Foundations of Mathematical Biology
Cellular Systems
- 1st Edition - January 1, 1972
- Imprint: Academic Press
- Editor: Robert J. Rosen
- Language: English
- Hardback ISBN:9 7 8 - 0 - 1 2 - 5 9 7 2 0 2 - 4
- Paperback ISBN:9 7 8 - 1 - 4 8 3 2 - 4 5 6 5 - 2
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 7 1 8 4 - 2
Foundations of Mathematical Biology, Volume II: Cellular Systems describes the properties of cellular systems and their relationship to the development of multicellular organisms.… Read more
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Request a sales quoteFoundations 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.
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"
Notes
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
References
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
- Edition: 1
- Published: January 1, 1972
- Imprint: Academic Press
- No. of pages: 348
- Language: English
- Hardback ISBN: 9780125972024
- Paperback ISBN: 9781483245652
- eBook ISBN: 9781483271842
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