Category Archives: Chemistry (relatively pure)

Kinetic traps and life

“It is well known that the thermodynamically stable state of proteins in a crowded environment is insoluble fibrils” [ Proc. Natl. Acad. Sci. vol. 119 pp. e2122078119 ’22 ].  However even under ideal conditions the time scale for their formation is hours to days [ Nat. Rev. Mol. Cell Biol. 15, 384–396 (2014) ].  Hopefully it’s even longer (decades) for senile plaques (abeta) neurofibrils (tau) and Lewy bodies (alpha-synuclein) to form.  The fact that equilibrium takes such a long time to reach, allows rapid synthesis and degradation of proteins to avoid their aggregation.  So we live because our proteins are trapped in a less the equilibrium (metastable) state by kinetics — e.g. a kinetic trap.

We now understand what amyloid actually is

Lately we have received an embarrassment of riches about amyloid and the diseases it causes.  I’ll start with the latest — the structure of TDP amyloid.

I must say it is a pleasure to get back to chemistry and away from the pandemic, however briefly.  So relax and prepare to enjoy some great chemistry and protein structure.

TDP43 (you don’t to know what the acronym stands for) is a protein which binds to RNA (among other things).  It also forms aggregates, and some 50 mutations are known producing FrontoTemporal  Dementia (FTD) and/or Amyotrophic Lateral Dementia (ALS).  I saw a case as a resident (before things were worked out) and knew something was screwy because while ALS is a horrible disease, patients are clear to the end (witness Stephen Hawking) and my patient was clearly dementing.

Mutations in TDP43 occur in 5% of familial ALS.  More to the point cytoplasmic aggregates of TDP43 occur in 95% of sporadic cases of ALS (no mutations), so neurologists have been fascinated with TDP43 for years.

Back before we knew much about the structure of amyloid, it was characterized by the dyes that would bind to it (Congo Red, thioflavin etc.) and birefringence (see below).  None of this is true for the aggregates of TDP43.

Well we now know what the structure of amyloid is.  You simply can’t do better than  Cell vol. 184 pp. 4857 – 4873 ’21 — but it might be behind a paywall.

So here’s the skinny about what amyloid actually is —

 

It is a significantly long polypeptide chain  flattening  out into a 4.8 Angstrom thick sheet, essentially living in 2 dimensions.  Thousands of sheets then pile on top of each other forming amyloid.  So amyloid is not a particular protein, but a type of conformation a protein can assume (like the alpha helices, beta pleated sheets etc. etc. ).

The structure also explained why planar molecules like Congo Red bind to amyloid (it slips between the sheets).   Or at least that’s what I thought.

 

Enter Nature vol. 601 pp. 29 – 30, 139 – 143 ’22 showing that some 79 amino acids of the 414 amino acids of TDP43 flatten out into single sheet in the aggregates, with the sheets piling on top of each other.  If that isn’t amyloid, what is?

 

Where are the beta strands producing birefringence if this is amyloid.  In fact where is the birefringence? (see below). The paper says that there are 10 beta strands in the 79 amino acids, but they are short with only two of them containing more than 3 amino acids (I guess they can see beta strands by measuring backbone angles a la Ramachandran plots).  The high number of glycine mediated turns prevents beta sheets from stacking next to each other precluding the crossBeta  structure (and birefringence).

 

Why doesn’t Congo Red bind?  My idea about how it binds to other amyloids (slipping between the sheets) clearly is incorrect.

 

There are all sorts of fascinating points about the amyloid of TDP43.  The filaments derived from patients are stable to heating to 65 C.   The structure of the TDP43 fibrils derived from patients with FTD/ALS are quite different in structure from synthetic filaments made from parts of TDP43, so possibly a lot of work will have to be done again.

