Bursting: the genesis of rhythm in the nervous system
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
New Jersey
World Scientific Publishing
2005
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 401 S. graph. Darst. |
| ISBN: | 9789812565068 981256506X |
Internformat
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| 245 | 1 | 0 | |a Bursting |b the genesis of rhythm in the nervous system |c edited by Stephen Coombes ... |
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Datensatz im Suchindex
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|---|---|
| adam_text | CONTENTS
Preface v
PART I: BURSTING AT THE SINGLE CELL LEVEL
1 THE DEVELOPMENT OF THE HINDMARSH
ROSE MODEL FOR BURSTING 3
Jim Hindmarsh and Philip Cornelius
1.1 Introduction 3
1.2 Tail Current Reversal 4
1.3 The 1982 Model 5
1.4 The 1984 Model 8
1.5 Subthreshold Oscillations 10
1.6 A Bifurcation Theorem 15
2 NEGATIVE CALCIUM FEEDBACK: THE ROAD
FROM CHAY KEIZER 19
Richard Bertram and Arthur Sherman
2.1 Introduction 19
2.2 Before the Beginning 20
2.3 The Beginning 24
2.4 The Demise of K(Ca) 32
2.5 The Return of K(Ca): Help from the Endoplasmic
Reticulum 34
2.6 Further Modifications to the Model 41
2.7 Discussion 43
ix
x Contents
3 AUTOREGULATION OF BURSTING OF AVP
NEURONS OF THE RAT HYPOTHALAMUS 49
Peter Roper, Colin H. Brown, Charles W. Bourque and
William E. Armstrong
3.1 Introduction 49
3.2 Electrical Properties of AVP Cells 52
3.3 Mathematical Model 55
3.4 Firing Patterns 58
3.5 Burst Structure 58
3.6 The Role of Calcium 62
3.7 The Action of Dynorphin 62
3.8 The Bursting Mechanism 66
3.9 The Dynamics of Dynorphin 71
3.10 Analysis of Bursting 73
3.10.1 FAST 73
3.10.2 SLOW 73
3.11 Discussion 81
3.11.1 A dual role for calcium 81
3.11.2 Alternative mechanisms for the plateau potential . . 81
3.11.3 Excitable bursting 82
4 BIFURCATIONS IN THE FAST DYNAMICS OF
NEURONS: IMPLICATIONS FOR BURSTING 89
John Guckenheimer, Joseph H. Tien and Allan R. Willms
4.1 Introduction 90
4.2 A Two Dimensional Model of Spiking Sodium Currents . . 91
4.3 Fast Slow Analysis of Bursting 104
4.3.1 Aplysia 106
4.3.2 Thalamic relay neurons 108
4.3.3 Leech heart interneurons 110
4.3.4 Plateau oscillations in leech heart interneurons ... 112
4.3.5 Neurons of the pre B6tzinger complex 113
4.4 Discussion 115
Contents xi
5 BURSTING IN 2 COMPARTMENT NEURONS:
A CASE STUDY OF THE PINSKY RINZEL
MODEL 123
Amitabha Bose and Victoria Booth
5.1 Introduction 123
5.2 The Pinsky Rinzel Model 125
5.2.1 Equations and qualitative description of the complex
burst 125
5.3 Dynamics of the Pinsky Rinzel Model 129
5.3.1 Burst initiation 129
5.3.2 Somatic dendritic ping pong 133
5.4 Morris Lecar Two Compartment Models 137
5.5 Discussion 140
6 GHOSTBURSTING: THE ROLE OF ACTIVE
DENDRITES IN ELECTROSENSORY
PROCESSING 145
Carlo R. Laing and Brent Doiron
6.1 Introduction 145
6.2 Bursting Mechanism 146
6.3 Ghostburster Dynamics 151
6.4 Unique Features 154
6.5 Extensions and Other Work 157
6.5.1 Reduced models 158
6.5.2 Periodic forcing 159
6.5.3 Burst excitability 160
6.5.4 Differential modulation of burst discharge 161
6.6 Parallel Processing with Bursts and Isolated Spikes .... 163
6.6.1 Ghostbusting the ghostburster 163
