Cryo–electron microscopy breaks the atomic resolution barrier | Hacker News Reader

Cryo–electron microscopy breaks the atomic resolution barrier

sciencemag.org

377 pointsnathandaly91 comments

Cryo-EM is such a powerful and important tool in biochemistry that any advancement is bound to have significant impacts. Its difficult to overstate how powerful a tool this is and how widely used it is to understand protein structures. Essentially, it let's you see what proteins look like, with some significant advantages over previous techniques like xray crystallography for many use cases. The technique won the 2017 chemistry nobel and was method of the year for nature in 2016, even without atomic resolution.

https://www.nature.com/articles/nmeth.4115

It's powerful, and a definite step up over crystallography in some ways, but personally I think structural biology has repeatedly been oversold as a method to understand the function of proteins at the molecular level. I say that as somebody who obtained a PhD in NMR spectroscopy and worked for 15 years on structural biology problems.

I've come to see SB as a visualization tool that helps form hypotheses, but not an actual method by which most protein structural/function problems can be directly solved.

The techniques which seem to provide the most utility are fluorescent imaging with light microscopy, often at low magnification. These are more amenable to scale-up and machine learning, both of which are likely to be necessary to unlock the next level of understanding biology.

I think your criticism of structural biology can be applied to any methods-focused investigation, as opposed to biology-focused. I've certainly been down the "okay we have the data, what does it mean?" path more times than I care to remember. Unfortunately I think this is a natural consequence of working on cutting-edge methods - structural biology has traditionally required a degree of over-specialization.

Sharing the OP’s position, and having worked in a biochemical technology development lab in grad school, I don’t think that’s quite right. Structural biology is disproportionately seductive as a data source because we are such visual creatures. You “see” it so it must be true. I’ve definitely been guilty of it while looking at protein structures, I doubt anyone in the field hasn’t. Hell there used to be 3D rigs you could buy with IR activated LED shutter glasses so you could see structures in 3D on your monitor and “better understand” the structure.

It’s easy to get misled, proteins are incredibly dynamic in solution. Binding pockets appear and disappear, change shape, add and remove water. Given a structure of an unknown enzyme, with little to no biochemical characterization, you can’t tell what the catalytic mechanism or rate is. You probably can’t tell what the crucial residues are for binding at all. You may be able to tell the binding pocket, and... generate some hypotheses!

That’s not to say protein structures aren’t helpful, they are! Especially things like co-crystals with drugs can help study that specific interaction. But I think the OP is totally right, we should back off strong conclusions on structure alone. It’s a great hypothesis generator, not a final answer in and of itself.

The awesome part of cryoem at atomic scale is that we can now get MORE hypotheses generated faster with tougher proteins than with X-ray crystallography and other methods.

I won't lie, I was thrilled the first time I saw the holes in aromatic rings in electron density from my experiment. But until the very end of last century, X-ray crystallography was still difficult enough to be a full-time occupation and a single crystal structure was a PhD thesis. In my experience that kind of narrow focus becomes self-propagating whether or not the method generates beautiful figures.

Oh yeah, X-ray crystallography used to be crazy hard, and still is for many many things. I can imagine those holes must have been so satisfying :)

> I've come to see SB as a visualization tool that helps form hypotheses, but not an actual method by which most protein structural/function problems can be directly solved.

This seems to understate the challenge and power of generating good hypotheses.

But structural biology can be very inefficient.

Let's say you want to know which residues in a protein are important for a particular function, so you can tweak them to improve function.

You could

- spend months or years solving a structure of the complex then look at the structure and look at the direct contacts - then mutate to various other resides to see if they affect function ( finding out that even with a structure of the complex your chosen list is far from 100% correct )

- look at sequence alignments and then make a library of millions of variants and screen in a couple of months.

The first feels better as the glorious scientist is doing 'rational design', however it can be much more hit and miss and slower and more expensive.

