Force in physics is very different from the way we think of it

I’m very lucky (and honored) that a friend asked me to read and comment on the galleys of a his book. He’s trying to explain some very advanced physics to laypeople (e.g. me). So he starts with force fields, gravitational, magnetic etc. etc. The physicist’s idea of force is so far from the way we usually think of it. Exert enough force long enough and you get tired, but the gravitational force never does, despite moving planets stars and whole galaxies around.

Then there’s the idea that the force is there all the time whether or not it’s doing something a la Star Wars. Even worse is the fact that force can push things around despite going through empty space where there’s nothing to push on, action at a distance if you will.

You’ve in good company if the idea bothers you. It bothered Isaac Newton who basically invented action at a distance. Here he is in a letter to a friend.


“That gravity should be innate inherent & {essential} to matter so that one body may act upon another at a distance through a vacuum without the mediation of any thing else by & through which their action or force {may} be conveyed from one to another is to me so great an absurdity that I beleive no man who has in philosophical matters any competent faculty of thinking can ever fall into it. “

So physicists invented the ether which was physical, and allowed objects to push each other around by pushing on the ether between them. 

But action at a distance without one atom pushing on the next etc. etc. is exactly what an incredible paper found [ Proc. Natl. Acad. Sci. vol. 117 pp. 25445 – 25454 ’20 ].

Allostery is an abstract concept in protein chemistry, far removed from everyday life. Far removed except if you like to breathe, or have ever used a benzodiazepine (Valium, Librium, Halcion, Ativan, Klonopin, Xanax) for anything. Breathing? Really? Yes — Hemoglobin, the red in red blood cells is really 4 separate proteins bound to each other. Each of the four can bind one oxygen molecule. Binding of oxygen to one of the 4 proteins produces a subtle change in the structure of the other 3, making it easier for another oxygen to bind. This produces another subtle change in structure of the other making it easier for a third oxygen to bind. Etc. 

This is what allostery is, binding of molecule to one part of a protein causing changes in structure all over the protein. 

Neurologists are familiar with the benzodiazepines, using them to stop continuous seizure activity (status epilepticus), treat anxiety (Xanax), or seizures (Klonopin). They all work the same way, binding to a complex of 5 proteins called the GABA receptor, which when it binds Gamma Amino Butyric Acid (GABA) in one place causes negative ions to flow into the neuron, inhibiting it from firing. The benzodiazepines bind to a completely different site, making the receptor more likely to open when it binds GABA. 

The assumption about all allostery is that something binds in one place, pushing the atoms around, which push on other atoms which push on other atoms, until the desired effect is produced. This is the opposite of action at a distance, where an effect is produced without the necessity of physical contact.

The paper studied TetR, a protein containing 203 amino acids. If you’ve ever thought about it, almost all the antibiotics we have come from bacteria, which they use on other bacteria. Since we still have bacteria around, the survivors must have developed a way to resist antibiotics, and they’ve been doing this long before we appeared on the scene. 

TetR helps bacteria resist tetracycline, an antibiotic produced by bacteria. When tetracycline binds to TetR it causes other parts of the protein to change so it binds DNA causing the bacterium, among other things, to make a pump which moves tetracyline out of the cell. Notice that site where tetracycline binds on TetR is not the business end where TetR binds DNA, just as where the benzodiazepines bind the GABA receptor is not where the ion channel is. 

This post is long enough already without describing the cleverness which allowed the authors to do the following. They were able to make TetRs containing every possible mutation of all 203 positions. How many is that — 203 x 19 = 3838 different proteins. Why 19? Because we have 20 amino acids, so there are 19 possible distinct changes at each of the 203 positions in TetR.  

Some of the mutants didn’t bind to DNA, implying they were non-functional. The 3 dimensional structure of TetR is known, and they chose 5 of nonfunctional mutants. Interestingly these were distributed all over the protein. 

Then, for each of the 5 mutants they made another 3838 mutants, to see if a mutation in another position would make the mutant functional again. You can see what a tremendous amount of work this was. 

