What the frack is fiber diffraction? And how does a blurry X Xplain DNA structure? You’ve likely seen “Photo 51” even if you didn’t know that’s what chemist Rosalind Franklin’s 1952 masterpiece is “titled.” It’s that blurry X that unlocked the structure of DNA. Franklin and grad student Raymond Gosling took this image using a technique called fiber diffraction, which uses x-rays to reveal information about “molecular architecture”  based on how the atoms in the molecules alter the waves’ paths. It’s related to crystal diffraction – but this famous Photo 51 is not from a crystal! And it was this non-crystal nature that provided the key to figuring out DNA’s structure.

I’m used to *crystal* diffraction, which I use to look at proteins, so I had to do some reading up on this very related but also different technique and hopefully I explain it okay! Both fiber & crystal x-ray diffraction have the same underlying phenomena, but they differ in some key ways (the most obvious being that fiber diffraction doesn’t require you to crystallize molecules – but does require the molecules meet strict conditions so you can’t just use it for anything – so don’t go ditching those crystal screens!)

The basic concept of x-ray diffraction – of any kind – is that x-ray waves get scattered when they run into the atoms making up molecules – an x-ray wave comes in, hits an atom and spreads out in all directions. And the scattered waves cross paths – sometimes constructively, adding together to give you a stronger wave – but sometimes destructively, effectively “canceling each other out.” We call the “scatter & add to strengthen” phenomenon diffraction and, if we capture the diffracted waves on a detector or a screen, we get marks called a diffraction pattern. The size & relative locations of these “hit marks” depends on the spacing of the atoms so, with some geometry & trig (don’t worry I won’t go too far into this!) you can work out things about how the atoms are arranged. 

But you’ll only get an interpretable pattern if strict geometric conditions are met – there has to be a repeating pattern of atomic spacings so that the waves don’t just all cancel each other out or add up unpredictably. 

In x-ray crystallography, the required symmetry is achieved by getting lots of individual molecules to ditch their full water coats (come out of solution) and organize themselves into an orderly 3D arrangement of “bricks” called “asymmetric units” (which can contain one or more individual proteins) called a lattice. The symmetry comes from comparing the asymmetric units – so for example an atom in one protein molecule is in the same place in its “asymmetric unit” as the corresponding atom in the protein molecule copies in each asymmetric unit. So even if the protein itself is wildly unsymmetrical (often the coolest ones are), you still have symmetry. So you’ll still get evenly-spaced wave scatterers leading to diffraction.

In fiber diffraction, the symmetry required for diffraction comes from inherent symmetry of the individual molecules, not from relationships between the molecules or units. For it to work, fibers have to have an axis of symmetry, such that you can “spin it” around that axis without changing the diffraction pattern. This axis of symmetry is sometimes referred to as the “fiber axis” or the “meridian” – and, since unlike in a crystal, the molecules in a fiber are free to rotate, a fiber can have a mix of different rotations around that central axis, but they’re all parallel to one another along that axis. 

So – we have these different ways to get symmetry. Now let me try to shine some light on why that symmetry matters. 

At the core of diffraction – from a crystal or from a fiber –  is light scattering. X-rays are “just” a really energetic form of “light” which is a term used to describe a broad spectrum of “ElectroMagnetic Radiation” (EMR). From low-energy, long-wavelength microwaves & infrared through the ROYGBIV of the visible rainbow, through ultraviolet (UV) & x-rays, we can think of EMR as consisting of little packets of energy called photons traveling in waves. Different kinds of light have different amounts of energy in their photons & the more energy the photons have, the shorter the wavelength (distance between peaks) & higher the frequency (peaks come closer together). 

more here: http://bit.ly/2QASc8h 

When x-rays hit atoms, they perturb those atoms’ electrons’ electric fields. Kinda like dropping some billiard balls in a pool, those electrons take the hit” and, instead of just reflecting the x-ray back, they absorb the energy & re-release it, becoming their own sources of waves. Since electrons orbit around the central core of atoms (the atomic nucleus), we can think of the atoms as a whole being the wave sources, which makes things easier to talk about/think of. 

So you have all those waves getting “broadcast” from the atoms – in all directions (we often just draw it in a single direction or in 2D for clarity, but these waves are spherical). And these broadcast waves will inevitably cross paths. 

When waves cross paths, it’s not like 2 physical walkers colliding with one another. Because these waves are *not* matter – they’re not physical stuff, they’re “just” energy. So they *can* occupy the same place at once. As a result, waves add through something called superposition – they can cross paths without changing one another, travel together, then come apart, then travel together – all without changing one another. They’re oblivious to the other’s existence. 