6.6.2 Spike train processing 166
6.7 Summary 169
xii Contents
PART II: BURSTING AT THE NETWORK LEVEL
7 ANALYSIS OF CIRCUITS CONTAINING
BURSTING NEURONS USING PHASE
RESETTING CURVES 175
Carmen Canavier
7.1 Introduction 175
7.2 Stability Analysis for Two Coupled Oscillators 178
7.3 Analysis of a Circuit of Two Model Neurons 181
7.4 Stability Analysis for a Three Neuron Ring Circuit 183
7.5 Analysis of a Circuit of Three Model Neurons 186
7.6 Analysis of a Two Neuron Hybrid Circuit 189
7.7 Effect of Changing Burst Durations in the Two Neuron
Circuit 191
7.8 Phenomenology of Resetting in a Biological Bursting
Neuron 193
7.9 Significance 195
8 BURSTING IN COUPLED CELL SYSTEMS 201
Martin Golubitsky, Kresimir Josic and LieJune Shiau
8.1 Introduction 201
8.2 Unfolding Theory and Bursting in Fast Slow Systems . . . 203
8.3 Bursting in Two Coupled Cells 205
8.4 Z2 Equivariant Bifurcations 207
8.5 Pitchfork Bifurcation 209
8.6 Hopf/Hopf Mode Interactions 211
8.7 Takens Bogdanov Bifurcation with Z2 Symmetry 213
8.8 Conclusion 219
9 MODULATORY EFFECTS OF COUPLING ON
BURSTING MAPS 223
Gerda de Vries
9.1 Introduction 223
9.2 Examples of Bursting Maps 225
Contents xiii
9.2.1 One dimensional maps 225
9.2.2 Two dimensional maps 226
9.3 Effects of Coupling 230
9.3.1 Effects of coupling on one dimensional maps 230
9.3.2 Effects of coupling on two dimensional maps .... 232
9.4 Rulkov s First Bursting Map: Explaining the Effect of
Coupling 234
9.5 Discussion 238
10 BEYOND SYNCHRONIZATION: MODULATORY
AND EMERGENT EFFECTS OF COUPLING IN
SQUARE WAVE BURSTING 243
Gerda de Vries and Arthur Sherman
10.1 Introduction 243
10.2 The Model 245
10.3 Effect of Coupling: Identical Cells 247
10.3.1 Effects of coupling on spike patterns 249
10.3.2 Effects of coupling on burst period 251
10.4 Normal Form Reduction 254
10.4.1 Identical cells: A = 1 255
10.4.1.1 Stability of the in phase and anti phase
steady states 256
10.4.2 Non identical cells: A ^ 1 257
10.5 Enhancement of the Period Extension with Heterogeneity . 258
10.6 Emergent Bursting 261
10.7 Synaptic Coupling 265
10.8 Discussion 267
10.8.1 Limitations and extensions 267
10.8.2 Comparison to other emergent oscillations 269
11 BURSTING IN EXCITATORY NEURAL
NETWORKS 273
Joel Tabak and John Rinzel
11.1 Introduction 274
11.2 Spontaneous Activity in the Developing Spinal Cord .... 274
xiv Contents
11.3 Model of the Spontaneous Activity in the Embryonic Chick
Spinal Cord 277
11.4 Properties and Applications of the Model 280
11.4.1 Bistability of the excitatory network with fixed
synaptic efficacy 280
11.4.2 Episodic and rhythmic behavior due to activity
dependent depression of network excitability .... 283
11.4.3 Relationship between episode duration and inter
episode interval 287
11.4.4 Recovery of the activity after blockade of excitatory
connections 289
11.5 Analogy between Network and Cellular Bursting 292
11.6 Discussion 294
11.6.1 Bursting activity in neural networks 295
11.6.2 Network vs cellular bursting 296
12 OSCILLATORY BURSTING MECHANISMS IN
RESPIRATORY PACEMAKER NEURONS AND
NETWORKS 303
Robert Butera, Jonathan Rubin, David Terman and
Jeffrey Smith
12.1 Introduction 304
