banana predicts bending of a normal (B) DNA double helix, using the method of Goodsell & Dickerson, NAR 1994 11;22(24):5497-5503. The program calculates the magnitude of local bending and macroscopic curvature at each point along an arbitrary B-DNA sequence, using any desired bending model that specifies values of twist, roll and tilt as a function of sequence. The program outputs both a graphical display and a text file of the results.
The default model (model 'a' from the Goodsell & Dickerson paper) is based on the nucleosome positioning data of Satchwell et al 1986 (J. Mol. Biol. 191, 659-675). It correctly predicts experimental A-tract curvature as measured by gel retardation and cyclization kinetics and successfully predicts curvature in regions containing phased GGGCCC sequences. The model shows local bending at mixed sequence DNA, strong bends at the sequence GGC, and straight, rigid A-tracts. It is the only model out of the six investigated that is consistent with both solution data from gel retardation and cyclization kinetics and structural data from x-ray crystallography.
banana reads a sequence and a matrix of standard twist, roll and tilt angles for each type of base pair step. The default matrix is described below (see "Bending Model") but some other can be specified (see "Data Files" below). The program creates a table or a graphical image of the bending and the curvature at each base step.
The indicated twist, roll and tilt angles are applied at each step along the sequence, and the resulting base pair normal vector calculated. The first base pair is aligned normal to the z axis, with a twist value of 0.0 degrees. The specified twist is applied to the second base pair, and roll and tilt values are use to calculate its normal vector relative to the first. If either roll or tilt is non-zero, the new normal vector will be angled away from the z axis, producing the first 'bend'. The process is continued along the sequence, applying the appropriate twist, roll and tilt to each new base pair relative to its predecessor. The result is a list of normal vectors for all base pairs in the sequence.
Local bends are then calculated from the normal vectors. The bend for base N is calculated across a window from N-1 to N+1.
Curvature is calculated in two steps. Base pair normals are first averaged over a 10-base-pair window to filter out the local writhing of the helix. The normals of the nine base pairs from N-4 to N+4, and the two base pairs N-5 and N+5 at half weight, are averaged and assigned to base pair N. Curvature then is calculated from these averaged normal vector values, using a bracket value, nc, with a value of 15. That is, the curvature at base pair N is the angle between averaged normal vectors at base pairs N-nc and N+nc.
banana reads by default a data file (Eangles_tri.dat) of twist, roll and tilt angles, as in Goodsell & Dickerson, NAR 1994 11;22(24):5497-503 and Drew and Travers (1986) JMB 191, 659. The roll-tilt-twist parameters of this bending model are objective and unbiased. They are derived purely from experimental observations of sequence location preferences of base trimers in small circles of DNA, without reference to solution techniques that measure curvature per se.
Satchwell, Drew and Travers studied the positioning of DNA sequences wrappped around nucleosome cores, and in closed circles of double-helical DNA of comparable size. From the sequence data they calculated a fractional preference of each base pair triplet for a position 'facing out', or with the major groove on the concave side of the curved helix.
The sequence GGC, for example, has a 45% preference for locations on a bent double helix in which its major groove faces inward and is compressed by the curvature (tending towards positive roll), whereas sequence AAA has a 36% preference for the opposite orientation, with major groove facing outward and with minor groove facing inward and compressed (tending toward negative roll).
These fractional variances are converted into roll angles in the following manner: Because x-ray cyrstal structure analysis uniformly indicates that AA steps are unbent, a zero roll is assigned to the AAA triplet; an arbitrary maximum roll of 10 degrees is asigned to GGC, and all other triplets are scaled in a lenear manner. Where % is the percent-out figure, then: Roll = 10 degrees * (% + 36)/(45 + 36)
Changing the maximum roll value will scale the entire profile up or down proportionately, but will not change the shape of the profile. Peaks will remain peaks, and valleys, valleys. The absolute magnitude of all the roll values is less important than their relative magnitude, or the order of roll preference. Twist angles were set to zero. Because these values correspond to base trimers, the values of roll, tilt and twist were applied to the first two bases for the calculation.
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The graphical display shows the sequence together with the local local bending (solid line) and macroscopic curvature (dotted line).
The data file consists of three columns separated by blanks or tab characters.
The first column is the sequence.
The second column is the local bending.
The third is the curvature.
