Electrical Dynamics of the Dendritic Space

by Sergiy Mikhailovich Korogod, Suzanne Tyc-Dumont

Overview

The authors explain how the whole dendritic arborization contributes to the generation of various output discharges and elucidate the mechanisms of the transfer function of all dendritic sites. Their alternative modelling approach to conventional models introduces the notion of a functional dendritic space, and they have concentrated on a detailed spatial description of the electrical states at all dendritic sites when the dendrites operate. By analyzing the electrical dendritic space in which all the signals are processed, the authors provide tools to explore the spatial dimension of the transient events well known by electrophysiologists. They demonstrate the mechanisms by which the operating dendrites decide how, in fine, the distributed synaptic inputs generate final various output discharges. Their approach reveals the mechanisms by which individual dendritic geometry determines the sequence of action potentials that is the neuronal code. An accompanying NeuronViewer allows readers to monitor the simulation of operating dendritic arborization.

Product Details

ISBN-13:	9780521896771
Publisher:	Cambridge University Press
Publication date:	12/17/2009
Pages:	224
Product dimensions:	7.00(w) x 9.80(h) x 0.70(d)

About the Author

Sergey Korogod is Professor and Head of Department of Experimental Physics at the Dniepropetrovsk National University, and Head of Dniepropetrovsk Division, International Center for Molecular Physiology at the National Academy of Science of the Ukraine.

Suzanne Tyč-Dumont is Director of Research Emeritus at CNRS, Paris. She has been active since the early 1980s in the promotion of the notion of the dendritic shape as one of the most critical factors in the understanding of dendritic processing, and introduced computational tools for the quantification of the geometry of dendritic arborizations in her laboratory.

Table of Contents

Preface ix

1 Definition of the neuron 1

1.1 The biologist 1

1.2 The physicist 8

1.3 The physicist and the biologist 9

References 10

2 3D geometry of dendritic arborizations 13

2.1 Brief historical background 13

2.2 Single neuron labelling 15

2.3 Dendritic quantification 17

2.4 Data quality and morphological noise 22

2.5 Models of neurons 25

References 31

3 Basics in bioelectricity 37

3.1 Ions as carriers of current 37

3.2 Selective ion permeability of neuronal membrane 38

3.3 Ion pumps 39

3.4 Ion channels 40

3.5 Voltage dependence of membrane conductance 41

3.6 Effective equilibrium potential of multicomponent ion current 41

3.7 Membrane capacitance and capacitive current 42

3.8 External sources 43

3.9 Local current-voltage (I-V) relations 43

Reference 46

4 Cable theory and dendrites 47

4.1 Dendrites as electrical cables 47

4.2 The cable equation 49

4.3 Additional conditions required for solution 53

4.4 Input-output (point-to-point) relations in dendritic cables 56

References 57

5 Voltage transfer over dendrites 59

5.1 Dendritic cables in the steady state 59

5.2 Voltage transients in dendritic cables 62

6 Current transfer over dendrites 65

6.1 Charge transfer ratio 65

6.2 Somatopetal current transfer and somatofugal voltage spread 66

6.3 Current transfer ratio for passive paths at different boundary conditions 71

6.4 Local electro-geometrical coupling in non-uniform paths 72

6.5 Current transfer from distributed dendritic sources 75

References 76

7 Electrical structure of an artificial dendritic path 77

7.1 Electrical structure of passive paths with single-site inputs 79

7.2 Electrical structure of paths with distributed tonic inputs 81

References 94

8 Electrical structure of a bifurcation 95

8.1 Theory for different configurations 95

8.2 Electrical structure of passive branching paths with single-site inputs 100

8.3 Electrical structure of a bifurcation receiving distributed tonic inputs 102

8.4 Recapitulation and conclusions 111

References 112

9 Geography of the dendritic space 113

9.1 Dendritic arborization in 3D and 2D representations 114

9.2 Distinct 3D dendritic landscapes 118

9.3 Digitized dendritic arborizations 121

References 125

10 Electrical structures of biological dendrites 127

10.1 Geometry of an example dendrite 127

10.2 Passive dendrite with single-site inputs 129

10.3 Dendrites with distributed inputs 130

10.4 Reconfigurations of passive electrical structures 136

References 139

11 Electrical structure of the whole arborization 141

11.1 Organization of the spatial electrical profiles 141

11.2 Robustness of the electrical bundles 150

11.3 Dynamic reconfigurations of the whole electrical structure 152

11.4 Spatial aspects of reconfigured electrical structure 156

11.5 Complexity of the whole arborization and its electrical domains 159

References 160

12 Electrical structures in 3D dendritic space 161

12.1 The 3D electrical structures of Purkinje neurons 162

12.2 The 3D electrical structure of pyramidal neurons 164

12.3 The 3D electrical structures of motoneurons 164

12.4 High-efficiency domain of the motoneuronal arborizations in 3D 166

12.5 Bistable dendritic field 168

References 171

13 Dendritic space as a coder of the temporal output patterns 173

13.1 Terminology to describe the repertoire of neuronal discharges 173

13.2 Geometry-induced features of Purkinje cell discharges 174

13.3 Geometry-dependent repertoire of pyramidal cell activity 189

13.4 Some general rules 193

References 194

14 Concluding remarks 197

14.1 Impact for interpretation of neuronal discharges 199

14.2 The dancing dendrites 200

14.3 Speculation for the future 200

References 202

Index 205

Editorial Reviews

'Dendritic trees come in all sorts of shapes and sizes. Their complexity and diversity lends a majesty and beauty to the task of understanding the brain. But are they more than just random protrusions? Could their very complexity and diversity be important for the computational properties of the brain? The authors are clear on this point, 'We strongly believe that the answer is yes indeed, as we attribute a specific role to every of these structural features in a harmonious working ensemble!' I am sure that readers of this book will also be convinced. The book progresses through careful treatment of the electrical properties of dendrites to how the geometry interacts with synaptic input to produce rich repertoires of firing output. It is an important book for experts and students of dendrites alike as well as an eye-opener for neuroscientists in every field.' Matthew Larkum, University of Bern

'Electrical Dynamics of the Dendritic Space is a compelling treatise on the electrical properties of neuronal dendrites, from a modeling perspective. The authors Serge Korogod and Suzanne Tyč-Dumont do a super job in writing comprehensively on a topic of profound relevance to present day neuroscience.' Rodolfo Llinas, New York University Medical School

'The complex geometry of neuronal dendrites is one of the greatest challenges facing neuroscientists today. Serge Korogod and Suzanne Tyc-Dumont characterize the dendrites as an immense unknown. They have been pioneers in exploring this frontier. In this book they have distilled lifetimes of work by themselves and colleagues in France and the Ukraine to formulate new rules for how the electrical states of dendritic arborizations represent space and time in generating the neural code. In clear language they show how the interactions between these passive and active properties and dendritic geometry create different scales of dynamical dendritic space. New insights are provided into the significance of the dendrites of motoneurons, cerebellar Purkinje cells, and cortical pyramidal neurons. Their models available online give dramatic evidence for these insights. This is a key book for all those interested in dendrites and in the neural basis of cognition and behavior.' Gordon M. Shepherd, Yale University School of Medicine

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