王青云生物神经元网络动力学的研究进展课件.ppt

1、7:03:051Some Recent Study in Biological Neuronal Oscillatory NetworksQingyun Wang(王青云)Department of Dynamics and Control,Beihang University,Beijing 100191Email:7:03:052 With complimentsa Prof.Lu Qishao(Beihang University)a Prof.Duan ZhiSheng(Peking University)a Prof.Chen GuanRong(City University of

2、HongKong)a Dr.Matjaz Perc(University of Maribor,Koroska cesta 160,SI-2000 Maribor,Slovenia)7:03:053ContentsFMotivationFNeuronal structure and networkFDynamics of a single neuronFSynchronization transition and Rhythm dynamics on networksFBursting Dynamics on Realistic Neuronal Networks FSpatial Reson

3、ance in Neuronal NetworksFOpen problems 7:03:054The 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.Neuronal informat

4、ion encoding and processing are reflected by oscillation patterns of electrical impulse sequences in neurons.Motivation7:03:055Neurodynamics deals with the dynamics and control problems of electrical activities and information processes in nervous systems and is important in the research of biologic

5、al 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 neurons can extra

6、ct the hindered information by stochastic resonance.7:03:0566 Neural Medicine and Engineering Neuronal firing and information encoding Biological ControlBiological complex neuronal networksIntelligent RobotsBiological structure of nervous systems Neural Cognitive ScienceNeural ComputersNeural Medica

7、l Techniques7:03:057Structure 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.7:03:058Model of neuron)()()(LLKKaNaNVVgVVgVVgdtdVCInVnVdtdnnn)()1)(mVmVdtdmmm)()1)(hVhVdtdhhh)()1)(1)(4)(3)(2)Ho

8、dgkin 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.7:03:069Diversity of firing patterns of a single neuro

9、n(in experimental neural pacemakers)(Li Li,Ren Wei,2003,2004)7:03:1110Bifurcation scenario (in theoretical model and experimental neural pacemakers)(Li Li,Ren Wei et al,IJBC,2004.Duan Li Xia et al,Neurocomputing 2008)Chay model7:03:1211Chaos(in experimental neural pacemakers)between period 2 and per

10、iod 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)7:03:13127:03:1313Neuronal networkso What is a Brain?dense networkmore than 104 cell bodies and several kilometers of wires per cubic millimete

11、r.Many types of cells:spiking neurons(1011 cells),glia cells(supporter cells not involved in the information processing)and analog neurons.7:03:1314Synapse and delay7:03:1315Dorsal and lateral views of the connectivity backbone of human brain.Labels indicating anatomical subregions are placed at the

12、ir 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 core of human cerebral cortex.PLoS Biology Vol.6,No.7,e159 7:03:1316Ne

13、uronal networksNeuronal networks involve a large number of individual neurons.Details of the connectivity not usually known.Hard to analyze how connectivity influences ODE dynamics.7:03:1317Neuronal synchronizationo Synchronization seems to be very crucial for the efficient processing and transmissi

14、on 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 for a reduction of synchronization in schizophrenia.7:03:1318Robert C.Elso

15、n et al,Phys.Review Lett 81 5692-5695 1998Two coupled neuron circuitSynchronized motions7:03:1419Hua Guang GU et al,CHIN.PHYS.LETT.Vol.26,No.11(2009)110501Experiment results7:03:1420PNAS 2010Listener-speaker can validly communication by means of neuronal coupling7:03:1421Classification of synchroniz

16、ation7:03:1422Burst synchronization and desynchronization in fold/homoclinic(square-wave)bursters.Shown are simulations of coupled Morris-Lecar systems with additional slow variables.Various regimes of synchronization of bursters(modied from Izhikevich,2000a).7:03:1423Singular phase locking7:03:1424

17、Analysis 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-cells.Each E-cell excitesone I-cell and each I-cell inhibits three E-cellsLimited:Network structure,conn

18、ection style7:03:1425o Phase response curve(discrete map method)Carmen Canavier7:03:1426There are still many other methods:Hilbert transformation of time series,Poincare map method(numerical computation)7:03:1427Incorporating noise and delayo Noise induced(enhanced)synchronization.(two coupled neuro

19、ns 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 (various synchronization transition and spatial coherence)7:03:1428Effect of delay on two coupled neuronsQ Y Wang et al,

20、IJBC,18,4(2008)118911987:03:1529Effect of delay on large scale neuronal networksDynamics model7:03:1530Zig-zag frontsAntiphase clustering sunhcronizationIn phase synchronization again7:03:1531Measure:Q.Y.Wang,Z.S Duan,M.Perc,G.R.Chen,EPL,83(2008)500087:03:1532(Continued)A.-L.Barabsi and R.Albert,Sci

21、ence 286,509 19997:03:1533Increasing delay7:03:15347:03:15357:03:15367:03:15377:03:1538Qingyun Wang,Matjaz Perc,Zhi Sheng Duan,Guan Rong Chen,Physical Review E,80,026206,2009.7:03:1539Attractive coupling7:03:1640Repulsive coupling7:03:1641Bursting periodo 7:03:1742Bursting synchronizationMacaque cor

22、tical network,consisting of 95 nodes and 2402 links7:03:1743Mathematical model7:03:1744Bursting synchronizationSpace-time plots of x(t)as obtained for D=2.0 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

23、spikes in burst increase as tau increases.Liang Xiao Ming et al,2009 PRE7:03:1745In order to quantitatively describe global network states,we define the quantity mThe more synchronous the neuronal network is,the larger is the parameter m.Further,it can also identify transition of different bursts.Th

24、us,it is called burst synchronization transition parameter.7:03:1746Dependence of the burst synchronization parameter m on$tau$for different values of diffusion D7:03:1747Dependence of the burst synchronization parameter m on$tau$for different values of the external stimulus I7:03:1748Resonance Reso

25、nance of a single HH neuron7:03:1749Resonance7:03:1750Spatial resonance of networks7:03:1751Spatial coherence resonanceModel Set-UpHodgkin and Huxley modelTransmission delaynoisethe Euler Maruyama method 7:03:1752Effect of delayAs the noise increases,pattern is destroyed.There is an intermediate noi

26、se,circular pattern can appear.7:03:1753Spatial structure function:Circular average:Signal-noise-ratio:Two dimensional Fourier Transform 7:03:1754Spatial structure function 7:03:1755Circular average and SNRMaximum indicating coherence7:03:1756For different delays,dependence of SNR on noise.7:03:1757

27、Effect of small world connectionAs q is increased,Snr decreases.7:03:1758Open problems?Dynamical mechanism of synchronization bifurcation:synchronization-antiphase synchronization-synchronization as the delay/link probability is varied on small world/scale free networks.?Dynamical bifurcation mechan

28、ism of bursting firing should be explored as the delay is increased.?Theory exploration of singular phase locking.?Dynamics of more realistic neuronal networks7:03:17591.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 P

29、hysics,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-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

30、networks,Phys.Lett.A,372(2008)5681.4.Qingyun Wang,Zhisheng Duan,Matja Perc,Guanrong Chen,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 Ron

31、g Chen,Synchronization transitions on scale-free neuronal networks due to finite 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 References7:03:1760o 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).7:03:1761Thanks for your interesting!