We’ve been “looking” a lot at proteins, the main workhorses of our cells, which do everything from provide structural support to help mediate and speed up (catalyze) complex reactions.  We’ve “looked” a lot at the amino acid “letters” that proteins are made up of – and at the smaller parts called atoms those letters themselves are made of (individual hydrogens, carbons, oxygens, etc.). But how do we actually *look* at proteins and their parts? One way is with a technique called X-ray crystallography

All those pretty protein models you see in figures might make it seem like you’re looking at proteins directly. But, we’re doing all this “seeing” of proteins without actually seeing them – the reason we can see things is that when light hits a solid object, like the two things we’re trying to tell apart, some light waves get reflected at us and it’s the cornea & lenses’ job to take those light waves and bend them to focus them onto our eyes’ retinas. And photoreceptors in the retina send signals to the brain to interpret. 

But the light waves we use for X-ray crystallography are way too energetic for such focusing – they don’t get slowed down enough when they travel through glass so they wouldn’t get “bent” by a lens like visible light does – and they’d basically fry any conventional lens we tried to use to focus them (they’d even fry our detector so we have a “beam stop” in the direct path of the beam to absorb any of the concentrated rays that go through undeflected). Therefore, we have to work with evidence from the waves that scatter from the protein in the crystal.

I’m going to start with a brief overview, so if some of the terms don’t make sense yet, bear with me and I will explain them in more depth later – I just want to give you a big picture view first…

Basically, with X-ray crystallography, you get a protein to organize into a regular repeating pattern (a lattice) which we call a crystal. In order to do that you have to get the protein really really pure and then you take that dissolved protein and (through a lot of screening for good conditions) convince the individual protein molecules to ditch their watery coats (come out of solution) in an orderly manner, swapping some of their protein-water contacts for protein-protein ones. As I’ll get into, this isn’t always easy, but once you get a crystal, you can shoot X-ray beams at it. 

X-rays are “just” really energetic light waves and when they run into the electrons of the atoms making up the proteins inside the crystal, they get scattered. Kinda like dropping a ball in a pool, the electric field of X-rays perturbs the electron clouds surrounding the nuclei of atoms, causing them to deflect the X-rays (which came in as a strong “united” wave) into little “mini waves” going in all directions. And this happens in each of the lots and lots of individual protein molecules inside the crystal. Since waves have consistent properties and a crystal has a defined spacing, for each wave scattered, there’s almost always another wave exactly out of phase (e.g. one’s at a high point (peak) when another’s at a low point (trough)). As a result, most of the scattered rays will cancel each other out (destructive interference), but some will add together to give you a stronger wave (constructive interference). 

A “diffraction pattern” consists of a series of spots showing us where those strong “diffracted” waves hit a detector – and then we (our computers) work backwards mathematically from those spots to figure out where the electrons are that scattered them. It’s not quite that easy because we’re still missing something called “phase” information – we can tell how strong a signal is when it hit the detector (from the intensity of the spot) but not where in the wave cycle a wave was when it hit to give you that spot (was it at a peak? A trough? Somewhere in between?). We can infer phase information by using additional evidence from similar known structures (a method called molecular replacement), or by adding heavy atoms (such as mercury) and comparing the patterns you get with and without them, Heavy atoms give stronger signals and thus put “place markers” in the data to help guide us.

Once we have the intensities (from the original diffraction pattern) and the phase information, we use that combined data to generate an “electron density map.” These are typically represented as a meshy-looking things. Tthen – since we know that electrons orbit around the dense central part of atoms (the atomic nuclei) – we can build an atomic model (those sticky or ribbony things) into that mesh indicating the location of the center of each of the atoms that make it up. 

It’s usually just that final model that the science consumer sees, but there’s so much more cool science (and hard work) behind getting it. So let’s get into some more detail, starting with the crystal-making itself, as the quality of the crystal is of upmost importance. So how do we get good crystals? Well, first off, what exactly is a crystal?

Crystal composition

A crystal is “just” an orderly 3D lattice of repeating units – kinda like floor tiles but in 3 dimensions – if you know where one spot is on one thing you know exactly where in space the corresponding spot is in every other copy of the thing because there’s a “recipe” to follow – like stick one copy down, take 2 steps left and 3 up, stick another copy down, etc. 

The “identical tiles” in a protein crystal are called “unit cells” and they are made up of 1 or more copies of some unique part called the “asymmetric unit.” That asymmetric unit may itself contain one or more individual copies of the protein. A space group is the recipe for making one unit cell from an asymmetric unit and lattice translations are the recipes for making a whole crystal from the unit cells. Don’t worry too much about these terms (and they probably make more sense if you look at the figure). The bottom line I want you to see is that if you know what’s in the asymmetric unit and you know the layout of the crystal, you can figure out the structure of the entire crystal. And you can use the symmetrical layout of the crystal to help you figure out the structure of the asymmetric unit.

