Introduction To Mathematical Biology

This volume is designed to cultivate in graduate biology students an awareness of and familiarity with applications of mathematical techniques and methods related to biology. This text explores five areas of mathematical biology, presented in a unified fashion: the first three subjects, cell growth, enzymatic reactions, and physiological tracers, are biological; the final two, biological fluid dynamics and diffusion, are biophysical. Introduced in an order of progressive mathematical complexity, the topics essentially follow a course in elementary differential equations, although linear algebra and graph theory are also touched upon. Free of mathematical jargon, the text requires only a knowledge of elementary calculus. A set of problems appears at the end of each chapter, with solutions at the end of the book. Unabridged republication of the edition published by John Wiley & Sons, New York, 1975. Preface. Solutions. References. Appendixes. Author Index. Subject Index.

Developed from the author s course in mathematical biology at Cornell University, this volume is designed to cultivate in graduate biology students an awareness of and familiarity with applications of mathematical techniques and methods related to biology.
This text explores five areas of mathematical biology, which are unified by their underlying mathematical structure. The first three subjects (cell growth, enzymatic reactions, and physiological tracers) are biological; the final two (biological fluid dynamics and diffusion) are biophysical. Introduced in an order of progressive mathematical complexity, the topics essentially follow a course in elementary differential equations, although linear algebra and graph theory are also touched upon.
Free of mathematical jargon, the text requires only a knowledge of elementary calculus. A set of problems appears at the end of each chapter, with solutions at the end of the book. In addition to its value to biology students, this text will also prove useful to students with backgrounds in mathematics, physics, and engineering, who possess little knowledge of biology but nevertheless take an interest in the quantitative approach."

Designed to explore the applications of mathematical techniques and methods related to biology, this text explores five areas: cell growth, enzymatic reactions, physiological tracers, biological fluid dynamics and diffusion. Topics essentially follow a course in elementary differential equations and#8212; some linear algebra and graph theory; requires only a knowledge of elementary calculus.

Chapter 1?Cell Growth

1.1 Exponential Growth or Decay

1.2 Determination of Growth or Decay Rates

1.3 The Method of Least Squares

1.4 Nutrient Uptake by a Cell

1.5 Inhomogeneous Differential Equations

1.6 Growth of a Microbial Colony

1.7 Growth in a Chemostat

1.8 Interacting Populations: Predator-Prey System

1.9 Mutation and Reversion in Bacterial Growth

and#160; Problems

Chapter 2?Enzyme Kinetics

2.1 The Michaelis-Menten Theory

2.2* Early Time Behavior of Enzymatic Reactions

2.3 Enzyme-Substrate-Inhibitor System

2.4 Cooperative Properties of Enzymes

2.5 The Cooperative Dimer

2.6 Allosteric Enzyme

2.7 Other Allosteric Theories

2.8 Hemoglobin

2.9 Graph Theory and Steady-State Enzyme Kinetics

2.10 Enzyme-Substrate-Modifier System

2.11 Enzyme-Substrate-Activator System

2.12 Aspartate Transcarbamylase

and#160; Problems

Chapter 3?Tracers in Physiological Systems

3.1 Compartment Systems

3.2 The One-Compartment System

3.3 Indicator-Dilution Theory

3.4 Continuous Infusion

3.5 The Two-Compartment System

3.6 Leaky Compartments and Closed Systems

3.7 The Method of Exponential Peeling

3.8 Creatinine Clearance: A Two-Compartment System

3.9 "The "Soaking Out" Experiment"

3.10 The Three-Compartment Catenary System

3.11* The n-Compartment System

and#160; Problems

Chapter 4?Biological Fluid Dynamics

4.1 The Equations of Motion of a Viscous Fluid

4.2 Poiseuille's Law

4.3 Properties of Blood

4.4 The Steady Flow of Blood through a Vessel

4.5 The Pulse Wave

4.6 The Swimming of Microorganisms

and#160; Problems

Chapter 5?Diffusion in Biology

5.1 Fick's Laws of Diffusion

5.2 The Fick Principle

5.3 The Unit One-Dimensional Source Solution

5.4 The Diffusion Constant

5.5 Olfactory Communication in Animals

5.6 Membrane Transport

5.7 Diffusion Through a Slab

5.8 Convective Transport: Ionic Flow in an Axon

5.9 The Gaussian Function

5.10 Ultracentrifugation

5.11 The Sedimentation Velocity Method

5.12* An Approximate Solution to the Lamm Equation

5.13 Sedimentation Equilibrium

5.14 Transcapillary Exchange

and#160; Problems

Solutions to Problems

References

Appendix A: Brief Review

"Appendix B: Determinants, Vectors, and Matrices"

Author Index

Subject Index