12.2 Single Cell Dynamics: Evidence, Motivation, and Models . 306
12.3 Coupling Effects in Two Cells: A Pathway to Larger
Populations 312
12.4 The Big Bang: Populations of Excitatory Pacemakers . . . 314
12.4.1 Synchronized bursting in a heterogeneous population 314
12.4.2 Dynamic range of network oscillations 316
12.4.3 Emergent rhythms: Pacemakers vs. group
pacemakers 317
12.5 Dynamic Range of Bursting Activity 318
12.5.1 Fast/slow analysis of a single cell 318
12.5.2 The transition from bursting to spiking in coupled
cells with hi = h2 323
Contents xv
12.5.3 The transition from bursting to tonic spiking in the
full model for two coupled cells 327
12.6 Effects of Heterogeneity 329
12.6.1 Motivation and introduction to modeling approach . 329
12.6.2 The role of fast threshold modulation 330
12.6.3 Analysis of a synchronized bursting in a
heterogeneous population 333
12.7 Contemporary Issues and Unresolved Problems 338
12.7.1 Single neuron properties and models 338
12.7.2 Analysis of coupled cells and networks 340
13 GEOMETRIC ANALYSIS OF BURSTING
NETWORKS 347
Janet Best and David Terman
13.1 Introduction 348
13.2 Existence, Uniqueness and Stability of Square Wave
Bursters 349
13.2.1 Assumptions on the geometric model 350
13.2.2 The main result 352
13.2.3 Bursting solution 352
13.2.4 When do trajectories jump down? 353
13.2.5 Return map and outline of the proof 355
13.3 Propagating Activity Patterns 358
13.3.1 The model 358
13.3.2 Numerical results 361
13.3.3 Singular construction of smooth waves 362
13.3.4 Estimating the wave speed 364
13.4 Transitions between Irregular and Clustered Activity . . . 367
13.4.1 The model 367
13.4.2 Two distinct activity patterns 369
13.4.3 Geometric analysis of irregular activity 370
13.4.4 Geometric analysis of clustered activity 375
13.4.5 Transitions and dependence on parameters 379
xvi Contents
14 ELLIPTIC BURSTERS, DEPOLARIZATION
BLOCK, AND WAVES 385
Bard Ermentrout, Joyeeta Dutta Moscato and David Pinto
14.1 Introduction 385
14.2 Methods 387
14.3 Results 388
14.3.1 The burster 388
14.3.2 Breaking up is easy to do 390
14.3.3 A normal form 392
14.3.4 Elliptic dentistry 393
14.4 Discussion 394
INDEX 397
|
| adam_txt |
CONTENTS
Preface v
PART I: BURSTING AT THE SINGLE CELL LEVEL
1 THE DEVELOPMENT OF THE HINDMARSH
ROSE MODEL FOR BURSTING 3
Jim Hindmarsh and Philip Cornelius
1.1 Introduction 3
1.2 Tail Current Reversal 4
1.3 The 1982 Model 5
1.4 The 1984 Model 8
1.5 Subthreshold Oscillations 10
1.6 A Bifurcation Theorem 15
2 NEGATIVE CALCIUM FEEDBACK: THE ROAD
FROM CHAY KEIZER 19
Richard Bertram and Arthur Sherman
2.1 Introduction 19
2.2 Before the Beginning 20
2.3 The Beginning 24
2.4 The Demise of K(Ca) 32
2.5 The Return of K(Ca): Help from the Endoplasmic
Reticulum 34
2.6 Further Modifications to the Model 41
2.7 Discussion 43
ix
x Contents
3 AUTOREGULATION OF BURSTING OF AVP
NEURONS OF THE RAT HYPOTHALAMUS 49
Peter Roper, Colin H. Brown, Charles W. Bourque and
William E. Armstrong
3.1 Introduction 49
3.2 Electrical Properties of AVP Cells 52
3.3 Mathematical Model 55
3.4 Firing Patterns 58
3.5 Burst Structure 58
3.6 The Role of Calcium 62
3.7 The Action of Dynorphin 62
3.8 The Bursting Mechanism 66
