The concept of curvature is best understood on the example of an ideally elastic rod exposed to bending stress:
Such an ideal rod curves along a perfect circular arch, and its curvature can be
defineded as the angle between the beginning and the end of the rod (i.e. the angle of the
two corresponding tangential vectors). This is identical with the central angle of the
arch. The curvature of a DNA molecule can be defined in an analogous manner:
The angle can be calculated as the angle of normal vectors of the first and last
basepair plains. In order to get values that are independent of the DNA length, one can
present curvature as degree/basepair or degree/helical turn. From this quantity it is easy
to calculate the number of nucleotides or helical turns necessary to form a full circle of
360°. For example a value18 °/helical turn defines a circle of 20 helical turns or 210
nucleotides (20x18=360, and 1 helical turn =10.5 residues).
The prediction of curvature is based on statistically derived roll, tilt and twist
angles of dinucleotide steps. We suppose that a dinucleotide step (i.e. two successive
basepairs) will curve to the same extent, no matter where it is in a DNA structure. This
big and not necessarily correct simplification allows one to derive statistical average
values from 3D structures, or from other measurements, such as electrophoretic mobility
analysis, nucleosome binding or DNaseI cutting assays.
The calculation is then rather simple: we divide the DNA sequence into overlapping dinucleotides, and assign the corresponding roll, tilt and twist angles to each step. We suppose (another simplification) that the molecule is an ideal B-DNA with successive basepairs 3.4 Angstroms apart. Then we can calculate the DNA path as a result of one vertical translation (3.4 A) and three rotations (roll, tilt, twist). In principle, this calculation is quite complicated, but i) for small angles, such as occur in DNA, and ii) for short DNA segments, the problem is simplified into a straightforward vectorial addition of the geometric parameters. This procedure is complemented with averaging [Goodsell and Dickerson, 1994], and the curvature is determined for a standard segment length, in our case 31 basepairs or approximately 3 helical turns. This value is assigned to the center of the segment. Plotting this value along the sequence one gets a curvature vs. sequence plot, that shows peaks at highly curved positions.
The prediction method is based on the bendability values determined from
nucleosome binding and DNaseI analysis [Gabrielian and Pongor, 1997]. The basic
observation is that bendability values are assymetrically distributed in intrinsicaly
curved segments, as can be shown here by a "helical wheel diagram" (similar to
that used for alpha helices in proteins):
In this figure, the arrows are proportional to the bendability value of the given
basepair, taken from a table of values determined for trinucleotides [Brukner et. al.]. The sequence represents a highly
curved sequence motif (A)AAATGTCAAA(A) from a Leishmania tarantolae class II
minicircle. The dark shading indicates the rigid part of the helix. In "average
DNA" we find a different, quasi random distribution, i.e. the arrows are not
asymmetrical. There are two extreme situations that correspond to highly bendable (B) and
rigid (C) sequences:
B: A straight sequence from the lambda phage OR3 operator region: (C)ACCGCAAGGG(A) C:
is a poly-A sequence.
In the following tables we listed a number of curved and straight sequences that you can use as a comparison to the maxima you find in your sequence.