Statistical Physics of DNA

The following sections are included:

• Dedication
• Foreword
• About the Author
• Contents

The following sections are included:

• Definitions and notation. Key quantities
  • The freely jointed chain (FJC)
  • Local stiffness. Elastic energy. The wormlike chain
• Statistical mechanics of the Kratky–Porod (KP) chain
  • The partition function
  • Correlations. Persistence length
  • Moments
  • Radius of gyration
• The end-to-end distance probability distribution
• The Gaussian chain
• Excluded volume effects
  • Characterization of the end-to-end distance distribution function
  • Critical exponents and observable quantities
  • Values of the critical exponents. Relationship to the self-avoiding walk problem

The elastic response of common polymeric materials, e.g. rubber, can be traced to entropic rather than enthalpic changes of their state[Flory (1953)]. A long, flexible polymer coiling randomly in solution will have a typical end-to-end distance far smaller than its contour length. Consequently, the work done by a force acting to stretch it will be mostly spent in changing the spatial conformation of the molecule; chemical bonding, and thus internal enthalpies, play a minor role.

The following sections are included:

• Packaging of genomic material in a DNA virus
  • Shape and parameters
  • Bending vs. hydration energies. Packaging force. Pressure on capsid walls
• Wrapping in nucleosomes
  • Genomic packaging
  • Bending energies at the nucleosome core
  • Unwrapping the nucleosome

The following sections are included:

• Elastic scattering from dilute solutions of macromolecules
• The structure factor of the Kratky–Porod chain
  • An intermediate result
  • Structure factor of the homogeneous KP chain
• Structure factor of the freely jointed chain (FJC)
• Structure factor of the WLC
  • The approach to the continuum limit
  • Numerical evaluation of the structure factor
• Numerical evaluation of the end-to-end distance probability distribution function
• Structure factors of simple geometrical molecules
  • Structure factor of a spherical molecule
  • Structure factor of a cylindrical molecule
• Light scattering from long DNA molecules
• Small angle neutron scattering (SANS) from short DNA molecules

The following sections are included:

• Introduction
  • Discovery
  • Basic Thermodynamics
• Base sequence and thermodynamic stability
  • The nearest-neighbor model
  • Enthalpies and entropies for neighboring base pairs
• Melting of longer DNA chains
  • Internal vs. external melting
  • Multistep melting
  • Melting of long, synthetic, homogeneous duplexes

The following sections are included:

• Unzipping
  • The experimental findings
  • Mean-field theory
• Overstretching
  • The overstretching transition
  • Enthalpic corrections to the force-extension curve
  • Force induced melting: the torsionally unconstrained case
  • Torsionally constrained forced-induced melting

The following sections are included:

• Statistical models of helix-coil equilibria
  • Synthetic polypeptides
  • Helix growth vs. helix initiation
  • The “all-or-nothing” (AON) model
  • The zipper model
  • The generalized zipper model
• Melting of infinitely long homogeneous DNA. The Poland–Scheraga model
  • A useful shortcut
  • Loop entropies
  • The phase transition
  • Bubbles and clusters
  • A thermodynamic phase transition in a one-dimensional system?

The following sections are included:

• Base pairs as dynamical entities
  • Functional requirements
  • Breathing of individual base pairs
  • Base pair lifetime
  • Low frequency vibrations
• The homogeneous Peyrard–Bishop model
  • Definitions and Notation
  • Dynamics
  • Statistical mechanics
  • The phase transition
  • Bubbles
  • DNA unzipping in the PB model

The following sections are included:

• The homogeneous Peyrard–Bishop–Dauxois (PBD) Hamiltonian
• A local thermally activated barrier
• Thermodynamic properties of the PBD Hamiltonian
• First-order transition: true or apparent?

The following sections are included:

• Heterogeneity in the PBD model framework
  • Theory describes internal melting
  • The Hamiltonian and its model parameters
• Statistical mechanics of the finite, heterogeneous chain
  • The partition function
  • The melting fraction
  • Computational issues
• Computed melting profiles
  • The T-7 phage
  • The pBR322 plasmid
• Predictive power of the PBD model
  • Dependence of the Morse depths on salt concentration
  • Parameter-free computation of melting profiles
  • Longer sequences
  • Unzipping

The following sections are included:

• Introduction
• Statistical mechanics of the heterogeneous KP chain
  • The partition function
  • Correlations
  • The second moment
• Flexibility and melting
  • Magnetic birefringence of DNA in solution
  • Birefringence in the premelting and melting regime
• Enhanced flexibility of a short sequence at elevated temperatures

According to the picture presented so far, DNA at the scale of a few hundred nm should appear at room temperature essentially as a stiff rod. However, experiments in the last ten years have cast considerable doubts on the general validity of such a sweeping statement. Cyclization experiments with some short sequences (≤ 200 bps)[Cloutier and Widom (2004, 2005); Vafabakhsh and Ha (2012)] have measured a significantly higher rate of ring closure than that expected from WLC model calculations with a 50 nm persistence length. SAXS-based measurements of even shorter sequences, 10-35bp [Mathew-Fenn et al. (2008)] and 15-89 bp [Yuan et al. (2008)] also suggest a notably softer structure at this scale…

The following sections are included:

• Self-complementary sequences
• Biomolecular beacons
  • Fluorescence resonance energy transfer (FRET) spectroscopy
  • Fluorescence upon hybridization
• Thermodynamic stability of hairpins
  • Open-closed equilibria
  • Hairpin statistical mechanics: stem vs loop
• Excluded volume, SAWs and electrostatic repulsion in ss-DNA

The following sections are included:

• Appendix A. Monte Carlo simulations of the Kratky–Porod chain
• Appendix B. Landau’s theorem on the absence of phase transitions in one-dimensional systems
• Appendix C. Dynamical theory of DNA melting: The soliton analogy
  • Soliton-like field configurations of the Peyrard–Bishop model
  • Thermal fluctuations and soliton stability
• Appendix D. Numerical solution of the transfer integral equation
  • Gauss–Legendre quadratures
  • Application to the TI equation

The following sections are included:

• Bibliography
• Index