Now having talked about how to obtain 3D information from projections, let's move on to the third fundamental challenge in biological EM, which is dose limitations. Dose limitations are imposed by the fact that the high energy imaging electrons break the bonds within the structure that we're trying to image. This is a movie that illustrates the kind of damage that happens to cells when they're bombarded by the imaging electrons. So in this movie, you'll see three bacterial cells. Here's one. Here's the second cell and here's the third cell. And these have been plunge frozen on an electron microscope grid and inserted into the microscope. And each frame of the image will be using ten electrons per square Angstrom. And we'll just take image after image after image and you'll see the results. So, as the electrons begin to hit the cells, you'll see that the density's inside become more fuzzy and then eventually the membranes first and then other density's inside begin to bubble. So clearly, after many, many electrons have hit the sample, the sample structure has been destroyed. What is happening is that as incident electrons come and hit the sample and they break covalent bonds. First of all, the atoms that used to be bonded together now are no longer bonded and they want to be further apart than they used to be. In addition, small fragments of molecules can be released as gases. For instance, methyl groups can be liberated or maybe carbon dioxide or a carbon monoxide or maybe an oxygen molecule could form within the ice as it's being irradiated. And in spot that these small molecules can diffuse through the water, but inside of a cell, sometimes the density is higher and so they can't move as quickly and so they build up and produce a little gas bubble that expands and produces those little bubbles. It's been noted that bubbles tend to aggregate on carbon surfaces and the onset and rate of bubbling are highly dependent on the nature of the buffer and also the material that's being irradiated. But in any case, these bubbles distort the structure of our sample and prohibit further imaging. Now, we could take a closer look of this damage by looking at specific images of protein complexes with different doses. So, in this first set of images here, I'm showing pictures of a protein complex called hemocyanin. Hemocyanin is a very large, barrel-shaped protein and these pictures are of eight different hemocyanin particles, four on the bottom and four on the top. And they were plunge frozen on an EM grid and imaged and they were in different locations of the grid, but we simply cut out the pictures of each of these particles and arranged them in two nice rows here, so that we could look at them carefully. And so this first image was taken with ten or twenty electrons per square angstrom, then we continued taking pictures of this same field of particles. And after we had exposed these particles with 120 electrons per square angstrom, now their structure looks a little bit degraded. If you look and carefully compare say, this top view of a barrel to this top view of a barrel, this is the, the same complex here in this image is the, the same complex down here, it's just after another 100 electrons per angstrom have been delivered. You can see that the crispness of the boundaries has been lost and the particles are starting to degrade. If we continue that process after we had invested another 80 electrons per square angstrom, we see that the particles were even further degraded more and more fuzzy, less distinct. And finally, we continued the dose series out to 350 electrons per square angstrom. And now you can see that the general shape of the particle is still evident, that it's a barrel, but the details are lost. For instance, here you can no longer see that it's a stack of six layers as you can see in the very first few images. You can see that the barrels are stacks of specific layers, and that's lost by the end. A good way to measure how quickly radiation damages the structure of an object is to image two-dimensional crystals. And so here's a picture of such a crystal. You can clearly see that the object in this pattern is arranged in a lattice with lattice lines like this and each of the unit cells here, in this case, happen to contain two molecules of RNA polymerase two. RNA polymerase two will form these two dimensional crystals and one of these crystals was prepared on EM grid and stained and this is an actual image of such a crystal. Now remember, from previously in the course that in the electron microscope if here is the object electrons will scatter off of the object and be collected in the back focal plane of the microscope and will then re-interfere below on an image plane. Now, if the object itself is a crystal, then its diffraction pattern will be a regular lattice of bright spots. And further remember that there are additional lenses in the microscope and ultimately, there's a detector. And if we put the microscope in diffraction mode, then the detector is on a conjugate plane with not the image, but rather the diffraction pattern of the sample. So the detector is made conjugate to the back focal plane where this diffraction pattern is present. And so, in such a situation where we're taking a picture of a crystal, what we see at the bottom of the microscope on the detector is a magnified image of the defraction pattern. And on this magnified defraction pattern, remember each spot represents one of the Fourier components of the crystal of the object here. And so, it has an amplitude and a phase and this spot represents how many densities are in the object at a particular spacing. Now further remember that here in our crystal, let's imagine this as a crystal of this pattern. There's one here and there's an, another unit cell right here. There's