Cellular Biophysics and Modeling - A Primer on the Computational Biology of Excitable Cells

Description

What every neuroscientist should know about the mathematical modeling of excitable cells. Combining empirical physiology and nonlinear dynamics, this text provides an introduction to the simulation and modeling of dynamic phenomena in cell biology and neuroscience. It introduces mathematical modeling techniques alongside cellular electrophysiology. Topics include membrane transport and diffusion, the biophysics of excitable membranes, the gating of voltage and ligand-gated ion channels, intracellular calcium signalling, and electrical bursting in neurons and other excitable cell types. It introduces mathematical modeling techniques such as ordinary differential equations, phase plane, and bifurcation analysis of single-compartment neuron models. With analytical and computational problem sets, this book is suitable for life sciences majors, in biology to neuroscience, with one year of calculus, as well as graduate students looking for a primer on membrane excitability and calcium signalling. Reviews 'In this text, Conradi Smith does an excellent job of teaching students with no mathematical training beyond calculus how to use differential equations to understand the basic principles of cell physiology and excitability. He skilfully walks students through the steps of modeling and analysis, all the while working to develop intuition and insight into how things work. His emphasis on computational methods for solution as well as graphical and geometrical means for interpretation enables him to communicate complex ideas in understandable ways. Furthermore, his patience and attention to detail will be appreciated by those students who have not had extensive exposure to the art of mathematical modeling. This text is a wonderful addition to the mathematical biology textbook literature.' James P. Keener - University of Utah Cellular Biophysics and Modeling......Page 1 Contents......Page 5 Preface......Page 11 1 Introduction......Page 13 PART I Models and Ordinary Differential Equations......Page 25 2 Compartmental Modeling......Page 27 3 Phase Diagrams......Page 54 4 Ligands, Receptors and Rate Laws......Page 71 5 Function Families and Characteristic Times......Page 93 6 Bifurcation Diagrams of Scalar ODEs......Page 110 PART II Passive Membranes......Page 125 7 The Nernst Equilibrium Potential......Page 127 8 The Current Balance Equation......Page 144 9 GHK Theory of Membrane Permeation......Page 166 PART III Voltage-Gated Currents......Page 181 10 Voltage-Gated Ionic Currents......Page 183 11 Regenerative Ionic Currents and Bistability......Page 197 12 Voltage-Clamp Recording......Page 211 13 Hodgkin-Huxley Model of the Action Potential......Page 228 PART IV Excitability and Phase Planes......Page 245 14 The Morris-Lecar Model......Page 247 16 Linear Stability Analysis......Page 264 15 Phase Plane Analysis......Page 284 PART V Oscillations and Bursting......Page 307 17 Type II Excitability and Oscillations (Hopf Bifurcation)......Page 309 18 Type I Excitability and Oscillations (SNIC and SHO Bifurcations)......Page 331 19 The Low-Threshold Calcium Spike......Page 350 20 Synaptic Currents......Page 365 References......Page 380 Afterword......Page 389 Index......Page 392