Category Archives: Chemistry (relatively pure)

Hydrogen bonding — again, again

I’ve been thinking about hydrogen bonding ever since my senior thesis in 1959. Although its’ role in the protein alpha helix had been known since ’51 and in the DNA double helix since ’53, little did we realize at the time just how important it would be for the workings of the cell. So I was lucky Dr. Schleyer put me at an IR spectrometer and had me make a bunch of compounds, to look for hydrogen bonding of OH, NH and SH to the pi electrons of the benzene ring. I had to make a few of them, which involved getting a (CH2)n chain between the benzene ring and the hydrogen donor. Just imagine the benzene as the body of a scorpion and the (CH2) groups as the length of the tail.  The SH compounds were particularly nasty, and people would look at their shoes when I’d walk into the eating club. Naturally the college yearbook screwed things up and titled my thesis “Studies in Hydrogen Bombing”, to which my parents’ friends would say — he looks like such a nice young man, why was he doing that?

At any rate I’m going to talk about a recent paper [ Science vol. 371 pp. 160 – 164 ’21 ] on the nature of the bond in the F H F – anion.  It’s going to be pretty hard core stuff with relatively little explanatory material. You’ve either been previously exposed to this stuff or you haven’t.  So this post is for the cognoscenti.  Hold on, it’s going to be wild ride.

In conventional hydrogen bonds, the donor (D) atom is separated from the Acceptor atom (A) by 2.7 Angstroms or more, and the hydrogen nucleus is found closer to A where the potential energy minimum is found.

So it looks like this D – H . .. A

The D-H bond isn’t normal, but is stretched  and weakened.  This means that it takes less energy to stretch it meaning that it absorbs infrared radiation at a lower frequency (higher wavelength) — red shift if you will. 

Such is what we were looking for and we found it comparing 

Benzene (CH2)n OH vibrations to butanol, pentanol, hexanol, etc etc. cyclohexane (CH2)n OH.

As the D – A distance shrinks there is ultimately a flat bottomed single well potential, where H becomes a confined particle (but still delocalized) betwen D and A.

The vibrations of protons in hydrogen bonds deviate markedly from the classic quantum harmonic oscillator beloved by physicists.  Here the energy levels on solving the classic H psi = E psi equation of quantum mechanics are evenly spaced (see Lancaster & Blundell “Quantum Field Theory” p. 20.)

However in real molecules, as you ascend the vibrational ladder, conventional hydrogen bonds show a decrease in the difference between energy levels (positive anharmonicity).  By contrast, when proton confinement dictates the potential shape in short hydrogen bonds (when D and A are close together, mimicking the particle in a box model in quantum mechanics) the spacing between states increases (negative anharmonicity).

The present work shows that in FHF- the proton motion is superharmonic — https://en.wikipedia.org/wiki/Subharmonic_function — which they don’t describe very well. 

When the F F distance gets below 2.4 Angstroms, covalent bonding starts to become a notable contributor to the short hydrogen bond, and the authors actually have evidence that there is overlap in FHF- between the 3s orbital of H and the 2 Pz orbitals of the donor and the acceptor atoms, yielding a stabilization of the resulting molecular orbital. 

Is that cool or what.  The bond sits right on the borderland between a covalent bond and a hydrogen bond, taking on aspects of both. 

 

Life at the edge of foldability

Insulin has contains 51 amino acids, split into two chains held together by disulfide bonds. The two chains come from a single gene and a single mRNA. Clearly a lot of processing is required. There is an A chain containing 21 amino acids and a B chain containing 30.

Mutations of phenylalanine at position #24 on the B chain results in MODY (Maturity Onset Diabetes of the Young) in which not enough insulin is made. Every known vertebrate insulin contains phenylalanine at B#24.

A fascinating paper [ Proc. Natl. Acad. Sci. vol. 117 pp. 29618 – 29628 ’20 ] explains why.