another unit cell right here. Remember that the scattering at low scattering angles, here's a low scattering angle. These low-scattering angles represents the number of scattering centers that are at this distance apart from each other. In other words, the low angle scattering represents how much of a pattern of density is there with this kind of distance between it in the sample. And scattering at higher angle, for instance, at that angle, reveals how many scattering centers are at in this case, a distance this far apart from each other. Because it's this distance that gives rise to constructive interference in this direction. And so, if there's a lot of scattering centers that are exactly this far apart in the object, then you get strong scattering in that direction. And finally, scattering at even higher angle represents how many scattering centers are at very small distances apart from each other. Okay. So the scattering to high angle represents the high resolution order within the sample. And so, as we look to this magnified image of the defraction pattern, a spot here represents a low resolution component of the crystal. Basically, how far apart are the unit cells and a spot out here at the periphery of the defraction pattern. Tells us how many scattering centers for instance, atoms or maybe alpha helices are in a regular pattern of a certain distance apart and, and this spot represents very small distances. What this all leads to is that, as this crystal is imaged in the electron microscope, the electrons will break the proteins forming the crystal. And as side chains are damaged and bonds are broken, the details of the structure will be destroyed first. But even though a lot of these bonds may be broken in all these proteins, nevertheless the nuclei of the atoms remain in roughly the same place. They start to smear out a little bit, but they remain roughly in place. And so the low resolution structure of the crystal remains. In other words, the idea that there is a protein there and a protein there and a protein there. That information remains within the crystal, even after extensive electron damage. So now, we're prepared to understand the results of an important experiment. That was published in 1996 where Holger Stark and his colleagues imaged a crystal like the one that I just shown. And what they did is they, they plotted the intensity of certain defraction spots as a function of dose. So, on this axis, they're plotting dose applied to the crystal in electrons per square angstrom. And so, it starts with no dose and then after one, two, three, four, five electrons per square angstrom were applied. And on this axis, they're graphing the spot intensities in on an arbitrary scale and notice that it's logarithmic. And so they're plotting the intensities of two particular spots. One of the spots represents structural order at seven angstroms. In other words, it represents a sine wave that oscillates up and down every seven angstroms. So for instance, alpha helices in a packed protein are, are close to seven angstroms apart. And so that spot tells you how, how well the original alpha helices are holding up to the radiation damage. And this experiment shows that after just about two and a half electrons per square angstrom, the intensity of that spot falls by orders of magnitude. And so, after just a couple electrons, even the relative positions of the alpha helices is destroyed. Now that part of the experiment was done at room temperature. And after methods have been developed to freeze samples, it was quickly noticed that cold samples seemed to resist radiation damage. Or at least, the effects of radiation damage are slowed in on a cold sample. And so Holger and his colleagues redid this experiment at 98 degrees Kelvin. And now the seven angstrom spot here, you can see is still the intensity is still decaying, it decays more slowly now than it did at room temperature. In fact, even after three electrons per square angstrom, it's only decayed by about half. They're also at this temperature able to measure the rate of decay of a spot that represents three angstrom structure within the sample. So this would be the details of the positions of the side chains, for instance. And what they were able to measure is that that information is lost rapidly after only three electrons per square angstrom it, it is lost by orders of magnitude. Now the preservation of structural detail at colder temperatures led people to wonder, what would happen if we cooled the sample to more like a few Kelvin? Could we then use even higher doses to image it before the structure was lost? This led to the development of microscopes that, where the sample could be kept in thermal contact with liquid helium. And when this experiment was repeated at four degrees Kelvin, now you see that the structure at seven Angstrom resolution is preserved even longer. So that it only falls by about 30% after five electrons per square angstrom, even the high resolution detail at three angstrom resolution, at least there was a tenth of it that still remained after four electrons per square angstrom. While liquid helium cooling appears to preserve fine protein structure against radiation damage, there are some disadvantages. These images that I showed previously were recorded at about 82 Kelvin under liquid nitrogen cooling. We repeated the experiment with liquid helium cooling, where the samples were kept at more like 12 Kelvin. In this case, what we're seeing is that the first images were very similar. But later, the protein density faded against the background and became less visible, lower contrast. Until the particles were nearly invisible against the water background. And finally, after 350 electrons per square angstrom. There was severe bubbling noticed in the locations of the protein