As I’ll talk about more in a minute, the reason why diffraction patterns from crystals are a series of distinct spots is because of a crystal’s symmetry. This symmetry is discussed in terms of 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 (the situation when waves constructively interfere to give a stronger signal).⠀

Unfortunately, getting these crystals to form from dissolved proteins is not always easy… 

Crystallization (hopefully without complication!)

When something is dissolved, each molecule has a full coat of water, but to crystallize, something (like our protein) needs to come out of solution. This means it needs to  “prioritize” contacts to things other than water – like other protein molecules. So, for instance, it swaps some of the water molecules it was coated in, for interactions with other protein molecules. But the tricky part about crystals is that, while they represent optimal packing layouts, they require coordination because all the molecules have to arrange themselves the same way. And if they do it in different ways you just get clumpy protein “aggregate”

Coordination takes time (think putting together a jigsaw puzzle “properly” vs just tossing all the pieces into a box). So if you don’t give molecules time to coordinate, they can’t crystallize. We can therefore use speed-up tactics to prevent crystallization when we don’t want it to occur, such as when we’re storing protein after purifying it and don’t want the water in and around the protein to crystallize and damage our protein. To prevent that unwanted water crystallization we can “flash freeze” our protein by dunking tiny tubes of it into liquid nitrogen to rapidly cool them, preventing the formation of ice crystals.  

But with X-ray crystallography, the situation’s different –  we *want* crystallization (but of our protein and not of water!) so we want to *slowly* promote grouping together. 

How do we slow things down? There are a lot of different techniques for doing this. The one that I’ve used the most is “vapor diffusion,” mostly “hanging drop” crystallization. Basically you stick a drop of liquid containing your protein on a glass slide and then you flip the slide over and use it as the “roof” for a well of protein-less liquid (reservoir). Since this reservoir liquid is more concentrated than the drop liquid (because the reservoir hasn’t been diluted with your protein), water evaporates from the drop to help “dilute out” the reservoir (that’s not really its goal – it’s trying to escape the well altogether but there’s a lid, so it gets pulled in by the reservoir). This leaves less water available to surround the protein molecules. So the protein molecules start binding to each other instead – hopefully in the coordinated fashion that leads to nice crystals. 

In addition to simply removing water, we promote crystallization by optimizing the pH (acidity), salt types & concentrations, protein concentrations, etc. When you see “optimize” think “troubleshooting” and LOTS and LOTS of “trial and error” – since each protein is different and has different binding opportunities to offer up to other protein molecules and different types of interactions are favored in different conditions, the ideal “crystallization cocktail” varies from protein to protein and is normally unpredictable. Therefore, we usually carry out extensive screening – we even have liquid dispensing robots to help us do this with tiny tiny volumes so that we can test hundreds of combinations without needing a ton of protein (you still need a lot of protein though because it needs to be at a high concentration so the molecules can find one another okay – and this can be a major limitation of crystallography).

We also have a microscope robot that takes pictures of our crystal trays for us over time so that we can see if crystals are forming in any of the wells. If we get any hits, we can then optimize around those conditions in order to get even better crystals. Once our crystals have grown and stop growing (could be days to weeks to months depending on the crystal) we have to fish them out with little loops, freeze them with cryoprotectants, and store them in liquid nitrogen dewars (basically really insulated giant thermoses) to keep them super cold until we’re ready to collect diffraction data from them. 

We put all that effort into getting great crystals because the quality of the crystal will influence the “resolution” of the data you collect.

Resolving confusion about resolution

Resolution refers to how close together 2 things can be before you stop being able to tell that they’re 2 separate things (so “higher resolution” has lower numbers). It’s like if you have 2 asterisks * & *. If they’re really far apart, it’s easy to see there are 2 of them: *_____________*. But as they get closer together, it becomes harder to tell them apart: *_*. And at some point, they’ll be so close together you’ll see it as a single thing **. Another way to visualize it is being able to tell two distant light sources apart; Is that one star or 2? Or a whole galaxy? The cutoff point will be slightly different for different people depending on how good their eyesight is. 

At low X-ray crystallography resolutions, it’s harder to be confident about the position of things like side chains (the unique parts of amino acids that stick off the generic backbone) because they move around more and tend not to produce as strong of a signalX, but we can make out things like the protein backbone and secondary structure (helices (like spiral staircases), strands, etc.). Once you get to higher resolutions, you start to be able to make out the side chains & their orientations. The exact cutoff point is a bit subjective, but we tend to call structures with resolution at or better than 1.2 Å (an angstrom is 10⁻¹⁰ meters, 0.1 nanometers (0.1 nm)) “atomic resolution” because we can confidently make out the location of all the atoms. BUT this is rare in protein crystallography. The average published structure is ~2 Å, but you only need about 3.5  Å to start making out those helices and stuff. Plus, resolution is not the only thing that matters, it’s just one of the easiest things to really quantify and report (and explain).

