Dynamic Phenomena in Cells

  • Christopher P. Fall
  • Joel E. Keizer
Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 20)


Over the past several decades, progress in the measurement of rates and interactions of molecular and cellular processes has initiated a revolution in our understanding of dynamic phenomena in cells. Spikes or bursts of plasma membrane electrical activity or intracellular signaling via receptors, second messengers, or other networked biochemical pathways in single cells, or more complex processes that involve small clusters of cells, organelles, or groups of neurons, are examples of the complex behaviors that we know take place on the cellular scale. The vast amount of quantitative information uncovered in recent years, leveraged by the intricate mechanisms already shown to exist, results in an array of possibilities that makes it quite hard to evaluate new hypotheses on an intuitive basis. Using mathematical analysis and computer simulation we can show that some seemingly reasonable hypotheses are not possible. Analysis and simulations that confirm that a given hypothesis is reasonable can often result in quantitative predictions for further experimental exploration. Rapid advances in computer hardware and software technology combined with pioneering work giving structure to the interface between mathematics and biology have put the ability to test hypotheses and evaluate mechanisms with simulations within the reach of all cell biologists and neuroscientists.


Phase Portrait Dynamic Phenomenon Spiral Wave Giant Axon Phase Plane Analysis 
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Suggestions for Further Reading

  1. Modeling Dynamic Phenomena in Molecular and Cellular Biology, Lee Segel. A great place to start for a more mathematical treatment of some of the contents of this book (Segel 1984).Google Scholar
  2. Mathematical Models in Biology, Leah Edelstein-Keshet. A classic introductory textbook for general mathematical biology, and a good source for a different perspective on topics such as time scales, phase plane analysis, and elementary numerical analysis as applied to biological problems (Edelstein-Keshet 1988).Google Scholar
  3. Understanding Nonlinear Dynamics, Daniel Kaplan and Leon Glass, and Nonlinear Dynamics and Chaos, Steven Strogatz. Extremely readable entry-level books on nonlinear dynamics, including sections on chaos, fractals, and data analysis (Kaplan and Glass 1995; Strogatz 1994).Google Scholar
  4. Mathematical Physiology, James Keener and James Sneyd. Keener and Sneyd treat many of the topics presented in this book from a more analytic perspective as opposed to the computational focus presented here (Keener and Sneyd 1998).Google Scholar
  5. Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations, U.M Acher and L.R. Petzold (Asher and Petzold 1998).Google Scholar
  6. Cellular Biophysics, Volumes 1 and 2, Thomas Weiss. These two volumes cover in more detail the biophysics of transport processes and electrical properties in cells (Weiss 1996).Google Scholar
  7. Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students, by Bard Ermentrout. A complete user’s manual for the public domain ODE package XPP (Ermentrout 2002).Google Scholar
  8. Mathematical Biology, James Murray. While not especially didactic, this volume is recognized as an essential handbook describing models throughout mathematical biology (Murray 1989).Google Scholar

Copyright information

© Springer-Verlag New York, Inc. 2002

Authors and Affiliations

  • Christopher P. Fall
  • Joel E. Keizer

There are no affiliations available

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