The reason is that having phenylalanine at B#24 appears to be crucial in folding of the insulin into its final form. We have 20 amino acids, and changing phenylalanine at B#24 to any of the other 19 amino acids results in poor insulin production.

Well we can now make any protein this long by automated peptide synthesis. Which amino acid is closest in shape and structure to phenylalanine? Tyrosine clearly. So the authors made insulin with tyrosine at B#24 (outside the cell).

Guess what — insulin synthesized (outside the cells) B#24 tyrosine bound to the insulin receptor almost as well (20 fold less well), but in terms of biological activity there was no difference. The 3 dimensional structures of B#24 tyrosine and B#24 phenylalanine were nearly identical.

The problem was in the processing of the parent protein (proinsulin) with something other than B#24 phenylalanine to insulin, which involves breaking the chain and forming 3 disulfide bonds between 6 cysteines. So it isn’t structures which evolution is conserving by B#24 phenylalanine but the ability to be processed and folded correctly.

Time to let the authors speak for themselves “Our results suggest that sequences required for insulin’s bioactivity (similar in all vertebrates) are frozen at the edge of nonfoldability.”

 

 

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

Neuroscience can no longer ignore phase separation

As a budding organic chemist, I always found physical chemistry rather dull, particularly phase diagrams. Organic reactions give you a very clear and intuitive picture of energy and entropy without the math.

In past few years cell biology has been finding phase changes everywhere. Now it comes to neuroscience as the synaptic active zone (where vesicles are released) is an example of a phase change (macromolecular condensation, liquid liquid phase separation, biomolecular condensates — it goes by a lot of names as the field is new). If you are new to the field, have a look at an excerpt from an earlier post before proceeding further — it is to be found after the ****

Although the work [ Nature vol. 588 pp. 454 – 458 ’20 ] was done in C. elegans with proteins SYD2 (aka liprinAlpha) and ELKS1, humans have similar proteins.

Phase separation accounts for a variety of cellular organelles not surrounded by membranes. The best known example is the nucleolus, but others include Cajal bodies, ProMyelocytic Leukemia Bodies (PML bodies), gemline P granules, processing bodies, stress granules.

These nonmembranous organelles have 3 properties in common

l. They arise as a phase separation from the surrounding milieu

2. They remain in a liquid state, but with properties distinct from those in the surrounding cellular material

3. They are dynamic. Proteins move in and out of them in seconds (rather than minutes, hours or longer as is typical for stable complexes.

They are usually made of proteins and RNA, and proteins in them usually have low complexity sequences (one example contains 60 amino acids of which 45 are one of alanine, serine, proline and arginine)

Back to the synaptic active zone. The ELKS1 and SYD2 both have phase separation regions (which aren’t of low complexity but they both have lots of amino acids capable of making pi pi contacts). They undergo phase separation during an early stage of synapse development. Later they solidify and bind other proteins found in the active presynaptic zone. You can make mutant ELKS1 and SYD2 lacking the low complexity regions, but the synapses they form are abnormal.

The liquid phase scaffold formed by SYD2 and ELK1 can be reconstituted in vitro. It binds and incorporates downstream synaptic components. Both proteins are large (SYD2 has 1,139 amino acids, ELKS1 has 836).

What is remarkable is that you can take a phase separation motif from human proteins (FUS which when mutated can cause ALS, or from hnRNPA2) put them into SYD2 and ELK1 mutants lacking their low complexity region and have the proteins form a normal presynaptic active zone.

This is remarkable and exciting stuff

*****

Advances in cellular biology have largely come from chemistry.  Think DNA and protein structure, enzyme analysis.  However, cell biology is now beginning to return the favor and instruct chemistry by giving it new objects to study. Think phase transitions in the cell, liquid liquid phase separation, liquid droplets, and many other names (the field is in flux) as chemists begin to explore them.  Unlike most chemical objects, they are big, or they wouldn’t have been visible microscopically, so they contain many, many more molecules than chemists are used to dealing with.