3.9 The Dynamics of Dynorphin 71
3.10 Analysis of Bursting 73
3.10.1 FAST 73
3.10.2 SLOW 73
3.11 Discussion 81
3.11.1 A dual role for calcium 81
3.11.2 Alternative mechanisms for the plateau potential . . 81
3.11.3 Excitable bursting 82
4 BIFURCATIONS IN THE FAST DYNAMICS OF
NEURONS: IMPLICATIONS FOR BURSTING 89
John Guckenheimer, Joseph H. Tien and Allan R. Willms
4.1 Introduction 90
4.2 A Two Dimensional Model of Spiking Sodium Currents . . 91
4.3 Fast Slow Analysis of Bursting 104
4.3.1 Aplysia 106
4.3.2 Thalamic relay neurons 108
4.3.3 Leech heart interneurons 110
4.3.4 Plateau oscillations in leech heart interneurons . 112
4.3.5 Neurons of the pre B6tzinger complex 113
4.4 Discussion 115
Contents xi
5 BURSTING IN 2 COMPARTMENT NEURONS:
A CASE STUDY OF THE PINSKY RINZEL
MODEL 123
Amitabha Bose and Victoria Booth
5.1 Introduction 123
5.2 The Pinsky Rinzel Model 125
5.2.1 Equations and qualitative description of the complex
burst 125
5.3 Dynamics of the Pinsky Rinzel Model 129
5.3.1 Burst initiation 129
5.3.2 Somatic dendritic ping pong 133
5.4 Morris Lecar Two Compartment Models 137
5.5 Discussion 140
6 GHOSTBURSTING: THE ROLE OF ACTIVE
DENDRITES IN ELECTROSENSORY
PROCESSING 145
Carlo R. Laing and Brent Doiron
6.1 Introduction 145
6.2 Bursting Mechanism 146
6.3 Ghostburster Dynamics 151
6.4 Unique Features 154
6.5 Extensions and Other Work 157
6.5.1 Reduced models 158
6.5.2 Periodic forcing 159
6.5.3 Burst excitability 160
6.5.4 Differential modulation of burst discharge 161
6.6 Parallel Processing with Bursts and Isolated Spikes . 163
6.6.1 Ghostbusting the ghostburster 163
6.6.2 Spike train processing 166
6.7 Summary 169
xii Contents
PART II: BURSTING AT THE NETWORK LEVEL
7 ANALYSIS OF CIRCUITS CONTAINING
BURSTING NEURONS USING PHASE
RESETTING CURVES 175
Carmen Canavier
7.1 Introduction 175
7.2 Stability Analysis for Two Coupled Oscillators 178
7.3 Analysis of a Circuit of Two Model Neurons 181
7.4 Stability Analysis for a Three Neuron Ring Circuit 183
7.5 Analysis of a Circuit of Three Model Neurons 186
7.6 Analysis of a Two Neuron Hybrid Circuit 189
7.7 Effect of Changing Burst Durations in the Two Neuron
Circuit 191
7.8 Phenomenology of Resetting in a Biological Bursting
Neuron 193
7.9 Significance 195
8 BURSTING IN COUPLED CELL SYSTEMS 201
Martin Golubitsky, Kresimir Josic and LieJune Shiau
8.1 Introduction 201
8.2 Unfolding Theory and Bursting in Fast Slow Systems . . . 203
8.3 Bursting in Two Coupled Cells 205
8.4 Z2 Equivariant Bifurcations 207
8.5 Pitchfork Bifurcation 209
8.6 Hopf/Hopf Mode Interactions 211
8.7 Takens Bogdanov Bifurcation with Z2 Symmetry 213
8.8 Conclusion 219
9 MODULATORY EFFECTS OF COUPLING ON
BURSTING MAPS 223
Gerda de Vries
9.1 Introduction 223
9.2 Examples of Bursting Maps 225
Contents xiii
9.2.1 One dimensional maps 225
9.2.2 Two dimensional maps 226
9.3 Effects of Coupling 230
9.3.1 Effects of coupling on one dimensional maps 230
9.3.2 Effects of coupling on two dimensional maps . 232
9.4 Rulkov's First Bursting Map: Explaining the Effect of
Coupling 234
9.5 Discussion 238
10 BEYOND SYNCHRONIZATION: MODULATORY
AND EMERGENT EFFECTS OF COUPLING IN
SQUARE WAVE BURSTING 243
Gerda de Vries and Arthur Sherman
