Modeling in the Neurosciences: From Biological Systems to Neuromimetic Robotics

0415328683......Page 1
Contents......Page 6
Preface to the Second Edition......Page 8
Contributors......Page 10
Foreword......Page 14
About the Editors......Page 16
1 Introduction to Modeling in the Neurosciences......Page 20
2.1.2 Genes Interact with Each Other......Page 28
2.2.1 Network Topologies......Page 30
2.2.2 Genomic Networks......Page 32
2.3 GENETIC NETWORKS......Page 34
2.4 INTEGRATIVE MODELING APPROACH......Page 35
2.4.1 The General Model......Page 36
2.4.2 Five Models of Genetic Networks......Page 37
2.4.3 EachModel Generates mRNA Levels with a Characteristic PDF......Page 38
2.5 BIOLOGICAL DATA......Page 41
APPENDIX: MULTI-HISTOGRAM ALGORITHM FOR DETERMINING THE PDF......Page 42
CONTENTS......Page 44
3.1 INTRODUCTION......Page 45
3.2.1 Calcium Diffusion......Page 46
3.2.2 Calcium Buffering......Page 47
3.2.4 Calcium Influx......Page 48
3.2.6 Summary......Page 49
3.3.3 Spine-Head Calcium (or CaMCa4) Concentration isa Good Predictor of LTP......Page 50
3.4.1 Calcium Pumps......Page 51
3.4.2 Calcium Buffers......Page 52
3.5.1 SpinesCompartmentalize Calcium Concentration Changes......Page 53
3.6 INSIGHTS......Page 54
3.6.1 Sourcesof Calcium in Spines......Page 55
3.6.3 Calcium Buffersin Spines......Page 57
3.7.1 Spine Motility......Page 58
3.8 SECOND-GENERATION SPINE MODELS: REACTIONS LEADING......Page 59
3.8.2 Characteristics of Second-Generation Models......Page 60
3.9.2 Different Stagesof CaMKII Activation......Page 67
3.9.3 CaMKII Activation asa Bistable Molecular Switch......Page 68
3.9.5 CaMKII Activation and Spine Shape......Page 69
3.10 FUTURE PERSPECTIVES......Page 70
PROBLEMS......Page 72
APPENDIX 1. TRANSLATING BIOCHEMICAL REACTION EQUATIONS TO DIFFERENTIAL EQUATIONS......Page 74
APPENDIX 2. STOCHASTIC RATE TRANSITIONS......Page 75
APPENDIX 3. USE OF MICHAELIS-MENTEN KINETICS IN DEPHOSPHORYLATION REACTIONS......Page 76
4.1.1 Modeling Synaptic Function in the CNS......Page 80
4.1.2 Complexity Introduced by Synaptic Heterogeneity and Plasticity......Page 82
4.1.3 Complexity Associated with Physiological Recordings......Page 84
4.1.4 Classical Statistical Models......Page 85
4.2.1 Introduction to the Bayesian Model and Comparison to Classical Models......Page 87
4.2.2 Bayesian Site Analysis......Page 88
4.2.3 Application of the Bayesian Site Model to Simulated Data......Page 89
4.2.4 Application of the Bayesian Model to Recorded Data......Page 90
4.3.1 Comparison of Simulations and Physiological Data Sets......Page 92
4.3.2 Analysis of Components in Contrast to Sites......Page 93
4.3.3 Analysis of Physiological Data Sets......Page 94
4.3.4 Conclusions and Future Perspectives......Page 95
APPENDIX: MATHEMATICAL DERIVATION OF THE MODEL......Page 97
4.A1.1 General Structure......Page 99
4.A1.2 Priors for m and Associated Hyperparameters q, a......Page 100
4.A1.3 Priors for p and Associated Hyperparameters b......Page 101
4.A2 POSTERIOR DISTRIBUTIONS......Page 102
4.A4 PARAMETER IDENTIFICATION......Page 103
4.A5 INCORPORATION......Page 105
5.1 INTRODUCTION......Page 108
5.2 DENDRITIC SHAPE PARAMETERS......Page 111
5.2.1 Dendritic Topology......Page 112
5.3.2 Variation in the Number of Dendritic Segments......Page 116