 

Here is some more detail on amyloid structure:

 

So start with NH – CO – CHR.  NH  CO and C in the structure all lie in the same plane (the H and the side chain of the amino acid < R >  project out of the plane).
Here’s a bit of elaboration for those of you whose organic chemistry is a distant memory.  The carbon in the carbonyl bond (CO) has 3 bonding orbitals in one plane 120 degrees apart, with the 4th orbital perpendicular to the plane — this is called sp2 hybridization.  The nitrogen can also be hybridized to sp2.  This lets the pair of electrons above the plane roam around moving toward the carbon.  Why is this good?  Because any time you let electrons roam around you increase their entropy (S) and anything increasing entropy lowers their free energy (F)which is given by the formula F = H – TS where H is enthalpy (a measure of bond strength, and T is the absolute temperature in Kelvin.

 

So N and CO are in one plane, and so are the bonds from  N and C to the adacent atoms (C in both cases).

 

You can fit the plane atoms into a  rectangle 4.8 Angstroms high.  Well that’s one 2 dimensional rectangle, but the peptide bond between NH and CO in adjacent rectangles allows you to tack NH – CO – C s together while keeping them in a 3 dimensional parallelopiped 4.8 Angstroms high

 

Notice that in the rectangle the NH and CO bonds are projecting toward the top and bottom of the rectangle, which means that in each plane  NH – CO – CHR s, the NH and CO are pointing out of the 2 dimensional plane (and in opposite directions to boot). This is unlike protein structure in which the backbone NHs and COs hydrogen bond to each other.  There is nothing in this structure for them to bond to

 

What they do is hydrogen bond to another 3 dimensional parallelopiped (call it a sheet, but keep in mind that this is NOT the beta sheet you know about from the 3 dimensional structures of proteins we’ve had for years).
So thousands of sheets stacked together form the amyloid fibril.

 

Where does the 9 Angstrom reflection of cross beta (and birefringence) come from?  Consider the  [ NH – CHR – CO ]  backbone as it lies in the 4.8  thick plane (Having studied proteins structure since entering med school in ’62, I never thought such a thing would even be possible ! ).  It curves around like a snake lying flat.  Where are the side chains?  They are in the 4.8 thick plane, separating parts of the meandering backbone from each other — by an average of 9 Angstroms.
Here is an excellent picture of the Alzheimer culprit — the aBeta42 peptide as it forms the amyloid of the senile plaque
You can see the meandering backbone and the side chains keeping the backbone apart.

Then Nature [ vol. 598,  pp. 359 – 363 ’21] blows the field wide open, finding 19 different conformations of tau in clinically distinct diseases. Each clinical disease appears to be associated with a distinct polymorphism.  This is also true for the polymorphisms of alpha-synuclein, with distinct conformations being seen in each of Parkinsonism, multiple system atrophy and Lewy body dementia.

In none of the above diseases is there a mutation (change in amino acid sequence) in the protein.

Henry J. Heinz claimed to have 57 varieties of pickles in 1896, but Cell [ vol. 184 pp. 4857 – 4873 ’21  ] Page 4862 claims that 24 amyloid polymorphs of alpha-synuclein have been found and structurally characterized.  Recall that alpha-synuclein amyloid is the principal component of the Lewy body of Parkinsonism  and Lewy Body disese

How did they get the 24 different conformations?  They incubated the protein under different conditions (e.g. different salt concentrations, different alpha-synuclein concentrations, different salts).

Why is this incredibly good news? 

Because it moves us past amyloid itself, to the conditions which cause amyloid to form.  Certainly, removing amyloid or attacking it hasn’t resulted in any clinical benefit for the Alzheimer patient despite billions being spent by Big Pharma to do so.

We will start to study the ‘root causes’ of amyloid formation.   The amino acid sequence of each protein is identical despite the different conformations of the chain in the amyloid. Clearly the causes must be different for each of the different polymorphs of the protein.  This just has to be true.

Amyloid Structure At Last ! 4 Polymorphs

Henry J. Heinz claimed to have 57 varieties of pickles in 1896, but Cell [ vol. 184 pp. 4857 – 4873 ’21  ] Page 4862 claims that 24 amyloid polymorphs of alpha-synuclein have been found and structurally characterized.

What does this actually mean in English? The previous 3 articles in this series have discussed the structure of amyloid — the most relevant being https://luysii.wordpress.com/2021/10/11/amyloid-structure-at-last/

Basically, in amyloid some of the protein backbone flattens out so it lies in a single plane, and thousands of the planes stack on top of each other producing the amyloid fiber.  In the case of alpha-synuclein some 56 of the 144 amino acids comprising the protein flatten out.   Just as throwing a chain with 56 links on the floor will give different conformations of the chain,  the conformation of alpha-synuclein is different in each of the polymorphs.

