CONTENTS (TABLE DES MATIÈRES)

Preface
Forword to Volume I

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PART I : MATERIALS AND METHODS IN BIOLOGICAL DYNAMICS
Introduction to Part I

Chapter I : Macromolecular Components and Interactions in Living Organisms
I. Structure of nucleic acids
II. Structure of proteins

1. Description of protein structure
2. Theory of the conformation of biological macromolecules

• a. Physical description of a macromolecular syslem in solution
• b. Free energy variation during a conformational change 1

3. Molecular conformation and biological activity

III. Molecular interactions in proteins: protein-ligand interactions

1. Thermodynamic theory of molecular interactions

• a. Protein-ligand associations (homotropic effects)
• b. Consequences
• c. Allosteric models generally used

2. The cooperative effect

• a. The concept of cooperativity
• b. Cooperativity and fhe binding polynomial
• c. An illustration of the cooperative effect

Chapter II : The Internal Chemistry of Cells
I. Catalytic function of the enzymic reaction

1. Henri-Michaelis-Menten Equations: equilibrium conditions
2. Briggs-Haldane Equations: Quasi-stationary state conditions
3. The mathematical viewpoint: the pseudo-steady state hypothesis

II. Regulatory function of the enzymic reaction
III. Molecular interactions and the active site concept
IV. Coupled chemical reactions: reaction-diffusion equations

1. General equation for a chemical transformation
2. The physics of diffusion: Fick's equation
3. The mathematics of a reactional-diffusional system
4. An autocatalytic reaction

Chapter III : Methods in Biological Dynamics
I. Biology and complexity
II. Relational theories

1. Rosen's theory of abstract biological systems
2. Delattre's theory of transformation systems

• a. Axioms
• b. Graph representation
• c. An application showing the impossibility of spontaneous undamped oscillations in physically linear systems and the existence of oscillations in non-catalytic systems

III. Thermodynamic theory

1. Principles of equilibrium thermodynamics
2. The entropy production term. Consequence in the linear field: non-equilibrium stationary states in the neighbourhood of equilibrium
3. Non-linear thermodynamics of chemical reactions: non-equilibrium stationary states far from equilibrium

• a. The universal criterion of evolution
• b. The Glansdorff-Prigogine functional
• c. Physical interpretation
• d. Network thermodynamics
• a.Characteristics of an element in a chemical network
• b. Bond graphs

IV. Thom's theory of elementary catastrophes

Summary of Part I

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PART II : THE MOLECULAR ORGANISATION OF LIVING MATTER
Introduction to Part II

Chapter IV : Organisation of Biological Systems

I. A formal definition of self-organisation

1. Organisation
2. Self-organisation

II. Biological organisation and information theory

1. Von Foerster’s self-organising system
2. The Yockey-Atlan theory of self-organisation

III. A theory of the functional organisation of formal biological systems some concepts and definitions

1. Introduction to the functional organisation of biological systems
2. The problem of representation in biology

• a. Notions of system, structure, function and evolution
• a . System: general considerations
• b . Structure and system
• g . Function
• d . Evolution
• b. A representation of physiological systems: the hypothesis of associative
• functional self-organisation
• a . Biological structure and systems
• b . The hypothesis of associative self-organisation
• g . The physiological system as a hierarchical system.
• c. Functional interactions, levels of organisation

3. Mathematical representation of the functional organisation
4. Dual representations: (N,a) and (y,r)

IV. Spatial organisation in the cell : concept of structural discontinuity

1. On the existence of non-local interactions: The concept of the active site re-examined
2. Enzyme organisation: microcompartmentation and the example of "channelling"

• a. Introduction to the problem of enzyme organisation
• b. Relation with physiology and physiological consequences
• c. Definitions of channeling on biophysical bases
• a . Metabolic organisation
• b . Application of Curie’s principle of symmetry
• g . The respective roles of diffusion and reaction
• d . How should the diffusion process be characterised in order to account for the existence of molecular channels in the absence of a physical limit such as a membrane ?

3. On the functional organisation in a biological structure: the example of enzyme organisation

• a. Definition of a metabolic pathway as a structural unit
• a . Michaelis enzymatic reactions: metabolic flux and transport between the local medium and the bulk phase
• b . Stability of the dynamics of a step in the metabolic chain
• g . Stability of a metabolic pathway with allosteric control of production

4. A paradigm for the creation of functional interactions: the self-association hypothesis

• a. The structural unit and the physiological function
• b. The self-association hypothesis
• c. On the nature of a break in the self-association
• a . A break in the functional interaction of the metabolic pathway
• b . Basic mechanisms of the association

5. Functional association between two metabolic pathways defined as structural units 168

• a. A general and generative schema of the association
• b. Mathematical study of the dynamics in a u₂-units: a specific system
• c. Mathematical study of the dynamics in a u₂-units: a general dynamical system

6. The paradigm of self-association applied to the enzyme organisation: role of local and bulk phase

Chapter V : The Replication-Translation Apparatus

I. The 'central dogma' of molecular biology

1. Genes and chromosomes
2. Replication, transcription and translation
3. Computational methods of determining the sequencing properties of DNA

II. Information theory and the genetic code

1. Measurement of the quantity of information in the genetic code
2. The genetic code

III. Chemical dynamics of heredity

1. Generalities
2. DNA replication
3. Protein synthesis

IV. Topological, structural and functional implications of nucleicacid chains

1. Topological concepts in DNA replication and structural consequences

• a. Topological findings
• b. Experimental data

2. Topology and protein biosynthesis

• a. The concept of contractibility and its consequences
• b. The concept of restorability and its consequences

