Introduction to Mathematical Biology

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