Front cover 1
Contents 6
Preface to the Second Edition 8
Contributors 10
Foreword 14
About the Editors 16
1 Introduction to Modeling in the Neurosciences 20
2 Patterns of Genetic Interactions: Analysis of mRNA Levels from cDNA Microarrays 28
CONTENTS 28
2.1 INTRODUCTION 2.1.1 Biological Organisms are Complex Systems 28
2.1.2 Genes Interact withEac hOth er 28
2.2 GENETIC INTERACTION 30
2.2.1 Network Topologies 30
2.2.2 Genomic Networks 32
2.3 GENETIC NETWORKS 34
2.4 INTEGRATIVE MODELING APPROACH 35
2.4.1 The General Model 36
2.4.2 Five Models of Genetic Networks 37
2.4.3 EachModel Generates mRNA Levels with a Characteristic PDF 38
2.5 BIOLOGICAL DATA 41
2.6 SUMMARY 42
ACKNOWLEDGMENTS 42
PROBLEMS 42
APPENDIX: MULTI-HISTOGRAM ALGORITHM FOR DETERMINING THE PDF 42
3 Calcium Signaling in Dendritic Spines 44
CONTENTS 44
3.1 INTRODUCTION 45
3.2 FIRST-GENERATION DENDRITIC-SPINE CALCIUM MODELS 46
3.2.1 Calcium Diffusion 46
3.2.2 Calcium Buffering 47
3.2.3 Calcium Pumps 48
3.2.4 Calcium Influx 48
3.2.5 Calcium from Intracellular Stores 49
3.2.6 Summary 49
3.3 INSIGHTS 50
3.3.1 SpinesCompartmentalize Calcium Concentration Changes 50
3.3.2 SpinesAmplify Calcium Concentration Changes 50
3.3.3 Spine-Head Calcium (or CaMCa4) Concentration isa Good Predictor of LTP 50
3.3.4 Spine Shape Playsan Important Role in the Ability of a Spine to Concentrate Calcium 51
3.4 ISSUES 51
3.4.1 Calcium Pumps 51
3.4.2 Calcium Buffers 52
3.4.3 Calcium Source 53
3.5 IMAGING STUDIES TEST MODEL PREDICTIONS 53
3.5.1 SpinesCompartmentalize Calcium Concentration Changes 53
3.5.2 Importance of Spine Geometry 54
3.6 INSIGHTS 54
3.6.1 Sourcesof Calcium in Spines 55
3.6.2 Calcium Extrusion via Pumps 57
3.6.3 Calcium Buffersin Spines 57
3.7 ADDITIONAL INSIGHTS 58
3.7.1 Spine Motility 58
3.7.2 Coincidence Detection with Backpropagating Action Potentials 59
3.8 SECOND-GENERATION SPINE MODELS: REACTIONS LEADING 59
3.8.1 Modeling CaMKII Activation isComplicated 60
3.8.2 Characteristics of Second-Generation Models 60
3.9 INSIGHTS 67
3.9.1 Frequency Dependence of CaMKII Activation 67
3.9.2 Different Stagesof CaMKII Activation 67
3.9.3 CaMKII Activation asa Bistable Molecular Switch 68
3.9.4 CaMKII and Bidirectional Plasticity 69
3.9.5 CaMKII Activation and Spine Shape 69
3.9.6 ModelsPr edict the Need for Repetition of Short TetanusT rains 70
3.10 FUTURE PERSPECTIVES 70
3.11 SUMMARY 72
PROBLEMS 72
APPENDIX 1. TRANSLATING BIOCHEMICAL REACTION EQUATIONS TO DIFFERENTIAL EQUATIONS 74
APPENDIX 2. STOCHASTIC RATE TRANSITIONS 75
APPENDIX 3. USE OF MICHAELIS\u2013MENTEN KINETICS IN DEPHOSPHORYLATION REACTIONS 76
4 Physiological and Statistical Approaches to Modeling of Synaptic Responses 80
CONTENTS 80
4.1 INTRODUCTION 4.1.1 Modeling Synaptic Function in the CNS 80
4.1.2 Complexity Introduced by Synaptic Heterogeneity and Plasticity 82
