22 December 1952

Mr. Roger Hayward

920 Linda Vista

Pasadena 2, Calif.

Dear Roger:

Here is the information about the drawings that I need for the nucleic acid paper,
in connection with the NFIP work.

The cylindrical coordinates for 20 atoms are given on the accompanying sheet. Here
ρ is the radial distance from the axis of the cylinder (the axis of the helix), Ф
is the azimuthal angle, and z is the coordinate in the direction of the axis. The
coordinates are on a right-handed system, so that increasing z and increasing Ф generates
a right-handed screw.

The first five coordinates, for P and four oxygen atoms, refer to the phosphate groups.
The four oxygen atoms are at the corners of a tetrahedron, which is, however, not
a regular tetrahedron. I think that so far as your drawings are concerned it would
be satisfactory, however, to indicate the tetrahedron as a regular tetrahedron, without
trying to take the relatively small distortions into consideration. The next three
sets of coordinates for C_{5'}, C_{4'}, and C_{3'}, represent three atoms
which connect the upper right outer corner of an tetrahedron with the lower left outer
corner of the tetrahedron that is in the layer above, and rotated 105° to the right.

I suggest that the first drawing indicate one helix, formed by one tetrahedron, the
link to another tetrahedron in the layer above, that tetrahedron, the link to the
tetrahedron in the layer above that, and so on. This helix is generated by taking
the tetrahedron represented by the four oxygen atoms, the inner edge being formed
by oxygen atoms with radius 2.00 A, and generating the next tetrahedron by translating
the distance 3.40 A along the z axis and rotating through the angle 105°. This helical
molecule executes seven turns in 24 tetrahedra. The pitch is 81.6 - that is, 24.
x 3.40 A. I suggest that 24 - probably better 25 - tetrahedra be shown in outline,
with arcs connecting them together, the arcs representing the atoms C_{5'}, C_{4'}, and C_{3'}. This would be just a diagrammatic representation. It might be worth while to
show the axis of the molecule, as a straight line, and to draw a radius out from the
axis to the center of the inner edge of each tetrahedron.

For the second figure, a representation of the three-chain structure should be drawn.
This can consist of 25 tetrahedra and the connecting

Mr. Hayward
22/12/52

arcs, as in the first figure, and the same repeated after rotation through 120° and
240°. The molecule consists of three helical chains that are related to one another
by the operations of a three-fold axis.

It would be good also to have a perspective drawing showing all 20 atoms, plus five
more - the phosphate group to which the first phosphate group is connected by the
chain of atoms C_{5'}, C_{4'}, and C_{3'}. In this
drawing bonds should be shown connecting the atoms. The phosphorus atom is bonded
to the four oxygen atoms that constitute the tetrahedron about it. Then O_{III} is bonded to C5'. The other bonds are C_{5'}-C_{4'}, C_{4'}-C_{3'}, C_{3'}-C_{2'}, C_{2'}-C_{1'}, C_{1'}-O_{1'}, O_{1'}-C_{4'} (forming a five-membered ring), C_{2'}-O_{2'}, C_{1'}-N_{3}, N_{3}-C_{4}, C_{4}-C_{5}, C_{5}-C_{6}, C_{6}-N_{6}, C_{6}-N_{1}, N_{1}-C_{2}, C_{2}-O_{2}, C_{2}-N_{3}. The other five atoms to be shown, the other phosphate tetrahedron, are obtained
from the coordinate for the phosphorus and the surrounding four oxygen atoms by increasing
z by 3.40 A and increasing by 105°. I think that it would be wise in this figure
to show the helical axis, and perhaps the radii from the axis to the centers of the
inner edges of the two tetrahedra.

Please telephone me if there is any question in your mind about the nature of this
structure, or if you think that I have made some mistake in this description.

Sincerely yours,

Linus Pauling: W