Introduction to Mathematical Biology

by S. I. Rubinow

Overview

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 - some linear algebra and graph theory; requires only a knowledge of elementary calculus.

Product Details

ISBN-13:	9780486425320
Publisher:	Dover Publications
Publication date:	01/13/2003
Series:	Dover Books on Biology Series
Edition description:	DOVER
Pages:	400
Product dimensions:	5.30(w) x 8.40(h) x 0.90(d)

Table of Contents

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
  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
  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
  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
  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
  Problems
Solutions to Problems
References
Appendix A: Brief Review
"Appendix B: Determinants, Vectors, and Matrices"
Author Index
Subject Index