complexes. So the visible contrast in the protein complexes was replaced by the same pattern of bubbles. It turns out that the lowest free energy state of water at very low temperatures like 12 Kelvin, it's a high density amorphous state. So, it's not crystalline, it's still amorphous just like liquid water or plunge frozen vitreous ice, but it's higher density. Meaning that if you take a protein solution at room temperature in liquid water and then you plunge freeze it into liquid ethane, the water and the protein molecules stop moving where they are and it's a native life-like state. But if you further cool the sample below about 40 Kelvin and then begin to illuminate the sample, so that the incoming electrons give the water molecules just enough energy to rearrange. They will rearrange and what they do is collapse into a more dense victorious state. When they collapse, their density more closely matches the density of protein. And therefore, proteins are contrast matched and become nearly invisible. Further more, it appears that the radiolytic fragments that are released by electron imaging are not able to escape outside of the high density amorphous ice that forms under liquid helium cooling. And because of this, many bubbles form right in the locations where the protein used to be. As a result, for imaging applications where. Significant doses are going to be used. Cooling with liquid nitrogen turns out to be optimal. It helps preserve the structure of the proteins without inducing the further collapse of the amorphous water. So, because the electrons destroy protein and other macromolecular structure as we're trying to image it. How will we overcome such a dose limitation? The answer is that it cannot be overcome if we have a unique object that we're trying to image. However, if we're interested in an object that we can purify so that we have a large number of identical copies. Then we can overcome radiation damage by imaging a large number of identical copies with low doses. So for instance, here's a picture of Hemocyanin. As I introduced before, it's a barrel-shaped protein. Here's the side view. Here's an end view. And as you can see, here's a field of purified Hemocyanin particles. And they were spread into a thin film and plunge frozen on an EM grid, and this is a projection image. And if we take a low dose image, we begin to see the structure of each of those particles. Now if we're able to average the information from each of the low dose images and combine all that information, we can achieve what is the equivalent of a single high-dose image. In each low-dose image, there's a lot of noise, shot noise. Because of the randomness of the electrons and how many electrons will hit one pixel verses the other. But each of these low dose images will have different shot noise present, and so by averaging a large number of low dose images, we can overcome that noise and obtain a high signal to noise ratio image of the object. Now, this is easiest when our object of interest can be coerced into forming a crystal, as in the example of the Arnay Pomeroy's two molecules that I brought up earlier. Because in this case, each of the objects is regularly arranged, it becomes much easier to average the information across that image. So our best idea of how to overcome dose limits is to record low-dose images of a very large number of identical objects and then average those images. And the combination of these three fundamental challenges, how to preserve native structure, how to obtain 3-D information from projections, and how to overcome dose limitations, leads to three basic approaches in Cryo-EM. In the case where we have a single unique object that we'd like to study, for instance, an entire cell, we'll never be able to find another cell that's exactly like this one, then we use the approach called Tomography. And we'll take this single cell and we'll image it from many different directions and combine all of that information into a single 3D reconstruction. The fundamental resolution limit in Tomography is radiation damage. Because we simply can't get a high signal-to-noise ratio 3D reconstruction to high resolution before the sample is destroyed by radiation damage. And so in practice, resolutions of about four nanometers are obtained on unique objects using Tomography. However, in the case where we can purify a large number of identical objects, then we can begin to overcome radiation damage by averaging low dose images. In single particle analysis, such a large number of identical objects are purified and then imaged. Here again is the image of Hemocyanin, and as you can see, each copy of this protein complex exhibits a different orientation in the ice. And by recording low dose images of all of these particles and then combining them, we can obtain a high resolution three dimensional reconstruction. Now here, a significant resolution limitation is how precisely we can determine the relative orientations of each of these particles and average their information. But in many cases now, this has been possible to allow near-atomic resolution reconstructions where atomic models can be built into the density. Finally, in the case where we can purify a large number of identical copies of our object of interest, and we can coerce them to crystallize. Then the precision to which we can orient each of the unit cells, the precision to which we can average the information present in the image of a crystal goes up. And so, we do what's called two dimensional crystallography. And two dimensional electron crystallography has produced some of the very highest resolution protein structures that are known to date. So now we'll turn our attention to the particulars of these three basic modalities of Cryo-EM. Tomography, Single particle analysis, and 2D crystallography.
