# DNA Structure: Puzzle Number 4

clive delmonte clived at ndirect.co.uk
Mon Nov 30 04:25:53 EST 1998

```Marvin et al. (5) drew fibres of the lithium salt of C-DNA in both hexagonal
and orthorhombic lattices. In a hexagonal lattice of side 3.5nm., systematic
absences followed  (-h+k) =/=3n for l=0, and (-h+k)=3n when l=1 or 2.

Streaks were found on several layer lines and could be explained by
molecules having a random axial translation of c/2, without using the
systematic absences, according to Marvin et al.

Fuller et al. (6) state that such a pattern of systematic absence allows the
choice of a hexagonal unit cell of side reduced by root 3.

Marvin et al. chose a unit cell large enough to accommodate a double helix.

If we elect to reduce the unit cell size, a double helix cannot be
accommodated, and we find that the maximum, outer helix diameter is

(3.5nm/root 3) x sin60 x 2/3 = 1.2 nm

In an orthorhombic lattice, where Marvin et al. found a=3.22nm and b=2.02nm,
large enough to accommodate a double hlix, they report that systematic
equatorial absences follow h+k=2n+1.  This pattern of absence is reported by
Langridge et al. (7) to allow the halving of the long side to form a new
reduced unit cell.   In an orthorhombic cell with a=2.02nm and b=1.61nm, a
double helix cannot be accommodated, and we find that the maximum outer
diameter of a helix is now 1.3nm.

Again, the observed streaks in the orthogonal pattern could result from a
random axial displacement of duplexes of c/2, according to Marvin et al.  If
we elect to explore the implications of a random axial translation of c/2,
utilising the layer line streaks as evidence, we are able to use the
systematic absences in both lattices to choose a smaller unit cell in each
case.

Applying Stokes' equation to the helical cross of Li DNA in the Langridge
paper, we find delta = 41 degrees and the helical diameter to be 1.22nm.

A DNA helical diameter of 1.2 to 1.3 nm is therefore deducible directly from
the STM work of Lee et al. (Puzzle 1, ref. 1) (and many other AFM &STM
studies), or by applying Stokes' equation to Franklin's B-DNA diffraction pa
ttern (Puzzle 2, ref. 2) and to diffraction from Li DNA in the C form (7),
or from James and Mazia's surface film of B-DNA (Puzzle 3, ref. 4).

A very wide range of entirely separate experiments suggests that the helical
diameter of the major diffractors (the sugar-phosphate chains) is 1.2 to 1.3
nm.

5        The Molecular Configuration of Deoxyribonucleic Acid.  III.  X-ray
Diffraction Study of the C form of the Lithium Salt; D.A. Marvin, M.
Spencer, M.H.F. Wilkins & L.D. Hamilton; J Mol Biol Vol 3 (1961) 547 - 565

6        Molecular and Crystal Structures of Double-helical RNA; W. Fuller,
F. Hutchinson, M. Spencer & M.H.F. Wilkins; J Mol Biol Vol 27 (1967) 507 -
524

7        The Molecular Configuration of Deoxyribonucleic Acid.   I.; R.
Langridge, H.R. Wilson, C.W. Hooper, M.H.F. Wilkins & L.D. Hamilton; J Mol
Biol Vol 2 (1960) 19 - 37
----------------------------------------------------------------------------
Clive Delmonte

```