5.3.3 Variation in Segment Length......Page 117
5.4 MODELING DENDRITIC BRANCHING PATTERNS......Page 119
5.4.1 Modeling Topological Variation (QS Model)......Page 120
5.4.2 Modeling the Variation in the Number of Terminal Segments per Dendrite (BE, BES, and BEST Models)......Page 122
5.4.3 Modeling the Variation in the Length of Dendritic Segments (BESTL Model and Simulation Procedure)......Page 125
5.4.4 Modeling the Variation in Segment Diameter......Page 130
5.5 DISCUSSION......Page 131
ACKNOWLEDGMENTS......Page 133
PROBLEMS......Page 134
6.1 INTRODUCTION......Page 136
6.2.1 The Mathematical Problem......Page 137
6.2.2 Problem Normalization and General Solution......Page 140
6.2.3 Synaptic Reversal Potentials and Quasi-Active Ionic Currents......Page 145
6.3.1 The Mathematical Problem......Page 156
6.3.2 Problem Normalization and General Solution......Page 159
6.3.3 Synaptic Reversal Potentials......Page 165
6.4 TWO GAP-JUNCTIONALLY COUPLED MULTICYLINDER MODELS TAPER......Page 168
6.4.1 Soma-Somatic Coupling......Page 169
6.4.2 Dendro-Dendritic Coupling......Page 182
6.5 DISCUSSION......Page 191
6.6 CONCLUSIONS......Page 194
PROBLEMS......Page 195
7.1 INTRODUCTION......Page 198
7.2.1 De.nition of the System......Page 199
7.2.2 Relationship between Tapering Multicylinder Model and Tapering Single Cylinder......Page 202
7.2.3 Separation of Variables Solution......Page 204
7.3.2 Approximate Solutions for Persistent (Na+P) Sodium Channels......Page 211
7.3.3 Approximate Solutions for Transient (Na+) Sodium Channels......Page 213
7.4 DISCUSSION......Page 215
7.5 SUMMARY......Page 216
PROBLEMS......Page 217
APPENDIX: CARLEMAN LINEARIZATION......Page 218
8.1 INTRODUCTION......Page 220
8.2 THE CABLE EQUATION......Page 223
8.3 SCALING THE MACROSCOPIC Na+ CURRENT DENSITY......Page 225
8.4 REFORMULATION......Page 226
8.6 VOLTAGE-DEPENDENT ACTIVATION......Page 229
8.7 STEADY-STATE INACTIVATION OF THE SODIUM CHANNEL......Page 231
8.8.1 Electrotonic Spread of bAP without Na+ Ion Channels......Page 232
8.8.2 How the Location of Hot Spots with Identical Strengths of Na+ Ion Channels Affects the bAP......Page 233
8.8.4 How the Conductance Strength of Na+ ion Channel Densities with Identical Regional Distribution of Hot Spots Affects the bAP......Page 235
8.9 DISCUSSION......Page 237
8.10 SUMMARY......Page 239
APPENDIX......Page 240
PROBLEMS......Page 243
9.1 INTRODUCTION......Page 246
9.2 CONDUCTANCE-BASED MODELING......Page 247
9.3.1 Recovering a Density in Passive Cable......Page 249
9.3.2 Recovering a Density in Active Cable......Page 251
9.3.3 Numerical Results......Page 252
9.4 DENDRITES WITH EXCITABLE APPENDAGES......Page 253
9.4.1 Recovering a Spatially Distributed Spine Density......Page 254
9.4.2 Recovering a Spatially Distributed Filopodia Density......Page 255
9.5 DISCUSSION......Page 257
9.6 CONCLUSIONS......Page 258
ACKNOWLEDGMENTS......Page 259
PROBLEMS......Page 260
CONTENTS......Page 262
10.2 CONSTRUCTION OF THE CONTINUOUS MODEL DENDRITE......Page 263
10.2.1 Construction of the Discrete Model Dendrite......Page 265
10.3 MATHEMATICAL MODEL OF UNIFORM CABLE......Page 266
10.3.2 Application to a Cable......Page 267
10.3.3 Symmetrizing a Cable Matrix......Page 269