4.1.3 Complexity Associated with Physiological Recordings 84
4.1.4 Classical Statistical Models 85
4.2 NONTRADITIONAL MODELS 87
4.2.1 Introduction to the Bayesian Model and Comparison to Classical Models 87
4.2.2 Bayesian Site Analysis 88
4.2.3 Application of the Bayesian Site Model to Simulated Data 89
4.2.4 Application of the Bayesian Model to Recorded Data 90
4.3 DISCUSSION 4.3.1 Comparison of Simulations and Physiological Data Sets 92
4.3.2 Analysis of Components in Contrast to Sites 93
4.3.3 Analysis of Physiological Data Sets 94
4.3.4 Conclusions and Future Perspectives 95
ACKNOWLEDGMENTS 97
APPENDIX: MATHEMATICAL DERIVATION OF THE MODEL 97
4.A1 PRIOR DISTRIBUTIONS 99
4.A1.1 General Structure 99
4.A1.2 100
4.A1.3 101
4.A1.4 Priors for Noise Moments m and v 102
4.A2 POSTERIOR DISTRIBUTIONS 102
4.A3 CONDITIONAL POSTERIORS 103
4.A4 PARAMETER IDENTIFICATION 103
4.A5 INCORPORATION 105
5 Natural Variability in the Geometry of Dendritic Branching Patterns 108
CONTENTS 108
5.1 INTRODUCTION 108
5.2 DENDRITIC SHAPE PARAMETERS 111
5.2.1 Dendritic Topology 112
5.2.2 Dendritic Metrics 116
5.3 OBSERVED VARIABILITY 116
5.3.1 Variation in Topological Structure 116
5.3.2 Variation in the Number of Dendritic Segments 116
5.3.3 Variation in Segment Length 117
5.3.4 Variation in Dendritic Diameter 119
5.4 MODELING DENDRITIC BRANCHING PATTERNS 119
5.4.1 Modeling Topological Variation (QS Model) 120
5.4.2 Modeling the Variation in the Number of Terminal Segments per Dendrite (BE, BES, and BEST Models) 122
5.4.3 Modeling the Variation in the Length of Dendritic Segments (BESTL Model and Simulation Procedure) 125
5.4.4 Modeling the Variation in Segment Diameter 130
5.5 DISCUSSION 131
5.6 CONCLUSIONS 133
5.7 SUMMARY 133
ACKNOWLEDGMENTS 133
PROBLEMS 134
6 Multicylinder Models for Synaptic and Gap-Junctional Integration 136
CONTENTS 136
6.1 INTRODUCTION 136
6.2 THE MULTICYLINDER MODEL 6.2.1 The Mathematical Problem 137
6.2.2 Problem Normalization and General Solution 140
6.2.3 Synaptic Reversal Potentials and Quasi-Active Ionic Currents 145
6.3 THE MULTICYLINDER MODEL WITH TAPER 156
6.3.1 The Mathematical Problem 156
6.3.2 Problem Normalization and General Solution 159
6.3.3 Synaptic Reversal Potentials 165
6.4 TWO GAP-JUNCTIONALLY COUPLED MULTICYLINDER MODELS TAPER 168
6.4.1 Soma\u2013Somatic Coupling 169
6.4.2 Dendro\u2013Dendritic Coupling 182
6.5 DISCUSSION 191
6.6 CONCLUSIONS 194
ACKNOWLEDGMENT 195
PROBLEMS 195
7 Voltage Transients in Branching Multipolar Neurons with Tapering Dendrites and Sodium Channels 198
CONTENTS 198
7.1 INTRODUCTION 198
7.2 SOLUTIONS FOR TRANSIENTS IN A FULL ARBOR MODEL WITH TAPERED BRANCHES AND BRANCH-SPECIFIC MEMBRANE RESISTIVITY 199
7.2.2 Relationship between Tapering Multicylinder Model and Tapering Single Cylinder 202
