Physical Thoughts, Biological Systems: The Application of Modeling Principles to Understanding Biological Systems

  • Peter R. Bergethon


Imagine yourself standing outside a country home on an early spring morning just before dawn. Take a deep breath and shiver to the taste of the sweet morning air. Listen carefully to hear the chirping of morning birds. As the sun reaches the horizon, glinting shafts of light reach your eyes. Another deep breath and you feel a peace that comes from a resonance between you and the world at your doorstep. Your eyes close and for a fleeting moment you understand the universe in its simplest, most basic terms. Savor that moment, for your eyes open again and you are drawn back to reality—you are reading the introduction to a book on physical chemistry. If you are mildly perturbed at being returned to this apparently less appealing reality, you have just demonstrated a facility for a key and exquisitely valuable tool in the study of science, the gedanken experiment (thought experiment). The use of thought trips will be of fundamental importance in the approach this book takes toward understanding biophysical processes. That virtually any student has access to one of the most profound and sophisticated theoretical techniques available to a scientist is an important lesson to learn.


State Space Natural System Abstract State Chaotic Attractor Symmetry Operation 
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Further Reading

General Modeling

  1. Casti J. L. (1992a) Reality rules I: Picturing the World in Mathematics—The Fundamentals. Wiley Interscience, New York. This volume is a delightful introduction to the intellectual approach to modeling. This chapter has used Casti’s approach in a simplified fashion, and his book is the logical next step to expand your horizons.Google Scholar
  2. Casti J. L. (1992b) Reality rules II: Picturing the World in Mathematics—The Frontier. Wiley Interscience, New York. Going beyond the first volume, this exposition is just as much fun and intellectually satisfying as the first volume.Google Scholar

Philosophy and Epistemology

  1. Feynman R. P., Leighton R. B., and Sands M. (1963) Atoms in Motion, Lecture #1 in The Feynman Lectures on Physics, vol. 1. Addison-Wesley Publishing Co., Reading, MA. In classic Feynman style, he explains the approach to theory, experiment, observable, and abstraction.Google Scholar
  2. Russell B. (1945) A History of Western Philosophy. Touchstone/Simon and Schuster, New York. Fun to read and accessible discourse on philosophy for the nonprofessional philosopher. Bertrand Russell was a mathematician, and his scientific tilt makes the scientist at ease with the subject.Google Scholar

Biological Modeling

  1. Murray J. D. (1991) Mathematical Biology, 2d ed. Springer Verlag, New York/Berlin/Heidelberg. This textbook devotes a detailed chapter to a selection of 20 fundamental processes of biological interest. Each chapter describes and explores these models. Included are models important to our study such as waves of diffusion, population growth, reaction mechanisms, enzyme kinetics, biological oscillators, and so on. Detailed and from the mathematician’s point of view.Google Scholar


  1. Atkins P. W. (1983) Group Theory, Chapter 7 in Molecular Quantum Mechanics. Oxford University Press, Oxford/New York. A good introduction to group theory and symmetry. P. W. Atkins also treats the subject nicely in his textbook, Physical Chemistry.Google Scholar
  2. Cotton F. A. (1990) Chemical Applications of Group Theory, 3rd ed. Wiley Interscience, New York. For the serious student. This is a book worth studying but cannot be picked up casually.Google Scholar
  3. Feynman R. P., Leighton R. B., and Sands M. (1963) Symmetry in Physical Laws, Lecture #52 in The Feynman Lectures on Physics, vol. 1. Addison-Wesley Publishing Co., Reading, MA. Clear, concise, illuminating; the first stop for those going further.Google Scholar

Dynamical Systems

  1. Abraham R. H., and Shaw C. D. (1984) Dynamics, The Geometry of Behavior: Part One: Periodic Behavior. Aerial Press, Inc, Santa Cruz, CA.Google Scholar
  2. Abraham R. H., and Shaw C. D. (1984) Dynamics, The Geometry of Behavior; Part Two: Chaotic Behavior, Aerial Press, Inc, Santa Cruz, CA.Google Scholar
  3. Beltrami E. (1987) Mathematics for Dynamic Modeling. Academic Press, Inc, Boston.Google Scholar

When you want more

  1. Bracewell R. N. (1990) Numerical transforms. Science, 248: 697–704.PubMedCrossRefGoogle Scholar
  2. Ditto W. L. and Pecora L. M. (1993) Mastering Chaos. Scientific American,269(2):78–84. Nontechnical general introduction to chaos theory.Google Scholar
  3. Ekeland I. (1988) Mathematics and the Unexpected. University of Chicago Press, Chicago. This volume discusses Kepler, chaos, and catastrophe and is a logical next step.Google Scholar
  4. Galasso F. (1993) The importance of understanding structure. J. Chem. Ed., 70: 287–90.CrossRefGoogle Scholar
  5. Grebogi C., Ott E., and Yorke J. A. (1987) Chaos, strange attractors and fractal basin boundaries in non-linear dynamics. Science, 238: 632–38.PubMedCrossRefGoogle Scholar
  6. Peitgen H. O., Jürgens H., and Saupe D. (1989) Fractals for the Classroom. Springer-Verlag, New York.Google Scholar
  7. Thom R. (1975) Structural Stability and Morphogenesis. W. A. Benjamin Co., Reading, MA. This volume is by the originator of the catastrophe theory.Google Scholar
  8. Thompson D’Arcy W. (1942) On Growth and Form. Cambridge University Press, Cambridge. This is his classic, revolutionary work on evolution and coordinate transformations.Google Scholar
  9. Weiner N. (1961) Cybernetics or Control and Communication in the Animal and the Machine, 2d ed. The MIT Press and John Wiley and Sons, New York. This is a classic and should be required reading for any scientist. Out of print but available in most academic libraries. Find a professor who has a copy and talk with her/him.Google Scholar
  10. Woodcock T. and Davis M. (1978) Catastrophe Theory. Dutton, New York. A good introduction to catastrophe theory for the nonmathematician.Google Scholar

Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Peter R. Bergethon
    • 1
  1. 1.Department of BiochemistryBoston University School of MedicineBostonUSA

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