So then why do we talk about waves adding and canceling each other out? That just has to do with our perception of the waves. You can think of waves as kinda like walkers  – with the right step/left step cycle making up a single wavelength. Where in the stride you are (e.g. right leg, left leg, in the air, on the ground) is the “phase”

If you have 2 waves traveling together but exactly out of phase, one will peak when the other troughs (e.g. right leg of one person hits the ground at the exact same time as the left leg of the other person), and, as a result, the signals we detect are canceled out, but the physical waves are unchanged. Kinda like how you can use a “white noise” generator to “cancel out” the sound that you hear without interrupting the sound itself. 

In the case of diffraction, the “walkers” (scattered waves) are getting sent out by atoms that get hit by x-rays. They send out walkers in all directions, each taking the same length strides (same wavelength). And this happens everywhere the x-rays hit, so you  have a bunch of walkers traveling in all directions starting from different places. Diffraction occurs when walkers from different places are in step with one another along the same path.

Diffraction happens in all 3D but our detector is only set up to capture scattered rays coming its direction. What it will capture depends on the spacing of the “wave generators” (the atomic structure of the molecule) and its position in relation to where the light source is coming from, where the detector is, and what the wavelength of light is.  

If you have evenly-spaced wave sources, almost all the waves will cancel out because, for each wave, there’s almost always one completely out of phase to “destruct” it. But there are special spacing/angle/wavelength combos where the waves are out of phase by multiples of a complete wavelength – so it’s kinda like being one step ahead but still in sync. So they add together constructively and you get that strong signal we call diffraction. You can get diffraction if you’re one step ahead, or 2 steps ahead, or 3, or 4, etc. etc. corresponding to a wave having to travel 1, 2, 3, 4, etc. whole wavelengths further before it reaches the detector.  Mathematically this is reflected (no pun intended) in Bragg’s law. 

Phase shift depends on wavelength (λ), angle incoming wave hits (θ) & distance between them (d) & BRAGG’S LAW says that in order for constructive interference to occur, nλ = 2dsinθ. And we’ll come back to this later. But now let’s get to Photo 51 (not Area 51 which a Google search on it might lead you to…) 

X-ray diffraction techniques were introduced in the 1910s by von Laue and Braggs. Crystallography was all the rage those days, so a lot of scientists had a crystallography mindset – and toolset – Franklin herself was an incredibly skilled crystallographer. But it was the non-crystalline , fiber diffraction pattern that would prove particularly powerful. Rosalind wasn’t the first to get x-ray diffraction patterns from DNA fibers – Astbury & Bell tried it out in the 1930s, but they couldn’t get good enough pictures to deduce much. Even though Franklin’s Photo 51 might look a little blurry, it was super “clear”!

Franklin & Gosling found that they could get 2 very different DNA diffraction patterns depending on how wet the DNA was – a “dry” fiber of mini crystals they called A-DNA & a “wet” fiber of dissolved B-DNA. And it was only by “non-crystallizing” the DNA to get the B form (by using saturated salt solutions to control the humidity in the camera chamber) that they were able to get the crucial information needed to solve DNA’s structure. And to get such a clean image she had to do a lot of troubleshooting to tease the DNA into super orderly yet freely rotating strands. 

It is this B form, the most common natural form in our bodies, that is shown in Photo 51, which comes from a fiber diffraction experiment. Later we’ll get back to the A form. But for now, let’s look at how Photo 51 led to an understanding of DNA as a double helix with antiparallel strands and specific geometry.

Unlike in crystals, which give distinct spots all over the place, fibers made of polymers (chains of repeating units) diffract to give spots along strait & equally-spaced lines that are referred to as layer lines, which are at a right angle to the fiber axis. 

The spacing between these layer lines is inversely related to the spacing behind repeating parts of the fiber. In DNA we have a couple different repeating things. We have a big repeating thing – a full turn of the helix. And we have small repeating parts – the nucleotides, These “DNA letters” have generic sugar (deoxyribose)-phosphate part and 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. 

The inverse relationship makes it so that the closer together the bases are (the more squished the helix) the further apart their corresponding layer lines are. This is because diffraction patterns show us “reciprocal space.” If you want to learn more about the details of this, check out this post: http://bit.ly/2OfOUnO 

But to get the general idea, you just need to know that in reciprocal space, things that are closer together in “real space” are further apart. So the closer together the marks on the diffraction pattern, the further the physical spacings of the things they’re getting scattered from. 

Just like we can use different terminology to describe wave “sizing.” we can give special names to the geometrical dimensions of a helix. Pitch refers to how far you have to travel linearly up the fiber axis to get to the start of the next turn. If you want to refer to how far up you travel per base, you use a small p or an h (I’m gonna use h). And if you want to refer to how much turning you do between bases, that angle gets the abbreviation (Π). You can also talk about the different axises of the diffraction pattern – the “vertical” one that’s parallel to the fiber axis is called the meridian. And the “horizontal” one is called the equatorial axis. 