7.2.3 Separation of Variables Solution 204
7.3 SOLUTIONS FOR TRANSIENTS IN A FULL AROR MODEL WITH LINEAR EMBEDDING OF SODIUM CHANNELS 211
7.3.1 Definition of the System 211
7.3.2 Approximate Solutions for Persistent (Na+P) Sodium Channels 211
7.3.3 Approximate Solutions for Transient (Na+) Sodium Channels 213
7.4 DISCUSSION 215
7.5 SUMMARY 216
ACKNOWLEDGMENT 217
PROBLEMS 217
APPENDIX: CARLEMAN LINEARIZATION 218
8 Analytical Solutions of the Frankenhaeuser\u2013Huxley Equations Modified for Dendritic Backpropagation of a Single SodiumSpike 220
CONTENTS 220
8.1 INTRODUCTION 220
8.2 THE CABLE EQUATION 223
8.3 SCALING THE MACROSCOPIC Na+ CURRENT DENSITY 225
8.4 REFORMULATION 226
8.5 A PERTURBATIVE EXPANSION 229
8.6 VOLTAGE-DEPENDENT ACTIVATION 229
8.7 STEADY-STATE INACTIVATION OF THE SODIUM CHANNEL 231
8.8 RESULTS 8.8.1 Electrotonic Spread of bAP without Na+ Ion Channels 232
8.8.2 How the Location of Hot Spots with Identical Strengths of Na+ Ion Channels Affects the bAP 233
8.8.3 How the Number (N) of Uniformly Distributed Hot Spots with Identical Strengths of Na+ Ion Channel Densities Affects the bAP 235
8.8.4 How the Conductance Strength of Na+ ion Channel Densities with Identical Regional Distribution of Hot Spots Affects the bAP 235
8.9 DISCUSSION 237
8.10 SUMMARY 239
8.11 CONCLUSIONS 240
ACKNOWLEDGMENTS 240
APPENDIX 240
PROBLEMS 243
9 Inverse Problems for Some Cable Models of Dendrites 246
CONTENTS 246
9.1 INTRODUCTION 246
9.2 CONDUCTANCE-BASED MODELING 247
9.3 NONUNIFORM ION-CHANNEL DENSITIES 249
9.3.1 Recovering a Density in Passive Cable 249
9.3.2 Recovering a Density in Active Cable 251
9.3.3 Numerical Results 252
9.4 DENDRITES WITH EXCITABLE APPENDAGES 253
9.4.1 Recovering a Spatially Distributed Spine Density 254
9.4.2 Recovering a Spatially Distributed Filopodia Density 255
9.5 DISCUSSION 257
9.6 CONCLUSIONS 258
9.7 SUMMARY 259
ACKNOWLEDGMENTS 259
PROBLEMS 260
10 Equivalent Cables \u2014 Analysis and Construction 262
CONTENTS 262
10.1 INTRODUCTION 263
10.2 CONSTRUCTION OF THE CONTINUOUS MODEL DENDRITE 263
10.2.1 Construction of the Discrete Model Dendrite 265
10.3 MATHEMATICAL MODEL OF UNIFORM CABLE 266
10.3.1 Notation 267
10.3.2 Application to a Cable 267
10.3.3 Symmetrizing a Cable Matrix 269
10.3.4 The Simple Y-Junction 270
10.3.5 Application to a Branched Dendrite 273
10.4 STRUCTURE OF TREE MATRICES 274
10.4.1 Self-Similarity Argument 275
10.4.2 Node Numbering 275
10.4.3 Symmetrizing the Tree Matrix 277
10.4.4 Concept of the Equivalent Cable 277
10.5 ILLUSTRATIVE EXAMPLES 278
10.5.1 A Simple Asymmetric Y-Junction 278
10.5.2 A Symmetric Y-Junction 282
10.5.3 Special Case: c1c4 = c2c3 286
10.6 HOUSEHOLDER TRANSFORMATIONS 290
10.6.1 Householder Matrices 290
10.7 EXAMPLES OF EQUIVALENT CABLES 291
10.7.1 Interneurons Receiving Unmyelinated Afferent Input 291