These objects do not have any sort of definite stiochiometry and are made of RNA and the proteins which bind them (and sometimes DNA).  They go by any number of names (processing bodies, stress granules, nuclear speckles, Cajal bodies, Promyelocytic leukemia bodies, germline P granules.  Recent work has shown that DNA may be compacted similarly using the linker histone [ PNAS vol.  115 pp.11964 – 11969 ’18 ]

The objects are defined essentially by looking at them.  By golly they look like liquid drops, and they fuse and separate just like drops of water.  Once this is done they are analyzed chemically to see what’s in them.  I don’t think theory can predict them now, and they were never predicted a priori as far as I know.

No chemist in their right mind would have made them to study.  For one thing they contain tens to hundreds of different molecules.  Imagine trying to get a grant to see what would happen if you threw that many different RNAs and proteins together in varying concentrations.  Physicists have worked for years on phase transitions (but usually with a single molecule — think water).  So have chemists — think crystallization.

Proteins move in and out of these bodies in seconds.  Proteins found in them do have low complexity of amino acids (mostly made of only a few of the 20), and unlike enzymes, their sequences are intrinsically disordered, so forget the key and lock and induced fit concepts for enzymes.

Are they a new form of matter?  Is there any limit to how big they can be?  Are the pathologic precipitates of neurologic disease (neurofibrillary tangles, senile plaques, Lewy bodies) similar.  There certainly are plenty of distinct proteins in the senile plaque, but they don’t look like liquid droplets.

It’s a fascinating field to study.  Although made of organic molecules, there seems to be little for the organic chemist to say, since the interactions aren’t covalent.  Time for physical chemists and polymer chemists to step up to the plate.

Maybe the backbone is more important than the side chains

I’m really embarrassed that I was unaware of the following work on protein design from Japan. Apparently, they were able to design proteins stable at 100 Centigrade using a methodology of which I was completely in the dark (N. Koga et al., Principles for designing ideal protein structures. Nature 491, 222–227 (2012), Y. R. Lin et al., Control over overall shape and size in de novo designed proteins. Proc. Natl. Acad. Sci. U.S.A. 112, E5478–E5485 (2015)). I read those journals but must have skipped the articles — I’ll have to go back and have a look.

A recent article (PNAS 117 31149 – 31156 ’20) brought it to my attention. Here’s what they say they’ve done.

“We proposed principles for designing ideal protein structures stabilized by completely consistent local and nonlocal interactions , based on a set of rules relating local backbone structures to preferred tertiary motifs (7, 10 — given above). These design rules describe the relation of the lengths or torsion patterns of two secondary structure elements and the connecting loop to favorable packing geometries . The design principles enable to encode strongly funneled energy landscapes into amino acid sequences, by the stabilization of folded structures (positive design) and by the destabilization of nonnative conformations (negative design) due to the restriction of folding conformational space by the rules”

Hard to believe but it works apparently. The paper also stands an idea about protein structure and stability on its head — the hydrophobic core of a compact protein, in this case a designed protein with a Rossmann fold (two pairs of alpha helices sandwiching a beta sheet is absolutely crucial to the ultimate 3 dimensional conformation of the protein backbone.

The protein is quite stable, not denaturing at 100 C. So then they mutated 10 of the large hydrophobic amino acids (leucine, isoleucine) to a small one (valine) so that 30 of the 34 amino acids in the core were valine and watched what happened.

What’s your guess? Mine would have been that the core was in a molten globule state and that backbone structure was lost.

That’s not what happened at all. The resulting protein was still stable over 100 C (although not quite as much by 5 KCal/mole)

To quote the authors again — “This result indicates that hydrophobic tight core packing may not be quite important for designed proteins: The folding ability and extremely high stability may arise from the restriction of conformational space to be searched during folding by the local backbone structures. This can lead to an exceptionally stable protein even in the absence of precise core packing.”

Astounding. However, this may not be true for proteins ‘designed’ by natural selection.
It’s time to try the same trick on some of them.