10.3.4 The Simple Y-Junction......Page 270
10.3.5 Application to a Branched Dendrite......Page 273
10.4 STRUCTURE OF TREE MATRICES......Page 274
10.4.2 Node Numbering......Page 275
10.4.4 Concept of the Equivalent Cable......Page 277
10.5.1 A Simple Asymmetric Y-Junction......Page 278
10.5.2 A Symmetric Y-Junction......Page 282
10.5.3 Special Case: c1c4 = c2c3......Page 286
10.6.1 Householder Matrices......Page 290
10.7.1 Interneurons Receiving Unmyelinated Afferent Input......Page 291
10.7.2 Neurons Receiving Myelinated Afferent Input......Page 292
10.8 DISCUSSION......Page 293
PROBLEMS......Page 295
APPENDIX......Page 296
CONTENTS......Page 298
11.1 INTRODUCTION......Page 299
11.2.2 Bioelectrical Considerations......Page 300
11.2.3 Specification of the Mathematical Problem......Page 301
11.3 IDENTIFICATION OF A ONE-DIMENSIONAL MEMBRANE POTENTIAL......Page 302
11.4 DEVELOPMENT OF A HIERARCHY OF MEMBRANE EQUATIONS......Page 303
11.4.1 The Membrane Boundary Conditions......Page 305
11.4.2 Consistency of Boundary Conditions......Page 307
11.5 THE MEMBRANE EQUATIONS......Page 308
11.5.1 First Membrane Equation......Page 309
11.5.2 Second Membrane Equation......Page 310
11.5.3 Computation of Axial Current......Page 312
11.6.2 SynapticCurr ent......Page 313
11.7 MEMBRANE EQUATIONS FOR SEGMENTS OF CONSTANT CONDUCTANCE......Page 314
11.7.1 Constant Conductance Dendritic Model......Page 315
11.8 SUMMARY OF THE MATHMATICAL MODEL......Page 316
11.9.1 Finite-Element Representation of Functions......Page 317
11.9.2 First Membrane Equation......Page 318
11.9.3 The Second Membrane Equation......Page 320
11.9.4 The Finite-Element Expansion of......Page 323
11.9.5 Time Integration......Page 324
11.10.1 Results......Page 325
PROBLEMS......Page 327
11.A1.2 Integration of Products of Three Basis Functions......Page 328
11.A1.3 Integrals of Basis Functions and their Derivatives......Page 329
11.A2 Notation and Definitions......Page 330
NOTES......Page 331
12.1 INTRODUCTION......Page 332
12.2.1 The Parallel Conductance Model......Page 333
12.2.2 Intracellular Calcium Concentration......Page 335
12.3.1 Photoreceptor......Page 341
12.3.2 Horizontal Cell......Page 346
12.3.3 Bipolar Cell......Page 348
12.3.4 Ganglion Cell......Page 349
12.4.2 Horizontal Cell Model......Page 355
12.5 CONCLUSIONS......Page 356
NOTE......Page 357
13.1 INTRODUCTION......Page 358
13.2 ODES FOR ASSOCIATION OF Ca2+ WITH BUFFER......Page 360
13.3 MICROFLUORIMETRY......Page 361
13.4 THE BUFFER EQUILIBRATION TIME......Page 362
13.5 CONCENTRATION FLUCTUATIONS......Page 363
13.6 PDES......Page 366
13.7 BUFFERED AXIAL DIFFUSION......Page 367
13.8 AN EXPLICIT NUMERICAL SCHEME......Page 368
13.9 AN IMPLICIT NUMERICAL SCHEME......Page 370
13.10 CALCULATIONS......Page 371
13.11 THE RAPID BUFFER APPROXIMATION......Page 372
13.12 THE VALIDITY......Page 373
13.13 DYNAMICS......Page 374
13.14 A MINIMAL INTRACELLULAR Ca2+ CHANNEL MODEL......Page 376
13.15 PROPAGATING WAVES......Page 380
13.16 TRAVELING FRONTS......Page 381
13.17 MODELING LOCALIZED Ca2+ ELEVATIONS......Page 383
13.18 ESTIMATES......Page 386
13.19 DOMAIN Ca2+- MEDIATED Ca2+ CHANNEL INACTIVATION......Page 388
13.20 CONCLUSION......Page 390
PROBLEMS......Page 391
