This textbook grew out of a course that the highly respected applied mathematician Lee Segel taught at the Weizmann Institute. This book represents the unique perspective on mathematical biology of Segel and his co-author Leah Edelstein-Keshet (author of the popular SIAM book, Mathematical Models in Biology). It introduces differential equations, biological applications, and simulations, with emphasis on molecular events (biochemistry and enzyme kinetics), excitable systems (neural signals), and small protein and genetic circuits. The exposition combines clear and useful mathematical methods with plenty of applications to illustrate the power of such tools, along with many exercises in reasoning, modelling and simulation. The reader will also find suggestions for further study and appendices containing useful background material. These features make the book ideal for students at the advanced undergraduate or graduate level in both biology and mathematics who wish to experience the application of mathematical techniques to the biological sciences.
Lee A. Segel (1932-2005) was a Professor at the Weizmann Institute of Science, Rehovot, Israel, where he served as Chairman of Applied Mathematics, Dean of Mathematical Sciences and Chairman of the Scientific Council. He was an Ulam Scholar at the Los Alamos National Laboratory, a Fellow of the American Association for the Advancement of Science and a member of the Santa Fe Institute, where he continued his work on complex adaptive systems. He served as editor or editorial board member of six journals. Leah Edelstein-Keshet is a Professor in the Department of Mathematics at the University of British Columbia, Vancouver, Canada. Her book Mathematical Models in Biology was republished in SIAM's Classics in Applied Mathematics series.
List of figures; List of tables; Acknowledgments; Preface; 1. Introduction; 2. Introduction to biochemical kinetics; 3. Review of linear differential equations; 4. Introduction to nondimensionalization and scaling; 5. Qualitative behavior of simple differential equation models; 6. Developing a model from the ground up: case study of the spread of an infection; 7. Phase plane analysis; 8. Quasi steady state and enzyme-mediated biochemical kinetics; 9. Multiple sub-unit enzymes and proteins: cooperativity; 10. Dynamic behavior of neuronal membranes; 11. Excitable systems and the FitzHugh-Nagumo equations; 12. Biochemical modules; 13. Discrete networks of genes and cells; 14. For further study; 15. Extended exercises and projects; Appendix A. The Taylor approximation and Taylor series; Appendix B. Complex numbers; Appendix C. A review of basic theory of electricity; Appendix D. Proofs of Boolean algebra rules; Appendix E. XPP files for models in this book; Bibliography; Index.
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