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SomeRecentStudyinBiologicalNeuronalOscillatoryNetworks
QingyunWang(王青云)DepartmentofDynamicsandControl,BeihangUniversity,Beijing100191Email:qingyunwang@7/29/20231WithcomplimentsProf.LuQishao(BeihangUniversity)Prof.Duan
ZhiSheng(PekingUniversity)Prof.ChenGuanRong(CityUniversityofHongKong)Dr.Matjaz
Perc(UniversityofMaribor,Koroska
cesta160,SI-2000Maribor,Slovenia)7/29/20232ContentsMotivationNeuronalstructureandnetworkDynamicsofasingleneuronSynchronizationtransitionandRhythmdynamicsonnetworksBurstingDynamicsonRealisticNeuronalNetworksSpatialResonanceinNeuronalNetworksOpenproblems
7/29/20233Thesingleneuroninthevertebratecortexconnectstomorethan10,000postsynapticneuronsviasynapsesformingcomplexnetworks.Thebiologicalnervoussystemcancommunicateandtransforminformationthroughinteractionofnetworks.Neuronalinformationencodingandprocessingarereflectedbyoscillationpatternsofelectricalimpulsesequencesinneurons.Motivation7/29/20234Neurodynamicsdealswiththedynamicsandcontrolproblemsofelectricalactivitiesandinformationprocessesinnervoussystemsandisimportantintheresearchofbiologicalmotionsandintelligentbehavior.Neurodynamicsisamulti-disciplinaryresearchareainnonlineardynamics,networkscienceandneuroscience.Synchronizationisofgreatimportanceforsignalencodingandtransductionininformationprocessingofneuronsintworespects.Biologicalneuronscanextractthehinderedinformationbystochasticresonance.7/29/202356
NeuralMedicineandEngineering
NeuronalfiringandinformationencodingBiologicalControlBiologicalcomplexneuronalnetworksIntelligentRobotsBiologicalstructureofnervoussystemsNeuralCognitiveScienceNeuralComputersNeuralMedicalTechniques7/29/20236StructureofSingleNeuron
Abasic
elementforinformationprocessinginnervoussystems.Thereareabout1011
neuronsinthehumanbrainand104synapsesforaneuron.7/29/20237Modelofneuron
(1)
(4)(3)(2)
HodgkinA.L.,HuxleyA.F.,J.physiol.(London),1952,(117)500-544Hodgkin-Huxleymodel(1952NobelPrize)Chaymodel,HRmodel,FHNmodel,Rulkovmapetc.NonlinearODEsinvolvingmultipletimescales.
Hardtoanalyzebothmathematicallyandcomputationally.7/29/20238Diversityoffiringpatternsofasingleneuron
(inexperimentalneuralpacemakers)
(LiLi,RenWei,2003,2004)
7/29/20239Bifurcationscenario
(intheoreticalmodelandexperimentalneuralpacemakers)
(LiLi,RenWeietal,IJBC,2004.DuanLiXiaetal,Neurocomputing2008)
Chaymodel7/29/202310Chaos(inexperimentalneuralpacemakers)
betweenperiod2andperiod3firings(RenWei,IJBC,1997)
7/29/2023117/29/202312NeuronalnetworksWhatisaBrain?densenetworkmorethan104cellbodiesandseveralkilometersof`wires'percubicmillimeter.Manytypesofcells:spikingneurons(1011cells),gliacells(`supporter'cellsnotinvolvedintheinformationprocessing)andanalogneurons.7/29/202313Synapseanddelay7/29/202314Dorsalandlateralviewsoftheconnectivitybackboneofhumanbrain.Labelsindicatinganatomicalsubregionsareplacedattheirrespectivecentersofmass.Nodes(individualROIs)arecodedaccordingtostrengthandedgesarecodedaccordingtoconnectionweight.HagmannP,CammounL,GigandetX,MeuliR,HoneyCJ,WedeenVJ,SpornsO(2008)Mappingthestructuralcoreofhumancerebralcortex.PLoSBiologyVol.6,No.7,e1597/29/202315NeuronalnetworksNeuronalnetworksinvolvealargenumberofindividualneurons.Detailsoftheconnectivitynotusuallyknown.HardtoanalyzehowconnectivityinfluencesODEdynamics.7/29/202316NeuronalsynchronizationSynchronizationseemstobeverycrucialfortheefficientprocessingandtransmissionofinformationacrossthenervesystem.Parkinson'stremorisrelatedtoneuronalsynchronization.Transientlysynchronizedassembliesofneuronsarebelievedtounderliecognitivefunctions.Thereisconsistentevidenceforareductionofsynchronizationinschizophrenia.7/29/202317RobertC.Elsonetal,Phys.ReviewLett
815692-56951998TwocoupledneuroncircuitSynchronizedmotions7/29/202318Hua
