Multiscale Analysis and Nonlinear Dynamics: From Genes to the Brain

325 Pages·7.896 MB·English

by  Misha (Meyer) Z. Pesenson(eds.)

Editedby
Misha(Meyer)Z.Pesenson
MultiscaleAnalysisand
NonlinearDynamics
ReviewsofNonlinearDynamicsandComplexity
Schuster,H.G.(ed.) Lüdge,K.(ed.)
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Edited by Misha (Meyer) Z. Pesenson
Multiscale Analysis and Nonlinear Dynamics
From Genes to the Brain
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V
Contents
ListofContributors XIII
Preface XVII
1 Introduction:MultiscaleAnalysis–Modeling,Data,Networks,and
NonlinearDynamics 1
Misha(Meyer)Z.Pesenson
1.1 MultiscaleModeling 5
1.1.1 Domain-SpecificModeling 6
1.1.2 Analysis 7
1.1.3 ModelInterpretationandVerification:Experimental/Simulation
Data 9
1.2 MultiresolutionAnalysisandProcessingofHigh-Dimensional
Information/Data 10
1.3 MultiscaleAnalysis,Networks,andNonlinearDynamics 11
1.4 Conclusions 14
References 14
PartOne MultiscaleAnalysis 19
2 ModelingAcrossScales:DiscreteGeometricStructuresin
HomogenizationandInverseHomogenization 21
MathieuDesbrun,RogerD.Donaldson,andHoumanOwhadi
2.1 Introduction 21
2.2 HomogenizationofConductivitySpace 23
2.2.1 HomogenizationasaNonlinearOperator 24
2.2.2 ParameterizationoftheConductivitySpace 26
2.3 DiscreteGeometricHomogenization 31
2.3.1 HomogenizationbyVolumeAveraging 32
2.3.2 HomogenizationbyLinearInterpolation 33
2.3.3 SemigroupPropertiesinGeometricHomogenization 37
2.4 OptimalWeightedDelaunayTriangulations 39
2.4.1 ConstructionofPositiveDirichletWeights 40
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VI Contents
2.4.2 WeightedDelaunayandQ-AdaptedTriangulations 43
2.4.3 ComputingOptimalWeightedDelaunayMeshes 44
2.5 RelationshiptoInverseHomogenization 47
2.6 ElectricalImpedanceTomography 49
2.6.1 NumericalTests 52
2.6.1.1 HarmonicCoordinateIteration 53
2.6.1.2 Divergence-FreeParameterizationRecovery 55
References 61
3 MultiresolutionAnalysisonCompactRiemannianManifolds 65
IsaacZ.Pesenson
3.1 Introduction 65
3.2 CompactManifoldsandOperators 66
3.2.1 ManifoldswithoutBoundary 66
3.2.2 CompactHomogeneousManifolds 67
3.2.3 BoundedDomainswithSmoothBoundaries 68
3.3 HilbertFrames 69
3.4 MultiresolutionandSampling 70
3.5 ShannonSamplingofBand-LimitedFunctionsonManifolds 72
3.6 LocalizedFramesonCompactManifolds 73
3.7 ParsevalFramesonHomogeneousManifolds 76
3.8 VariationalSplinesonManifolds 79
3.9 Conclusions 81
References 81
PartTwo NonlinearDynamics:GeneletsandSyntheticBiochemicalCircuits 83
4 TranscriptionalOscillators 85
ElisaFranco,JongminKim,andFriedrichC.Simmel
4.1 Introduction 85
4.2 SyntheticTranscriptionalModules 86
4.2.1 ElementaryActivationandInhibitionPathways,andSimpleLoops 87
4.2.2 ExperimentalImplementation 88
4.3 MolecularClocks 89
4.3.1 ATwo-NodeMolecularOscillator 90
4.3.2 AnalysisoftheOscillatoryRegime 91
4.3.3 ExperimentalImplementationandData 95
4.4 ScalingUpMolecularCircuits:SynchronizationofMolecular
Processes 96
4.4.1 AnalysisoftheLoadDynamics 97
4.4.1.1 QuasisteadyStateApproximationoftheLoadDynamics 99
4.4.1.2 EfficiencyofSignalTransmission 99
4.4.2 PerturbationoftheOscillatorCausedbytheLoad 100