10.7.2 Neurons Receiving Myelinated Afferent Input 292
10.8 DISCUSSION 293
ACKNOWLEDGMENTS 295
PROBLEMS 295
APPENDIX 296
11 The Representation of Three-Dimensional Dendritic Structure by a One-Dimensional Model \u2014 The Conventional Cable Equation as the First Member of a Hierarchy of Equations 298
CONTENTS 298
11.1 INTRODUCTION 299
11.2 BIOPHYSICAL PRELIMINARIES 300
11.2.1 Geometrical Considerations 300
11.2.2 Bioelectrical Considerations 300
11.2.3 Specification of the Mathematical Problem 301
11.3 IDENTIFICATION OF A ONE-DIMENSIONAL MEMBRANE POTENTIAL 302
11.4 DEVELOPMENT OF A HIERARCHY OF MEMBRANE EQUATIONS 303
11.4.1 The Membrane Boundary Conditions 305
11.4.2 Consistency of Boundary Conditions 307
11.5 THE MEMBRANE EQUATIONS 308
11.5.1 First Membrane Equation 309
11.5.2 Second Membrane Equation 310
11.5.3 Computation of Axial Current 312
11.6 CONSTITUTIVE EQUATIONS FOR TRANSMEMBRANE CURRENT 313
11.6.1 IntrinsicV oltage-Dependent Current 313
11.6.2 SynapticCurr ent 313
11.7 MEMBRANE EQUATIONS FOR SEGMENTS OF CONSTANT CONDUCTANCE 314
11.7.1 Constant Conductance Dendritic Model 315
11.8 SUMMARY OF THE MATHMATICAL MODEL 316
11.9 APPLICATION TO AN EXTRACELLULAR REGION AT CONSTANT POTENTIAL 317
11.9.1 Finite-Element Representation of Functions 317
11.9.2 First Membrane Equation 318
11.9.3 The Second Membrane Equation 320
11.9.4 The Finite-Element Expansion of 323
11.9.5 Time Integration 324
11.10 APPLICATION TO A UNIFORM DENDRITE 325
11.10.1 Results 325
11.11 CONCLUDING REMARKS 327
ACKNOWLEDGMENTS 327
PROBLEMS 327
APPENDIX 328
11.A1.1 Integration of Products of Two Basis Functions 328
11.A1.2 Integration of Products of Three Basis Functions 328
11.A1.3 Integrals of Basis Functions and their Derivatives 329
11.A2 Notation and Definitions 330
NOTES 331
12 Simulation Analyses of Retinal Cell Responses 332
CONTENTS 332
12.1 INTRODUCTION 332
12.2 DESCRIPTION OF IONIC CURRENTS 333
12.2.1 The Parallel Conductance Model 333
12.2.2 Intracellular Calcium Concentration 335
12.3 MODEL OF RETINAL CELLS 341
12.3.1 Photoreceptor 341
12.3.2 Horizontal Cell 346
12.3.3 Bipolar Cell 348
12.3.4 Ganglion Cell 349
12.4 DISCUSSION 12.4.1 Photoreceptor Model 355
12.4.2 Horizontal Cell Model 355
12.4.3 Bipolar Cell Model 356
12.4.4 Ganglion Cell Model 356
12.5 CONCLUSIONS 356
ACKNOWLEDGMENTS 357
PROBLEMS 357
NOTE 357
13 Modeling Intracellular Calcium: Diffusion, Dynamics, and Domains 358
CONTENTS 358
13.1 INTRODUCTION 358
13.2 ODES FOR ASSOCIATION OF Ca2+ WITH BUFFER 360
13.3 MICROFLUORIMETRY 361
13.4 THE BUFFER EQUILIBRATION TIME 362
13.5 CONCENTRATION FLUCTUATIONS 363
13.6 PDES 366
13.7 BUFFERED AXIAL DIFFUSION 367
13.8 AN EXPLICIT NUMERICAL SCHEME 368
13.9 AN IMPLICIT NUMERICAL SCHEME 370
13.10 CALCULATIONS 371
13.11 THE RAPID BUFFER APPROXIMATION 372
