22 December 1952
Mr. Roger Hayward
920 Linda Vista
Pasadena 2, Calif.
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 C5', C4', and C3', 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
C5', C4', and C3'. 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
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 C5', C4', and C3'. 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 OIII is bonded to C5'. The other bonds are C5'-C4', C4'-C3', C3'-C2', C2'-C1', C1'-O1', O1'-C4' (forming a five-membered ring), C2'-O2', C1'-N3, N3-C4, C4-C5, C5-C6, C6-N6, C6-N1, N1-C2, C2-O2, C2-N3. 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.
Linus Pauling: W