Tutorials in Mathematical Biosciences II:

This book presents a series of models in the general area of cell physiology and signal transduction, with particular attention being paid to intracellular calcium dynamics, and the role played by calcium in a variety of cell types. Calcium plays a crucial role in cell physiology, and the study of its dynamics lends insight into many different cellular processes. In particular, calcium plays a central role in muscular contraction, olfactory transduction and synaptic communication, three of the topics to be addressed in detail in this book. In addition to the models, much of the underlying physiology is presented, so that readers may learn both the mathematics and the physiology, and see how the models are applied to specific biological questions. It is intended primarily as a graduate text or a research reference. It will serve as a concise and up-to-date introduction to all those who wish to learn about the state of calcium dynamics modeling, and how such models are applied to physiological questions.

James Sneyd already published one book with Springer which won a prize for best math book in 1998 (American Association of Publishers). Achi Dosanjh will have copies of any reviews of this book, which have been favourable in general: Mathematical PhysiologySeries: Interdisciplinary Applied Mathematics, Vol. 8 Keener, James, Sneyd, James 1st ed. 1998. Corr. 2nd printing, 2001, XIX, 766 p. 347 illus., HardcoverISBN: 0-387-98381-3He is also an author of: S. Camazine, J.-L. Deneubourg, N. Franks, J. Sneyd, Guy Theraulaz, Eric Bonabeau, Self-Organization in Biological Systems, Princeton University Press, 2001. Winner of Best Professional/Scholarly Book in Biological Science (2001), American Association of Publishers. One of Choice's Outstanding Academic Titles for 2002.

Basic Concepts of Ca²+ Signaling in Cells and Tissues

M.J. Sanderson

1

(14)

1 Introduction

1

(1)

2 Ca²+ Stores and Pumps

1

(2)

3 Ca²+ Release Channels

3

(1)

4 Signaling by Ca²+ Transients

4

(1)

5 Cell Signaling by Ca²+ Oscillations

5

(3)

5.1 FM Regulation of Cell Activity

6

(2)

6 Spatial Aspects of Ca²+ Signaling

8

(4)

6.1 Elemental Ca²+ Signals

8

(1)

6.2 Microdomains of Ca²+ Signaling

8

(1)

6.3 Intracellular Ca²+ Waves

9

(1)

6.4 Intercellular Ca²+ Waves

10

(2)

6.5 Extracellular Ca²+ Waves

12

(1)

7 Summary

12

(1)

References

12

(3)

Modeling IP3-Dependent Calcium Dynamics in Non-Excitable Cells

J. Sneyd

15

(48)

1 Introduction

15

(3)

2 Calcium Oscillations and Waves

18

(4)

3 Well-Mixed Cell Models: Calcium Oscillations

22

(18)

3.1 Influx

23

(1)

3.2 Mitochondria

24

(1)

3.3 Calcium Buffers

24

(1)

3.4 Calcium Pumps and Exchangers

24

(4)

3.4.1 Calcium ATPases

24

(4)

3.4.2 Calcium Exchangers

28

(1)

3.5 IP3 Receptors

28

(7)

3.5.1 An 8-State IP3 Receptor Model

29

(1)

3.5.2 A Model with Saturating Binding Rates

30

(5)

3.6 Putting the Pieces Together: a Model of Calcium Oscillations

35

(2)

3.7 IP3 Dynamics

37

(3)

4 Calcium Waves

40

(6)

4.1 Simulation of Spiral Waves in Xenopus

42

(1)

4.2 Traveling Wave Equations and Bifurcation Analysis

42

(4)

5 Calcium Buffering

46

(3)

5.1 Fast Buffers or Excess Buffers

46

(3)

6 Calcium Puffs and Stochastic Modeling

49

(4)

6.1 Stochastic IPR Models

49

(3)

6.2 Stochastic Models of Calcium Waves

52

(1)

7 Intercellular Calcium Waves

53

(1)

References

54

(9)

Integrated Calcium Management in Cardiac Myocytes

T.R. Shannon

63

(1)

1 Introduction

63

(1)

2 Geometry of the Cardiac Myocyte

63

(3)

3 Overview of Excitation-Contraction Coupling

66

(1)

4 Action Potentials

67

(30)

4.1 The Resting Potential

68

(3)

4.2 Construction of the AP Waveform

71

(2)

5 Ca Channels

73

(3)

