Foundations of Mathematical Biology - 1st Edition - ISBN: 9780125972017, 9781483272139

Foundations of Mathematical Biology

1st Edition

Subcellular Systems

Editors: Robert Rosen
eBook ISBN: 9781483272139
Imprint: Academic Press
Published Date: 1st January 1972
Page Count: 316
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Foundations of Mathematical Biology, Volume 1, Subcellular Systems, provides an introduction the place of mathematical biology in relation to the other biological, physical, and organizational sciences. It discusses the use of mathematical tools and techniques to solve biological problems.
The book contains four chapters and begins with a discussion of the nature of hierarchical control in living matter. This is followed by a chapter on chemical kinetics and enzyme kinetics, covering the physicomathematical principles, models, and approximations underlying transition-state theory and the unimolecular reaction. Subsequent chapters deal with quantum genetics and membrane excitability.

Table of Contents

List of Contributors


Contents of Other Volumes

Chapter 1 The Nature of Hierarchical Control in Living Matter

I. The Significance of Hierarchical Control

II. General Nature of Hierarchical Organizations

III. Hierarchical Control Implies a Language

IV. Some Basic Properties of Language and Control Hierarchies

A. Some Properties of Language

B. Some Properties of Control Hierarchies

V. Physical Conditions for Language and Control Hierarchies

VI. Conclusions


Chapter 2 Chemical Kinetics and Enzyme Kinetics

I. Introduction

II. The Transition-State Theory

A. Origins of the Method

B. Quantum Mechanical Calculations of Energy Terms

C. Passage of "Activated Complex" over the Potential Energy Barrier

D. Equilibrium and Thermodynamic Aspects of the Transition-State Rate

E. Completion of the Derivation of the Rate Expression, Thermodynamic Aspects of the Rate Constant

III. The Unimolecular Reaction

A. The Lindemann-Hinshelwood Mechanism

B. Possible Precursor to the Lindemann-Hinshelwood Hypothesis

C. Subsequent Analysis and Study of the Pseudounimolecular Rate Constant

D. The Rice-Ramsperger-Kassel and Rice-Ramsperger-Kassel-Marcus Theories of the Unimolecular Reaction

E. Origins of the Stochastic Approach to Microscopic Chemical Kinetics

F. Macroscopic Stochastic Models of the Unimolecular Reaction

IV. Enzyme Kinetics

A. The Enzyme-Substrate System

B. The Classical Mathematical Model of the Elementary Enzyme-Catalyzed Reaction

C. A Closer Look at Some Active Site Characterizations

D. Kinetic Significance of Active Site

E. Stochastic Models of the Michaelis-Menten Mechanism

F. Some Further Examples of the Use of Stochastic Models in Dealing with Complex Biochemical Kinetics


Chapter 3 Quantum Genetics

I. The Basic Genetic Questions

II. Systems, States, and Observables

A. Macrophysical and Microphysical Systems

B. A More Accurate Formation of the Notion of State

C. Some Properties of p(A, α, E)

D. "Questions"

E. Some Properties of the Set of Questions

F. Questions and Observables

G. Expected Values of Observables on States

H. Simultaneous Observations, Commutation and the Uncertainty Relations

III. The Usual Form of Quantum Theory

The Universality Postulate of Microphysics and Its Consequences

IV. The Genetic Systems

A. The Phenotypic Observable A

B. Limit Points in σ(A) and Resolving Power

C. An Example: Lysogeny

D. Degeneracy, Perturbation, and Allelism

V. The Operators B and C, and Their Interrelationships with the Genetic Observable A

VI. Interpretation


Chapter 4 Excitability Phenomena in Membranes

I. Introduction

II. Squid Axon and the Hodgkin-Huxley Equations: concerning Models and Theories

III. Descriptive Equations for the Axon Membrane

IV. Research Objectives

V. The Movement of Charged Particles across Potential Barriers

VI. The Equations of Electrodiffusion

VII. Physical Systems with Negative Conductance

A. Tunnel Effects

B. Oxide Films

C. Passivated Iron

D. Teorell Oscillator

E. Black Lipid Membranes and Organic Films

VIII. A Steady-State Model Involving Fixed Charges

IX. The Nonstationary State


Author Index

Subject Index


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© Academic Press 1972
Academic Press
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About the Editor

Robert Rosen

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