Here is where it gets really interesting. The restoring mutant (revertants if you want to get fancy) were all over the protein and up to 40 – 50 Angstroms away from the site of the dead mutation. Recall that 1 Angstrom is the size of a hydrogen atom, a turn of the alpha helix is 5.4 Angstroms and contains 3.5 amino acids per turn.The revertant mutants weren’t close to the part of the protein binding tetracycline or the part binding to DNA. 

Even worse the authors couldn’t find a contiguous path of atom pushing atom pushing atom, to explain why TetR was able to bind DNA again. So there you have it — allosteric action at a distance.

There is much more in the paper, but after all the work they did it’s time to let the authors speak for themselves. “Several important insights emerged from these results. First, TetR exhibits a high degree of allosteric plasticity evidenced by the ease of disrupting and restoring function through several mutational paths. This suggests the functional landscape of al- lostery is dense with fitness peaks, unlike binding or catalysis where fitness peaks are sparse. Second, allosterically coupled residues may not lie along the shortest path linking allosteric and active sites but can occur over long distances “

But there is still more to think about, particularly for drug development. Normally, in developing a drug for X, we have a particular site on a particular protein as a target, say the site on a neurotransmitter receptor where a neurotransmitter binds. But the work shows that sites far removed from the actual target might have the same effect

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Comments

  • Peter Shenkin  On December 30, 2020 at 7:32 pm

    For what it’s worth, I would not have guessed that the center would become a molten globule when large hydrophobic residues are replaced by smaller ones. I would have guessed that those proteins that do fold would become more compact and more stable because they would pack more closely. This is consistent with the common observation that replacing a small internal residue with a larger one of the same type (say, hydrophobic) generally destabilizes the structure if indeed it folds to something resembling the native form in the first place.

    It’s long been known that changes even to surface residues can destabilize proteins. There was a study of shotgun mutagenesis of lysozyme in the ’80s by John Schellman at Oregon state (I think!) in the ’80s that showed that. I think it was published in Nature. I don’t think that the overall results have ever been rationalized. At least, they weren’t at the time.

    It’s worth considering that the potential between uncharged atoms attract (as potentials) as 1/r^6 and repel as 1/r^12, called a Lennard-Jones potential. This gives a very short range repulsion as atoms collide and a longer-range cutoff for attraction. (Max Born, I think, first derived the 1/r^6 dependence as an induced dipole – induced-dipole interaction, but the 1/r^12 model is purely empirical and computationally convenient.) But charge-charge interactions go energetically as (1/r^2) – that is, they continue to be important over very long distances – and become successively shorter-range for charge-dipole then dipole-dipole, then dipole-inudced-dipole interactions).

    So charge-charge and charge-dipole interactions are significant even at long interatomic distances. This has been a major stumbling block in computing protein-ligand interactions, especially for a charged ligands, partly because these simulations often assume a rigid protein, but also because there is significant contribution from surrounding solvent. However, I understand that in practice, progress has been made on this problem this in recent years.

    But either way, a charge-charge interaction between two charged centers on the opposite sides of a protein can certainly be modeled as interacting through space, with appropriate compensation due to the effective dielectric constant created by the atoms of the interior and the solvent outside. Of course that potential has to be added to the other potentials involved, which include the Lennard-Jones terms and also bond-length and -angle potentials, such as those which tend to keep sp3 carbons tetrahedral,. Similarly with the accompanying forces.

  • Steve Curry  On January 2, 2021 at 1:09 pm

    As a neurologist and admirer of allosteric interactions at GABA receptors, you may enjoy this exploration of GABA receptors and idiopathic stupor.
    https://emcrit.org/toxhound/ff-endozepines/

  • Crowley  On January 3, 2021 at 7:00 pm

    Looks like an interesting paper.

    If I might be a bit pedantic, I think what you’re describing as allostery in hemoglobin is better described as cooperativity.

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

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