NONLINEAR PHYSICS OF DNA

The first edition of this book was the first on the physics of DNA to go beyond the simple (simplified) 'linear' approach, and it has since been found that the inclusion of nonlinear effects leads to a significantly improved interpretation of experimental data. This new edition naturally retains this approach, but has been completely revised, updated and expanded to cover recent developments.

Beginning with introductory chapters on DNA structure and dynamics, the book also includes a comparison between linear and nonlinear approaches to the DNA molecule, a chapter devoted to the statistics of nonlinear excitations of DNA, and examples for the interpretation of experimental data on the dynamics of DNA in terms of nonlinear theory.

Essential reading for researchers in biophysics and nonlinear physics, allowing biologists, chemists and physicists to continue developing new and improved techniques of investigating the DNA molecule.

Ludmila V. Yakushevich is a Doctor of Science and leading research worker of the Laboratory of Physical and Chemical Mechanisms of Gene Expression, which is part of the Institute of Cell Biophysics of the Russian Academy of Sciences. The main research field is the dynamics of biopolymers, especially the nonlinear dynamics of DNA. The principal methods of investigations include theoretical physics and mathematical modeling.

Preface to the First Edition.

Preface to the Second Edition.

1 DNA Structure.

1.1 Chemical Composition and Primary Structur.

1.2 Spatial Geometry and Secondary Structure.

1.3 Forces Stabilizing the Secondary DNA Structure.

1.3.1 Hydrogen Interactions.

1.3.2 Stacking Interactions.

1.3.3 Long-range Intra- and Inter-backbone Forces.

1.3.4 Electrostatic Field of DNA.

1.4 Polymorphism.

1.5 Tertiary Structure.

1.5.1 Superhelicity.

1.5.2 Structural Organization in Cells.

1.6 Approximate Models of DNA Structure.

1.6.1 General Comments.

1.6.2 Hierarchy of Structural Models.

1.7 Experimental Methods of Studying DNA Structure.

2 DNA Dynamics.

2.1 General Picture of the DNA Internal Mobility.

2.2 Twisting and Bending Motions.

2.3 Dynamics of the Bases.

2.3.1 Equilibrium State.

2.3.2 Possible Motions of the Bases.

2.4 Dynamics of the Sugar–Phosphate Backbon e.

2.4.1 Equilibrium State.

2.4.2 Possible Motions of the Sugar–Phosphate Backbone.

2.5 Conformational Transitions.

2.5.1B->A Transition.

2.5.2B->Z Transition.

