Abstract
One of the hallmarks of cellular processes is their complexity. For example, in Chapter 3 we described a detailed model for the SERCA pump that might require 11 ODEs and 22 kinetic constants for its analysis. Similarly, the Hodgkin-Huxley model, which includes only three currents in the squid giant axon, involves 4 differential equations and information about three voltage gated currents. As complex as these processes are, they do not begin to represent the true complexity of cellular processes like muscle contraction or insulin secretion, which depend on the coupling of numerous dynamic components. In Chapter 5 we describe some examples of “whole-cell” modeling that attempt to deal with these larger issues.
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Suggestions for Further Reading
Mathematical Models in Biology, Leah Edelstein-Keshet. This is a great introductory textbook on general mathematical biology. Chapter 7 contains material on reduction of scale and molecular events (Edelstein-Keshet 1988).
Principles of Applied Mathematics, James Keener. This book contains a good treatment of perturbation theory as well as other approximation techniques (Keener 1999).
Applied Mathematics, J. David Logan. This book also contains a good treatment of perturbation theory (Logan 1997).
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© 2002 Springer-Verlag New York, Inc.
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Keener, J.P., Keizer, J.E. (2002). Fast and Slow Time Scales. In: Fall, C.P., Marland, E.S., Wagner, J.M., Tyson, J.J. (eds) Computational Cell Biology. Interdisciplinary Applied Mathematics, vol 20. Springer, New York, NY. https://doi.org/10.1007/978-0-387-22459-6_4
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DOI: https://doi.org/10.1007/978-0-387-22459-6_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-95369-4
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