Double helix formula
Thomas Gramstad
of the DNA-type? I'd appreciate some explanation or reference to
literature as well.
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Thomas Gramstad b...@ifi.uio.no
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Robert Langridge%CGL
>Can somebody tell me the mathematical formula for a double helix
>of the DNA-type? I'd appreciate some explanation or reference to
>literature as well.
>
the connections to the helical sugar-phophate chain, which, in the
early models follows the regular helical repeat of 10 base-pairs
per turn and 34A per turn, or 3.4A rise and 36 degrees rotation
per base pair. The general structure, refined against the best X-ray
fiber diffraction data at that time is in our paper, Langridge et al
Journal of Molecular Biology, Vol 2, p 19-38, 1960.
More recently, crystals of DNA fragments have been made in which the X-ray
crystal structure shows that the precise conformation is irregular and
depends on the base sequence, although for many purposes the regular
double helix is sufficient.
Bob Langridge Phone: +1 415 476-2630, -1540, -5128
Computer Graphics Laboratory FAX: +1 415 476-0688
University of California E-Mail: r...@cgl.ucsf.edu
San Francisco CA 94143-0446
Thomas Gramstad
helix structure; I believe this is the answer to my question:
(quoting from a letter to me:)
A helix is a circle that moves up with time. Hence the equations
x(t) = sin t
y(t) = cos t
z(t) = t
describe a helix. A double helix is two helices that are offset by half
a turn. The equations for the second helix would then be
x(t) = sin t
y(t) = cos t
z(t) = t + \pi
Roy Smith
> x(t) = sin t, y(t) = cos t, z(t) = t describe a helix. A double helix is
> two helices that are offset by half a turn. The equations for the second
No quite, since the original question referred to a DNA double
helix. First, the double helix is not symetric. This gives rise to a
major and minor groove. The way to represent this, using the parametric
formss you give, is to have for the second helix, z(t) = t + k*pi. I'm not
sure what the exact value for k should be, but something like 0.7 would be
about right. Second, to be really correct, you should incorporate the fact
that the two strands are anti-parallel (i.e. one goes up andd the other
goes down). You need a sign-inversion in there somewhere (but don't just
change the sign of z; that would change the helical sense from right to
left handed).
--
Roy Smith, Public Health Research Institute
455 First Avenue, New York, NY 10016
{att,philabs,cmcl2,rutgers,hombre}!phri!roy -or- r...@alanine.phri.nyu.edu
"The connector is the network"
Gary Murphy
of tetrahedron column, pointing out that this is not an 'official'
description, but yet another amazing similarity between his geometrical
games and the real world. This model accounts not only for the 36
degree twist, but also includes a slight error in the alignment of the
two columns which Bucky termed the 'unzipping' angle and speculated
that the tension of this error could be the mechanism which causes
the strands to split.
I've made dozens of these models for my kids: take a sheet of paper
and fold it lengthwise to give 3 parallel creases each bending the
same direction (a flat tube). Fold it up so that you have this flat
tube as one strip 1/4th the width and then fold that into equilateral
triangles by starting at one end and folding in alternate directions
along a 60 degree crease, bringing one side flush with one of the
sides of the strip; when done, the strip should be an accordian of
equilateral triangles. Unfold the paper and overlap the outside
strips (from the first three creases) - the paper will need to be
skewed to do this (one top corner is pulled out further than the
other). This should form a tube-like column of tetrahedrons.
--
Gary Murphy decvax!utzoo!dciem!nrcaer!cognos!garym
(garym%cogno...@uunet.uu.net)
(613) 738-1338 x5537 Cognos Inc. P.O. Box 9707 Ottawa K1G 3N3
"There are many things which do not concern the process" - Joan of Arc