Cells are not bags of cytoplasm

How Ya Gonna Keep ’em Down on the Farm (After They’ve Seen Paree) is a song of 100+ years ago when World War I had just ended. In 1920, for the first time America was 50/50 urban/rural. Now it’s 82%.

What does this have to do with cellular biology? A lot. One of the first second messengers to be discovered was cyclic adenosine monophosphate (CAMP). It binds to an enzyme complex called protein kinase A (PKA), activating it, making it phosphorylate all sorts of proteins changing their activity. But PKA doesn’t float free in the cell. We have some 47 genes for proteins (called AKAPs for protein A Kinase Anchoring Protein) which bind PKA and localize it to various places in the cell. CAMP is made by an enzyme called adenyl cyclase of which we have 10 types, each localized to various places in the cell (because most of them are membrane embedded). We also have hundreds of G Protein Coupled Receptors (GPCRs) localized in various parts of the cell (apical, basal, primary cilia, adhesion structures etc. etc.) many of which when activated stimulate (by yet another complicated mechanism) adenyl cyclase to make CAMP.

So the cell tries to keep CAMP when it is formed relatively localized (down on the farm if you will). Why have all these ways of making it if its going to run all over the cell after all.

Actually the existence of localized signaling by CAMP is rather controversial, particularly when you can measure how fast it is moving around. All studies previous to Cell vol. 182 pp. 1379 – 1381, 1519 – 1530 ’20 found free diffusion of CAMP.

This study, found that CAMP (in low concentrations) was essentially immobile, remaining down on the farm where it was formed.

The authors used a fluorescent analog of CAMP which allowed them to use fluorescence fluctuation spectroscopy which gives the probability distribution function of an individual molecule occupying a given position in space and time (SpatioTemporal Image correlation Spectroscopy — STICS).

Fascinating as the study is, it is ligh tyears away from physiologic — the fluorescent CAMP analog was not formed by anything resembling a physiologic mechanism (e.g. by adenyl cyclase). A precursor to the fluorescent CAMP was injected into the cell and broken down by ‘intracellular esterases’ to form the fluorescent CAMP analog.

Then the authors constructed a protein made of three parts (1) a phosphodiesterase (PDE) which broke down the fluorescent CAMP analog and (2) another protein — the signaler — which fluoresced when it bound the CAMP analog. The two were connected by (3) a flexible protein linker e.g. the ‘ruler’ of the previous post. The ruler could be made of various lengths.

Then levels of fluorescent CAMP were obtained by injecting it into the cell, or stimulating a receptor.

If the sensor was 100 Angstroms away from the PDE, it never showed signs of CAMP, implying the the PDE was destroying it before it could get to the linker implying that diffusion was quite slow. This was at low concentrations of the fluorescent CAMP analog. At high injection concentrations the CAMP overcame the sites which were binding it in the cell and moved past the signaler.

It was a lot of work but it convincingly (to me) showed that CAMP doesn’t move freely in the cell unless it is of such high concentration that it overcomes the binding sites available to it.

They made another molecule containing (1) protein kinase A (2) a ruler (3) a phophodiesterase. If the kinase and phosphodiesterase were close enough together, CAMP never got to PKA at all.

Another proof that phosphodiesterase enzymes can create a zone where there is no free CAMP (although there is still some bound to proteins).

Hard stuff (to explain) but nonetheless impressive, and shows why we must consider the cell a bunch of tiny principalities jealously guarding their turf like medieval city states.

*****

A molecular ruler

Time to cleanse your mind by leaving the contentious world of social issues and entering the realm of pure thought with some elegant chemistry. 

You are asked to construct a molecular ruler with a persistence length of 150 Angstroms. 

Hint #1: use a protein

Hint #2; use alpha helices

Spoiler alert — nature got there first. 

The ruler was constructed and used in an interesting paper on CAMP nanoDomains (about which more on the next post).

It’s been around since 2011 [ Proc. Natl. Acad. Sci. vol. 108 pp. 20467 – 20472 ’11 ] and I’m embarrassed to admit I’d never heard of it.