So what?

Well, different polymorphs of another protein, the tau protein which forms the neurofibrillary tangle in Alzheimer’s give rise to at least 25 clinically distinct neurological diseases called tauopathies (3 more are chronic traumatic encephalopathy, corticobasal degeneration, and Pick’s disease).  In each of the these four diseases, a different conformation of tau is seen.

Then Nature [ vol. 598,  pp. 359 – 363 ’21] blows the field wide open, finding 19 different conformations of tau in clinically distinct diseases. Each clinical disease appears to be associated with a distinct polymorphism.  This is also true for the polymorphisms of alpha-synuclein, with distinct conformations being seen in each of Parkinsonism, multiple system atrophy and Lewy body dementia.

In none of the above diseases is there a mutation (change in amino acid sequence) in the protein

Back to alpha-synuclein.  How did they get the 24 different conformations?  They incubated the protein under different conditions (e.g. different salt concentrations, different alpha-synuclein concentrations, different salts).

Why is this incredibly good news? 

Because it moves us past amyloid itself, to the conditions which cause amyloid to form.  Certainly, removing amyloid or attacking it hasn’t resulted in any clinical benefit for the Alzheimer patient despite billions being spent by Big Pharma to do so.

We will start to study the ‘root causes’ of amyloid formation.   The amino acid sequence of each protein is identical despite the different conformations of the chain in the amyloid. Clearly the causes must be different for each of the different polymorphs of the protein.  This just has to be true.

Some cynic said that people who talk about the root causes of crime never get their hands dirty.  Hopefully neuroscience is about to take off its gloves.

This is why alternative approaches to Alzheimer’s disease, such as Cassava Biosciences manipulation of filamin A, might bear fruit.   For details please see — https://luysii.wordpress.com/2021/03/25/the-science-behind-cassava-sciences-sava/

Just got this back from one of the authors of the Nature paper

“Yes, studying the conditions that lead to all these different structures
is certainly high on our to-do list now.”

 

Amyloid Structure at Last ! 3 The Alzheimer mutations

The structure of the amyloid fibril formed by the aBeta42 peptide exactly shows why certain mutations are associated with hereditary Alzheimer’s disease.   Here is a picture

https://www.alzforum.org/news/research-news/danger-s-bends-new-structure-av42-fibrils-comes-view

Scroll down to the picture above “Bonds that Tie”

If you need some refreshing on the general structure of amyloid, have a look at the first post in the series — https://luysii.wordpress.com/2021/10/11/amyloid-structure-at-last/

Recall that in amyloid fibrils the peptide backbone is flat as a flounder (well in a box 4.8 Angstroms high) with the amino acid side chains confined to this plane.  The backbone winds around in this plane like a snake.  The area in the leftmost loop is particularly crowded with bulky side chains of glutamic acid (single letter E) at position 22 and aspartic acid (single letter D) at position 23 crowding each other.  If that wasn’t enough, at the physiologic pH of 7 both acids are ionized, hence negatively charged.  Putting two negative charges next to each other costs energy and makes the sheet making up the fibril less stable.

The marvelous paper (the source for much of this) Cell vol. 184 pp. 4857 – 4873 ’21 notes that there are 3 types of amyloid — pathological, artificial, and functional, and that the pathological amyloids are the most stable. The most stable amyloids are the pathological ones.  Why this should be so will be the subject of a future post, but accept it as fact for now

In 2007 there were 7 mutations associated with familial Alzheimer’s disease (10 years later there were 11). Here are 5 of them.

Glutamic Acid at 22 to Glycine (Arctic)

Glutamic Acid at 22 to Glutamine (Dutch)

Glutamic Acid at 22 to Lysine (Italian)

Aspartic Acid at 23 to Asparagine (Iowa)

Alanine at 21 to Glycine (Flemish)

All of them lower the energy of the amyloid fiber.

