance for signal encoding and transduction in information processing of neurons in two respects.Biological ne
6、urons can extract the hindered information by stochastic resonance.9:37:2766 Neural Medicine and Engineering Neuronal firing and information encoding Biological ControlBiological complex neuronal networksIntelligent RobotsBiological structure of nervous systems Neural Cognitive ScienceNeural Compute
7、rsNeural Medical Techniques9:37:277Structure of Single Neuron A basic element for information processing in nervous systems.There are about 1011 neurons in the human brain and 104 synapses for a neuron.9:37:278Model of neuron)()()(LLKKaNaNVVgVVgVVgdtdVCInVnVdtdnnn)()1)( mVmVdtdmmm)()1)( hVhVdtdhhh)(
8、)1)( (1) (4) (3) (2) Hodgkin A. L., Huxley A. F., J. physiol.(London), 1952, (117) 500-544oHodgkin-Huxley model (1952 Nobel Prize)nChay model, HR model, FHN model, Rulkov map etc.Nonlinear ODEs involving multiple time scales. Hard to analyze both mathematically and computationally.9:37:289Diversity
9、of firing patterns of a single neuron(in experimental neural pacemakers) (Li Li, Ren Wei, 2003, 2004 ) 9:37:3110Bifurcation scenario (in theoretical model and experimental neural pacemakers)(Li Li, Ren Wei et al, IJBC, 2004. Duan Li Xia et al, Neurocomputing 2008)Chay model9:37:3211Chaos (in experim
10、ental neural pacemakers) between period 2 and period 3 firings (Ren Wei, IJBC, 1997) 01000200030000.000.030.060.090.12(a)ISI(sec)Number0.0000.0250.0500.0750.1000.0000.0250.0500.0750.100ISI(n+1)(sec)ISI(n)(sec)9:37:32129:37:3213Neuronal networkso What is a Brain?dense networkmore than 104 cell bodies
11、 and several kilometers of wires per cubic millimeter.Many types of cells: spiking neurons (1011 cells), glia cells (supporter cells not involved in the information processing) and analog neurons.9:37:3214Synapse and delay9:37:3215Dorsal and lateral views of the connectivity backbone of human brain.
12、 Labels indicating anatomical subregions are placed at their respective centers of mass. Nodes (individual ROIs) are coded according to strength and edges are coded according to connection weight .Hagmann P, Cammoun L, Gigandet X, Meuli R, Honey CJ, Wedeen VJ, Sporns O (2008) Mapping the structural
13、core of human cerebral cortex. PLoS Biology Vol. 6, No. 7, e159 9:37:3216Neuronal networksNeuronal networks involve a large number of individual neurons.Details of the connectivity not usually known.Hard to analyze how connectivity influences ODE dynamics.9:37:3217Neuronal synchronizationo Synchroni
14、zation seems to be very crucial for the efficient processing and transmission of information across the nerve system.o Parkinsons tremor is related to neuronal synchronization.o Transiently synchronized assemblies of neurons are believed to underlie cognitive functions.o There is consistent evidence
15、 for a reduction of synchronization in schizophrenia.9:37:3218Robert C. Elson et al, Phys. Review Lett 81 5692-5695 1998Two coupled neuron circuitSynchronized motions9:37:3319Hua Guang GU et al, CHIN. PHYS. LETT. Vol. 26, No. 11 (2009) 110501Experiment results9:37:3320PNAS 2010Listener-speaker can v
16、alidly communication by means of neuronal coupling9:37:3321Classification of synchronization9:37:3322Burst synchronization and desynchronization in fold/homoclinic (square-wave) bursters. Shown are simulations of coupled Morris-Lecar systems with additional slow variables.Various regimes of synchron
17、ization of bursters (modied from Izhikevich, 2000a).9:37:3323Singular phase locking9:37:3324Analysis method of phase lockingo Singular perturbation theory (Terman etal, J Comput Neurosci (2007) 23:217235)Dynamic clustering in the (a) full and (b) reduced models.There are twenty pairs of E- and I-cel
18、ls. Each E-cell excitesone I-cell and each I-cell inhibits three E-cellsLimited: Network structure, connection style9:37:3325o Phase response curve (discrete map method)Carmen Canavier9:37:3326There are still many other methods: Hilbert transformation of time series, Poincare map method (numerical c
19、omputation)9:37:3327Incorporating noise and delayo Noise induced (enhanced) synchronization. (two coupled neurons and large scale neuronal networks)o Noise induced spatiotemporal wave patterns (target wave, spiral wave (Ma jun), spatial coherence)o Delay induced complexity in neuronal networks (vari