As I understand it, one of the things about Cryo-EM is it's potentially much faster/easier than previous methods - but even so, looking at the structure doesn't get you to the answer direct - it's still very much hit and miss.

Brute-forcing the problem with a variant library and high-throughput screening could easily end up being far more inefficient. At least with crystallography it's easy to set up the experiment, whether or not it actually works.

You can even buy robots that do grid searches for crystallography (IE, if you're desperate, can't find conditions to make a crystal, and you've exhausted your postdocs, the robot will be able to try more possibilities in shorter time). Unfortunately they don't work very well and end up being a real pain to clean.

“Easy” is rarely a word I’ve heard associated with crystallography. Hence cryo-em! Easier and faster sample prep.

In the very best case, it is indeed easy! I've seen the entire process take less than a month for a completely novel structure - those were extremely lucky cases of course, but my point is that it costs very little to set up some screens and see what happens. (Small globular proteins of course, not ribosomes or ion channels.)

Nice! I always assumed unless there was a known crystal, you’d be in for pain. “Good and globular” is the way to go I guess.

Exactly.

There are obviously famous exceptions - like the structure of DNA revealing key functional aspects.

But for the most part it's like claiming photography is the key to understanding how animals really behave.

Single pictures in isolation are typically not very helpful in understand the biology.

Even the promise of having a structure and therefore being able to calculate physio-chemical properties has been much harder and slower than the hype.

Wouldn't a single image of an animal greatly improve understanding of animal behavior if previously we were unable to see the animal at all?

Yes, hopelessly extending this analogy, see the change in the way artists represented galloping horses before and after photography.

https://www.amusingplanet.com/2019/06/the-galloping-horse-pr...

And yet that was a snapshot of a dynamic process. Seeing an image of the horse didn’t actually reveal how it galloped, we had plenty of those and got it wrong. Seeing many images of the dynamics did, that’s a subtle but important difference. Movies are way more helpful than photographs. A crystal (or cryoem) structure is a snapshot of a horse standing still. We rarely care about that, though maybe we can guess that it uses its hind legs intensely because it’s very muscular. We do care about how it gallops, and don’t have a clue how with a single picture.

Put another way, we have “pictures” of dinosaurs, but have limited understanding of how they socialized, interacted, moved. We have ideas and guesses, sure, most based on descendants and modern context. Hypotheses, but few answers. Now if we had a movie of a dinosaur...

If we have its scat and see footprints we can learn a lot: where it lives, what it eats, what's related to. The fluorescence methods+knockout/expression can get you that sort of thing.

I'm just an interested layman but it seems like this technology might be useful in developing therapies that either suppress or amplify immune response (e.g. diabetes, vaccines, cancer). For example, it may be possible to optimize the targeting of PD-1 inhibitors by comparing the PD-L1 ligands of healthy and diseased tissues in a cancer patient (edit: found something [2]). There was also a story [1] about how more advanced imaging was used to help identify antibodies that would be effective against SARS-CoV-2.

[1]

https://www.diagnosticimaging.com/view/role-emerges-imaging-...

https://www.nih.gov/news-events/nih-research-matters/novel-c...

[2]

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5050107/

It's absolutely useful for drug development and pharma companies appear to be getting heavily invested in the technique. The problem is that they've been trying to use structural biology this way for close to four decades now, and there are still many obstacles to this that have nothing to do with the structural biology methods themselves. Biology is messy, human biology particularly so. There are success stories of course but it's never been a magical solution.

Ah ok. That type of problem has to be orders of magnitude more difficult, especially when this still doesn't give us a great view into how everything interacts in a living creature.

We need to know the elemental sequence of every human protein at some point, so we might as well start now.

Deepmind has made some interesting progress on modeling molecular structure from first principles using advanced ML architectures. Hopefully years from now these types of tools will let us understand the in vivo structural dynamics of these amazing molecular machines that give rise to life.

