Principles of Biological Regulation: An Introduction to Feedback Systems presents some understanding of control, regulatory, and feedback mechanisms in biological systems. This book discusses concepts related to the dynamic behavior of both individual biological processes and systems of processes that make up an organism. Comprised of 10 chapters, the book also describes the characteristics of biological feedback systems, focusing on the physical concepts. After briefly dealing with involved regulatory processes in biological systems, the book goes on discussing the flow or transport of material through a series of processes in the steady-state. Next chapter uses superposition principle to explain the changes that biological systems undergo following a disturbance or under dynamic behavior. The subsequent chapters cover the fundamental principles of negative biological feedback and to the effects it produces both under steady-state and dynamic behavior. Other chapters describe the effect of sinusoid signals on biological processes and present some stability criteria applied to technological systems and also their value in the study of homeostatic processes. The book also discusses some aspects of homeostats that seem to distinguish them from technological feedback systems. These features include not only the components themselves and their organization, but also the experimental problems involved in their study. The concluding chapters describe nonlinear behavior with great relevance to homeostatic systems and rate processes (production or destruction) for which the roles of stimulus and initial conditions are different. Mathematical relations developed from the conservation of mass and the mass action for chemical reactions are also presented. The book is an invaluable resource for life scientists and researchers.

Preface
Acknowledgments

1. Regulatory Processes in Biological Systems

1.1 Biology as a Science of Organization

1.2 Regulatory Biology

1.3 Historical Development

1.4 Epitome

References

2. Flow Processes in the Steady State

2.1 Introduction

2.2 Cellular Diffusion of CO2

2.3 Heat Flow in a Muscle; Definition of a Compartment

2.4 Flow through a Compartment: the Storage Function

2.5 Loss Functions

2.6 Single-Compartment Process in the Steady State

2.7 Factors Affecting the Steady State; Variables and Parameters

2.8 Multicompartment Systems; Noninteracting Processes

2.9 Interacting Processes

2.10 Aqueous Flow through the Eye; Two-Compartment Model

2.11 Disturbances to the Steady State

2.12 Transmission Function, Gain

2.13 Flow Graphs and Block Diagrams

2.14 Glucose Transport with Intravenous Feeding

2.15 Steady-State Control of the Extraoculär Muscles

2.16 Mathematical Treatment of the Steady State

2.17 Glands as Transducers; Biological Fluxes

2.18 Epitome

Problems

References

3. Dynamic Behavior; the Transient Response

3.1 Introduction

3.2 Compartment Filling at a Prescribed Rate; No Losses

3.3 Compartment Emptying

3.4 Properties of the Exponential Curve

3.5 Single Compartment; Transient and Steady-State Solution

3.6 First-Order Dynamics

3.7 Second-Order System; Noninteracting Processes

3.8 Noninteracting and Interacting Processes

3.9 Signal Transmission through Several Compartments

3.10 Second-Order Transient; Oscillatory Case

3.11 Oscillations in Limb Movement, Dysmetria

3.12 Systems of Higher Order

3.13 Modes of Free Vibration

3.14 Block Diagram Symbols for First-Order Processes

3.15 Responses to Pulse Disturbances

3.16 Muscle Dynamics

3.17 Mathematical Analysis of Linear Dynamical Systems

3.18 Epitome

Problems

References

4. Introduction to Feedback; the Steady State

4.1 Introduction

4.2 Feedback in a Two-Compartment System

4.3 The Steady-State Operating Point; Definition of a Negative Feedback System

4.4 Effect of Disturbances upon the Operating Point

4.5 Open-Loop and Closed-Loop Gain

4.6 The Control Mechanism; Reference Input and Sign Reversal

4.7 Further Discussion of Loop Gain

4.8 Reducing the Effects of Disturbances

4.9 Effect of Loop Gain on Perturbations; Sensitivity

4.10 Further Aspects of Sensitivity

4.11 Operating Point, Reference Input, and Summing Point in Nonlinear Systems

4.12 The Error Concept

4.13 Temperature Regulation under Heat Stress; Sweating

4.14 Regulation of Thyroxine; the Thyroid-Pituitary System

4.15 Types of Regulator; the Servomechanism

4.16 Steady-State Relations in a Type 1 System

4.17 Mechanisms of Sign Reversal

4.18 Generalized Block Diagram

4.19 Blood Pressure Regulation

4.20 The Stretch Reflex

4.21 Epitome

Problems

References

5. Feedback Systems; Dynamic Behavior

5.1 Introduction

5.2 Changes in the System Behavior with Feedback

5.3 Block Diagrams; Open- and Closed-Loop Behavior

5.4 First-Order Systems; Change in the Operating Point

5.5 Types of Disturbances; System Trajectory

5.6 Second-Order System; Responses to an Input Disturbance

5.7 Second-Order System; Parametric Disturbance

5.8 The Complex s-Plane; Pole Location and Transient Response

5.9 Second-Order Systems; Poles on the s-Plane

5.10 Complex Poles; Damped Oscillatory Modes

5.11 Second-Order System; Effect of Increased Gain

5.12 Signal Transmission through a Feedback System Having an Oscillatory Response

5.13 Effect of Time Constant Ratio on the Transient Modes

5.14 Oscillations in Neuromuscular Control

5.15 Baroreceptor Reflex

5.16 Further Discussion of Feedback System Dynamics

5.17 Epitome

Problems

References

6. Sinusoidal Signals

6.1 Introduction

6.2 Properties of a Sinusoid

6.3 Sinusoidal Transmission; First-Order Process

6.4 Sinusoidal Response of a Single Compartment at Different Frequencies

6.5 Sinusoidal Modulation

6.6 Frequency Spectrum; First-Order Process

6.7 Logarithmic Coordinates

6.8 Frequency Spectrum of a Second-Order System

6.9 Sign Inversion and Its Frequency Spectrum

6.10 Open-Loop Frequency Spectrum

6.11 Effect of Loop Gain on the Open-Loop Spectrum

6.12 Frequency Spectrum; Nerve-Muscle Preparation

6.13 Frequency Spectrum; the Wolf Spider Eye

6.14 Transmission of a Periodic Signal

6.15 Development of the Fourier Transform

6.16 System Analysis with the Fourier Transform

6.17 Properties of the Baroreceptor

6.18 Spectra of the Stretch Reflex

6.19 Open- and Closed-Loop Frequency Spectra

6.20 Resonance in a Second-Order Feedback System

6.21 Algebra of Complex Numbers

6.22 Further Discussion of Sinusoidal Signals and Frequency Spectra

6.23 Epitome

Problems

References

7. Stability

7.1 Introduction

7.2 Instability in a Liquid Level Regulator

7.3 Transients in a Third-Order Feedback System; Critical Gain

7.4 Stability and the Sinusoidal Domain

7.5 Nystagmus; an Example of Physiological Instability

7.6 Factors Contributing to Instability; Stability Boundaries

7.7 Stability Criteria in the Time Domain

7.8 Ideal Transport Lag

7.9 Feedback System Having Transport Lag

7…