Bursting

The Genesis Of Rhythm In The Nervous System

By: Paul Bressloff (Editor), Steve Coombes (Editor)

Write A Review

Hardcover | 4 October 2005

At a Glance

Hardcover
420 Pages

Dimensions(cm)
22.86 x 15.24 x 2.54

Hardcover

RRP $306.99

$276.75

10%OFF

or 4 interest-free payments of $69.19 with

Ships in 15 to 25 business days

Neurons in the brain communicate with each other by transmitting sequences of electrical spikes or action potentials. One of the major challenges in neuroscience is to understand the basic physiological mechanisms underlying the complex spatiotemporal patterns of spiking activity observed during normal brain functioning, and to determine the origins of pathological dynamical states such as epileptic seizures and Parkinsonian tremors. A second major challenge is to understand how the patterns of spiking activity provide a substrate for the encoding and transmission of information, that is, how do neurons compute with spikes? It is likely that an important element of both the dynamical and computational properties of neurons is that they can exhibit bursting, which is a relatively slow rhythmic alternation between an active phase of rapid spiking and a quiescent phase without spiking. This book provides a detailed overview of the current state-of-the-art in the mathematical and computational modeling of bursting, with contributions from many of the leading researchers in the field.

Industry Reviews

"All of the chapters are clearly written and for the most part would be accessible to readers who have taken at least an undergraduate course that covers modeling of neuronal dynamics ... The excitement generated by this collection of papers stems from the demonstration that appropriate interdisciplinary teams are indeed forming to tackle the outstanding issues."Mathematical Reviews

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

Orders over $0.00 qualify for free shipping.

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

You Can Find This Book In

Non-Fiction Science Biology, Life Sciences Life Sciences in General Neurosciences Medicine Clinical & Internal Medicine Neurology & Clinical Neurophysiology Pre-Clinical Medicine & Basic Sciences Physiology Cellular Physiology Mathematics