It’s basically a run of 4 negatively charged amino acids (glutamic acid or aspartic acid) followed by a run of 4 positively charged amino acids (lysine, arginine). This is a naturally occurring motif found in a variety of species. 

My initial (incorrect) thought was that this couldn’t work as the 4 positively charged amino acids would bend at the end and bind to the 4 negatively charged ones. This can’t work even if you make the peptide chain planar, as the positive charges would alternate sides on the planar peptide backbone.

Recall that there are 3.5 amino acids/turn of the alpha helix, meaning that between a run of 4 Glutamic acid/Aspartic acids and an adjacent run of 4 lysines/arginines, an ionic bond is certain to form between the side chains (and not between adjacent amino acids on the backbone, but probably one 3 or 4 amino acids away)

Since a complete turn of the alpha helix is only 5.4 Angstroms, a persistence length of 150 means about 28 turns of the helix using 28 * 3.5 = 98 amino acids or about 12 blocks of ++++—- charged amino acids. 

The beauty of the technique is that by starting with an 8 amino acid ++++—- block, you can add length to your ruler in 12 Angstrom increments. This is exactly what Cell vol. 182 pp. 1519 – 1530 ’20 did. But that’s for the next post. 

247 ZeptoSeconds

247 ZeptoSeconds is not the track time of the fastest Marx brother. It is the time a wavelength of light takes to travel across a hydrogen molecule (H2) before it kicks out an electron — the photoelectric effect.

But what is a zeptosecond anyway? There are 10^21 zeptoSeconds in a second. That’s a lot. A thousand times more than the number of seconds since the big bang which is only 60 x 60 x 24 x 365 x 13.8 x 10^9 = 4. 35 x 10^17. Not that big a deal to a chemist anyway since 10^21 is 1/600th of the number of molecules in a mole.

You can read all about it in Science vol. 370 pp. 339 – 341 ’20 — https://science.sciencemag.org/content/sci/370/6514/339.full.pdf it you have a subscription.

Studying photoionization allows you to study the way light is absorbed by molecules, something important to any chemist. The 247 zeptoseconds is the birth time of the emitted electron. It depends on the travel time of the photon across the hydrogen molecule.

They don’t quite say trajectory of the photon, but it is implied even though in quantum mechanics (which we’re dealing with here), there is no such a thing as a trajectory. All we have is measurements at time t1 and time t2. We are not permitted to say what the photon is doing between these two times when we’ve done measurements. Our experience in the much larger classical physics world makes us think that there is such a thing.

It is the peculiar doublethink quantum mechanics forces on us. Chemists know this when they think about something as simple as the S2 orbital, something spherically symmetric, with electron density on either side of a node. The node is where you never find an electron. Well if you don’t, find it here, how can it have a trajectory from one side to the other.

Quantum mechanics is full of conundrums like that. Feynman warned us not to think about them, but it will take your mind off the pandemic (and if you’re good, off the election as well)..

It’s worth reading the article in Quanta which asks if wavefunctions tunnel through a barrier at speeds faster than light — here’s a link — https://www.quantamagazine.org/quantum-tunnel-shows-particles-can-break-the-speed-of-light-20201020/. It will make your head spin.

Here’s a link to an earlier post about the doublethink quantum mechanics forces on us

https://luysii.wordpress.com/2009/12/10/doublethink-and-angular-momentum-why-chemists-must-be-adept-at-it/

Here’s the post itself

Doublethink and angular momentum — why chemists must be adept at it

Chemists really should know lots and lots about angular momentum which is intimately involved in 3 of the 4 quantum numbers needed to describe atomic electronic structure. Despite this, I never really understood what was going until taking the QM course, and digging into chapters 10 and 11 of Giancoli’s physics book (pp. 248 -310 4th Edition).