10.1 Introduction 243
10.2 The Model 245
10.3 Effect of Coupling: Identical Cells 247
10.3.1 Effects of coupling on spike patterns 249
10.3.2 Effects of coupling on burst period 251
10.4 Normal Form Reduction 254
10.4.1 Identical cells: A = 1 255
10.4.1.1 Stability of the in phase and anti phase
steady states 256
10.4.2 Non identical cells: A ^ 1 257
10.5 Enhancement of the Period Extension with Heterogeneity . 258
10.6 Emergent Bursting 261
10.7 Synaptic Coupling 265
10.8 Discussion 267
10.8.1 Limitations and extensions 267
10.8.2 Comparison to other emergent oscillations 269
11 BURSTING IN EXCITATORY NEURAL
NETWORKS 273
Joel Tabak and John Rinzel
11.1 Introduction 274
11.2 Spontaneous Activity in the Developing Spinal Cord . 274
xiv Contents
11.3 Model of the Spontaneous Activity in the Embryonic Chick
Spinal Cord 277
11.4 Properties and Applications of the Model 280
11.4.1 Bistability of the excitatory network with fixed
synaptic efficacy 280
11.4.2 Episodic and rhythmic behavior due to activity
dependent depression of network excitability . 283
11.4.3 Relationship between episode duration and inter
episode interval 287
11.4.4 Recovery of the activity after blockade of excitatory
connections 289
11.5 Analogy between Network and Cellular Bursting 292
11.6 Discussion 294
11.6.1 Bursting activity in neural networks 295
11.6.2 Network vs cellular bursting 296
12 OSCILLATORY BURSTING MECHANISMS IN
RESPIRATORY PACEMAKER NEURONS AND
NETWORKS 303
Robert Butera, Jonathan Rubin, David Terman and
Jeffrey Smith
12.1 Introduction 304
12.2 Single Cell Dynamics: Evidence, Motivation, and Models . 306
12.3 Coupling Effects in Two Cells: A Pathway to Larger
Populations 312
12.4 The Big Bang: Populations of Excitatory Pacemakers . . . 314
12.4.1 Synchronized bursting in a heterogeneous population 314
12.4.2 Dynamic range of network oscillations 316
12.4.3 Emergent rhythms: Pacemakers vs. group
pacemakers 317
12.5 Dynamic Range of Bursting Activity 318
12.5.1 Fast/slow analysis of a single cell 318
12.5.2 The transition from bursting to spiking in coupled
cells with hi = h2 323
Contents xv
12.5.3 The transition from bursting to tonic spiking in the
full model for two coupled cells 327
12.6 Effects of Heterogeneity 329
12.6.1 Motivation and introduction to modeling approach . 329
12.6.2 The role of fast threshold modulation 330
12.6.3 Analysis of a synchronized bursting in a
heterogeneous population 333
12.7 Contemporary Issues and Unresolved Problems 338
12.7.1 Single neuron properties and models 338
12.7.2 Analysis of coupled cells and networks 340
13 GEOMETRIC ANALYSIS OF BURSTING
NETWORKS 347
Janet Best and David Terman
13.1 Introduction 348
13.2 Existence, Uniqueness and Stability of Square Wave
Bursters 349
13.2.1 Assumptions on the geometric model 350
13.2.2 The main result 352
13.2.3 Bursting solution 352
13.2.4 When do trajectories jump down? 353
13.2.5 Return map and outline of the proof 355
13.3 Propagating Activity Patterns 358
13.3.1 The model 358
13.3.2 Numerical results 361
13.3.3 Singular construction of smooth waves 362
13.3.4 Estimating the wave speed 364
13.4 Transitions between Irregular and Clustered Activity . . . 367