With that helix vocabulary now introduced, let’s put this new jargon to use!

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). If for example, you look at the A-form DNA diffraction pattern, this is a lot less clear because crystal diffraction spots are getting in the way… Later I will show you why a helix leads to an X but first let’s figure out the fundamental dimensions of this helix just by taking measurements from the diffraction pattern.

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. A nanometer (nm) is a millionth of a meter. Structural biologists prefer to talk in terms of Angstroms (Å). One Å is 0.1nm, so 34Å is the distance between the further apart repeating units – the single helical turn.

What about the distance between the middle and the top (or bottom) where there are those big arcs? What are those anyway? They come from the bases themselves and I will talk more about them in a minute. But, 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). 

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. 

That was the kinda math I like! Now for a little less comfortable stuff… To get our helix’s complete dimensions, we need to figure out its radius. So you have to add some trig to your Bragg’s law. But as a reward you get to see why we see an X!

I’m not one to brag about my trig, so I’m not gonna detail it out much, but basically, you might remember how we could pretend that our protein crystals where made up of families of planes bouncing off light. Well, we can do the same sort of thing with these fibers – 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. 

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)

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. 

Or not quite full… 

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?! What the frack happened to the 4th layer line?! Its signal must be getting stolen! This told them that there’s a second strand to the helix – and it’s destructively interfering! But why is only the 4th line’s signal getting “erased?” It has to do with how the strands are spaced! 

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 (molecules take up room so need enough space to fit). So, take 3/8 of P, where P is 34Å and you get a shift of 12.75 Å

There’s another region you don’t see signal – and once again, this nothingness is significant. Because there isn’t signal seen inside the meridian diamond, as would be expected if the phosphates were in the center (as early models by several scientists proposed), they figured out that the phosphates must be on the outside of the helix, with the bases facing in – which the “large” radius (a whole 10 Å!) told them there was room to accommodate. 

Many scientists thought that the bases would stick out, as this would allow easy access for reading. But facing in protects them from damage, which is good! But poses the issue of readability – thankfully, this picture cryptically revealed a solution to that problem too. The shift of 3/8P instead of 1/2 P makes it so that there’s an “offset” in the helix. While the diffraction consequence is a line lost, the biochemical consequence of this is sequence information more easily gained! The offset gives DNA a minor groove and a more open major groove. Proteins are able to “read out” the sequence of bases from the DNA from this major groove without having to unzip it. 

In Photo 51, there are big north and south meridian arcs – these come from scattering from the bases themselves. And their mere existence is informative – it tells us that in this B-form DNA, the bases are nearly horizontal. If they weren’t, the different bases would “look” too different to the incoming x-rays – and, since DNA has different letter combos, they’d cancel each other out. But, instead we get these big arcs at the top and bottom – if the bases were perfectly horizontal, these lines would be straight, so the arc-iness of it tells us they’re not quite flat. 

And this takes us back to the A-form DNA, the “dry form” – in the A-DNA, the DNA molecules were “partially dehydrated” – they had ditched some water contacts in favor of DNA-DNA contacts, leading to “micro crystals” in their fibers. So they actually saw some crystal diffraction spots in the first few layer lines.

In the A form, the pitch shrinks by ~20%  (P = 2.8 nm for A-DNA) with the squishing down accompanied by a “squishing in” of a another base, so that there are 11 instead of 10 nucleotides per helical period. And the squishing disrupts the horizontal-ness of the bases – they adopt a 20° tilt that makes it so that only 2 bases per turn are hit “edge-on” so you don’t get those strong meridian arcs. 

The crystal form was still useful – from it Franklin & Gosling figured out that it crystallized with a form of twofold symmetry perpendicular to the backbone axis. Knowing that DNA strands have a directionality, Crick deduced that in order to be a double helix, the strands must be antiparallel. 

And this takes us to the real downer part of the story – a coworker of Franklin’s – Maurice Wilkins – shared Photo 51 with Watson and Crick while Franklin was still collecting evidence and interpreting it, not quite ready to publish until she was more sure.  Watson and Crick then published their famous paper describing their interpretation of the image as the double helical structure of DNA, spelling out the geometry the picture revealed. Franklin died tragically young in 1958 & Watson, Crick, & Wilkins got the Nobel Prize in 1962. 

There are other DNA forms too – including a weird “Z form” that you can get with polynucleotides of alternating purine-pyrimidine bases like GCGCGC or ATATATAT and is actually left-handed. 

So I really hope that all made sense and I didn’t just confuse you! 

photo 51 paper: https://www.nature.com/articles/171740a0.pdf

more on topics mentioned (& others) #366DaysOfScience All (with topics listed) 👉 http://bit.ly/2OllAB0

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