Quick, what is the angular momemtum of a single particle (say a planet) moving around a central object (say the sun)? Well, its magnitude is the current speed of the particle times its mass, but what is its direction? There must be a direction since angular momentum is a vector. The (unintuitive to me) answer is that the angular momemtum vector points upward (resp. downward) from the plane of motion of the planet around the center of mass of the sun planet system, if the planet is moving counterclockwise (resp. clockwise) according to the right hand rule. On the other hand, the momentum of a particle moving in a straight line is just its mass times its velocity vector (e.g. in the same direction).

Why the difference? This unintuitive answer makes sense if, instead of a single point mass, you consider the rotation of a solid (e.g. rigid) object around an axis. All the velocity vectors of the object at a given time either point in different directions, or if they point in the same direction have different magnitudes. Since the object is solid, points farther away from the axis are moving faster. The only sensible thing to do is point the angular momentum vector along the axis of rotation (it’s the only thing which has a constant direction).

Mathematically, this is fairly simple to do (but only in 3 dimensions). The vector from the axis of rotation to the planet (call it r), and the vector of instantaneous linear velocity of the planet (call it v) do not point in the same direction, so they define a plane (if they do point in the same direction the planet is either hurtling into the sun or speeding directly away, hence not rotating). In 3 dimensions, there is a unique direction at 90 degrees to the plane. The vector cross product of r and v gives a vector pointing in this direction (to get a unique vector, you must use the right or the left hand rule). Nicely, the larger r and v, the larger the angular momentum vector (which makes sense). In more than 3 dimensions there isn’t a unique direction away from a plane, which is why the cross product doesn’t work there (although there are mathematical analogies to it).

This also explains why I never understood momentum (angular or otherwise) till now. It’s very easy to conflate linear momentum with force and I did. Get hit by a speeding bullet and you feel a force in the same direction as the bullet — actually the force you feel is what you’ve done to the bullet to change its momentum (force is basically defined as anything that changes momentum).

So the angular momentum of an object is never in the direction of its instantaneous linear velocity. But why should chemists care about angular momentum? Solid state physicists, particle physicists etc. etc. get along just fine without it pretty much, although quantum mechanics is just as crucial for them. The answer is simply because the electrons in a stable atom hang around the nucleus and do not wander off to infinity. This means that their trajectories must continually bend around the nucleus, giving each trajectory an angular momentum.

Did I say trajectory? This is where the doublethink comes in. Trajectory is a notion of the classical world we experience. Consider any atomic orbital containing a node (e.g. everything but a 1 s orbital). Zeno would have had a field day with them. Nodes are surfaces in space where the electron is never to be found. They separate the various lobes of the orbital from each other. How does the electron get from one lobe to the other by a trajectory? We do know that the electron is in all the lobes because a series of measurements will find the electron in each lobe of the orbital (but only in one lobe per measurement). The electron can’t make the trip, because there is no trip possible. Goodbye to the classical notion of trajectory, and with it the classical notion of angular momentum.

But the classical notions of trajectory and angular momentum still help you think about what’s going on (assuming anything IS in fact going on down there between measurements). We know quite a lot about angular momentum in atoms. Why? Because the angular momentum operators of QM commute with the Hamiltonian operator of QM, meaning that they have a common set of eigenfunctions, hence a common set of eigenvalues (e.g. energies). We can measure these energies (really the differences between them — that’s what a spectrum really is) and quantum mechanics predicts this better than anything else.

Further doublethink — a moving charge creates a magnetic field, and a magnetic field affects a moving charge, so placing a moving charge in a magnetic field should alter its energy. This accounts for the Zeeman effect (the splitting of spectral lines in a magnetic field). Trajectories help you understand this (even if they can’t really exist in the confines of the atom).

Action at a distance comes to chemistry

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.

Even though Newton invented a theory of gravity, which worked beautifully, he was disturbed by the fact that it acted through empty space. Here’s what he wrote in a letter to Bentley

“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 ]. Here’s a link but it’s probably behind a paywall — https://www.pnas.org/content/pnas/117/41/25445.full.pdf

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

A molecular ruler

Time to cleanse your mind by leaving the contentious world of social issues and entering the realm of pure thought with some elegant chemistry.