Applied Mathematics Booktopia Publisher Services World Scientific Publishing

Preface	p. v
Bursting at the Single Cell Level
The Development of the Hindmarsh-Rose Model for Bursting	p. 3
Introduction	p. 3
Tail Current Reversal	p. 4
The 1982 Model	p. 5
The 1984 Model	p. 8
Subthreshold Oscillations	p. 10
A Bifurcation Theorem	p. 15
Negative Calcium Feedback: The Road from Chay-Keizer	p. 19
Introduction	p. 19
Before the Beginning	p. 20
The Beginning	p. 24
The Demise of K(Ca)	p. 32
The Return of K(Ca): Help from the Endoplasmic Reticulum	p. 34
Further Modifications to the Model	p. 41
Discussion	p. 43
Autoregulation of Bursting of AVP Neurons of the Rat Hypothalamus	p. 49
Introduction	p. 49
Electrical Properties of AVP Cells	p. 52
Mathematical Model	p. 55
Firing Patterns	p. 58
Burst Structure	p. 58
The Role of Calcium	p. 62
The Action of Dynorphin	p. 62
The Bursting Mechanism	p. 66
The Dynamics of Dynorphin	p. 71
Analysis of Bursting	p. 73
Fast	p. 73
Slow	p. 73
Discussion	p. 81
A dual role for calcium	p. 81
Alternative mechanisms for the plateau potential	p. 81
Excitable bursting	p. 82
Bifurcations in the Fast Dynamics of Neurons: Implications for Bursting	p. 89
Introduction	p. 90
A Two Dimensional Model of Spiking Sodium Currents	p. 91
Fast-Slow Analysis of Bursting	p. 104
Aplysia	p. 106
Thalamic relay neurons	p. 108
Leech heart interneurons	p. 110
Plateau oscillations in leech heart interneurons	p. 112
Neurons of the pre-B&:otzinger complex	p. 113
Discussion	p. 115
Bursting in 2-Compartment Neurons: A Case Study of the Pinsky-Rinzel Model	p. 123
Introduction	p. 123
The Pinsky-Rinzel Model	p. 125
Equations and qualitative description of the complex burst	p. 125
Dynamics of the Pinsky-Rinzel Model	p. 129
Burst initiation	p. 129
Somatic-dendritic ping-pong	p. 133
Morris-Lecar Two-Compartment Models	p. 137
Discussion	p. 140
Ghostbursting: The Role of Active Dendrites in Electrosensory Processing	p. 145
Introduction	p. 145
Bursting Mechanism	p. 146
Ghostburster Dynamics	p. 151
Unique Features	p. 154
Extensions and Other Work	p. 157
Reduced models	p. 158
Periodic forcing	p. 159
Burst excitability	p. 160
Differential modulation of burst discharge	p. 161
Parallel Processing with Bursts and Isolated Spikes	p. 163
Ghostbursting the ghostburster	p. 163
Spike train processing	p. 166
Summary	p. 169
Bursting at the Network Level
Analysis of Circuits Containing Bursting Neurons Using Phase Resetting Curves	p. 175
Introduction	p. 175
Stability Analysis for Two Coupled Oscillators	p. 178
Analysis of a Circuit of Two Model Neurons	p. 181
Stability Analysis for a Three Neuron Ring Circuit	p. 183
Analysis of a Circuit of Three Model Neurons	p. 186
Analysis of a Two Neuron Hybrid Circuit	p. 189
Effect of Changing Burst Durations in the Two Neuron Circuit	p. 191
Phenomenology of Resetting in a Biological Bursting Neuron	p. 193
Significance	p. 195
Bursting in Coupled Cell Systems	p. 201
Introduction	p. 201
Unfolding Theory and Bursting in Fast-Slow Systems	p. 203
Bursting in Two Coupled Cells	p. 205
Z[subscript 2]-Equivariant Bifurcations	p. 207
Pitchfork Bifurcation	p. 209
Hopf/Hopf Mode Interactions	p. 211
Takens-Bogdanov Bifurcation with Z[subscript 2] Symmetry	p. 213
Conclusion	p. 219
Modulatory Effects of Coupling on Bursting Maps	p. 223
Introduction	p. 223
Examples of Bursting Maps	p. 225
One-dimensional maps	p. 225
Two-dimensional maps	p. 226
Effects of Coupling	p. 230
Effects of coupling on one-dimensional maps	p. 230
Effects of coupling on two-dimensional maps	p. 232
Rulkov's First Bursting Map: Explaining the Effect of Coupling	p. 234
Discussion	p. 238
Beyond Synchronization: Modulatory and Emergent Effects of Coupling in Square-Wave Bursting	p. 243
Introduction	p. 243
The Model	p. 245
Effect of Coupling: Identical Cells	p. 247
Effects of coupling on spike patterns	p. 249
Effects of coupling on burst period	p. 251
Normal Form Reduction	p. 254
Identical cells: [Delta] = 1	p. 255
Stability of the in-phase and anti-phase steady states	p. 256
Non-identical cells: [Delta not equal] 1	p. 257
Enhancement of the Period Extension with Heterogeneity	p. 258
Emergent Bursting	p. 261
Synaptic Coupling	p. 265
Discussion	p. 267
Limitations and extensions	p. 267
Comparison to other emergent oscillations	p. 269
Bursting in Excitatory Neural Networks	p. 273
Introduction	p. 274
Spontaneous Activity in the Developing Spinal Cord	p. 274
Model of the Spontaneous Activity in the Embryonic Chick Spinal Cord	p. 277
Properties and Applications of the Model	p. 280
Bistability of the excitatory network with fixed synaptic efficacy	p. 280
Episodic and rhythmic behavior due to activity-dependent depression of network excitability	p. 283
Relationship between episode duration and inter-episode interval	p. 287
Recovery of the activity after blockade of excitatory connections	p. 289
Analogy between Network and Cellular Bursting	p. 292
Discussion	p. 294
Bursting activity in neural networks	p. 295
Network vs cellular bursting	p. 296
Oscillatory Bursting Mechanisms in Respiratory Pacemaker Neurons and Networks	p. 303
Introduction	p. 304
Single Cell Dynamics: Evidence, Motivation, and Models	p. 306
Coupling Effects in Two Cells: A Pathway to Larger Populations	p. 312
The Big Bang: Populations of Excitatory Pacemakers	p. 314
Synchronized bursting in a heterogeneous population	p. 314
Dynamic range of network oscillations	p. 316
Emergent rhythms: Pacemakers vs. group pacemakers	p. 317
Dynamic Range of Bursting Activity	p. 318
Fast/slow analysis of a single cell	p. 318
The transition from bursting to spiking in coupled cells with h[subscript 1] = h[subscript 2]	p. 323
The transition from bursting to tonic spiking in the full model for two coupled cells	p. 327
Effects of Heterogeneity	p. 329
Motivation and introduction to modeling approach	p. 329
The role of fast threshold modulation	p. 330
Analysis of a synchronized bursting in a heterogeneous population	p. 333
Contemporary Issues and Unresolved Problems	p. 338
Single neuron properties and models	p. 338
Analysis of coupled cells and networks	p. 340
Geometric Analysis of Bursting Networks	p. 347
Introduction	p. 348
Existence, Uniqueness and Stability of Square-Wave Bursters	p. 349
Assumptions on the geometric model	p. 350
The main result	p. 352
Bursting solution	p. 352
When do trajectories jump down?	p. 353
Return map and outline of the proof	p. 355
Propagating Activity Patterns	p. 358
The model	p. 358
Numerical results	p. 361
Singular construction of smooth waves	p. 362
Estimating the wave speed	p. 364
Transitions between Irregular and Clustered Activity	p. 367
The model	p. 367
Two distinct activity patterns	p. 369
Geometric analysis of irregular activity	p. 370
Geometric analysis of clustered activity	p. 375
Transitions and dependence on parameters	p. 379
Elliptic Bursters, Depolarization Block, and Waves	p. 385
Introduction	p. 385
Methods	p. 387
Results	p. 388
The burster	p. 388
Breaking up is easy to do	p. 390
A normal form	p. 392
Elliptic dentistry	p. 393
Discussion	p. 394
Index	p. 397
Table of Contents provided by Ingram. All Rights Reserved.