In practice, our resolution is usually limited by our samples (any tiny defects in the crystal lattice or slight variations between individual protein molecules can get them to deflect light slightly differently and thus “fuzzy up” the signals a little, making them harder to interpret). But, assuming you have a perfect sample, you are still limited in the resolution – this time from your light source, so let’s talk about that next. 

Let there be really energetic light!

X-rays and visible light might sound like 2 really different things, but X-rays are really just a much more energetic form of visible light – or visible light is just a much less energetic X-ray. They’re both forms of ElectroMagnetic Radiation (EMR), a spectrum which includes everything from microwaves, radio waves, and infrared through visible light and ultraviolet (UV) light and X-rays. The reason we have to use X-rays and can’t just use visible light which is so much easier to work with is that the wavelength of visible light (distance between 2 peaks) is way bigger than the distances between the things we’re wanting to resolve. Kinda like how you wouldn’t use a yardstick to measure a hair, you can’t use radio waves to look at proteins. 

All of these types of light are made up of little packets of energy called photons that travel in waves, but they differ in how much energy they have in those packets and thus how much they “wiggle.” All forms of EMR travel at the same linear speed in a vacuum (the speed of light through air is c=3*108 m/s). So if you were to beam a laser and an X-ray from the same place at the same time, the wavefront would arrive at a detector at the same time (though you would only be able to see the laser). BUT the photons in the X-ray beam will have traveled up and down many more times on the way there because they have more energy. It’s a bit like if an energetic little kid goes on a pogo-stick walk with his less-energetic grandpa. The kid might hop up and down more on the way to use up some of that energy without getting ahead of grandpa. Similarly, the more energy a photon has, the higher frequency the waves are (the pogo stick hits the ground more times in any given period) and, since it’s traveling the same overall distance, the peaks have to come closer together (shorter hops).

In more formal, less pogo-sticky terms, we can describe waves in terms of their wavelength (λ) (the peak-to-peak distance), their frequency (# of peaks that will pass through a fixed point in a certain amount of time), or the energy of their photons (E). The energy of a photon is directly correlated to the frequency via Planck’s constant (h = 6.626*10-34 Js) via the equation E=hf. And the frequency is speed of light over wavelength (c/λ) – put that into the equation and you get 

E=hf=hc/λ

In words,

higher frequency light requires higher energy photons and corresponds to shorter wavelengths

lower frequency light -> lower energy photons -> longer wavelengths

So how does this relate to resolution? Optical physics says you cannot achieve better resolution than ~1/2 the wavelength of the light you’re using to tell things apart. And in crystallography we want to tell apart things that are REALLY close together – the length of an average carbon-carbon single bond is ~1.54Å and the length of an average carbon-hydrogen bond is ~1.09Å. The most energetic visible light has a wavelength of ~700 nanometers, so ~7000 Å. We need something on the same order of magnitude as what we’re looking at, so we turn to X-rays, which range from 0.01-10 nanometers (so 0.1-100Å). For protein crystallography, we usually use X-rays with wavelengths of ~1 Å.

Getting that high energy light requires a lot of energy input. A LOT of energy – and you need the X-rays to be traveling in a really straight path and all have the exact same energy, so you can’t just go to Home Depot and buy yourself an X-ray flashlight. Instead, we usually go to synchrotrons (though we also have a less powerful “home source” at our lab). I’ve gone to Brookhaven National Laboratory (BNL)’s NSLSII synchrotron a couple of times and have collected data remotely from Lawrence Berkeley National Laboratory (LBNL)’s ALS synchrotron once – in such “remote collection” situations you ship your protein crystals to them and then you control the robot from any computer. Remote collection has become all the more important these days because robots are great at social distancing!

A quick overview of how a synchrotron works (cuz it’s cool) – electrons (e⁻) are produced by an electron gun (similar to those in cathode ray TVs but on a MUCH bigger scale). It generates e⁻ through thermionic emission – basically if you get a metal super hot it starts to lose e⁻. And since electrons are negatively charged, if you put a positively charged electric field nearby it will yank them away. In this case, it yanks them into a linear accelerator (LINAC) which has chambers of positive charge that attract the e⁻ & cause them to accelerate (near the speed of light) towards a booster ring where a series of magnets direct them to travel in circles. Some of the e⁻ are then fed into the storage ring which uses a series of magnets to get the electrons to change course and give off photons of different wavelengths that get separated and sent to “beam lines” & workstations where we can stick protein crystals in their path. More here: http://bit.ly/2z0JjwR

So, you have the protein being beamed with X-rays. Now what?