A few things here- first, we know the sequence of most proteins already. This is about structure, which is very different. It is entirely unclear that we "need" to know every structure to solve most important problems in biology (either basic research or applied).

As for Deepmind... they made an incremental improvement over the existing field (and everybody will be doing the same thing in 2 years). This ignores and underweights the decades of contributions from a wide range of people to bring us to this point in protein structure prediction and design.

Doesn't your disclaimer kind of also explain a bias against SB, as NMR is mostly used for protein dynamics elucidation (vs. the more rigid structures of Cryo-EM)? Or do you actually mean all fields of SB?

I mean all fields of SB. NMR is one of the worst- my PhD is in NMR structural biology. NMR gives you some dynamics information, but it's not great, hard to deconvolve and it's limited to very small molecules. of all the techniques, cryo is probably the best right now in terms of ease of sample prep and utility of data, but my point is much more that we don't even really need to know the structure of many things to make useful progress- fluorescence microscopy is far easier than any structural biology technique and provides far more useful signal.

Interesting!

> the most utility are fluorescent imaging with light microscopy, often at low magnification. These are more amenable to scale-up and machine learning

Any particular problems there, that you think can be tackled well by machine learning? I just recently started my first ML project in a fluorescence microscopy lab (biochem undergrad with previous software engineering experience), and while I see a lot of things that could benefit from ML for incremental improvements (which often need to be really tailored for each project), as is the case with most disciplines, I haven't really seen anything where I thought that there was potential for something groundbreaking.

there's good stuff here https://www.nature.com/collections/cfcdjceech if you have access to Nature.

It's a bit trickier than that as the flash freezing process is on the scale of milliseconds iirc which can affect what ensemble of folds are seen via cryo-em

When I was in grad school I was a TA for a biochemistry class and the prof asked me to deliver the lecture on crystallography while he was on vaca. Part of the lecture was about how electron microscopy was easier but pretty inaccurate compared to x-ray crystallography. But the slides were 10 years out of date, the accuracy of EM was still not as good but the gap was much smaller. So I updated them with more recent EM results from the same labs.

When the prof came back he spent the first 5m of the next lecture "correcting" me, explaining that EM sucked, x-ray was the only good technique. I realized that he had basically made up his mind decades earlier and no matter what changed in the technology he wasn't going to change his opinion. Science has its own politics, similar to actual politics in that conclusions drive observations, but instead of being about minimum wage or housing supply it's about arcane scientific techniques.

Wondering if we should go with some straight name and shaming so as to any future students can avoid things like this, be a real waste of PhD students to follow him and go into areas without any prospects

This is quite typical in academia, especially in biology and medicine.

I finished my PhD recently. Examiners asked me to rewrite some sections and resubmit my thesis because one of them didn't "believe" my results. Believing in this context actually meant I made lots of his stuff outdated / irrelevant using mathematical models instead of hand waving. Models led to precise findings, which had some lab validation by the time I submitted.

At the same time my university, which is a really famous one, was encouraging me to patent my results. And my supervisor applied for massive funding as if all was his idea. 2 major clinical trials are now recruiting to test my findings.

Least to say, I refused and got a new exam with some honest people.

Academic scientists can be intensely conservative, even reactionary, when confronted with new ideas and methods. If you want to see something really horrific, try digging up some of the original debate on whether experimental data deposition should be mandatory for structural biology publications. Here is the one bit I know that's online still (PDF is free): https://www.nature.com/articles/nsb0698-407

The fact that there had to be a debate on this issue at all tells you everything. The forces of good triumphed in the end but it probably took a full generation for everyone to get in line. (I've heard legends of computer-vision software being written just to decode the figures in protein structure publications from competitors. Would love to know if this is actually true, but again, the fact that it even sounds plausible tells you a lot about the broken incentives.)

This is true - I work in a related field.

This is a some sort of scream for money. These "scientists" do it on purpose in hope that one day a new tech company will pay them millions to change their mind. These "scientists" should be rooted out.