13.4.1 The model 367
13.4.2 Two distinct activity patterns 369
13.4.3 Geometric analysis of irregular activity 370
13.4.4 Geometric analysis of clustered activity 375
13.4.5 Transitions and dependence on parameters 379
xvi Contents
14 ELLIPTIC BURSTERS, DEPOLARIZATION
BLOCK, AND WAVES 385
Bard Ermentrout, Joyeeta Dutta Moscato and David Pinto
14.1 Introduction 385
14.2 Methods 387
14.3 Results 388
14.3.1 The burster 388
14.3.2 Breaking up is easy to do 390
14.3.3 A normal form 392
14.3.4 Elliptic dentistry 393
14.4 Discussion 394
INDEX 397 |
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| discipline_str_mv | Physik Biologie Medizin |
| format | Book |
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| id | DE-604.BV021280774 |
| illustrated | Illustrated |
| index_date | 2024-07-02T13:47:05Z |
| indexdate | 2024-07-09T20:34:36Z |
| institution | BVB |
| isbn | 9789812565068 981256506X |
| language | English |
| lccn | 2005051845 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014601782 |
| oclc_num | 61130877 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM |
| owner_facet | DE-91G DE-BY-TUM |
| physical | XVI, 401 S. graph. Darst. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | World Scientific Publishing |
| record_format | marc |
| spelling | Bursting the genesis of rhythm in the nervous system edited by Stephen Coombes ... New Jersey World Scientific Publishing 2005 XVI, 401 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Neural transmission Sensory neurons Aktionspotenzial (DE-588)4141745-8 gnd rswk-swf Biorhythmus (DE-588)4006896-1 gnd rswk-swf Aktionspotenzial (DE-588)4141745-8 s Biorhythmus (DE-588)4006896-1 s DE-604 Coombes, Stephen Sonstige oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014601782&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bursting the genesis of rhythm in the nervous system Neural transmission Sensory neurons Aktionspotenzial (DE-588)4141745-8 gnd Biorhythmus (DE-588)4006896-1 gnd |
| subject_GND | (DE-588)4141745-8 (DE-588)4006896-1 |
| title | Bursting the genesis of rhythm in the nervous system |
| title_auth | Bursting the genesis of rhythm in the nervous system |
| title_exact_search | Bursting the genesis of rhythm in the nervous system |
| title_exact_search_txtP | Bursting the genesis of rhythm in the nervous system |
| title_full | Bursting the genesis of rhythm in the nervous system edited by Stephen Coombes ... |
| title_fullStr | Bursting the genesis of rhythm in the nervous system edited by Stephen Coombes ... |
| title_full_unstemmed | Bursting the genesis of rhythm in the nervous system edited by Stephen Coombes ... |
| title_short | Bursting |
| title_sort | bursting the genesis of rhythm in the nervous system |
| title_sub | the genesis of rhythm in the nervous system |
| topic | Neural transmission Sensory neurons Aktionspotenzial (DE-588)4141745-8 gnd Biorhythmus (DE-588)4006896-1 gnd |
| topic_facet | Neural transmission Sensory neurons Aktionspotenzial Biorhythmus |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014601782&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT coombesstephen burstingthegenesisofrhythminthenervoussystem |