20、ous synchronization transition and spatial coherence)9:37:3328Effect of delay on two coupled neuronsQ Y Wang et al, IJBC, 18, 4 (2008) 118911989:37:3329Effect of delay on large scale neuronal networksDynamics model9:37:3330Zig-zag frontsAntiphase clustering sunhcronizationIn phase synchronization ag
21、ain9:37:3331Measure:Q.Y. Wang, Z.S Duan, M. Perc, G. R. Chen, EPL, 83 (2008) 500089:37:3432(Continued)A.-L. Barabsi and R. Albert, Science 286, 509 19999:37:3433Increasing delay9:37:34349:37:34359:37:34369:37:34379:37:3438Qingyun Wang, Matjaz Perc, Zhi Sheng Duan, Guan Rong Chen, Physical Review E,
22、80, 026206,2009.9:37:3439Attractive coupling9:37:3440Repulsive coupling9:37:3541Bursting periodo 9:37:3542Bursting synchronizationMacaque cortical network, consisting of 95 nodes and 2402 links9:37:3543Mathematical model9:37:3544Bursting synchronizationSpace-time plots of x(t) as obtained for D=2.0
23、and I_ext=3.2 with different information transmission delays tau, equalling: (a) 0, (b) 7, (c) 14, (d) 22, (e) 30. Notice the bursting synchronization and spikes in burst increase as tau increases.Liang Xiao Ming et al, 2009 PRE9:37:3545In order to quantitatively describe global network states, we d
24、efine the quantity mThe more synchronous the neuronal network is, the larger is the parameter m. Further, it can also identify transition of different bursts. Thus, it is called burst synchronization transition parameter.9:37:3546Dependence of the burst synchronization parameter m on $tau$ for diffe
25、rent values of diffusion D9:37:3547Dependence of the burst synchronization parameter m on $tau$ for different values of the external stimulus I9:37:3548Resonance Resonance of a single HH neuron9:37:3549Resonance9:37:3550Spatial resonance of networks9:37:3551Spatial coherence resonanceModel Set-UpHod
26、gkin and Huxley modelTransmission delaynoisethe Euler Maruyama method 9:37:3552Effect of delayAs the noise increases, pattern is destroyed. There is an intermediate noise, circular pattern can appear.9:37:3553Spatial structure function:Circular average:Signal-noise-ratio:Two dimensional Fourier Tran
27、sform 9:37:3554Spatial structure function 9:37:3555Circular average and SNRMaximum indicating coherence9:37:3556For different delays, dependence of SNR on noise.9:37:3557Effect of small world connectionAs q is increased, Snr decreases.9:37:3558Open problems?Dynamical mechanism of synchronization bif
28、urcation: synchronization-antiphase synchronization-synchronization as the delay/link probability is varied on small world/scale free networks.?Dynamical bifurcation mechanism of bursting firing should be explored as the delay is increased.?Theory exploration of singular phase locking.?Dynamics of m
29、ore realistic neuronal networks9:37:35591.Q.Y. Wang, Z.S. Duan, L. Huang, G.R. Chen, Q.S. Lu, Pattern formation and firing synchronization in networks of map neurons, New Journal of Physics, 9(383): 1-11, 2007.2.Q.Y. Wang, Z.S. Duan, Z.S. Feng, G.R. Chen and Q.S. Lu，Synchronization transition in Gap
30、-Junction-Coupled leech neurons, Physica A, 2008, 387 4404-4410. 3.Q. Y. Wang, Matja Perc, Zhisheng Duan, Guanrong Chen, Delay-enhanced coherence resonance of spiral wave in noisy Hodgkin-Huxley neuronal networks, Phys. Lett.A, 372 (2008) 5681.4.Qingyun Wang, Zhisheng Duan, Matja Perc, Guanrong Chen
31、, Synchronization transitions on small-world neuronal networks: effects of information transmission delay and rewiring probability, Europhysics Letters, 83 (2008) 500085.Qingyun Wang, Matjaz Perc, Zhi Sheng Duan, Guan Rong Chen, Synchronization transitions on scale-free neuronal networks due to fini
32、te information transmission delays, Physical Review E, 80, 026206,2009. 6.Qingyun Wang, Matjaz Perc, Zhisheng Duan, Guanrong Chen, Delay-induced multiple stochastic resonances on scale-free neuronal networks, Chaos, 19, 023112 2009 References9:37:3560o This work was supported by the National Science Foundation of China (Funds No. 10702023, 10832006 and 10972001), China Doctoral Science Special Foundation (Fund No. 200801020).9:37:3561Thanks for your interesting!
