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A Continuum Rod Model of Sequence-Dependent DNA Structure
J. Chem. Phys.105, pp. 5626-5646, 1 October 1996.
Robert S. Manning, John H. Maddocks
Institute for Physical Science and Technology and
Department of Mathematics
University of Maryland, College Park, MD 20742
Jason D. Kahn
Department of Chemistry and Biochemistry
University of Maryland, College Park, MD 20742
Abstract
Experimentally motivated parameters from a base-pair-level discrete
DNA model are averaged to yield parameters for a continuum elastic
rod with a curved unstressed shape reflecting the local DNA geometry.
The continuum model permits computations with discretization lengths
longer than the intrinsic discretization of the base-pair model, and,
for this and other reasons, yields an efficient computational formulation.
Obtaining continuum stiffnesses is straightforward, but obtaining a
continuum unstressed shape is hindered by the "noisy" small-scale structure
and rapid helix twist of the discrete unstressed shape. Filtering of the
discrete data and an analytic transformation from the true normal-vector
field to a natural (untwisted) frame allows a stable continuum fit.
Equilibrium energies of closed rings predicted by the continuum model are
found to match the energies of the underlying discrete model to within
0.5%. The model is applied to a set of 11 short DNA molecules (~150 bp) and
properly distinguishes their cyclization probabilities (J factors)
when compared both to experimental cyclization rates and to Monte Carlo
simulations. The continuum model does not include entropic contributions
to the free energy. However, because of its rapid and accurate computation
of internal energy, the continuum model should, when combined with further
work on entropic effects, be a useful method for computing experimental
DNA free energies.