Here’s why

Glutamic Acid at 22 to Glycine (Arctic) — glycine is the smallest amino acid (side chain hydrogen) so this relieves crowding.  It also removes a negatively charged amino acid next to the aspartic acid.  Both lower the energy

Glutamic Acid at 22 to Glutamine (Dutch) — really no change in crowding, but it removes a negative charge next to the negatively charged Aspartic acid

Glutamic Acid at 22 to Lysine (Italian)– no change in crowding, but the lysine is positively charged at physiologic pH, so we have a positive charge next to the negatively charged Aspartic acid, lowering the energy

Aspartic Acid at 23 to Asparagine (Iowa) –really no change in crowding, but it removes a negative charge next to the negatively charged Glutamic acid next door

Alanine at 21 to Glycine (Flemish) — no change in charge, but a reduction in crowding as alanine has a methyl group and glycine a hydrogen.

As a chemist, I find this immensely satisfying.  The structure explains why the mutations in the 42 amino acid aBeta peptide are where they are, and the chemistry explains why the mutations are what they are.

 

 

 

 

 

 

Amyloid Structure at Last ! – 2 Birefringence

This was the state of the art 19 years ago in a PNAS paper (vol. 99 pp. 16742 – 16747 ’02).  “Amyloid fibrils are filamentous structures with typical diameters of 10 nanoMeters and lengths up to several microns.  No high resolution molecular structure of an amyloid fibril has yet been determined experimentally because amyloid fibrils are noncrystalline solid materials and are therefore incompatible with Xray crystallography and liquid state NMR.”

Well solid state NMR and cryo electron microscopy have changed all that and we now have structures for many amyloids at near atomic resolution.  It’s probably behind a pay wall but look at Cell vol. 184 pp. 4857 – 4873 ’21 if you have a chance.  I’ve spent the last week or so with it, and a series of posts on various aspects of the paper will be forthcoming.  The paper contains far too much to cram into a single post.

So lacking an Xray machine to do diffraction, what did we have 57 years ago when I started getting seriously interested in neurology?  To find amyloid we threw a dye called Congo Red on a slide, found that it bound amyloid and became birefringent when it did so.

Although the Cell paper doesn’t even mention Congo Red, the structure of amyloid they give explains why this worked.

What is birefringence anyway?  It means that light moving through a material travels at different speeds in different directions.  The refractive index of a material is the relative speed of light through that material versus the speed of light in a vacuum.   Stand in a shallow pool.  Your legs look funny because light travels slower in water than in air (which is nearly a vacuum).

Look at the structure of Congo Red — https://en.wikipedia.org/wiki/Congo_red.  It’s a long thin planar molecule, containing 6 aromatic rings, kept planar with each other by pi electron delocalization.

The previous post contained a more detailed description of amyloid — but suffice it to say that instead of wandering around in 3 dimensional space, the protein backbone in amyloid is confined to a single plane 4.8 Angstroms thick — here’s a link — https://luysii.wordpress.com/2021/10/11/amyloid-structure-at-last/

Plane after plane stacks on top of each other in amyloid.  So a micron (which is 10,000 Angstroms) can contain over 5,000 such planes, and an amyloid fibril can be several microns long.

It isn’t hard to imagine the Congo Red molecule slipping between the sheets, making it’s orientation fixed.  Sounds almost pornographic doesn’t it? This orients the molecule and clearly light moving perpendicular to the long axis of Congo Red will move at a different speed than light going parallel to the long axis of Congo Red, hence its birefringence when the dye binds amyloid.

Well B-DNA (the form we all know and love as the double helix) has its aromatic bases stacked on top of each other every 3.4 Angstroms.  So why isn’t it birefringent with Congo Red?  It has a persistence length of 150 basePairs or about .05 microns, which means that the average orientation is averaged out, unlike the amyloid in a senile plaque

There is tons more to come.  The Cell paper is full of fascinating stuff.

Amyloid structure at last !

As a neurologist, I’ve been extremely interested in amyloid  since I started in the late 60s.  The senile plaque of Alzheimers disease is made of amyloid.  The stuff was insoluble gunk. All we had back in the day was Xray diffraction patterns showing two prominent reflections at 4 and 9 Angstroms, so we knew there was some sort of repetitive structure.