14.1 INTRODUCTION......Page 394
14.2.2 Electromagnetic Analysis of Nervous Tissue......Page 395
14.2.3 The Boundary Conditions......Page 397
14.3.1 The MathematicalModel......Page 399
14.3.2 A Simplification of the Model......Page 401
14.4 MATHEMATICAL METHODS FOR SOLVING THE RESULTING PARTIAL DIFFERENTIAL EQUATIONS (PDEs)......Page 403
14.4.1 Analytical Methods in One Dimension: Field Effects in Nerve Trunks and Parallel Dendrites......Page 404
14.4.2 Example: Electric Field Effects from Synaptic Potentials......Page 405
14.4.3 NumericalMethods in Three Dimensions: Field Effects in Populations of Active Neurons......Page 408
14.5 CONDUCTION IN BUNDLES OF MYELINATED NERVE FIBERS......Page 414
14.6.2 Electrical Field Effects in the Hippocampus and the CerebralCorte x......Page 417
14.7 CONCLUSIONS......Page 419
ACKNOWLEDGMENT......Page 420
15.1 INTRODUCTION......Page 422
15.2.1 Cable Model of Dendrites......Page 424
15.2.2 Compartmental Model of Dendrites......Page 425
15.2.3 Model of Dendritic Spines......Page 428
15.3.1 Modeling Adaptive Receptors......Page 430
15.3.2 Modeling Active Conduction......Page 431
15.4.1 Structure of the Model......Page 433
15.4.2 BehaviorF ollowing Simple Input Patterns......Page 435
15.4.3 Response to Active Conduction......Page 436
15.4.4 Control of Apical Influence......Page 437
15.5 PREDICTED RESPONSE OF THE MODEL NEURON TO PAIRED PATTERNS: LEARNING IN THE DENDRITES......Page 438
15.5.1 Interactions Between Different Regions of the Cell During Learning......Page 440
15.6.2 Key Features Indicated by a Comprehensive Model......Page 441
15.6.3 Structure of a Simple Model......Page 442
15.6.4 Basic Behaviorof the Simple Model......Page 443
15.6.6 Computation Speeds......Page 444
15.7 DISCUSSION......Page 446
15.8 CONCLUSIONS......Page 448
15.A1 USE OF SHIFT OPERATORS......Page 449
15.A3 CONDUCTANCE-BASED INTEGRATE-AND-FIRE NEURON MODELS......Page 450
16.1 INTRODUCTION......Page 454
16.2 BISTABLE DENDRITES......Page 455
16.3 POTENTIAL-DEPENDENT FACILITATION (WIND-UP)......Page 463
16.4 DISCUSSION......Page 466
16.5 CONCLUSIONS and FUTURE PERSPECTIVES......Page 471
16.6 SUMMARY......Page 472
16.A1 LIST OF SYMBOLS AND ABBREVIATIONS......Page 473
16.A2 WAVE PROPAGATION......Page 475
16.A3 WAVE PROPAGATION......Page 476
17.1 INTRODUCTION......Page 478
17.2 THE HODGKIN-HUXLEY EQUATIONS......Page 479
17.2.2 Reduction of the Hodgkin-Huxley Equations......Page 481
17.3.1 Bifurcation dueto Iext......Page 482
17.3.2 Why Study theGlobal Organization of Bifurcations?......Page 485
17.3.4 Bifurcation Diagram of Iext and VK......Page 486
17.4 DISCUSSION......Page 491
PROBLEMS......Page 493
17.A1 ANALYSIS AND TOOLS......Page 494
17.A3 THE DEGENERATE HOPF BIFURCATION......Page 496
NOTE......Page 497
CONTENTS......Page 498
18.1 INTRODUCTION......Page 499
18.1.1 Computational Considerations......Page 500
18.2.2 Propagation of Random Action Potential Trains through Serial Branch Points......Page 509
18.2.3 Discussion......Page 514
18.3.1 Periaxonal K+ Accumulation Model......Page 515
18.3.2 Effects of Periaxonal K+ Accumulation......Page 516
18.3.3 Differential Propagation Due to Periaxonal K+ Accumulation......Page 518
18.3.4 Modifications of Random Impulse Trains by Periaxonal K+ Accumulation......Page 525