"Science advances one funeral at a time" - Max Planck

Some readers here might be interested in the history of the technology that has enabled cryo-EM. One of the key innovations was the development of CMOS direct detection devices that are able to detect electrons with extremely high signal to noise ratio, operating very close to the thermal limit of the DDD itself. I think it is an excellent example of the fundamental interdependence of cutting edge research and cutting edge engineering. Some (maybe most?) of the initial research and development [0, 1] on the cameras was done in my grandadvisor's lab. Another part of the story is related to the massive improvements in algorithms that in some cases have enabled nearly real time reconstruction and visualization of viruses from cryo-EM samples (I don't have links for these handy), and the work to increase the resolution of the reconstructions presented in the linked article.

0. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2359769/ 1. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3210420/

What's "DDD"?

Direct Detection Device.

FYI - This means they're able to image individual atoms, not that they're imagining WITHIN atoms as the title somewhat implies.

That is: atomic resolution, not sub-atomic resolution

This is helpful context. I am not a scientist in any way, shape or form, but this is cool stuff. Appreciate the translation to layman’s terms!

Pedantic note: they're not really imaging individual atoms directly; it's a composite view of the structure based on averaging thousands of different images of copies of the molecule in different orientations. This is true of other structure determination methods such as crystallography of course. The breakthrough here is that these are exceptionally accurate measurements; when I tried learning EM in the early 2000s it was still mostly just vague blobs.

I remember when those vague blobs were a monumental achievement. It’s very cool to see these kinds of technologies break through and get refined like this.

In terms of either sample prep or data processing, how time consuming is this relative to X-ray crystallography?

Setting aside entirely the enormous benefit of not needing crystals.

I’m a (former) chemist that has only ever had to use X-ray crystallography for small molecules. I’m just trying to get a sense of what the practice of doing this is like?

I do not know what it's like in practice now, but on a purely theoretical basis, if you are trying to solve a completely novel structure with no known homologs, especially if it's something on the scale of a ribosome, direct imaging is always going to be easier than trying to solve the phase problem, both experimentally and computationally.

I don't do much experimentation, but I am pretty sure that you can very easily distinguish individual atoms with electron beam microscopy, and get pretty close using atomic force microscopy. And I am not sure what exactly is the resolving power of synchrotron radiation, but I expect if to be pretty high.

However, the breakthrough here seems being able to do so using a low-energy electron beam. All the methods I quoted above are probably impractical or damaging with biological samples.

With hard xrays you can visualize interatomic densities and lone pairs. I know there are structures down to 0.5Å resolution now but that must have required careful setup. I've seen diffraction out to 0.75Å but I could never collect complete data at that resolution.

I’m imagining a collector plate the size of my dining room table, with a staff of crazy-haired scrawny physicists clambering around some sort of neo-Victorian rube-Goldbergesque X-ray source — like a wine-barrel-sized copper anode and a small nuclear power plant for the arc.

This is not far from the truth, except the detectors are actually relatively small (and very expensive), there's more aluminum foil than the Victorians used, and we have slightly better hair on average. The last time I used one of these facilities, it looked like this (and still does): https://lcls.slac.stanford.edu/sites/lcls.slac.stanford.edu/... Compared to this electron microscopy is downright boring - and a couple of orders of magnitude cheaper to set up.

That's pretty much correct. Single-atom imaging is possible using aberration-corrected scanning TEM, but the beam doses used will typically obliterate anything organic through radiolysis or ionization damage (although there are emerging ways around that using some interesting compressive sensing techniques).

Most "atomic resolution" EM images you see are actually images of columns of atoms, since the imaging mode is transmission, so necessarily the image is summed through the plane of the sample (so atomic resolution is only in the perpendicular plane).

The techniques used in this paper get around the dose issue by taking many images of very many presumably identical proteins (called dose fractionation) at very low dose. Computer algorithms are then used to stitch together a 3D model based on the low-dose individual images. Making it really cold also helps things from breaking down under the beam.