V. The hierarchical organisation of the replication-translation apparatus

Chapter VI : Molecular Evolution and Organisation

I. Evolution of self-instructing information carriers

1. Phenomenological description of the evolution of chemical species
2. Solution of the system of equations
3. Explicit solutions
4. Consequence: selection in molecular systems

II. Evolution with complementary instruction. The case of DNA or RNA replication
III. Protein biosynthesis: self-organising enzymic cycles

1. Catalytic protein cycles
2. Self-reproducing hypercycle

Chapter VII : Evolution and Physiology

I. Evolution and self-organisation of molecular systems

1. Introduction
2. The three phases of evolution
3. Darwinian systems

II. A coherent interpretation of evolution

1. Creation of thermodynamically stable spatiotemporal structures
2. Self-organisation and the evolution of molecular bioystems
3. Evolution of the species in terms of information theory
4. Recapitulation: the scenario of evolution

III. Functional biology and evolutionary biology

1. Darwinism and physiology: the principle of vital coherence
2. An elementary model of evolution

• a. Formalisation of the principle of vital coherence in term of the level of organisation
• b. Description of an elementary model of evolution
• c. Discussion and results: can this model be generalised ?

Summary of Part II

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PART III : CELLULAR ORGANISATION OF LIVING MATTER
Introduction to Part II

Chapter VIII : Cellular Organisation

I. Cell description
II. Cell organisation and regulation

1. Formation of structures at the cellular level
2. Regulation and metabolic pathways

• a. The glucose-6-phosphate pathway
• b. The Krebs cycle (the citric acid cycle)
• c. Interpretation of regulatory phenomena
• d. The phenomenon of inverse regulation

III. Cell growth: an introduction

1. Growth
2. Development
3. Differentiation
4. Morphogenesis

Chapter IX : Regulation of Cell Function through Enzvme Activity

I. Introduction to the regulation of enzyme synthesis
II. Theoretical model of regulation
III. Regulation of protein biosynthesis in higher organisms

Chapter X : Cell Growth and Morphogenesis

I. General aspects
II. Unicellular organisms

1. Differentiation in the Acrasiales
2. Human red blood cells
3. Some examples of cell differentiation at the molecular level

III. Higher organisms

1. Embryogenesis

• a. Principal steps of embryogenesis
• b. Concepts of cell differentiation

2. Positional information and cell differentiation

3. Control and cell differentiation

• a. Transcriptional control
• b. Post-transcriptional control
• c. Post-translational control
• d. Mathematical models of control in cell differentiation

IV. Morphogenesis: Turing's theory

1. General aspects
2. Theoretical models of morphogenesis

• a. Creation of the gradient
• b. Interpretation of the gradient of positional information

3. Morphogenesis: local theory and global theory

• a. Turing's theory: a synthesis of theoretical models
• b. Thom's theory: towards a general theory of development

V. A description of growth for functional organisation

1. A break in the functional interaction: consequences on the stability of biological systems

• a. A break in the functional interaction: the choice between Life and Death
• b. Functional hierarchical organisation: the consequence of the choice

2. Evidence for the existence of self-association: An increase in stability

Chapter XI : Cell Division

I. The cell cycle

1. Description
2. Models of the cell cycle
3. The limit cycle model of biochemical oscillations

II. Development of a cell population

1. Kinetics with variables (t, a)
2. Kinetics with variables (t,m)

III. Analysis of the cell cycle: population theory

1. Leslie matrices applied to population studies
2. Interpretation of the FLM curve by population theory

Chapter XII : Cell Growth, Division and Differentiation

I. Asymmetrical cell division
II. Cell growth

1. Analytical description: mass and volume
2. Global description of the behaviour of a cell

III. Mechano-chemical approach to morphogenesis: Murray's mechanical model for mesenchymal morphogenesis

IV. Topological description of developmental dynamics: potential of functional organisation

1. Introduction: Variational principles in biology
2. The potential of functional organisation

• a. The nature of the concept: the combinatorial approach and non-symmetry
• b. Definition and formulation

3. Criterion of maximality for the potential of organisation: a class of biological systems

• a. State of maximum of organisation
• b. The extremum hypothesis: a class of biological systems
• a . The organisational state is an attractor
• b . Consequence: the extremum hypothesis for the time- variation of the number of sinks

4. Criterion of evolution for the functional organization: orgatropy

• a. The concept of ‘orgatropy’ 414
• b. Does orgatropy provide a criterion for the time-variation of the (O-FBS) ? 417

5. Criterion of specialisation and re-organization of the (O-FBS) during development

• a. Criterion of specialisation
• a . The concept of specialisation
• b . The relation between specialisation and hierarchisation
• b. Consequence: mathematical expressions of specialisation and emergence of a level of organisation
• c. Functional order
• d. Time-variation of an (O-FBS) during development

V. A comparison between biological and physical systems

1. Structural entropy and functional orgatropy
2. The consequence of the optimum principle
3. On the meaning of the optimum principle

Summary of Part III

Conclusion to Volume I : Unity at the Gene Level

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Mathematical Appendices

Appendix A : Vector analysis

1. Gradient of a function U(x,y,z)
2. Divergence of a vector
3. Green's theorem
4. The Laplace function: the second order scalar operator
5. Summary

Appendix B : Dynamic systems

1. Notion of a dynamic system
2. The Hamiltonian form. Conservative systems
3. Stability: Lyapunov functions
4. Limit cycles, critical points, Jacobian, Hessian
5. Partial differential equations
6. Some notes on the terrninology of ordinary differential equations.
Compact differential manifolds

Appendix C : Notations in matrix algebra

Appendix D : Probability and information theory

1. Probability
2. The Shannon function of information

Symbols and constants (mainly in CGS units)

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General reading
Bibliography
Index

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