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Abstracts and Talk Materials
Mathematics of Nucleic Acids
September 15, 2007


Wilma K. Olson (Rutgers, The State University of New Jersey)
http://dnaserver.rutgers.edu/

Sequence-Dependent Helical Structure and Global Responses of DNA Part I.
September 15, 2007

(Towards understanding the processing and packaging of genetic information at the molecular level)

Part I. Information content in known three-dimensional structures of nucleic acids: sequence-dependent conformation, deformation, interactions
    A. The classic B-DNA double helix: Watson-Crick base pair side groups vs. the polyanionic sugar-phosphate backbone

    B. DNA phase transitions and RNA double helices
    1. The A/B double helical transition and DNA bending Structural discriminants of A vs. B DNA Protein-induced A/B transitions
    2. The B/C double helical transition and DNA packaging Nucleosome core particle: a striking example of protein-induced DNA deformation via concerted changes in kinking and base-pair displacement Tight bending of DNA via B→A and B→C helical transitions
    3. The A-RNA double helix, including non-canonical base pairs


    C. Chemical basis of DNA sequence-dependent properties: structure, deformability, recognition
    1. Indirect (electrostatic) mechanism of nucleosomal DNA folding vs. sequence-dependent character of known positioning sequences
    2. Indirect recognition of sequences: pyrimidine-purine base-pair steps as sites of DNA deformability
    3. Patterns of base-amino acid contacts: direct recognition of specific DNA sequences by proteins
    4. DNA electrostatics, amino acid binding propensities, intrinsic curvature
    5. Recognition and structural roles of non-canonical base pairs

Wilma K. Olson (Rutgers, The State University of New Jersey)
http://dnaserver.rutgers.edu/

Part II: Implications of Base Sequence-Dependent Structural Information on Larger-Scale Genetic Control
September 15, 2007

    A. Quantitation of local, sequence-dependent properties of DNA
    1. Low resolution models, including knowledge-based potentials
    2. Linear, sequence-dependent three-dimensional structures


    B. Effects of sequence on ring closure properties of closed molecules
    1. Sequence-dependent factors that enhance the formation of tight minicircles and loops
    2. Mechanics of superhelix formation: roles of bending, twisting, and base-pair displacement
    3. Nucleotide looping and global folding of RNA


    C. Effects of sequence on the equilibrium structures and normal modes of cyclized DNA
    1. Constrains of bound proteins on global structure and motions
    2. Nucleosome positioning sequences and minichromosomes

David Swigon (University of Pittsburgh)
http://www.math.pitt.edu/~swigon/

Part II: DNA Statistical Mechanics/DNA Dynamics
September 15, 2007

  • Worm-like chain model, ring closure, J factor
  • Statistical mechanics of DNA supercoiling
  • Monte Carlo simulations of DNA
  • DNA stretching
  • Extraction of sequence-dependent parameters from statistical ensembles
  • DNA denaturation, effect of topological constraints, role in transcription regulation
  • Probability of knotting and catenation, removal of knots/catenanes


DNA dynamics
  • Dynamics of supercoiling
  • Kinetics of site juxtaposition
  • DNA in microchannels and porous media

David Swigon (University of Pittsburgh)
http://www.math.pitt.edu/~swigon/

Part I: DNA Topology and Geometry/DNA Elasticity
September 15, 2007

DNA topology and geometry
  • Linking number, writhe, twist
  • The theorem of Calugareanu and White, DNA supercoiling
  • Methods for calculating and estimating writhe
  • Surface linking number, linking number paradox
  • DNA knots and catenanes, topoisomerases, recombination


DNA elasticity
  • Idealized elastic rod model, equilibrium configurations, supercoiling of rings, bifurcations
  • Elastic rod models with intrinsic curvature, kinetoplast DNA
  • Higher order continuum models, kinkable DNA
  • Base-pair level models, sequence-dependence of DNA
  • elasticity
  • DNA looping, role of looping in transcription regulation
  • Electrostatic effects

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