18.3.5 Discussion......Page 528
18.4.1 The "PC" Model......Page 533
18.4.3 Propagation of Random Action Potential Trains in the PC Model......Page 535
18.4.4 Discussion......Page 538
18.5 DIRECTIONS FOR FUTURE RESEARCH......Page 541
APPENDIX......Page 546
NOTES......Page 548
19.1 INTRODUCTION......Page 550
19.2.2 Representation of Noninactivating Voltage-Dependent Ionic Currents......Page 552
19.2.3 Representation of Axodendritic Chemical Synapses......Page 553
19.2.4 Network Equations without Synaptic Weights......Page 554
19.3.1 Linearization of the Persistent Sodium Current......Page 556
19.3.2 Electrotonic Potential in the Stimulated Neuron......Page 558
19.3.3 Dendritic Potentials in the Stimulated Neuron with Synaptic Feedback......Page 560
19.3.4 Dendritic Potentials in the Nonstimulated Neuron via Feedforward Synapses......Page 562
19.3.5 Illustrative Simulation without Repetitive Firing (i.e., y = 1)......Page 564
19.4 DISCUSSION......Page 568
19.5 CONCLUSIONS......Page 569
APPENDIX: THE GREEN'S FUNCTION FOR A PASSIVE CABLE......Page 570
20.1 INTRODUCTION......Page 574
20.2 LINEAR NONLINEAR TIME-DOMAIN POINT-PROCESS ANALYSIS......Page 575
20.3 LINEAR NONLINEAR FREQUENCY-DOMAIN POINT-PROCESS ANALYSIS......Page 580
20.4 CORTICAL NEURAL NETWORK SIMULATION......Page 585
20.5 RESULTS......Page 587
20.6 CONCLUDING REMARKS......Page 594
PROBLEMS......Page 597
21.1 INTRODUCTION......Page 600
21.2 MODELS OF TREMOR DATA......Page 601
21.3 MODELS OF MULTIDIMENSIONAL (MULTIAXIAL) TREMOR DATA......Page 604
21.4 HARMONICS AND PHASE......Page 605
21.5 TEMPORAL STABILITY......Page 607
21.6 MODELS OF OTHER COMPLEX TREMOR DATA......Page 610
RESEARCH PROBLEMS9......Page 613
NOTES......Page 614
22.1 INTRODUCTION......Page 618
22.2.1 AnatomicalConnecti vity......Page 619
22.2.3 Effective Connectivity......Page 620
22.3.1 Segregation......Page 621
22.3.2 Integration......Page 622
22.4 ANALYSIS OF ANATOMICAL CONNECTIVITY......Page 623
22.5 ANALYSIS OF FUNCTIONAL CONNECTIVITY......Page 625
22.6 ANALYSIS OF EFFECTIVE CONNECTIVITY......Page 628
22.7 DISCUSSION: BRAIN NETWORKS, COMPLEXITY, AND COGNITION......Page 629
PROBLEMS......Page 630
23.1 INTRODUCTION......Page 632
23.1.1 Summary of the Theory of Neuronal Group Selection......Page 633
23.1.2 Synthetic Neural Modeling and Brain-Based Devices......Page 636
23.1.3 The Single-Cell or Neuronal Group Model......Page 637
23.1.5 Embodying the Brain......Page 639
23.1.6 Software Simulator......Page 641
23.2.1 A Totally Synthetic Model: Darwin III......Page 642
23.2.2 Darwin VII - Multimodal Sensing and Conditioning......Page 644
23.2.3 Darwin VIII - Visual Cortex Model with Reentrant Signaling......Page 647
23.2.4 Darwin IX - Whisker Barrel Model and Texture Discrimination......Page 651
23.3 CONCLUSIONS......Page 654
ACKNOWLEDGMENT......Page 655
PROBLEMS......Page 656
24.1 INTRODUCTION......Page 658
24.2 THE SYNTHETIC APPROACH......Page 659
24.3 COMPLEXITY AND COGNITION......Page 661
24.4 INFORMATION AND MORPHOLOGY......Page 662
24.5 HYBRID SYSTEMS: REAL NEURONS MOVING ROBOTS......Page 663
24.7 OUTLOOK......Page 664
ACKNOWLEDGMENT......Page 665
Bibliography......Page 666
Index......Page 724
Back cover......Page 742