My notes on papers on the subject over the past 20 years contain  about 100,000 characters (but relatively little enlightenment until recently).

A while ago I posted some more homework problems — https://luysii.wordpress.com/2021/09/30/another-homework-assignment/

Homework assignment #1:  design a sequence of 10 amino acids which binds to the same sequence in the reverse order forming a plane 4.8 Angstroms thick.

Homework assignment #2 design a sequence of 60 amino acids which forms a similar plane 4.8 Angstroms thick, such that two 60 amino acid monomers bind to each other.

Feel free to use any computational or theoretical devices currently at our disposal, density functional theory, force fields, rosetta etc. etc.

Answers to follow shortly

Hint:  hundreds to thousands of planes can stack on top of each other.

 

If you have a subscription to Cell take a look at a marvelous review full of great pictures and diagrams [ Cell vol. 184 pp. 4857 – 4873 ’21 ].

 

Despite all that reading I never heard anyone predict that a significantly long polypeptide chain could flatten out into a 4.8 Angstrom thick sheet, essentially living in 2 dimensions.  All the structures we had  (alpha helix, beta pleated sheet < they were curved >, beta barrel, solenoid, Greek key) live in 3 dimensions.

 

 

So amyloid is not a particular protein, but a type of conformation a protein can assume (like the structures mentioned above).

 

 

So start with NH – CO – CHR.  NH  CO and C in the structure all lie in the same plane (the H and the side chain of the amino acid < R >  project out of the plane).

 

Here’s a bit of elaboration for those of you whose organic chemistry is a distant memory.  The carbon in the carbonyl bond (CO) has 3 bonding orbitals in one plane 120 degrees apart, with the 4th orbital perpendicular to the plane — this is called sp2 hybridization.  The nitrogen can also be hybridized to sp2.  This lets the pair of electrons above the plane roam around moving toward the carbon.  Why is this good?  Because any time you let electrons roam around you increase their entropy (S) and anything increasing entropy lowers their free energy (F)which is given by the formula F = H – TS where H is enthalpy (a measure of bond strength, and T is the absolute temperature in Kelvin.

 

 

So N and CO are in one plane, and so are the bonds from  N and C to the adacent atoms (C in both cases).

 

You can fit the plane atoms into a  rectangle 4.8 Angstroms high.  Well that’s one 2 dimensional rectangle, but the peptide bond between NH and CO in adjacent rectangles allows you to tack NH – CO – C s together while keeping them in a 3 dimensional parallelopiped 4.8 Angstroms high.

 

 

Notice that in the rectangle the NH and CO bonds are projecting toward the top and bottom of the rectangle, which means that in each plane  NH – CO – CHR s, the NH and CO are pointing out of the 2 dimensional plane (and in opposite directions to boot). This is unlike protein structure in which the backbone NHs and COs hydrogen bond to each other.  There is nothing in this structure for them to bond to.

 

 

What they do is hydrogen bond to another 3 dimensional parallelopiped (call it a sheet, but keep in mind that this is NOT the beta sheet you know about from the 3 dimensional structures of proteins we’ve had for years).

 

 

So thousands of sheets stacked together form the amyloid fibril.

 

Where does the 9 Angstrom reflection of cross beta come from?  Consider the  [ NH – CHR – CO ]  backbone as it lies in the 4.8  thick plane (I never thought such a thing would be even possible ! ).  It curves around like a snake lying flat.  Where are the side chains?  They are in the 4.8 thick plane, separating parts of the meandering backbone from each other — by an average of 9 Angstroms

 

Here is an excellent picture of the Alzheimer culprit — the aBeta42 peptide as it forms the amyloid of the senile plaque

 

 

You can see the meandering backbone and the side chains keeping the backbone apart.

 

 

That’s just the beginning of the paper, and I’ll have lots more to say about amyloid as I read further.   Once again, biology instructs chemistry and biochemistry giving it more “things in heaven and earth, Horatio, than are dreamt of in your philosophy.”

More homework assignments

Homework assignment #1:  design a sequence of 10 amino acids which binds to the same sequence in the reverse order forming a plane 4.8 Angstroms thick.

