Note: Intro -- Preface -- Acknowledgements -- Contents -- Acronyms -- Part I Basic Theory -- 1 Some Background Physiology -- 1.1 Introduction -- 1.2 Common Features of Calcium Dynamics:The Calcium Toolbox -- 1.2.1 Agonists, Receptors, and Second Messengers -- 1.2.2 Internal Compartments -- 1.2.3 Internal Calcium Channels: IPR and RyR -- 1.2.4 IP3 Metabolism -- 1.2.5 Calcium Influx -- 1.2.6 Calcium Removal from the Cytoplasm -- 1.2.7 Calcium-Binding Proteins and Fluorescent Dyes -- 1.2.8 Microdomains and Nanodomains -- 1.3 Spatiotemporal and Hierarchical Organisation -- 1.4 Examples of Calcium Signalling -- 1.4.1 Cardiac Myocytes -- 1.4.2 Airway Smooth Muscle -- 1.4.3 Xenopus Oocytes -- 1.4.4 Pancreatic and Parotid Acinar Cells -- 1.4.5 Airway Epithelial Cells -- 2 The Calcium Toolbox -- 2.1 G Protein-Coupled Receptors -- 2.1.1 A Simple GPCR Model -- 2.1.2 More Complex Receptor Models -- 2.1.3 A Kinetic Model of GPCR Signalling -- 2.2 SERCA and PMCA -- 2.2.1 Unidirectional Models -- 2.2.2 Bidirectional Models -- 2.2.3 Coupling to ATP and pH -- 2.3 The Sodium/Calcium Exchanger -- 2.3.1 Unidirectional Enzyme Model -- 2.3.2 Bidirectional Markov Model -- 2.3.3 Modelling an Electrogenic Exchanger -- 2.3.4 Bidirectional Enzyme Model -- 2.3.5 A Model with Variable Stoichiometry -- 2.4 Mitochondria -- 2.4.1 The Mitochondrial Uniporter -- 2.4.2 The Mitochondrial Sodium/Calcium Exchanger -- 2.5 Voltage-Gated Calcium Channels -- 2.5.1 The Simplest Models -- 2.5.2 Permeation Models of Calcium Channels -- 2.5.3 Inactivation of Calcium Channels by Calcium -- 2.5.4 A Two-Mode Model of Calcium-InducedInactivation -- 2.6 Receptor-Operated and Store-Operated Channels -- 2.6.1 Receptor-Operated Channels -- 2.6.2 Store-Operated Channels -- 2.6.3 STIM-Orai Binding -- 2.7 Inositol Trisphosphate Receptors -- 2.7.1 An Eight-State Markov Model. , 2.7.2 Reduction of the Eight-State Markov Model -- 2.7.3 Gating Models -- 2.7.4 Modal Models -- 2.7.5 Simplifying the Modal Model -- 2.7.6 The Question of Local Calcium Concentration -- 2.7.7 Open Probability and Flux -- 2.8 Ryanodine Receptors -- 2.8.1 An Algebraic Model -- 2.8.2 A Markov Model of RyR Inactivation -- 2.8.3 Luminal Gating -- 2.8.4 Markov Models with Adaptation -- 2.8.5 Two-State Models -- 2.8.6 Modal Gating Model -- 2.9 Calcium Buffers -- 2.9.1 Fast Buffers or Excess Buffers -- 2.9.1.1 A Simplifying Transformation -- 2.10 Inositol Trisphosphate Metabolism -- 2.10.1 IP3 Production -- 2.10.2 IP3 Removal -- 3 Basic Modelling Principles: Deterministic Models -- 3.1 Types of Models -- 3.2 Spatially Homogeneous Models -- 3.2.1 A Model Based on IPR Dynamics -- 3.2.1.1 Steady States and Oscillations -- 3.2.2 A Model Based on ER Refilling -- 3.2.3 A Model That Incorporates MicrodomainsAround IPR -- 3.2.4 Calcium Excitability: Calcium-Induced CalciumRelease -- 3.2.5 Open-Cell and Closed-Cell Models -- 3.2.6 The Importance of Calcium Influx -- 3.2.7 IP3 Dynamics: Class I and Class II Models -- 3.2.7.1 Hybrid Models -- 3.2.7.2 Pulse Experiments -- 3.3 Spatially Distributed Models -- 3.3.1 A Brief Note on Terminology -- 3.3.2 Homogenisation -- 3.3.3 Membrane Fluxes -- 3.3.4 Closed-Cell Spatial Models -- 3.4 Microdomains -- 3.4.1 Calcium at the Mouth of an Open Channel -- 3.4.1.1 The Excess Buffer Approximation -- 3.4.1.2 The Rapid Buffer Approximation -- 3.4.2 Incorporating ER Depletion -- 3.4.3 The Channel as a Disk -- 3.4.4 Calcium Concentration Changes Quickly in Microdomains -- 3.4.5 Microdomains Between Organelles -- 3.4.6 Connecting a Microdomain to the Cell -- 3.4.7 Can Microdomains Be Modelled Deterministically? -- 3.5 Calcium Waves -- 3.5.1 The Fire-Diffuse-Fire Model -- 3.5.2 Continuous Release Sites. , 3.5.3 Waves in Multiple Dimensions -- 3.5.4 Phase Waves -- 3.6 Intercellular Waves -- 3.6.1 Mechanisms of Intercellular Wave Propagation -- 3.6.2 Propagation by Gap Junctions -- 3.6.2.1 An Example: Mechanically-Stimulated Waves in Airway Epithelial Cells -- 3.6.3 Regenerative and Partially Regenerative Waves -- 3.6.4 Paracrine Propagation -- 3.7 Connecting the Cytosol to the Membrane -- 3.8 The Effects of Buffers -- 3.8.1 Qualitative Effects -- 3.8.2 Quantitative Effects -- 4 Hierarchical and Stochastic Modelling -- 4.1 Introduction -- 4.1.1 Hierarchical Modelling Across Different Structural Levels -- 4.1.2 Distributions, Blips, and Puffs -- 4.2 Characteristics of Puffs -- 4.2.1 Interpuff Interval Distributions -- 4.2.2 The Coefficient of Variation -- 4.2.3 Puffs are not Periodic -- 4.3 Properties of Sequences of Cellular Spikes -- 4.3.1 Wave Nucleation -- 4.3.2 The Effects of Buffers on Wave Nucleation -- 4.3.3 Information Content and Signal Encoding -- 4.3.4 Summary -- 4.4 Appendix: An Incomplete Theory of Calcium Spiking -- 4.4.1 Semi-Markov Processes -- 4.4.2 Interpuff Interval Distributions, Puff Duration Distributions and Their Dependencies on Cellular Parameters -- 4.4.3 Detailed Derivation of the First Passage TimeDensity -- 4.4.3.1 Calculations Based on the Laplace Transform of Waiting Time Distributions -- 4.4.3.2 Resampling an IPI Distribution to Obtain an ISI Distribution -- 4.4.4 Some Formulae -- 4.4.5 Summary -- 5 Nonlinear Dynamics of Calcium -- 5.1 An Illustrative Model: The Hybrid Model -- 5.2 Bifurcation Analysis for ODE Models -- 5.3 Model Reduction -- 5.3.1 Identifying Time Scales -- 5.3.2 Reduction Based on Timescale Separation -- 5.4 Analysis Based on Timescale Separation -- 5.4.1 Freezing Slow Variables -- 5.4.2 Geometric Singular Perturbation Theory -- 5.5 Understanding Transient Dynamics. , 5.6 Coupled Voltage and Calcium Models -- 5.7 Calcium Waves -- 5.8 Calcium Excitability and the FitzHugh-Nagumo Equations -- Part II Specific Models -- 6 Nonexcitable Cells -- 6.1 Xenopus Oocytes -- 6.1.1 A Heuristic Model for Calcium Oscillationsand Waves -- 6.1.2 Mitochondria and