Pedantic note: At this scale, a particle is nothing more than a distribution of the probability of making some kind of measurement. So composites of multiple samples aren't a suboptimal means of imaging atomic structure, they're the only way. To do anything else would be to show only part of the probability field that is the atom.

(Right? I've been going back and forth about this since I saw those "videos" in 2015 of "individual photons". My gut reaction was that those aren't videos, they're simulations that cleverly represent the probability of measuring a photon as the brightness of of the "photon", but since we're measuring inherently probabilistic things maybe that's the only honest way to do it, in which case perhaps we ought to accept them as images.)

at around 0.7A resolution, you start to be able to see electron density between atoms. Nobody using these methods cares about intranuclear structure, just the electronic structure around the nucleus.

Indeed. For comparison: atoms are about four orders of magnitude larger than atomic nuclei. The size of the former is generally a few tens to low hundreds of picometers (1 pm = 1e-12 m) while the size of the latter is just a few femtometers (1 fm = 1e-15 m).

See, e.g. https://en.wikipedia.org/wiki/Atomic_nucleus for concrete example sizes.

People have used electron diffraction using cryo-em scopes to do sub-angstrom resolution. For example, my colleague Jose Rodridguez published this a few years ago.

https://www.nature.com/articles/s41594-017-0018-0

See also neutron diffraction- it's been used for decades to get fine structure info.

It’s 7 orders for the protium isotope of hydrogen:

https://www.wolframalpha.com/input/?i=diameter+of+hydrogen+a...

One reason hydrogen is so hard to see...

The electron wavefunction scatters primarily off the nucleus potential. The electron cloud acts to screen the potential, but this effect is weak and not easily detected in the scattered wave.

Naive question: these images are made at low but finite temperatures, so each atom would fluctuate within its position such that there should be an uncertainty. Is that uncertainty lower than 1 angstrom? Otherwise, how can one talk about atomic resolution if fluctuations are larger?

The uncertainty also comes from averaging many images together. But yes, it's less than 1 Angstrom; the deposited structures (for example https://www.rcsb.org/structure/7A6A) record atomic uncertainties, "B-factors" or "temperature factors" in crystallographer-speak. In the example I pulled out the B-factors are in the low-double digits for the main-chain atoms, and if I'm remembering the math correctly, this will correspond to atomic displacements with a radius around 0.5 Angstrom. (Of course that's just an estimate by the software that performed the model optimization, but my understanding is that this part is relatively straightforward.)

Hmm, but then the b-factor (and therefore also resolution) is dependent on the flexibility of molecule you want to look at? Does that mean that these guys just found a system for which the main chain was rigid enough such that the thermal fluctuations are low enough?

Oh absolutely, they picked a model system that is both very rigid and has extremely high internal symmetry, and I assume they did rotational averaging to use fewer images. But these ideal systems are very useful for determining the limitations of the underlying technology like electron detectors; 15 years ago the best you could do with a molecule like this was around 4 Angstrom resolution.

Ok, that’s fair. But, then the number makes more sense in relative terms than in absolute. Still, absolutely impressive.

Can I just say how amazingly well articulated this article was?

It was so clear, lacked fluff and explained enough of an extremely complex area of science to have basic grasp of the limitations, difficulties and gains that were made in the latest advancement.

I really wish more articles would be like this.

The progress of Cryo EM has been extremely impressive. I wouldn't have thought you could push it to actual atomic resolution. Even with X-Ray you don't achieve that for typical protein structures.

It'll be interesting to see if and how quickly these advances can be put into routine use.

The paper Atomic-resolution protein structure determination by cryo-EM [1]:

> Single-particle electron cryo-microscopy (cryo-EM) is a powerful method for solving the three-dimensional structures of biological macromolecules.

