Chemists tie a trefoil knot using only 54 atoms | Hacker News Reader

Chemists tie a trefoil knot using only 54 atoms

phys.org

96 pointswglb25 comments

In grad school I got interested in knots while doing structural biology and asked my advisor (extremely well known chemist) if it would be possible to make proteins that fold into knots and he pointed out (correctly) that entropy makes it very unlikely this would happen, as the process of folding into a knot typically decreases the degrees of freedom a protein can adopt. It was a reasonable point and I ignored the problem for some time.

It turned out later that a small number of proteins are found in a knotted conformation experimentally, https://en.wikipedia.org/wiki/Knotted_protein and alphafold even helped design a knotted protein. I can imagine there are also enzymatic modifications you can make to proteins that would generate knots without paying the entropic cost of threading the needle, so to speak.

> if it would be possible to make proteins that fold into knots and he pointed out (correctly) that entropy makes it very unlikely this would happen

This is exactly the opposite argument I'd make from entropy:

https://www.npr.org/sections/bryantpark/2008/01/knot_theory_...

There's many ways that a string can be knotted and only one way it can not be knotted.

Note I am talking about entropy of "folding" as a verb- the process by which a fold is adopted. Not the entropy of the final state (which is confusing called a "fold" by some practioners, although that habit is decreasing).

the argument is that the folding process would require the protein to go through an intermediate: forming a loop and then getting one end to go through the loop requires a very specific set of conformations, and reducing the number of conformations has an "entropic cost". Note also that the final post-folding form of a knotted protein isn't really a continuum of many different conformations, but probably one "locked" one which means there really is only a small set of conformations the protein can adopt once locked into the folded, knotted state.

In protein folding, there is not "only one way it can not be knotted"; you have to include all the degrees of freedom in the backbone available in the unfolded state (I am ignoring hydrophobicity and other important sources of entropy which help proteins fold rapidly to the "correct" final state). We already know this pretty well from more basic polymer physics,

but, entropy being subtle, I'm sure there are many different forces at play.

I think with proteins the ways it can be "not knotted" are basically infinite. Topologically-speaking, yeah, it's just a deformed ring. But the deformations (folds) are the huge thing that makes a protein do its job.

So there are tons of folding configurations, and entering a knotted state restricts a lot of the freedom-to-fold a protein would have

Topology gets its utility from collapsing lots of degrees of freedom into a small number of equivalence classes. That's great for reasoning about topological properties, where those degrees of freedom are not relevant, but it doesn't mean those degrees of freedom just go away.

Is there any evidence that the entropic restraints on a knotted protein are greater than the entropic restraints from the hydrophobic effect?

What would be the benefit of this?

Thermal stability, as far as I know. So hyperthermophiles, presumably.

edit: hmmm. from this interesting review - https://www.sciencedirect.com/science/article/pii/S0959440X2... (open article) - it looks like some knots might increase mechanical stability and resitance to proteolysis

Oh, cool- they turned a not-truly-a-knot (open ends) protein into a truly knotted one (connected ends) and then unfolded it using urea and it stayed knotted. That's what you'd expect but it's also pretty cool.

It's interesting. That's the benefit.

Protein design is a multi-billion dollar field.

A single observation- thermostable proteases- was incorporated into modern laundry detergents, making Genentech and Corning billions of dollars in IP.

A category theory textbook opens the "motivation and use cases" section with the following poem:

There's a tiresome young man in Bayshore. / When his fiance cried 'I adore / the beautiful sea' / he replied 'I agree, / it's pretty, but what is it for?'

If several of these could be looped together, could you get a structure stronger (or at least more resilient to tension) than carbon nanotubes?

[stub for offtopicness]

This is a good idea. Some sort of special handling for archive links might work too.

dang's been doing this for a few years now (<https://hn.algolia.com/?dateRange=all&page=0&prefix=true&que...>).

I'd stumbled across him doing it within the past year or so and noted on its appropriateness, effectiveness, genius, and simplicity at some point (either via email or in a comment I cannot presently find).

Huh, captivating concept. A catch-all comment to corall the chitchat.

I thought it might be something like the Emperor's New Wedding where the wedding ring was invisible and everyone is pretending to see it.

(coming to theatres soon!)

He thought he had clothes.

He didn't.

Now, his secret is exposed. And he is KNOT amused.

The Emperor's Tiny Ring

IMO they should have to reproduce it intentionally to get the “record.”

I'd be inclined to agree, now that I think about it. They discovered the knot, they did not intentionally tie it. When your headphones get knotted in your pockets, you don't say "I tied my headphones", you say "my headphones got tangled".

Damn, that's a really small wedding.

They invited Helium as well but you know it can be hard to get Helium to stick around anywhere.

They have a bond that cannot be broken.

Well, the split would be explosive.

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