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E-raamat: Bursting: The Genesis of Rhythm in the Nervous System illustrated edition [World Scientific e-raamat]

Edited by (Univ Of Nottingham & Loughborogh Univ, Uk), Edited by (Univ Of Utah, Usa)
  • Formaat: 420 pages
  • Ilmumisaeg: 04-Oct-2005
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • ISBN-13: 9789812703231
  • World Scientific e-raamat
  • Hind: 203,28 €*
  • * hind, mis tagab piiramatu üheaegsete kasutajate arvuga ligipääsu piiramatuks ajaks
  • Formaat: 420 pages
  • Ilmumisaeg: 04-Oct-2005
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • ISBN-13: 9789812703231
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.
Preface v
PART I: BURSTING AT THE SINGLE CELL LEVEL
The Development of the Hindmarsh-Rose Model for Bursting
3(16)
Jim Hindmarsh
Philip Cornelius
Introduction
3(1)
Tail Current Reversal
4(1)
The 1982 Model
5(3)
The 1984 Model
8(2)
Subthreshold Oscillations
10(5)
A Bifurcation Theorem
15(4)
Negative Calcium Feedback: The Road from Chay-Keizer
19(30)
Richard Bertram
Arthur Sherman
Introduction
19(1)
Before the Beginning
20(4)
The Beginning
24(8)
The Demise of K(Ca)
32(2)
The Return of K(Ca): Help from the Endoplasmic Reticulum
34(7)
Further Modifications to the Model
41(2)
Discussion
43(6)
Autoregulation of Bursting of AVP Neurons of the Rat Hypothalamus
49(40)
Peter Roper
Colin H. Brown
Charles W. Bourque
William E. Armstrong
Introduction
49(3)
Electrical Properties of AVP Cells
52(3)
Mathematical Model
55(3)
Firing Patterns
58(1)
Burst Structure
58(4)
The Role of Calcium
62(1)
The Action of Dynorphin
62(4)
The Bursting Mechanism
66(5)
The Dynamics of Dynorphin
71(2)
Analysis of Bursting
73(8)
Fast
73(1)
Slow
73(8)
Discussion
81(8)
A dual role for calcium
81(1)
Alternative mechanisms for the plateau potential
81(1)
Excitable bursting
82(7)
Bifurcations in the Fast Dynamics of Neurons: Implications for Bursting
89(34)
John Guckenheimer
Joseph H. Tien
Allan R. Willms
Introduction
90(1)
A Two Dimensional Model of Spiking Sodium Currents
91(13)
Fast-Slow Analysis of Bursting
104(11)
Aplysia
106(2)
Thalamic relay neurons
108(2)
Leech heart interneurons
110(2)
Plateau oscillations in leech heart interneurons
112(1)
Neurons of the pre-Botzinger complex
113(2)
Discussion
115(8)
Bursting in 2-Compartment Neurons: A Case Study of the Pinsky-Rinzel Model
123(22)
Amitabha Bose
Victoria Booth
Introduction
123(2)
The Pinsky-Rinzel Model
125(4)
Equations and qualitative description of the complex burst
125(4)
Dynamics of the Pinsky-Rinzel Model
129(8)
Burst initiation
129(4)
Somatic-dendritic ping-pong
133(4)
Morris-Lecar Two-Compartment Models
137(3)
Discussion
140(5)
Ghostbursting: The Role of Active Dendrites in Electrosensory Processing
145(30)
Carlo R. Laing
Brent Doiron
Introduction
145(1)
Bursting Mechanism
146(5)
Ghostburster Dynamics
151(3)
Unique Features
154(3)
Extensions and Other Work
157(6)
Reduced models
158(1)
Periodic forcing
159(1)
Burst excitability
160(1)
Differential modulation of burst discharge
161(2)
Parallel Processing with Bursts and Isolated Spikes
163(6)
Ghostbusting the ghostburster
163(3)
Spike train processing
166(3)
Summary
169(6)
PART II: BURSTING AT THE NETWORK LEVEL
Analysis of Circuits Containing Bursting Neurons Using Phase Resetting Curves
175(26)
Carmen Canavier
Introduction
175(3)
Stability Analysis for Two Coupled Oscillators
178(3)
Analysis of a Circuit of Two Model Neurons
181(2)
Stability Analysis for a Three Neuron Ring Circuit
183(3)
Analysis of a Circuit of Three Model Neurons
186(3)
Analysis of a Two Neuron Hybrid Circuit
189(2)
Effect of Changing Burst Durations in the Two Neuron Circuit
191(2)
Phenomenology of Resetting in a Biological Bursting, Neuron
193(2)
Significance
195(6)
Bursting in Coupled Cell Systems
201(22)
Martin Golubitsky
Kresimir Josic
LieJune Shiau
Introduction
201(2)
Unfolding Theory and Bursting in Fast-Slow Systems
203(2)
Bursting in Two Coupled Cells
205(2)
Z2-Equivariant Bifurcations
207(2)
Pitchfork Bifurcation
209(2)
