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Models of Calcium Signalling

Authors: Geneviève Dupont, Martin Falcke, Vivien Kirk, James Sneyd

Publisher: Springer International Publishing

Book Series : Interdisciplinary Applied Mathematics

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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About this book

This book discusses the ways in which mathematical, computational, and modelling methods can be used to help understand the dynamics of intracellular calcium. The concentration of free intracellular calcium is vital for controlling a wide range of cellular processes, and is thus of great physiological importance. However, because of the complex ways in which the calcium concentration varies, it is also of great mathematical interest.This book presents the general modelling theory as well as a large number of specific case examples, to show how mathematical modelling can interact with experimental approaches, in an interdisciplinary and multifaceted approach to the study of an important physiological control mechanism.

Geneviève Dupont is FNRS Research Director at the Unit of Theoretical Chronobiology of the Université Libre de Bruxelles; Martin Falcke is head of the Mathematical Cell Physiology group at the Max Delbrück Center for Molecular Medicine, Berlin; Vivien Kirk is an Associate Professor in the Department of Mathematics at the University of Auckland, New Zealand; James Sneyd is a Professor in the Department of Mathematics at The University of Auckland, New Zealand.

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Table of Contents

Frontmatter

Basic Theory

Frontmatter

Chapter 1. Some Background Physiology

Abstract

Calcium physiology is a vast field, far too large for us to do it justice in this book. Here, instead, we shall be concerned almost entirely with the physiology and dynamical behaviour of ionised intracellular calcium (Ca²⁺).

Geneviève Dupont, Martin Falcke, Vivien Kirk, James Sneyd

Chapter 2. The Calcium Toolbox

Abstract

The toolbox concept that was introduced in the previous chapter is a particularly useful way to approach Ca²⁺ modelling.

Geneviève Dupont, Martin Falcke, Vivien Kirk, James Sneyd

Chapter 3. Basic Modelling Principles: Deterministic Models

Abstract

The task of combining toolbox components into an overall model is neither simple nor easy.

Geneviève Dupont, Martin Falcke, Vivien Kirk, James Sneyd

Chapter 4. Hierarchical and Stochastic Modelling

Abstract

As we have already pointed out (Section 1.3), the basic building block of a Ca²⁺ response is a stochastic event at the level of an individual Ca²⁺ channel, whether an IP₃ receptor, a ryanodine receptor, or a voltage-gated Ca²⁺ channel. The behaviours that we call oscillations, or spiking, or waves, or microdomain transients, are merely emergent properties of the interaction of channel-level stochastic processes.

Geneviève Dupont, Martin Falcke, Vivien Kirk, James Sneyd

Chapter 5. Nonlinear Dynamics of Calcium

Abstract

The focus of the earlier chapters of this book has been on the construction of mathematical models based on information about the underlying physiology, and on comparison of model predictions with experimental data. A recurrent theme has been that a relatively small number of broad principles are applicable in the construction of a wide variety of different Ca²⁺ models in different physiological contexts. This chapter has a different focus, and instead looks at some mathematical methods that have proved useful for the analysis of Ca²⁺ models. However, there is an analogous theme, which is that a relatively small number of mathematical methods underlie much of current practice in model analysis.

Geneviève Dupont, Martin Falcke, Vivien Kirk, James Sneyd

Specific Models

Frontmatter

Chapter 6. Nonexcitable Cells

Abstract

In the remainder of this book we present a small number of examples, from a range of specific cell types, in more depth. Of course, it is not possible to give a complete overview of all the Ca²⁺ models that have been constructed, and so our choice here is based on a mixture of convenience and personal preference. However, the selected examples cover a broad range of modelling styles, in many qualitatively different types of cells, and should give a reasonably comprehensive picture of the types of models that have proved useful.

Geneviève Dupont, Martin Falcke, Vivien Kirk, James Sneyd

Chapter 7. Muscle

Abstract

In all three types of muscle cells – skeletal, cardiac, and smooth – Ca²⁺ plays a major role in excitation-contraction (EC) coupling, i.e., the sequence of events that links electrical stimulation to contraction (or, in nonexcitable smooth muscle, the events that link agonist stimulation to contraction). In skeletal and cardiac muscle, an action potential arriving from a neuron is propagated along the membrane of the muscle cell, and penetrates deep into the interior of the cell via invaginations of the cell membrane, called T-tubules. This action potential causes the release of Ca²⁺ from the sarcoplasmic reticulum, which then allows the crossbridge cycle to develop force (Huxley, 1957; Bers, 2001).

Geneviève Dupont, Martin Falcke, Vivien Kirk, James Sneyd

Chapter 8. Neurons and Other Excitable Cells

Abstract

Calcium plays a major role in every neuron. Not only does it play a part in controlling the membrane potential, but it is also a crucial ingredient of both the pre-synaptic and post-synaptic terminals. At the pre-synaptic terminal the secretion of neurotransmitter is controlled by Ca²⁺, as is short-term plasticity, while in the post-synaptic terminal Ca²⁺ is both necessary and sufficient for long-term synaptic plasticity, i.e., long-term depression, long-term potentiation, and spike-timing-dependent plasticity. In neuroendocrine cells from the hypothalamus and pituitary, as well as in the endocrine pancreas, Ca²⁺ controls the membrane potential, the shape of the bursts of electrical spiking, and the secretion of hormones. In photoreceptors and olfactory receptors, Ca²⁺ is at the centre of the biochemical networks that control adaptation to a maintained stimulus, while in interstitial cells of Cajal Ca²⁺ controls the membrane potential in ways that we do not yet fully understand. There are many other examples of the importance of Ca²⁺ in neurons and excitable cells.

Geneviève Dupont, Martin Falcke, Vivien Kirk, James Sneyd

Backmatter

Title: Models of Calcium Signalling
Authors: Geneviève Dupont
Martin Falcke
Vivien Kirk
James Sneyd
Copyright Year: 2016
Publisher: Springer International Publishing
Electronic ISBN: 978-3-319-29647-0
Print ISBN: 978-3-319-29645-6
DOI: https://doi.org/10.1007/978-3-319-29647-0

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