13.12 THE VALIDITY 373
13.13 DYNAMICS 374
13.14 A MINIMAL INTRACELLULAR Ca2+ CHANNEL MODEL 376
13.15 PROPAGATING WAVES 380
13.16 TRAVELING FRONTS 381
13.17 MODELING LOCALIZED Ca2+ ELEVATIONS 383
13.18 ESTIMATES 386
13.19 DOMAIN Ca2+- MEDIATED Ca2+ CHANNEL INACTIVATION 388
13.20 CONCLUSION 390
ACKNOWLEDGMENTS 391
PROBLEMS 391
14 Ephaptic Interactions Between Neurons 394
CONTENTS 394
14.1 INTRODUCTION 394
14.2 BIOPHYSICAL BASIS 14.2.1 Definitions 395
14.2.2 Electromagnetic Analysis of Nervous Tissue 395
14.2.3 The Boundary Conditions 397
14.3 THE MATHEMATICAL MODEL AND ITS SIMPLIFICATION 399
14.3.1 The MathematicalModel 399
14.3.2 A Simplification of the Model 401
14.4 MATHEMATICAL METHODS FOR SOLVING THE RESULTING PARTIAL DIFFERENTIAL EQUATIONS (PDEs) 403
14.4.1 Analytical Methods in One Dimension: Field Effects in Nerve Trunks and Parallel Dendrites 404
14.4.2 Example: Electric Field Effects from Synaptic Potentials 405
14.4.3 NumericalMethods in Three Dimensions: Field Effects in Populations of Active Neurons 408
14.5 CONDUCTION IN BUNDLES OF MYELINATED NERVE FIBERS 414
14.6 DISCUSSION 14.6.1 Biophysicaland MathematicalMethods 417
14.6.2 Electrical Field Effects in the Hippocampus and the CerebralCorte x 417
14.7 CONCLUSIONS 419
14.8 SUMMARY 420
ACKNOWLEDGMENT 420
15 Cortical Pyramidal Cells 422
CONTENTS 422
15.1 INTRODUCTION 422
15.2 COMPARTMENTALIZATION OF DENDRITES AND DENDRITC SPINES 424
15.2.1 Cable Model of Dendrites 424
15.2.2 Compartmental Model of Dendrites 425
15.2.3 Model of Dendritic Spines 428
15.3 RECEPTOR DYNAMICS AND ACTIVE CONDUCTANCES 430
15.3.1 Modeling Adaptive Receptors 430
15.3.2 Modeling Active Conduction 431
15.4 PREDICTED RESPONSE TO SIMPLE INPUT PATTERNS 433
15.4.1 Structure of the Model 433
15.4.2 BehaviorF ollowing Simple Input Patterns 435
15.4.3 Response to Active Conduction 436
15.4.4 Control of Apical Influence 437
15.5 PREDICTED RESPONSE OF THE MODEL NEURON TO PAIRED PATTERNS: LEARNING IN THE DENDRITES 438
15.5.1 Interactions Between Different Regions of the Cell During Learning 440
15.6 A REDUCED PYRAMIDAL CELL MODEL 15.6.1 The Need fora Simple Model 441
15.6.2 Key Features Indicated by a Comprehensive Model 441
15.6.3 Structure of a Simple Model 442
15.6.4 Basic Behaviorof the Simple Model 443
15.6.5 Adaptive Response 444
15.6.6 Computation Speeds 444
15.6.7 Integrate-and-Fire Neuron Models 446
15.7 DISCUSSION 446
15.8 CONCLUSIONS 448
PROBLEMS 449
APPENDIX 15. A1 USE OF SHIFT OPERATORS 449
15.A2 LEAKY INTEGRATE-AND-FIRE NEURON MODELS 450
15.A3 CONDUCTANCE-BASED INTEGRATE-AND-FIRE NEURON MODELS 450
16 Semi-Quantitative Theory of Bistable Dendrites with Potential-Dependent Facilitation of Inward Current 454
CONTENTS 454
16.1 INTRODUCTION 454
16.2 BISTABLE DENDRITES 455
16.3 POTENTIAL-DEPENDENT FACILITATION (WIND-UP) 463
