Now that we've discussed tomography and single particle analysis. The third basic modality in 3D EM is electron crystallography or sometimes, 2D crystallography and two-dimensional crystallography is the preferred approach when you can purify a large number of copies of your object of interest and you coerce it to crystallize. And the first thing we'll talk about is how do you get a protein to crystallize into a two-dimensional crystal. So part of the answer is that some proteins naturally assemble into 2D arrays that are immediately useful for 2D crystallography. So, an example of this is the protein bacteriorhodopsin. Bacteriorhodopsin is a integral membrane protein with seven transmembrane helices and certain bacteria express so much bacteriorhodopsin that they pack their membranes full of it and it spontaneously forms a well ordered 2D crystal. As can be seen in this image from Niko Grigorieff where one of these crystals was imaged and so you can see this is a bacteriorhodopsin molecule. Here's another one and here's another one. So they form trimers and then these trimers organize themselves. They're closely packed into a beautiful 2D crystal. Another example of a protein that naturally assembles into a well ordered thin 2D array is aquoporin. Aquoporin is found in many places. In one case, it's present in the membranes of the lens of your eye. And there it's found to bridge between two membranes. So here's one membrane and then there's a gap and there's another membrane. And aquoporin is found to bind across these membranes. Here's one aquoporin molecule binding to one in the other membrane and link them close together. And in addition to linking close together across the membranes, they also self-assemble in to well ordered arrays within each membrane. And so looking at them in the electron microscope, this is an aquoporin crystal. It's very flat and large and the proteins are already well ordered. If however, you want to crystallize a protein that doesn't naturally self-assemble into well ordered 2D arrays, one approach that can be taken has been called the Lipid Layer Crystallization technique. And here, you have a solution of your protein and you deposit a monolayer of lipds on the interface betweenthe water and the air. The hydrophobic tails stick up towards the air and the hydrophilic heads embed into the solution and form this nice monolayer. Then if your protein of interest has some affinity for the hydrophilic head groups, the protein will concentrate right on the air water interface. And because the lipid monolayer is still fluid, the proteins can still rearrange. And so, if there's by chance a nice contact that causes one to bind in a regular pattern up to its neighbor, this can propagate and into forming a 2D crystal. So here, for example is an image of a 2D crystal of RNA polymerase two, which was formed by this Lipid Layer Crystallization technique. One of the ways to engineer a nice interface between the lipids and the protein of interest is to use nickel NTA lipids and then a his tag to your protein of interest. And once the crystal forms on the air, water interface, then sections of that crystal can be picked up on EM grids, represented here by this slab. You can carefully pick up those crystals onto the EM grid. Now, once the 2D crystals are on the EM grid, they can be stabilized by being embedded in either some material that can dry and remain at room temperature or they can be embedded in vitreous ice through plunge freezing. So here's an example for instance, from this paper in Methods in Entomology, where several 2D crystal seen here. Here's another 2D crystal, here's a third 2D crystal have been embedded between two layers of continuous carbon film in a trehalose solution. So you might have a continuous layer of carbon and then a solution with your 2D crystals in it and into that solution, you can add a sugar like trehalose. And then as that dries, you can add another carbon film on top of that and let the water dry and it embeds the 2D crystal in the sugar sandwiched between two layers of carbon and that's one way that they can be observed. Alternatively, the 2D crystals can be spread into a thin film on the EM grid and plunge-frozen, just like we've described in other circumstances. So here is the extent of a 2D crystal that has been plunge-frozen on a quantifoil grid. You can see the regular pattern of holes in that carbon surface. This is just a beam stop that's been inserted into the field of view, but this is what a frozen hydrated 2D crystal looks like.