GuangGUetal,CHIN.PHYS.LETT.Vol.26,No.11(2009)110501Experimentresults7/29/202319PNAS2010Listener-speakercanvalidlycommunicationbymeansofneuronalcoupling7/29/202320Classificationofsynchronization7/29/202321Burstsynchronizationanddesynchronizationin\fold/homoclinic"(\square-wave")bursters.ShownaresimulationsofcoupledMorris-Lecarsystemswithadditionalslowvariables.Variousregimesofsynchronizationofbursters(modiedfrom[Izhikevich,2000a]).7/29/202322Singularphaselocking7/29/202323AnalysismethodofphaselockingSingularperturbationtheory(Terman
etal,JComput
Neurosci(2007)23:217–235)Dynamicclusteringinthe(a)fulland(b)reducedmodels.TherearetwentypairsofE-andI-cells.EachE-cellexcitesoneI-cellandeachI-cellinhibitsthreeE-cellsLimited:Networkstructure,connectionstyle7/29/202324Phaseresponsecurve(discretemapmethod)CarmenCanavier7/29/202325Therearestillmanyothermethods:
Hilberttransformationoftimeseries,Poincaremapmethod(numericalcomputation)7/29/202326IncorporatingnoiseanddelayNoiseinduced(enhanced)synchronization.(twocoupledneuronsandlargescaleneuronalnetworks)Noiseinducedspatiotemporalwavepatterns(targetwave,spiralwave(Majun),spatialcoherence)Delayinducedcomplexityinneuronalnetworks(varioussynchronizationtransitionandspatialcoherence)7/29/202327EffectofdelayontwocoupledneuronsQYWangetal,IJBC,18,4(2008)1189–11987/29/202328EffectofdelayonlargescaleneuronalnetworksDynamicsmodel7/29/202329Zig-zagfrontsAntiphaseclusteringsunhcronizationInphasesynchronizationagain7/29/202330Measure:Q.Y.Wang,Z.SDuan,M.Perc,G.R.Chen,EPL,83(2008)500087/29/202331(Continued)A.-L.BarabásiandR.Albert,Science286,50919997/29/202332Increasingdelay7/29/2023337/29/2023347/29/2023357/29/2023367/29/202337QingyunWang,
Matjaz
Perc,Zhi
Sheng
Duan,GuanRongChen,PhysicalReviewE,80,026206,2009.7/29/202338Attractivecoupling7/29/202339Repulsivecoupling7/29/202340Burstingperiod
7/29/202341BurstingsynchronizationMacaquecorticalnetwork,consistingof95nodesand2402links7/29/202342Mathematicalmodel7/29/202343BurstingsynchronizationSpace-timeplotsofx(t)asobtainedforD=2.0andI_{ext}=3.2withdifferentinformationtransmissiondelays\tau,equalling:(a)0,(b)7,(c)14,(d)22,(e)30.Noticetheburstingsynchronizationandspikesinburstincreaseas\tauincreases.LiangXiaoMingetal,2009PRE7/29/202344Inordertoquantitativelydescribeglobalnetworkstates,we
definethequantitymThemoresynchronoustheneuronalnetworkis,thelargeristheparameterm.Further,itcanalsoidentifytransitionofdifferentbursts.Thus,itiscalledburstsynchronizationtransitionparameter.7/29/202345Dependenceoftheburstsynchronizationparametermon$\tau$fordifferentvaluesofdiffusionD7/29/202346Dependenceoftheburstsynchronizationparametermon$\tau$fordifferentvaluesoftheexternalstimulusI7/29/202347
Resonance
ResonanceofasingleHHneuron7/29/202348Resonance7/29/202349Spatialresonanceofnetworks7/29/202350SpatialcoherenceresonanceModelSet-UpHodgkinandHuxleymodelTransmissiondelaynoisetheEulerMaruyamamethod7/29/202351EffectofdelayAsthenoiseincreases,patternisdestroyed.
Thereisanintermediatenoise,circularpatterncanappear.7/29/202352Spatialstructurefunction:Circularaverage:Signal-noise-ratio:TwodimensionalFourierTransform7/29/202353Spatialstructurefunction
7/29/202354CircularaverageandSNRMaximumindicatingcoherence7/29/202355Fordifferentdelays,dependenceofSNRonnoise.7/29/202356EffectofsmallworldconnectionAsqisincreased,Snrdecreases.7/29/202357OpenproblemsDynamicalmechanismofsynchronizationbifurcation:synchronization-antiphasesynchronization---synchronizationasthedelay/linkprobabilityisvariedonsmallworld/scalefreenetworks.Dynamicalbifurcationmechanismofburstingfiringshouldbeexploredasthedelayisincreased.Theoryexplorationofsingularphaselocking.Dynamicsofmorerealisticneuronalnetworks7/29/202358Q.Y.Wang,Z.S.Duan,L.Huang,G.R.Chen,Q.S.Lu,Patternformationandfiringsynchronizationinnetworksofmapneurons,NewJournalofPhysics,9(383):1-11,2007.Q.Y.Wang,Z.S.Duan,Z.S.Feng,G.R.ChenandQ.S.Lu,SynchronizationtransitioninGap-Junction-Coupledleechneurons,PhysicaA,2008,3874404-4410.Q.Y.Wang,Matja?
Perc,Zhisheng
D
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