16.4 DISCUSSION 466
16.5 CONCLUSIONS and FUTURE PERSPECTIVES 471
16.6 SUMMARY 472
ACKNOWLEDGMENT 473
PROBLEMS 473
APPENDIX 473
16.A2 WAVE PROPAGATION 475
16.A3 WAVE PROPAGATION 476
17 Bifurcation Analysis of the Hodgkin\u2013Huxley Equations 478
CONTENTS 478
17.1 INTRODUCTION 478
17.2 THE HODGKIN\u2013HUXLEY EQUATIONS 479
17.2.1 Linearization of the Hodgkin\u2013Huxley Equations 481
17.2.2 Reduction of the Hodgkin\u2013Huxley Equations 481
17.3 GLOBAL STRUCTURE OF BIFURCATION IN THE HODGKIN-HUXLEY EQUATIONS 482
17.3.1 Bifurcation dueto Iext 482
17.3.2 Why Study theGlobal Organization of Bifurcations? 485
17.3.3 Bifurcation Diagram for Iext at VK = 10 mV 486
17.3.4 Bifurcation Diagram of Iext and VK 486
17.3.5 Codimension and Organizing Center 491
17.3.6 Bifurcation in the Iext\u2013VK\u2013VNa Parameter Space 491
17.4 DISCUSSION 491
17.5 CONCLUSION 493
PROBLEMS 493
APPENDIX 17.A1 ANALYSIS AND TOOLS 494
17.A2 THE HOPF BIFURCATION 496
17.A3 THE DEGENERATE HOPF BIFURCATION 496
NOTE 497
18 Highly Efficient Propagation of Random Impulse Trains Across Unmyelinated Axonal Branch Points:Modifications by Periaxonal K+ Accumulation and Sodium Channel Kinetics 498
CONTENTS 498
18.1 INTRODUCTION 499
18.1.1 Computational Considerations 500
18.2 IMPULSE PROPAGATION THROGH BRANCH POINTS 509
18.2.1 Single Action Potential Propagation through Serial Branch Points 509
18.2.2 Propagation of Random Action Potential Trains through Serial Branch Points 509
18.2.3 Discussion 514
18.3 ROLE PERIAXONAL K+ ACCUMULATION 515
18.3.1 Periaxonal K+ Accumulation Model 515
18.3.2 Effects of Periaxonal K+ Accumulation 516
18.3.3 Differential Propagation Due to Periaxonal K+ Accumulation 518
18.3.4 Modifications of Random Impulse Trains by Periaxonal K+ Accumulation 525
18.3.5 Discussion 528
18.4 ROLE OF A MORE COMPLETE AND ACCURATE DESCRIPTION OF SODIUM CHANNEL POPULATION KINETICS 533
18.4.2 PC Model\u2019s Basic Properties 535
18.4.3 Propagation of Random Action Potential Trains in the PC Model 535
18.4.4 Discussion 538
18.5 DIRECTIONS FOR FUTURE RESEARCH 541
ACKNOWLEDGMENTS 546
PROBLEMS 546
APPENDIX 546
NOTES 548
19 Dendritic Integration in a Two-Neuron Recurrent Excitatory Network Model 550
CONTENTS 550
19.1 INTRODUCTION 550
19.2 IONIC CABLE THEORY FOR CONDUCTION OF DENDRITIC POTENTIALS 552
19.2.1 Ionic Cable Equation for a Single Neuron 552
19.2.2 Representation of Noninactivating Voltage-Dependent Ionic Currents 552
19.2.3 Representation of Axodendritic Chemical Synapses 553
19.2.4 Network Equations without Synaptic Weights 554
19.3 RECURRENT DYNAMICS OF TWO SYNAPTICALLY COUPLED NEURONS 556
19.3.2 Electrotonic Potential in the Stimulated Neuron 558
19.3.3 Dendritic Potentials in the Stimulated Neuron with Synaptic Feedback 560
