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depends only on the DNA sequence. In contrast to alternative DNA conformations (such as
A and Z-DNA), curvature can be viewed as a slight distortion of the B-DNA geometry that
is manifested in the bending of the DNA-trajectory. Such a curvature can be quantitatively
described using an analogy of a smoothly bent rod, and in the case of a DNA model, it can
be expressed in terms of degree per base pair, or degree per helical turn. In the latter case,
the repeat of the helical turn has to be specified. (Figure 1B).
Figure 2.
DNA curvature as asymmetric bendability. The diagram is a top-view of
the DNA helix with the Z-axis perpendicular to the plain of the paper. DNA
bendability of subsequent trinucleotides is represented as an arrow perpendicular to
the Z-axis. In curved segments, such as the one in the figure, the distribution of the
bendability vectors is asymmetrical and the vector-sum (red arrow) is non-zero. In
most parts of the genomes the vector sum is small [5].
The discovery of DNA curvature was a slow process. The first evidence that there is
an influence of base composition on the average twist between adjacent base pairs came
from DNA X-ray fiber diagrams, 20 years after the double-helix paper of Watson and Crick
[11]. Subsequent studies by gel-electrophoresis [12], nucleotide/digestions [13] and finally
the first X-ray structure of DNA [14] confirmed this view. In 1980, Trifonov and Sussman
suggested a correlation between the helical repeat of the DNA and spacing of certain
dinucleotides (especially AA and TT) along the sequence which indicated that a substantial
part of eukaryotic DNA may in fact be curved [15]. Subsequent experimental data by
Marini et al. [16] indicated that periodic A-tracts repeating in phase with the helical repeats
cause curvature, which was confirmed both by electron microscopy [17] and by enzymatic
circularisation experiments [18]. By the mid nineties, the concept of DNA curvature
became generally accepted, and even the apparent controversy between X-ray
crystallography and solution experiments could be reconciled by the discovery that divalent
cations induce a sequence dependent curvature in DNA [3].
A “curvature model” is a way to derive sequence-dependent DNA geometry
parameters from experimental data. The models are different both in terms of the
experimental data and the method of calculation. For example, it is common to fix some of
the base-pair parameters at the values corresponding to straight B-DNA while letting others
vary in a sequence-dependent fashion. In addition, the angles can be assigned to
dinucleotides or to trinucleotides; these datasets are referred to as dinucleotide or
trinucleotide scales. (All the models described here refer to double-stranded DNA
molecules with “classic” phosphate orientations.)