Bursting

The Genesis Of Rhythm In The Nervous System

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

More in Cellular Physiology

Good Energy

The Surprising Connection Between Glucose, Metabolism and Limitless Health

BRS Physiology

8th Edition

Essentials of Stem Cell Biology

Recent Advances in Targeting Inflammation

Ion channels, GPCR Signaling Tools, Therapies, and Beyond

The Life Machines

How Taking Care of Your Mitochondria Can Transform Your Health

Extracellular Vesicles

From the Laboratory to the Clinic

Proteostasis and Cancer

Supramolecular Protein Assemblies In Cells

Advances in Experimental Medicine and Biology

Cellular and Molecular Mechanisms in Alzheimer's Disease Therapeutics

Vol. 2: Molecular Mechanisms

Cellular and Molecular Mechanisms in Alzheimer's Disease Therapeutics

2-volume set

Cellular and Molecular Mechanisms in Alzheimer"s Disease Therapeutics

Volume 1: Cellular Mechanisms

Cellular Signaling and Apoptosis Research

Molecular Diagnostics

Fundamentals of Biomedical Science

Cell Biology of Addiction

Monograph

Visualization of Receptors In Situ

Applications of Radioligand Binding

Glycans in Cell Interaction and Recognition

Apoptosis in Health and Disease

New Horizons in Therpeutics : Smithkline Beecham Pharmaceuticals U.S. reseaRch Symposia Series

Protein Formulation and Delivery

Drugs and the Pharmaceutical Sciences

Y Chromosome And Male Germ Cell Biology In Health And Diseases, The

Endothelial Biomedicine

Bursting

The Genesis Of Rhythm In The Nervous System

Photoreceptor Cell Biology And Inherited Retinal Degenerations

Recent Ad ances in Human Biology

IgE and Anti-IgE Therapy in Asthma and Allergic Disease

Lung Biology in Health and Disease

Drug Discovery

Drug Discovery Series

This product is categorised by