> At resolutions better than 4 Å, atomic model building starts to become possible, but the direct visualization of true atomic positions in protein structure determination requires much higher (better than 1.5 Å) resolution, which so far has not been attained by cryo-EM.

> Here we report a 1.25 Å-resolution structure of apoferritin obtained by cryo-EM with a newly developed electron microscope that provides, to our knowledge, unprecedented structural detail.

[1] https://www.nature.com/articles/s41586-020-2833-4

There are actually two papers being cited. The other one is titled Single-particle cryo-EM at atomic resolution: https://www.nature.com/articles/s41586-020-2829-0

Since people might not be familiar with the unit Angstrom used in the article: it is a shorthand for 10^-10 m = 0.1 nm = 1 Å (Ångström).

Edit: Wikipedia entry: https://en.wikipedia.org/wiki/Angstrom

The original paper: https://www.nature.com/articles/s41586-020-2829-0

Published: 21 October 2020

Single-particle cryo-EM at atomic resolution

Takanori Nakane, Abhay Kotecha, Andrija Sente, Greg McMullan, Simonas Masiulis, Patricia M. G. E. Brown, Ioana T. Grigoras, Lina Malinauskaite, Tomas Malinauskas, Jonas Miehling, Tomasz Uchański, Lingbo Yu, Dimple Karia, Evgeniya V. Pechnikova, Erwin de Jong, Jeroen Keizer, Maarten Bischoff, Jamie McCormack, Peter Tiemeijer, Steven W. Hardwick, Dimitri Y. Chirgadze, Garib Murshudov, A. Radu Aricescu & Sjors H. W. Scheres

Nature (2020)

Interesting to see the work being done to try to move structural biology towards a place where we can observe biological processes more easily. Crystal structures (Especially with ligands) were really useful to determine structure and function, but you sometimes get artifacts and it is hard to see exactly how things transition (Assuming you even get it to crystallized in the first place).

Techniques like cryo-EM and smFRET are definitely helping bridge this toolset gap to do better functional analysis of proteins and complexes. Definitely worth the Nobel Prize it won a few years back.

You can still get artifacts due to freezing. But the lack of crystal packing makes it much easier to detect functional conformational changes in different copies of the molecule on an EM grid.

Sort of off-topic but I recall the first time I ran a scan on an atomic force microscope back in the early 90’s. I was totally blown away by the ability to “see” individual atoms.

The whole system was so high tech for its day; including the computer hardware which I think was a Sun workstation. It even had magneto optical drives for storing images and a high resolution color printer for printing images out. Given that I had only used DOS up to this time, it felt like to I had been teleported into the future.

Layman's question: if we know the precise shapes of two molecules, is that enough information for us to compute every interesting detail about how they'll interact?

No, not by a long shot unfortunately.

Especially for proteins there is not a single "precise shape" for the whole protein. It might take on slightly different shapes dependent on a number of factors (e.g. pH of the environment). Interactions between a protein and some other molecule might also alter the shape of the protein. So overall, a slight change in any of those values can have cascading effects in how it interacts with any other molecule (which themselves share the same problem).

So you're saying that given a particular instance of a protein molecule, the surrounding environment can cause its shape to change, but the set of bonds stays constant?

Or are you saying that the shape change involves a change to the set of bonds, but for some reason we continue to call it the same "kind" of protein?

The covalent bonds stay the same (which is why it's still the same molecule), apart for sometimes localized modification (e.g. protonation).

The 3D structure (= shape) however, is mostly dependent on the hydrogen bonds (among other things like bisulfide bonds) between the amino acids that make up a protein. So the deprotonated variant of a amino acid side chain might not be able to interact in the same way as its protonated form, which will cause a different 3D structure for the whole protein, which in turn influences how it interacts with other molecules.

> The 3D structure (= shape) however, is mostly dependent on the hydrogen bonds (among other things) between the amino acids that make up a protein.