X-ray scattering and diffraction

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 and re-release it, becoming their own sources of waves. Since electrons orbit around the central core of atoms (the atomic nucleus which contains positively-charged protons and neutral neutrons), 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 combine (“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 almost like walkers, with the right step/left step cycle making up a single wavelength, and 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 an active noise canceler 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” is a term we use to describe the situation where walkers from different places are in step with one another along the same path and it requires certain conditions as we’ll see.⠀

Diffraction happens in all directions (at least in theory…) but our detector is only set up to capture scattered rays coming in 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 (and how big) the detector is, and what the wavelength of light is.  ⠀

If you have evenly-spaced wave sources, almost all the waves will be canceled 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 (how far ahead a wave is compared to another) depends on wavelength (λ), the angle the incoming wave hits (θ) & the distance between them (d). Bragg’s Law says that in order for constructive interference to occur, nλ = 2dsinθ.

Although this is *not* what’s happening on the single atom level, we can think of “slicing” crystals into families of evenly-spaced planes called Bragg planes which correspond to positions where the conditions would make Bragg happy (places where constructive interference can occur). We can mathematically imagine these planes acting as mirrors, bouncing off incoming X-rays (but remember scattering is really atoms giving off their own “mini waves”). The reason such virtual slicing works is that an incoming X-ray wave hits one plane before the one under it, so it has to travel further to reach the lower plane & the reflected ray has to travel further to reach the detector. Bragg conditions are those needed for combined length of “detour” to be an integer # (n) of λ so waves get back in sync.

The waves diffracted from the planes represent the sum of signal from all the atoms in between that plane and the one under it. So the closer together the planes are, the more you can learn about individual atoms – like looking at the average income of everyone in the US vs the average income of a neighborhood. Going back to the concept of “resolution” we can say that the thinner the slicing of the Bragg planes, the higher the resolution. 

A crucial thing to keep in mind though is that each family of Bragg planes is giving you info about a “virtual slab”: // or || or \\. And you need to get slabs in all different directions in order to really get a sense of what’s going on, so you rotate your crystal a bit when it’s getting X-ray hit :). And then you measure diffraction from different angles. 

The signal from each family of planes will show up as a spot on the detector (in the olden days they actually used films, but now-a-days detectors measure the photons directly). The thinner the slicing of a family, the further from the center of the diffraction pattern the spot will be (and typically the fainter it will be sadly…) This means that the highest resolution information is found in the outermost part of the diffraction pattern. But the lower res (but “high quality”) information in the center of the pattern is crucial for doing all the computational work in the next step…

Figuring out what the diffraction data means…

This next step is working backwards from that diffraction data to figure out where the molecules are that created the pattern. First you have to process the data, which involves combining information from images of the diffraction pattern from different angles. Then, in order to reconstruct the molecule based on the waves it gives off, you need to “determine phases” which can be really difficult….We can measure the intensity of each spot to get that wave’s amplitude (peak height) but not its PHASE (how “in step” it is relative to all the other waves the crystal is giving off) & we need both! There are different ways to solve this phase problem including strategies such as SAD (Single-wavelength Anomalous Diffraction) or MAD (Multi-wavelength Anomalous Diffraction) which use heavy atoms (things like selenium and mercury which have a lot of electrons so they offer the X-rays more things to run into & get deflected from) or using a similar protein as a reference (a method called molecular replacement). 

Once you figure out the phases you can generate an electron density map (the thing that looks like a mesh). The electron density map shows locations of the atoms that caused the scattering . After this you can build an atomic model into that map – you put in the sticks or balls or cartoons or however you want to visually represent the location of the atoms which the electrons surrounded. 

cool sidenote: you might be familiar with the “ribbon diagram” representation of proteins, where alpha helices show as beautiful coiled ribbons and beta strands as flat arrows. That system of representation was developed by a brilliant scientist and artist named Jane Richardson whom I have had the pleasure of meeting several times when she’s come to teach in the CSHL X-ray crystallography course. http://bit.ly/2Qcqmhn 

However, you can’t just stick atoms in your map willy-nilly, you have to refine it using software (such as Coot, Phenix, CCP4) and then validate it (with software such as MolProbity and your knowledge of biochemistry) to make sure it makes sense biochemically & fits experimental data. 

Finally you can deposit the coordinates to the Protein Data Bank (PDB) so anyone can view & analyze them. I recommend people check out PDB 101 if they want to learn more. https://pdb101.rcsb.org/learn/guide-to-understanding-pdb-data/introduction

⠀Huge thanks to everyone who provided feedback and suggestions during the making of this post!

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