The description of this bending model is as follows:
The roll-tilt-twist parameters of this model are derived purely from experimental observations of sequence location preferences of base trimers in small circles of DNA, without reference to solution techniques that measure curvature per se. For this reason, they may be the most objective and unbiased parameters of all. Satchwell, Drew and Travers studied the positioning of DNA sequences wrappped around nucleosome cores, and in closed circles of double-helical DNA of comparable size. From the sequence data they calculated a fractional preference of each base pair triplet for a position 'facing out', or with the major groove on the concave side of the curved helix. The sequence GGC, for example, has a 45% preference for locations on a bent double helix in which its major groove faces inward and is compressed by the curvature (tending towards positive roll), whereas sequence AAA has a 36% preference for the opposite orientation, with major groove facing outward and with minor groove facing inward and compressed (tending toward negative roll). These fractional variances have been converted into roll angles in the following manner: Because x-ray cyrstal structure analysis uniformly indicates that AA steps are unbent, a zero roll is assigned to the AAA triplet; an arbitrary maximum roll of 10 degrees is asigned to GGC, and all other triplets are scaled in a lenear manner. Where % is the percent-out figure, then:
Roll = 10 degrees * (% + 36)/(45 + 36)
Changing the maximum roll value will scale the entire profile up or down proportionately, but will not change the shape of the profile. Peaks will remain peaks, and valleys, valleys. The absolute magnitide of all the roll values is less important than their relative magnitude, or the order of roll preference. Twist angles were set to zero. Because these values correspond to base trimers, the values of roll, tilt and twist were applied to the first two bases for the calculation.
DNA bending is vital for the winding of DNA in nucleosomes, and the recognition of particular DNA loci by restriction enzymes, repressors and other control proteins. For example, the binding of the catabolite gene activator protein and of the TATA-box recognition protein to a double DNA helix both rely on major bends in the helix induced at specific sequence loci. Whether the particular recognition sequences are bent even in the absence of proteins is not always clear: a preformed bend in the DNA would form a custom site for protein binding, or an enhanced bendability of a given sequence would facilitate protein-induced bending. Sadly, the rules of sequence-dependent DNA bending remain elusive.
Two models of sequence-dependent bending in free DNA have been proposed. Nearest neighbor models propose that large-scale measurable curvature may arise by the accumulation of many small local deformations in helical twist, roll, tilt and slide at individual steps between base pairs. In contrast, junction models propose that bending occurs at the interface between two different structural variants of the B-DNA double helix.
In both models, sequences which are anisotropically bendable - for instance, sequences with steps that preferentially bend only to compress the major groove - will lead to an average structure which is similar to a sequence with a rigid, intrinsic bend. The default bending model (see below) used by banana does not distinguish between these two possibilities.
B-DNA has the special property of having its base pairs very nearly perpendicular to the overall helix axis. Hence the normal vector to each base pair can be taken as representing the local helix at that point, and curvature and bending can be studied simply by observing the behaviour of the normal vectors from one base to another along the helix. This is both easy to calculate and simple to interpret. This program display the magnitude of bending and curvature at each point along the sequence. It is not intended as a substitute for more elaborate three-dimensional trajectory calculations, but only to express bending tendencies as a function of sequence. This affords easy screening for regions of a given DNA sequence where phased local bends add constructively to form an overall curve.
The terms bending and curvature are used in a restricted sense here. Bending of DNA describes the tendency for successive base pairs to be non-parallel in an additive manner over several base pair steps. Bending most commonly is produced by a rolling of adjacent base pairs over one another about thir long axis, although in principle, tilting of base pairs about their short axis could make a contribution. In contrast curvature of DNA represents the tendency of the helix axis to follow a non-linear pathway over an appreciable length, in a manner that contributes to macroscopic behaviour such as gel retardation or ease of cyclization into DNA minicircles.
The distinction between local bending and macroscopic curvature is illustrated (poorly) in the following figure (see figure 1 of the Goodsell & Dickerson paper for a better view).
bend bend bend
- - -
uncurved / \ / \ / \
-----/ \-/ \-/ \-----
bend bend
bend bend
/-------\
/ \
curved |bend |bend
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X-ray crystal structure analysis cannot show curvature, but can and often does show local bending. Conversely, gel electrophoresis and cyclization kinetics can detect macroscopic curvature, but not bending. A complete knowledge of local bending would permit the precise calculation of curvature, but a knowledge of macroscopic curvature alone does not allow one to specify precisely the local bending elements that produce it. This paradox has plagued the DNA conformation field resembles the familiar problem of classical statistical mechanics, where a complete knowledge of positions and velocities of all molecules of a gas would allow one to calculate bulk properties such as temperature, pressure and volume, but knowledge of bulk properties cannot lead one to precise molecular positions. Many molecular arrangements can produce identical bulk properties, and in the present case, many bending combinations can produce identical macroscopic curvature.
The consensus sequence for DNA bending is 5 As and 5 non-As alternating. "N" is an ambiguity code for any base, and "B" is the ambiguity code for "not A" so "BANANA" is itself a bent sequence - hence the name of this program.