You are asked to construct a molecular ruler with a persistence length of 150 Angstroms.

Hint #1: use a protein

Hint #2; use alpha helices

Spoiler alert — nature got there first.

The ruler was constructed and used in an interesting paper on CAMP nanoDomains (about which more on the next post).

It’s been around since 2011 [ Proc. Natl. Acad. Sci. vol. 108 pp. 20467 – 20472 ’11 ] and I’m embarrassed to admit I’d never heard of it.

It’s basically a run of 4 negatively charged amino acids (glutamic acid or aspartic acid) followed by a run of 4 positively charged amino acids (lysine, arginine). This is a naturally occurring motif found in a variety of species.

My initial (incorrect) thought was that this couldn’t work as the 4 positively charged amino acids would bend at the end and bind to the 4 negatively charged ones. This can’t work even if you make the peptide chain planar, as the positive charges would alternate sides on the planar peptide backbone.

Recall that there are 3.5 amino acids/turn of the alpha helix, meaning that between a run of 4 Glutamic acid/Aspartic acids and an adjacent run of 4 lysines/arginines, an ionic bond is certain to form between the side chains (and not between adjacent amino acids on the backbone, but probably one 3 or 4 amino acids away)

Since a complete turn of the alpha helix is only 5.4 Angstroms, a persistence length of 150 means about 28 turns of the helix using 28 * 3.5 = 98 amino acids or about 12 blocks of ++++—- charged amino acids.

The beauty of the technique is that by starting with an 8 amino acid ++++—- block, you can add length to your ruler in 12 Angstrom increments. This is exactly what Cell vol. 182 pp. 1519 – 1530 ’20 did. But that’s for the next post.

Why drug development is hard #34 — designer hallucinogens

NBOMe (2-(4-Bromo-2,5-dimethoxyphenyl)-N-[(2-methoxyphenyl) methyl]ethanamine to you) is a potent hallucinogen, a member of the phenylethylamine series of hallucinogens.  Well that’s the same as saying the current Intel chips are a member of the Intel class of starting with the 8080. https://psychonautwiki.org/wiki/25B-NBOMe has the structure, but I count 2 methoxy groups and a bromine on the phenyl group and a methoxy benzyl group making the amine group a secondary amine.

How anyone came up with the structure will remain unknown to me as it was part of a PhD thesis written in 2003 — unfortunately in German —Ralf Heim (February 28, 2010). “Synthese und Pharmakologie potenter 5-HT2A-Rezeptoragonisten mit N-2-Methoxybenzyl-Partialstruktur. Entwicklung eines neuen Struktur-Wirkungskonzepts.” (in German). diss.fu-berlin.de. Retrieved 2013-05-10.

Like other hallucinogens (LSD, mescaline, psilocin) NBOMe binds to the 2A variety of serotonin receptor (aka 5HT2A — at least 16 serotonin receptors are known) and acts like LSD as an agonist.

Which brings me to Cell vol. 182 pp. 1574 – 1588 ’20 — https://www.cell.com/cell/fulltext/S0092-8674(20)31066-7, probably behind a paywall.  Which has beautiful cryoEM structures of 5HT2A bound to LSD, NBOMe and methiothepin, an inverse agonist.  To get pictures they had to stabilize the structure with a single chain variable fragment of an antibody (something that always makes me wonder how physiologic the structure obtained actually is).

Why use NBOMe as an example of how hard drug discovery is?  Well the binding site of LSD to 5HT2A is well known, and the paper has some beautiful pictures of LSD snuggled between the 7 transmembrane segments of 5HT2A.  What is remarkable about NBOMe is that it lies in the binding site in a completely different orientation.  Moreover NBOMe fits in a previously undescribed pocket between transmembrane segments #3 and #6 (TM3, TM6).  Actually I think NBOMe actually produces the pocket.

So even if you know the target of your drug (5HT2A) and how another drug hits the target you’re aiming for, this doesn’t help you in designing a newer and more potent drug.