6 The SR Ca Release Channel

76

(3)

7 Ca-Induced Ca Release

79

(2)

8 Na-Ca Exchange

81

(4)

9 SL Ca Pump

85

(1)

10 SR Ca Pump

85

(3)

11 The Balance of Fluxes

88

(1)

12 Myocyte Contraction

89

(3)

References

92

(5)

Mechanisms and Models of Cardiac Excitation-Contraction Coupling

R.L. Winslow, R. Hinch, J.L. Greenstein

97

(36)

1 Introduction

97

(1)

2 The Molecular and Structural Basis of Cardiac EC Coupling

98

(6)

2.1 Structural Basis of EC Coupling

98

(1)

2.2 The Molecular Basis of Cardiac EC Coupling

99

(5)

2.2.1 Properties of LCCs

99

(1)

2.2.2 Properties of RyRs

100

(2)

2.2.3 Calcium-Induced Calcium-Release

102

(1)

2.2.4 Ca²+ Re-Uptake and Extrusion

103

(1)

3 Computational Models of Cardiac EC Coupling

104

(17)

3.1 Common Pool Models of CICR

104

(3)

3.1.1 Strengths of Common Pool Models

105

(1)

3.1.2 Weaknesses of Common Pool Models

105

(2)

3.2 A Stochastic Local-Control Model of CICR

107

(5)

3.3 Coupled LCC-RyR Gating Models of CICR

112

(9)

3.3.1 A "Minimal" Coupled LCC-RyR Gating Model

112

(6)

3.3.2 Generalized Coupled LCC-RyR Gating Models

118

(3)

4 Modeling Applications

121

(4)

4.1 AP Duration Regulation in Heart Failure

121

(2)

4.2 A General Mechanism for Regulation of AP Duration

123

(2)

5 Discussion

125

(2)

5.1 Regulation of Cardiac EC Coupling by Signaling Pathways

125

(1)

5.2 Dyadic Ca²+ Dynamics

126

(1)

5.3 Localized Signaling within Molecular Complexes

126

(1)

References

127

(6)

Mathematical Analysis of the Generation of Force and Motion in Contracting Muscle

E. Pate

133

(22)

1 Introduction

133

(2)

2 A.F. Huxley's Cross-Bridge Model

135

(3)

3 Isometric Contraction

138

(3)

4 Isotonic Contraction

141

(5)

5 Transient Simulations

146

(2)

6 Analysis of Systems of Small Numbers of Cross-Bridges

148

(4)

References

152

(3)

Signal Transduction in Vertebrate Olfactory Receptor Cells

J. Reisert

155

(18)

1 The Odour-Induced Response in Olfactory Receptor Cells

155

(3)

2 Olfactory Signal Transduction

158

(6)

2.1 The Olfactory G Protein-Coupled Cascade

158

(1)

2.2 The Olfactory Cyclic Nucleotide-Gated Channel: A Source of Ca²+

159

(1)

2.3 The Olfactory Ca²+-activated Cl- Channel: A Large Secondary Current

160

(2)

2.4 Adaptation and Modulation of the Odour Response

162

(2)

3 Mathematical Approaches in Olfaction

164

(1)

References

165

(8)

Mathematical Models of Synaptic Transmission and Short-Term Plasticity

R. Bertram

173

(1)

1 Introduction

173

(1)

2 Neurotransmitter Release is Evoked by Ca²+ Influx

174

(1)

3 Primed Vesicles are Located Close to Ca²+ Channels

175

(1)

4 Reaction-Diffusion Equations

175

(1)

5 The Simon and Llinás Model

176

(1)

6 Steady-State Approximations for Ca²+ Microdomains

177

(3)

7 Modeling the Postsynaptic Response

180

(2)

8 A Simple Model

182

(2)

9 Short-Term Plasticity

184

(1)

10 Mathematical Models for Facilitation

185

(1)

11 Residual Free Ca²+ Models

186

(4)

12 A Residual Bound Ca²+ Model for Facilitation

190

(2)

13 A Model for Facilitation Based on Buffer Saturation

192

(1)

14 Synaptic Depression

193

(2)

15 G Protein Inhibition of Presynaptic Ca²+ Channels

195

(2)

16 Conclusion

197

(1)

References

198

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Tutorials in Mathematical Biosciences II: Mathematical Modeling of Calcium Dynamics and Signal Transduction

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