2.6 Motions Associated with Local Strands Separation.

2.6.1 Base-pair Opening Due to Rotations of Bases.

2.6.2 Transverse Displacements in Strands.

2.7 Approximate Models of DNA Dynamics.

2.7.1 The Main Principles of Modeling.

2.7.2 Hierarchy of Dynamical Models.

2.8 Experimental Methods for Studying DNA Dynamics.

2.8.1 Raman Scattering.

2.8.2 Neutron Scattering.

2.8.3 Infrared Spectroscopy.

2.8.4 Hydrogen–Deuterium (–Tritium) Exchange.

2.8.5 Microwave Absorption.

2.8.6 NMR.

2.8.7 Charge-transfer Experiments.

2.8.8 Single Molecule Experiments.

3 DNA Function.

3.1 Physical Aspects of DNA Function.

3.2 Intercalation.

3.3 DNA–Protein Recognition.

3.4 Gene Expression.

3.5 Regulation of Gene Expression.

3.6 Replication.

4 Linear Theory of DNA.

4.1 The Main Mathematical Models.

4.1.1 Linear Rod-like Model.

4.1.1.1 Longitudinal and Torsional Dynamics: Discrete Case.

4.1.1.2 Longitudinal and Torsional Dynamics: Continuous Case.

4.1.1.3 Bending Motions.

4.1.2 Linear Double Rod-like Model.

4.1.2.1 Discrete Case.

4.1.2.2 Continuous Case.

4.1.3 Linear Models of Higher Levels.

4.1.3.1 The Third-Level Models.

4.1.3.2 The Fourth-level (Lattice) Models.

4.2 Statistics of Linear Excitations.

4.2.1 Phonons in the Rod-like Model.

4.2.1.1 General Solution of the Model Equations.

4.2.1.2 Secondary Quantum Representation.

4.2.1.3 Correlation Functions.

4.2.2 Phonons in the Double Rod-like Model.

4.2.2.1 General Solution of the Model Equations.

4.2.2.2 Secondary Quantum Representation.

4.2.2.3 Correlation Functions.

4.2.3 Phonons in the Higher-level Models.

4.3 Scattering Problem.

4.3.1 Scattering by "Frozen" DNA.

4.3.2 Elastic Scattering.

4.3.3 Inelastic Scattering.

4.4 Linear Theory and Experiment.

4.4.1 Fluorescence Depolarization.

4.4.2 Low-frequency Spectra: Neutron Scattering, Infrared scattering, Raman Scattering, Speed of Sound.

5 Nonlinear Theory of DNA: Ideal Dynamical Models.

5.1 Nonlinear Mathematical Modeling: General Principles and Restrictions.

5.2 Nonlinear Rod-like Models.

5.2.1 The Rod-like Model of Muto.

5.2.2 The Model of Christiansen.

5.2.3 The Rod-like Model of Ichikawa.

5.3 Nonlinear Double Rod-like Models.

5.3.1 General Case: Hamiltonian.

5.3.2 General Case: Dynamical Equations.

5.3.3 The Y-model.

5.3.3.1 Discrete Case.

5.3.3.2 Continuous Case.

5.3.3.3 Linear Approximation.

5.3.3.4 The First Integral.

5.3.3.5 Kink-like Solutions Found by Newton’s Method.

5.3.3.6 Kink-like Solutions Found by the Method of Hereman.

5.3.4 The Model of Peyrard and Bishop.

5.3.5 The Double Rod-like Model of Muto.

5.3.6 The Model of Barbi.

5.3.7 The Model of Campa.

5.4 Nonlinear Models of Higher Levels.

5.4.1 The Model of Krumhansl and Alexander.

5.4.2 The Model of Volkov.

6 Nonlinear Theory of DNA: Non-ideal Models.

6.1 Effects of Environment.

6.1.1 General Approach.

6.1.2 Particular Examples.

6.1.3 DNA in a Thermal Bath.

6.2 Effects of Inhomogeneity.

6.2.1 Boundary.

6.2.2 Local Region.

6.2.3 Sequence of Bases.

6.3 Effects of Helicity.

6.4 Effects of Asymmetry.

7 Nonlinear Theory of DNA: Statistics of Nonlinear Excitations.

7.1 PBD Approach.

7.2 Ideal Gas Approximation.

7.3 The Scattering Problem and Nonlinear Mathematical Models.

7.3.1 The Simple Sine-Gordon Model.

7.3.2 Helical Sine-Gordon Model.

7.3.3 The Y-model.

8 Experimental Tests of DNA Nonlinearity.

8.1 Hydrogen–Tritium (or Hydrogen–Deuterium) Exchange &feE;.

8.2 Resonant Microwave Absorption.

8.3 Scattering of Neutrons and Light.

8.3.1 Interpretation of Fedyanin and Yakushevich.

8.3.2 Interpretation of Cundall and Baverstock.

8.4 Fluorescence Depolarization.

9 Nonlinearity and Function.

9.1 Nonlinear Mechanism of Conformational Transitions.

9.2 Nonlinear Conformational Waves and Long-range Effects.

9.3 Nonlinear Mechanism of Regulation of Transcription.

9.4 Direction of Transcription Process.

9.5 Nonlinear Model of DNA Denaturation.

Appendix.

Appendix 1: Mathematical Description of Torsional and Bending Motions.

Appendix 2: Structural and Dynamical Properties of DNA.

References.

Index.