Hopf/Hopf Mode Interactions
211(2)
Takens-Bogdanov Bifurcation with Z2 Symmetry
213(6)
Conclusion
219(4)
Modulatory Effects of Coupling on Bursting Maps
223(20)
Gerda de Vries
Introduction
223(2)
Examples of Bursting Maps
225(5)
One-dimensional maps
225(1)
Two-dimensional maps
226(4)
Effects of Coupling
230(4)
Effects of coupling on one-dimensional maps
230(2)
Effects of coupling on two-dimensional maps
232(2)
Rulkov's First Bursting Map: Explaining the Effect of Coupling
234(4)
Discussion
238(5)
Beyond Synchronization: Modulatory and Emergent Effects of Coupling in Square-Wave Bursting
243(30)
Gerda de Vries
Arthur Sherman
Introduction
243(2)
The Model
245(2)
Effect of Coupling: Identical Cells
247(7)
Effects of coupling on spike patterns
249(2)
Effects of coupling on burst period
251(3)
Normal Form Reduction
254(4)
Identical cells: Δ = 1
255(1)
Stability of the in-phase and anti-phase steady states
256(1)
Non-identical cells: Δ ≠ 1
257(1)
Enhancement of the Period Extension with Heterogeneity
258(3)
Emergent Bursting
261(4)
Synaptic Coupling
265(2)
Discussion
267(6)
Limitations and extensions
267(2)
Comparison to other emergent oscillations
269(4)
Bursting in Excitatory Neural Networks
273(30)
Joel Tabak
John Rinzel
Introduction
274(1)
Spontaneous Activity in the Developing Spinal Cord
274(3)
Model of the Spontaneous Activity in the Embryonic Chick Spinal Cord
277(3)
Properties and Applications of the Model
280(12)
Bistability of the excitatory network with fixed synaptic efficacy
280(3)
Episodic and rhythmic behavior due to activity-dependent depression of network excitability
283(4)
Relationship between episode duration and inter-episode interval
287(2)
Recovery of the activity after blockade of excitatory connections
289(3)
Analogy between Network and Cellular Bursting
292(2)
Discussion
294(9)
Bursting activity in neural networks
295(1)
Network vs cellular bursting
296(7)
Oscillatory Bursting Mechanisms in Respiratory Pacemaker Neurons and Networks
303(44)
Robert Butera
Jonathan Rubin
David Terman
Jeffrey Smith
Introduction
304(2)
Single Cell Dynamics: Evidence, Motivation, and Models
306(6)
Coupling Effects in Two Cells: A Pathway to Larger Populations
312(2)
The Big Bang: Populations of Excitatory Pacemakers
314(4)
Synchronized bursting in a heterogeneous population
314(2)
Dynamic range of network oscillations
316(1)
Emergent rhythms: Pacemakers vs. group pacemakers
317(1)
Dynamic Range of Bursting Activity
318(11)
Fast/slow analysis of a single cell
318(5)
The transition from bursting to spiking in coupled cells with h1 = h2
323(4)
The transition from bursting to tonic spiking in the full model for two coupled cells
327(2)
Effects of Heterogeneity
329(9)
Motivation and introduction to modeling approach
329(1)
The role of fast threshold modulation
330(3)
Analysis of a synchronized bursting in a heterogeneous population
333(5)
Contemporary Issues and Unresolved Problems
338(9)
Single neuron properties and models
338(2)
Analysis of coupled cells and networks
340(7)
Geometric Analysis of Bursting Networks
347(38)
Janet Best
David Terman
Introduction
348(1)
Existence, Uniqueness and Stability of Square-Wave Bursters
349(9)
Assumptions on the geometric model
350(2)
The main result
352(1)
Bursting solution
352(1)
When do trajectories jump down?
353(2)
Return map and outline of the proof
355(3)
Propagating Activity Patterns
358(9)
The model
358(3)
Numerical results
361(1)
Singular construction of smooth waves
362(2)
Estimating the wave speed
364(3)
Transitions between Irregular and Clustered Activity
367(18)
The model
367(2)
Two distinct activity patterns
369(1)
Geometric analysis of irregular activity
370(5)
Geometric analysis of clustered activity
375(4)
Transitions and dependence on parameters
379(6)
Elliptic Bursters, Depolarization Block, and Waves
385(12)
Bard Ermentrout
Joyeeta Dutta-Moscalo
David Pinto
Introduction
385(2)
Methods
387(1)
Results
388(6)
The burster
388(2)
Breaking up is easy to do
390(2)
A normal form
392(1)
Elliptic dentistry
393(1)
Discussion
394(3)
Index 397