"reading" Photo 51: Franklin & Gosling's fiber x-ray diffraction pattern of the double helix

You’ve likely seen “Photo 51” even if you didn’t know that’s what chemist Rosalind Franklin & Raymond Gosling’s 1952 masterpiece is “titled.” It’s that blurry X that unlocked the structure of DNA. Franklin and grad student Gosling took this image using a technique called fiber diffraction, which uses x-rays to reveal information about “molecular architecture”  based on how atoms in the molecules alter the waves’ paths. It’s related to crystal diffraction - but this famous Photo 51 is'nt from a crystal! Unlike in crystals, which give distinct spots all over the place, fibers made of polymers (chains of repeating units) diffract to give spots along straight & equally-spaced lines that are referred to as layer lines, which are at a right angle to the fiber axis http://bit.ly/fiberdiffractiondna
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The spacing between layer lines is inversely related to spacing behind repeating parts of the fiber. In DNA we have a couple different repeating things. A big repeating thing - a full turn of the helix. And small repeating parts - the nucleotides, These “DNA letters” have generic sugar (deoxyribose)-phosphate part & one of 4 ring-y “bases.” Although the bases are slightly different, they still have the same spacing and act similarly in terms of diffraction, because as we’ll see, the predominant scattering comes from the sugar-phosphate backbone (phosphorus has a lot of electrons to scatter from). And the bases are flat and hit “edge on” by the x-rays. So we can just consider all the bases to be the same for now. ⠀
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The inverse relationship makes it so that the closer together the bases are (more squished the helix) the further apart their layer lines are because diffraction patterns show us “reciprocal space.”
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X-shaped diffraction is characteristic of a helix - and comes from scattering from an individual, angularly averaged molecule (which is one way they knew they had a soluble fiber and not a crystal). By measuring the distance between the layer lines, and using Bragg’s law defining the conditions required for diffraction to occur, they figured out that the pitch, P, was 3.4 nanometers. One Å is 10nm, so 34Å is the distance between the further apart repeating units - the single helical turn.⠀
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What about the distance between the middle and the top (or bottom) where there are those big arcs? Those come from the bases themselves. Their further spacing in the diffraction pattern corresponds to closer spacing in the actual DNA. And if you measure this distance and plug it into Bragg’s law like we did above for pitch, you get an interbase distance of 3.4 Å (34nm). ⠀
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So, 34 Å per complete turn. And 3.4 Å per nucleotide. 34/3.4 = 10 nucleotides per turn. And a turn is 360°, so 360/10 = 36° turned per nucleotide step. ⠀
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To get our helix’s complete dimensions, we need to figure out its radius.
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We can pretend that we have 2 series of planes perpendicular to each other. The spacing between the planes is d and - getting trig-gy with it, it’s equal to Pcos(α), where P is our pitch & a is the angle in relationship to the horizontal. ⠀
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That’s in real space (what the x-rays encounter) - now we need to get back to reciprocal space (what we see in the diffraction pattern). So it’s back to inverting things. So our horizontal angle turns into a vertical angle - the fatter the pitch, the larger the real angle and the smaller the reciprocal pattern angle and vice versa. And we can measure this (now vertical) angle directly from the diffraction pattern, find it’s 40° and use the trig relationship tan α = P/4r to calculate that the radius is r = (34Å)/(4 tan 40°) = 10 Å (1nm)⠀
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Now to the Xtra bonus of figuring out what makes the X an X… So if we pretend we have mirror-like plates we’re bouncing x-rays off of, we can picture these waves bouncing off one family of planes and giving us one top leg of the X. And waves bouncing off the other family of planes to give us the other top leg. But we see 4 legs… And that’s because we don’t really have bouncing rays. Instead we have those wave generators broadcasting in all directions, so it’s also like you have x-rays bouncing off the planes from below - so this diffraction pattern repeats on the bottom and we get our full X. ⠀
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Or not quite full… ⠀
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Layer lines are evenly-spaced. And, based on the fact that these lines corresponded to the nucleotides being 3.4 Å apart, and the pitch being 34 Å, there should be 10 layer lines - but they only saw 9?! This told them that there’s a second strand to the helix - and it’s destructively interfering! In order to get complete destructive interference, the second strand needs to be shifted some fraction of P that results in their waves getting out of step by some multiple of half a wavelength so the peak of one is canceled out by the trough of another. Geometrically, this works out to needing to be one of a few different fractions, of which only 3/8 P made sense biochemically So, take 3/8 of P, where P is 34Å and you get a shift of 12.75 Å⠀