That's really interesting. So now that this new microscopy technique is available, is it practical for chemists to determine every useful detail about the covalent bonds and hydrogen bonds in the imaged molecule?

No, because presumably they're solvated and that will change things dramatically. We have no idea, for instant, what the dielectric constant of water is in the middle of a protein, and therefore, no way to do these calculations.

What does the color information represent in the image?

Such color schemes usually represent the position of the amino acid in the protein sequence, from blue (start, or N-terminus) to red (end, or C-terminus). Keep in mind that the figure shows an oligomer of apoferritin, formed by several individual protein chains.

It's also possible it's colored by uncertainty in the atomic positions - what crystallographers call the "B-factor".

That is true, but B-factors are mostly shown in a ribbon, cartoon, or "putty" (e.g. https://www.researchgate.net/figure/B-factor-diagram-of-prot...) representation, not as ball-and-sticks.

Looks like it's just distance from the center, probably for the sake of visualizing 3D space in a press release.

That's another plausible option that I forgot to consider.

So at what point do we hit the Uncertainty Principle of disturbing atoms so strongly that we're no longer sure of their velocity or position?

Do you mean the uncertainty principle or the observer effect? From Wikipedia:

https://en.wikipedia.org/wiki/Uncertainty_principle

> In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which the values for certain pairs of physical quantities of a particle ... can be predicted from initial conditions.

> Historically, the uncertainty principle has been confused with a related effect in physics, called the observer effect, which notes that measurements of certain systems cannot be made without affecting the system, that is, without changing something in a system.

The former just means that the more precisely we know the location, the less precisely we can predict the momentum given the initial information of the system. It has nothing to do with "disturbing the atoms"; as Wikipedia explains it's a property of wave-like systems.

https://en.wikipedia.org/wiki/Observer_effect_(physics)

On the other hand, the observer effect simply says that measurements involve active processes and those can effect the system. But it has nothing to do with velocity or position per se, just the fact that measurements can have effects.

UP doesn't really apply here. The data the underlies the reconstructions requires massive averaging of individual objects as part of the tomography (see Radon transform for the core approach). In addition those objects/particles need to have the requisite symmetry/similarity/regularity in structure (not universally applicable), or the population of them needs to be completely homogeneous (hard to achieve). I suspect that there are now better techniques for detecting outliers so homogeneity might not be as important.

So in some sense that's what this is all about. The resolution of an electron microsocope is dependant on the energy of the electron, but higher energy electrons rip your sample apart. The trick that cryo-em does is to stiffen the structure of the protein by embedding it in a glass matrix (the glass is actually just really cold water that is prevented from freezing). Since the protein is stiff, you can use higher energy electrons, and thus get a higher resolution.

Are things besides water used? Like a vacuum or something else? Would the stiffness be dependent on the energy density gradient between what it is embedded in?

The technique reminds of those i've seen in sparse eigen decomposition of a matrix, where some non square matrix X is embedded in a larger sparse matrix of zeros of the form:

⎡ zeros(X.n_rows, X.n_rows) X ⎤

⎣ X.t() zeros(X.n_cols, X.n_cols) ⎦

Except for in this case the larger matrix of zeros would be replaced by a repeated structure. Though I can't help but think that using non zeros would get some weird energy feedbacks (due to the interaction of the protein with the embedding matrix molecules) that would require some renormalizations.

Next, researchers will strive to achieve similar sharp resolution with less rigid, large protein complexes, such as the spliceosome

Does this mean we don't currently have a good picture of what the spliceosome looks like? That seems important!

We do. For the entire splicing cycle, via cryoEM:

"Molecular Mechanisms of Splicing: Spliceosome Machinery and Pre-Messenger RNA Splicing Cycle"

https://youtube.com/watch?v=OuAGeQYjfus

Most of these still count as low-resolution - I don't see anything better than 3 Angstrom in the PDB, most are much worse. More than good enough for movies and functional assays, but some of the fine details will be guesses.

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