Foundations of Mathematical Biology - 1st Edition - ISBN: 9780125972024, 9781483271842

Foundations of Mathematical Biology

1st Edition

Cellular Systems

Editors: Robert Rosen
eBook ISBN: 9781483271842
Imprint: Academic Press
Published Date: 1st January 1972
Page Count: 348
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Foundations of Mathematical Biology, Volume II: Cellular Systems describes the properties of cellular systems and their relationship to the development of multicellular organisms. This volume is composed of five chapters that present the mathematical tools applied in evaluating these systems.

Chapters 1 illustrates the use of continuous time systems to examine the relationship between the properties of individual cells and the general problems of morphogenesis in developing systems, specifically how these properties could manifest themselves in morphological terms. Chapter 2 demonstrates the systems of rate equations or first-order differential equations to deal with the regulation of individual chemical processes and sequences of such processes, at both the genetic and metabolic levels. Chapter 3 discusses the application of the theory of automata to the evaluation of the concept and principles of embryology, while Chapter 4 presents some relational cell models to study the metabolism-repair cellular systems. Chapter 5 looks into the concept and systems of a compartment.

This book will prove useful to mathematical and cell biologists and researchers.

Table of Contents

List of Contributions

Preface to Volume II

Content of other Volumes

Chapter 1 Morphogenesis

I. Introduction

II. Morphogenetic Movements

A. Subunits and Subunit Assemblies

B. Prerequisites for Self-Assembly

C. The Efficiency of Subassembly Processes

III. Kinetic and Geometric Aspects of Self-Assembly

A. Spherical and Helical Viruses

B. "Sorting Out" in Mixed Cell Populations

IV. Differentiation

A. Asymmetries and Their Generation

B. Rashevsky's Model for Cell Polarities

C. The Turing Models

D. The Keller-Segel Models

E. Morphogenesis and Epigenesis

General References

Chapter 2 Mechanics of Epigenetic Control

I. Introduction

II. Regulatory Behavior in Open Chemical Systems

III. Parametric Changes in Open Chemical Systems

IV. Reaction Rate Control in Catalyzed Open Systems

A. Uncatalyzed Reactions

B. Catalyzed Reactions

C. Activation and Inhibition of Catalyzed Reactions

V. Examples of Epigenetic Controls

A. Rate Control in Enzyme Systems

B. Rate Control of Genetic Catalysis

VI. Some Specific Epigenetic Circuits

A. "Discrimination Network"

B. "Learning Network"

C. "Size Regulation Network"


General References

Chapter 3 Automata Theory in the Context of Theoretical Embryology

I. Programs in Biological Systems

II. Positional Information

III. Relative Position and Synchronization in Arrays of Automata

A. Synchronization of Arrays of Automata

B. Relative Position-A Slightly Embryological View

IV. An Introduction to Turing Machines and Formal Languages

A. Turing Machines

B. Biological String Processing

C. Formal Languages

D. Tessellation Automata

V. Automata Which Construct as Well as Compute

A. Self-Reproducing Automata

B. Modified Modules for Greater Biological Relevance

VI. Evolution and Entropy


Chapter 4 Some Relational Cell Models: The Metabolism-Repair Systems

I. Introduction

II. General Input-Output Systems

A. Components and Component Networks

B. Some Examples of Input-Output Systems

C. Dependency Structure in Block Diagrams

D. The Roles of Time in General Input-Output Systems

III. Theory of a Single Metabolism-Repair System

A. The Basic Idea of Metabolism-Repair Systems

B. The Conversion of Input-Output Systems to Metabolism-Repair Systems

C. The Dependency Structure of Metabolism-Repair Systems

D. Replication of Repair Components

IV. Global Theory of Metabolism-Repair Systems

A. The Theory of Categories

B. Metabolism-Repair Systems in Arbitrary Categories

C. The Behavior of Abstract Metabolism-Repair Systems in Changing Environments

D. The Problem of Control and Reversibility in Metabolism-Repair Systems

V. Structural and Relational Models Compared

General References

Chapter 5 Compartments

I. The Concept of Compartment

A. Physiology

B. Pharmacology

C. Tracer Kinetics

II. General System Properties

A. Definition of a System

B. Linear Systems

C. State-Determined Systems

D. Holonomic Systems

III. Systems of Compartments

A. The Operational Definition of a Compartment

B. Pools versus Compartments

C. Classification of Systems

D. Topological Properties

IV. Integration of the System Equations

Α. The Operational Calculus of Mikusinski

B. Differential Equations in Operational Notation

C. The Flow Graph

D. Partial Fraction Expansion

E. The Operational Form of Some Simple Functions

F. The Algebraic Derivative of an Operator

G. The Operational Form of Other Trigonometric Functions

H. The Transfer Function

V. Analysis of the Precursor-Successor Relationship

VI. Material Transport through Compartments

A. Turnover

B. Graphs and Turnover

VII. Noncompartmented Systems

VIII. Dimensional Analysis of the System Equations

IX. The Use and Abuse of Compartment Analysis

General References

Author Index

Subject Index


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© Academic Press 1972
Academic Press
eBook ISBN:

About the Editor

Robert Rosen

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