19.3.4 Dendritic Potentials in the Nonstimulated Neuron via Feedforward Synapses 562
19.3.5 Illustrative Simulation without Repetitive Firing (i.e., y = 1) 564
19.4 DISCUSSION 568
19.5 CONCLUSIONS 569
ACKNOWLEDGMENTS 570
PROBLEMS 570
APPENDIX: THE GREEN\u2019S FUNCTION FOR A PASSIVE CABLE 570
20 Spike-Train Analysis for Neural Systems 574
CONTENTS 574
20.1 INTRODUCTION 574
20.2 LINEAR NONLINEAR TIME-DOMAIN POINT-PROCESS ANALYSIS 575
20.3 LINEAR NONLINEAR FREQUENCY-DOMAIN POINT-PROCESS ANALYSIS 580
20.4 CORTICAL NEURAL NETWORK SIMULATION 585
20.5 RESULTS 587
20.6 CONCLUDING REMARKS 594
ACKNOWLEDGMENTS 597
SOFTWARE ARCHIVE 597
PROBLEMS 597
21 The Poetics of Tremor 600
CONTENTS 600
21.1 INTRODUCTION 600
21.2 MODELS OF TREMOR DATA 601
21.3 MODELS OF MULTIDIMENSIONAL (MULTIAXIAL) TREMOR DATA 604
21.4 HARMONICS AND PHASE 605
21.5 TEMPORAL STABILITY 607
21.6 MODELS OF OTHER COMPLEX TREMOR DATA 610
21.7 FUTURE ISSUES 613
RESEARCH PROBLEMS9 613
NOTES 614
22 Principles and Methods in the Analysis of Brain Networks 618
CONTENTS 618
22.1 INTRODUCTION 618
22.2 ANATOMICAL, FUNCTIONAL, AND EFFECTIVE CONNECTIVITY 619
22.2.1 AnatomicalConnecti vity 619
22.2.2 FunctionalConnecti vity 620
22.2.3 Effective Connectivity 620
22.2.4 Relationships between Anatomical, Functional, and Effective Connectivity 621
22.3 SEGREGATION AND INTEGRATION AS PRINCIPLES OF BRAIN ORGANIZATION 621
22.3.1 Segregation 621
22.3.2 Integration 622
22.4 ANALYSIS OF ANATOMICAL CONNECTIVITY 623
22.5 ANALYSIS OF FUNCTIONAL CONNECTIVITY 625
22.6 ANALYSIS OF EFFECTIVE CONNECTIVITY 628
22.7 DISCUSSION: BRAIN NETWORKS, COMPLEXITY, AND COGNITION 629
ACKNOWLEDGMENT 630
PROBLEMS 630
23 The Darwin Brain-Based Automata: Synthetic Neural Models and Real-World Devices 632
CONTENTS 632
23.1 INTRODUCTION 632
23.1.1 Summary of the Theory of Neuronal Group Selection 633
23.1.2 Synthetic Neural Modeling and Brain-Based Devices 636
23.1.3 The Single-Cell or Neuronal Group Model 637
23.1.4 Neural Areas and Network Architecture 639
23.1.6 Software Simulator 641
23.1.5 Embodying the Brain 639
23.2 THE DARWIN SERIES OF MODEL 642
23.2.1 A Totally Synthetic Model: Darwin III 642
23.2.2 Darwin VII \u2014 Multimodal Sensing and Conditioning 644
23.2.3 Darwin VIII \u2014 Visual Cortex Model with Reentrant Signaling 647
23.2.4 Darwin IX \u2014 Whisker Barrel Model and Texture Discrimination 651
23.3 CONCLUSIONS 654
ACKNOWLEDGMENT 655
PROBLEMS 656
24 Toward Neural Robotics: From Synthetic Models to Neuromimetic Implementations 658
CONTENTS 658
24.1 INTRODUCTION 658
24.2 THE SYNTHETIC APPROACH 659
24.3 COMPLEXITY AND COGNITION 661
24.4 INFORMATION AND MORPHOLOGY 662
24.5 HYBRID SYSTEMS: REAL NEURONS MOVING ROBOTS 663
24.6 HUMANOID ROBOTS: THE SEARCH FOR PRINCIPLES OF DEVELOPMENT 664
24.7 OUTLOOK 664
ACKNOWLEDGMENT 665
Bibliography 666
Index 724
Back cover 742