4.4.2.1 ConsumptiveCoupling 100
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Contents VII
4.4.2.2 NonconsumptiveCouplingandRetroactivity 100
4.4.3 Insulation 102
4.4.3.1 ReductionofPerturbationsontheOscillatorDynamics 103
4.4.3.2 SignalTransmissiontotheInsulatedLoad 104
4.5 OscillatorDrivingaLoad:ExperimentalImplementationandData 105
4.6 DeterministicPredictiveModelsforComplexReactionNetworks 105
4.7 StochasticEffects 107
4.8 Conclusions 110
References 110
5 SyntheticBiochemicalDynamicCircuits 113
Rapha€elPlassonandYannickRondelez
5.1 Introduction 113
5.2 Out-of-EquilibriumChemicalSystems 114
5.2.1 AShortHistoricalOverview 114
5.2.1.1 DiscoveryofNonlinearChemicalSystems 114
5.2.1.2 UnexpectedOscillatingChemicalSystems 115
5.2.2 BuildingNonequilibriumSystems 116
5.2.2.1 EnergeticRequirements 116
5.2.2.2 SystemClosure 116
5.2.2.3 InstabilitiesandDynamicStability 118
5.2.3 DesignPrinciples 119
5.2.3.1 Dynamism 119
5.2.3.2 InteractingFeedbacksProcesses 121
5.2.3.3 Modularity 122
5.3 BiologicalCircuits 123
5.3.1 BiologicalNetworksModeledbyChemistry 123
5.3.2 Biosystems:AMultilevelComplexity 124
5.3.3 AFirstExampleofaBiologicalReactionCircuit 124
5.3.4 BiologicalNetworkingStrategy 125
5.3.4.1 GRNsAreTemplatedNetworks 125
5.3.4.2 RegulationandFeedbackLoops 125
5.3.4.3 NonlinearitiesinGeneticRegulation 127
5.3.4.4 Delays 128
5.3.4.5 TitrationEffects 129
5.3.5 HigherLevelMotifsandModularityofBiochemicalNetworks 129
5.4 ProgrammableInVitroDynamics 130
5.4.1 EnzymaticSystems 130
5.4.1.1 DNA–RNASequenceAmplification 131
5.4.1.2 TheGeneletSystem 131
5.4.1.3 ThePENToolbox 132
5.4.2 NonenzymaticNetworks:StrandDisplacementSystems 134
5.4.3 NumericalModeling 135
5.4.3.1 MathematicalDescriptions 135
5.4.3.2 LSAandBifurcationAnalysisforDesign 137
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VIII Contents
5.4.3.3 TimeEvolutions 138
5.4.3.4 RobustnessAnalysisandInSilicoEvolutions 138
5.5 Perspectives 139
5.5.1 DNAComputing 140
5.5.2 SelfOrganizingSpatialPatterns 140
5.5.3 ModelsofBiologicalNetworks 141
5.5.4 OriginofLife 141
References 142
PartThree NonlinearDynamics:theBrainandtheHeart 147
6 TheoreticalandExperimentalElectrophysiologyinHumanNeocortex:
MultiscaleDynamicCorrelatesofConsciousExperience 149
PaulL.Nunez,RameshSrinivasan,andLesterIngber
6.1 IntroductiontoBrainComplexity 149
6.1.1 HumanBrainsandOtherComplexAdaptiveSystems 149
6.1.2 Is“Consciousness”aFour-LetterWord? 150
6.1.3 MotivationsandTargetAudiencesforthisChapter 151
6.1.4 BrainImagingatMultipleSpatialandTemporalScales 151
6.1.5 MultipleScalesofBrainDynamicsinConsciousness 153
6.2 BriefOverviewofNeocorticalAnatomyandPhysiology 154
6.2.1 TheHumanBrainatLargeScales 154
6.2.2 ChemicalControlofBrainandBehavior 155
6.2.3 ElectricalTransmission 156
6.2.4 Neocortex 156
6.2.5 TheNestedHierarchyofNeocortex:MultipleScalesofBrain
Tissue 158
6.2.6 CorticocorticalConnectionsAreNonlocaland“SmallWorld” 159
6.3 MultiscaleTheoryinElectrophysiology 160
6.3.1 CharacteristicEEGandPhysiologicalTimeScales 160
6.3.2 LocalversusGlobalBrainModelsandSpatialScale 161
6.3.3 ALarge-ScaleModelofEEGStandingWaves 162
6.3.4 RelationshipsbetweenSmall,Intermediate,andLargeScales:ASimple
