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.
Chapter 1: Introduction Chapter 2: Introduction to Biochemical Kinetics Chapter 3: Review of Linear Differential Equations Chapter 4: Introduction to Nondimensionalization and Scaling Chapter 5: Qualitative Behavior of Simple Differential Equation Models Chapter 6: Developing a Model from the Ground Up: Case Study of the Spread of an Infection Chapter 7: Phase plane Analysis Chapter 8: Quasi Steady State and Enzyme-Mediated Biochemical Kinetics Chapter 9: Multiple Subunit Enzymes and Proteins: Cooperativity Chapter 10: Dynamic Behavior of Neuronal Membranes Chapter 11: Excitable Systems and the FitzHughaEUR"Nagumo Equations Chapter 12: Biochemical Modules Chapter 13: Discrete Networks of Genes and Cells Chapter 14: For Further Study Chapter 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
