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

$40.00 USD

  • Date Published: March 2019
  • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • format: Adobe eBook Reader
  • isbn: 9781108683265

$ 40.00 USD
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About the Authors
  • 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.

    • The seamless integration of empirical and mathematical tools, and their introduction in a familiar biological context, enables students to appreciate the significance and utility of these tools
    • Includes numerous illustrations focused on graphical aspects of modelling and encourages a hands-on, problem solving approach through both pencil and paper analysis and user-friendly computational assignments
    • Provides mathematics instruction at a basic level appropriate for undergraduate life science majors with one year of calculus, but with an accompanying depth of knowledge and relevance to biology
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    Reviews & endorsements

    '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

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    Product details

    • Date Published: March 2019
    • format: Adobe eBook Reader
    • isbn: 9781108683265
    • contains: 21 b/w illus. 248 colour illus. 6 tables
    • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • Table of Contents

    1. Introduction
    Part I. Models and Odes:
    2. Compartmental modeling
    3. Phase diagrams
    4. Ligands, receptors and rate laws
    5. Function families and characteristic times
    6. Bifurcation diagrams of scalar ODEs
    Part II. Passive Membranes:
    7. The Nernst equilibrium potential
    8. The current balance equation
    9. GHK theory of membrane permeation
    Part III. Voltage-Gated Currents:
    10. Voltage-gated ionic currents
    11. Regenerative ionic currents and bistability
    12. Voltage-clamp recording
    13. Hodgkin-Huxley model of the action potential
    Part IV. Excitability and Phase Planes:
    14. The Morris-Lecar model
    15. Phase plane analysis
    16. Linear stability analysis
    Part V. Oscillations and Bursting:
    17. Type II excitability and oscillations
    18. Type I excitability and oscillations
    19. The low-threshold calcium spike
    20. Synaptic currents.

  • Author

    Greg Conradi Smith, College of William and Mary, Virginia
    Greg Conradi Smith is a Professor in the Department of Applied Science and Neuroscience Program Faculty Affiliate at the College of William and Mary, Virginia. He was organizer of the Cold Spring Harbor Laboratory Summer School on Computational Cell Biology (2008–14). His research focuses on mathematical aspects of cell physiology and neuroscience.

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