MechanicalAnalog 164
6.4 StatisticalMechanicsofNeocorticalInteractions 166
6.4.1 SMNIonShort-TermMemoryandEEG 166
6.4.1.1 SMNISTM 167
6.4.1.2 SMNIEEG 168
6.4.2 Euler–LagrangeEquations 168
6.4.2.1 ColumnarEL 169
6.4.2.2 StringsEL 170
6.4.2.3 SpringsEL 171
6.4.3 SmokingGun 171
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Contents IX
6.4.3.1 NeocorticalMagneticFields 172
6.4.3.2 SMNIVectorPotential 172
6.5 ConcludingRemarks 173
References 174
7 MultiscaleNetworkOrganizationintheHumanBrain 179
DanielleS.BassettandFelixSiebenhu€hner
7.1 Introduction 179
7.2 MathematicalConcepts 181
7.3 StructuralMultiscaleOrganization 182
7.4 FunctionalMultiscaleOrganization 187
7.5 Discussion 191
7.5.1 StructureandFunction 191
7.5.2 HierarchicalModularity 193
7.5.3 Power-LawScaling 194
7.5.4 NetworkModelsofMultiscaleStructure 194
References 195
8 NeuronalOscillationsScaleUpandScaleDown
BrainDynamics 205
MichelLeVanQuyen,VicenteBotella-Soler,andMarioValderrama
8.1 Introduction 205
8.2 TheBrainWebofCross-ScaleInteractions 206
8.3 MultiscaleRecordingsoftheHumanBrain 208
8.4 PhysiologicalCorrelatesofCross-LevelInteractions 210
8.5 LevelEntanglementandCross-ScaleCouplingofNeuronal
Oscillations 212
8.6 Conclusions 213
References 214
9 LinkingNonlinearNeuralDynamicstoSingle-TrialHuman
Behavior 217
MichaelXCohenandBradleyVoytek
9.1 NeuralDynamicsAreComplex 217
9.2 DataAnalysisTechniquesandPossibilitiesAreExpanding
Rapidly 218
9.3 TheImportanceofLinkingNeuralDynamicstoBehavior
Dynamics 219
9.4 LinearApproachesofLinkingNeuralandBehavior
Dynamics 220
9.5 NonlinearDynamicsandBehavior:PhaseModulations 221
9.6 Cross-FrequencyCoupling 224
9.7 LinkingCross-FrequencyCouplingtoBehavior 226
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X Contents
9.8 TestingforCausalInvolvementofNonlinearDynamicsinCognition
andBehavior 228
9.9 Conclusions 229
References 229
10 BrainDynamicsatRest:HowStructureShapesDynamics 233
EtienneHugues,JuanR.Vidal,Jean-PhilippeLachaux,andGustavoDeco
10.1 Introduction 233
10.2 Model 234
10.3 Results 236
10.3.1 NeuralDynamics 236
10.3.1.1 CaseofInfiniteConductionVelocity 236
10.3.1.2 CaseofFiniteConductionVelocity 238
10.3.2 BOLDDynamics 238
10.4 ComparisonwithExperimentalData 239
10.5 Discussion 240
References 242
11 AdaptiveMultiscaleEncoding:AComputationalFunctionofNeuronal
Synchronization 245
Misha(Meyer)Z.Pesenson
11.1 Introduction 245
11.2 SomeBasicMathematicalConcepts 247
11.3 NeuralSynchronization 247
11.3.1 ConnectionswithSomeExistingApproachestoMRA 253
11.4 ConcludingRemarks 253
References 254
12 MultiscaleNonlinearDynamicsinCardiacElectrophysiology:
FromSparkstoSuddenDeath 257
ZhilinQuandMichaelNivala
12.1 Introduction 257
12.2 SubcellularScale:CriticalityintheTransitionfromCaSparkstoCa
Waves 258
12.3 CellularScale:ActionPotentialandCaCyclingDynamics 260
12.3.1 IntracellularCaAlternans 260
12.3.2 FastPacing-InducedComplexAPDDynamics 262
12.3.3 EAD-MediatedNonlinearDynamicsatSlowHeartRates 264
12.4 ExcitationDynamicsontheTissueandOrganScales 266
12.4.1 SpatiallyDiscordantAPDAlternans 266
12.4.2 SpiralandScrollWaveDynamics 267
12.4.3 ChaosSynchronization 269
12.5 Conclusions 271
References 271