Spiral Wave Stability -- 6.1.3 Bistability and the Fertilisation Calcium Wave -- 6.1.4 Increased IP3 Sensitivity During Egg Maturation -- 6.2 Hepatocytes -- 6.2.1 Effect of IP3 Metabolism on Calcium Oscillations -- 6.2.1.1 Simulation Results -- 6.2.1.2 Testing the Model Predictions -- 6.2.2 Deterministic Versus Stochastic Aspects of Calcium Oscillations -- 6.2.3 Phase Waves Coordinate Calcium Spiking Between Connected Hepatocytes -- 6.2.4 Amplitude-Coded Calcium Oscillations in Fish Hepatocytes -- 6.3 Pancreatic and Parotid Acinar Cells -- 6.3.1 Introduction -- 6.3.2 Calcium Oscillations and Waves in Acinar Cells -- 6.3.3 Calcium Waves and Water Secretion -- 6.3.4 Detailed Spatial Structure of an Acinus -- 6.4 Astrocytes -- 6.4.1 Introduction -- 6.4.2 Calcium Oscillations Induced by Stimulation of mGlu5 Receptors -- 6.4.3 Towards Modelling Calcium Oscillationsin Astrocytes -- 7 Muscle -- 7.1 Introduction -- 7.2 Cardiac Myocytes -- 7.2.1 Cardiac Excitation-Contraction Coupling -- 7.2.2 Common-Pool and Local-Control Models -- 7.2.3 Calcium Sparks -- 7.2.4 The Diadic Cleft Can Be Described by a Continuous and Deterministic Model -- 7.2.5 Integrative Models -- 7.2.6 Simplified Approaches -- 7.2.6.1 The Probability Density Approach -- 7.2.7 Atrial Myocytes -- 7.3 Skeletal Myocytes -- 7.4 Smooth Muscle -- 7.4.1 Airway Smooth Muscle -- 7.4.1.1 Stochastic or Deterministic? -- 7.4.1.2 The Cytosolic Oscillator -- 7.4.1.3 The Interplay Between IP3R and RyR -- 7.4.1.4 Periodic Waves in the Model -- 7.4.1.5 More Detailed Treatment of the Membrane Currents. , 7.4.2 Vascular Smooth Muscle -- 7.5 Calcium and the Generation of Force in Smooth Muscle -- 7.5.1 The Hai-Murphy Model -- 7.5.2 Calcium, Calmodulin, and MLCK -- 7.5.3 The Frequency Response of Airway Smooth Muscle -- 8 Neurons and Other Excitable Cells -- 8.1 Introduction -- 8.2 Pre-synaptic Calcium Dynamics -- 8.2.1 Facilitation -- 8.2.2 A Model of the Residual Bound Calcium Hypothesis -- 8.2.3 A More Complex Version -- 8.3 Post-Synaptic Plasticity -- 8.3.1 Calcium/Calmodulin-Dependent Protein Kinase II as a Bistable Switch -- 8.3.2 Phenomenological Models -- 8.3.3 CaMKII as a Frequency Decoder in the Absence of Dephosphorylation -- 8.4 Pancreatic Beta Cells -- 8.4.1 Bursting in the Pancreatic Beta Cell -- 8.4.1.1 Phase-Plane Analysis -- 8.4.2 ER Calcium as a Slow Controlling Variable -- 8.4.3 Other Models -- 8.5 Pancreatic Alpha Cells -- 8.5.1 Electrical Activity of Pancreatic Alpha Cells -- 8.5.2 Calcium Dynamics in Pancreatic Alpha Cells -- 8.6 Calcium-Mediated Secretion -- 8.6.1 Prototypic Model for Calcium-Mediated Secretion -- 8.6.2 Secretion of Insulin by Pancreatic Beta Cells -- 8.6.3 Secretion of Glucagon by Pancreatic Alpha Cells -- 8.7 Hypothalamic and Pituitary Cells -- 8.7.1 The Gonadotroph -- 8.7.1.1 The Membrane Model -- 8.7.1.2 The Calcium Model -- 8.7.1.3 Results -- 8.7.2 GnRH Neurons -- References -- Index.