Homework assignment #2 design a sequence of 60 amino acids which forms a similar plane 4.8 Angstroms thick, such that two 60 amino acid monomers bind to each other.

Feel free to use any computational or theoretical devices currently at our disposal, density functional theory, force fields, rosetta etc. etc.

Answers to follow shortly

Hint:  hundreds to thousands of planes can stack on top of each other.

Also I’ve written about phase changes in the past — https://luysii.wordpress.com/2020/12/20/neuroscience-can-no-longer-ignore-phase-separation/

A superb review of the subject is available if you have a subscription to Neuron [ Neuron vol. 109 pp. 2663 – 2681 ’21 ]

A possible new way to attack Parkinson’s disease

Alpha-synuclein is the main component of the Lewy body of Parkinson’s disease.  It contains 140 amino acids, and is ‘natively unfolded’ in that it has no apparent ordered secondary structure (alpha helices, beta pleated sheets) detectable by a variety of methods — far ultraviolet circular dichroism, Fourier transform infrared spectroscopy or NMR spectroscopy. When the protein binds to artificial membranes half of it forms alpha helices.   Amazingly, after a huge amount of work we don’t know what alpha-Synuclein actually does.  Knockouts have only minor CNS abnormalities.

However, alpha synuclein forms fibrils which bind to cell surface receptors with internalization and transmission to other cells, just like prions.   Two such receptors for alpha-synuclein fibrils are Lymphocyte Activation Gene E (LAG3) and Amyloid PrecursorLike Protein 1 (ALPL1).

LAG3 has 4 immunoglobulin like domains (D1 – D4).  It uses D1 to capture the carboxy terminus which is exposed and concentrated on the surface of the alpha-synuclein fibrils.

Interestingly the monomers are said to adopt a self-shielded conformation which impedes the exposure of the carboxy terminus.  Phosphorylation of serine #129 enhances the binding of alpha-synuclein preformed fibrils to LAG3 and APLP1.  So the carboxy terminus of alpha-synuclein is a promising traget to block Parkinson’s disease progression.

Mathematics and the periodic table

It isn’t surprising that math is involved in the periodic table. Decades before the existence of atoms was shown for sure (Einstein in 1905 on Brownian motion — https://physicsworld.com/a/einsteins-random-walk/) Mendeleev arranged the known elements in a table according to their chemical properties. Math is great at studying and describing structure, and the periodic table is full of it. 

What is surprising, is how periodic table structure arises from math that ostensibly has absolutely nothing to do with chemistry.  Here are 3 examples.

The first occurred exactly 60 years ago to the month in grad school.  The instructor was taking a class of budding chemists through the solution of the Schrodinger equation for the hydrogen atom. 

Recursion relations are no stranger to the differential equations course, where you learn to (tediously) find them for a polynomial series solution for the differential equation at hand. I never really understood them, but I could use them (like far too much math that I took back then).

So it wasn’t a shock when the QM instructor back then got to them in the course of solving the hydrogen atom (with it’s radially symmetric potential). First the equation had to be expressed in spherical coordinates (r, theta and phi) which made the Laplacian look rather fierce. Then the equation was split into 3, each involving one of r, theta or phi. The easiest to solve was the one involving phi which involved only a complex exponential. But periodic nature of the solution made the magnetic quantum number fall out. Pretty good, but nothing earthshaking.

Recursion relations made their appearance with the solution of the radial and the theta equations. So it was plug and chug time with series solutions and recursion relations so things wouldn’t blow up (or as Dr. Gouterman put it, the electron has to be somewhere, so the wavefunction must be zero at infinity). MEGO (My Eyes Glazed Over) until all of a sudden there were the main quantum number (n) and the azimuthal quantum number (l) coming directly out of the recursions.

When I first realized what was going on, it really hit me. I can still see the room and the people in it (just as people can remember exactly where they were and what they were doing when they heard about 9/11 or (for the oldsters among you) when Kennedy was shot — I was cutting a physiology class in med school). The realization that what I had considered mathematical diddle, in some way was giving us the quantum numbers and the periodic table, and the shape of orbitals, was a glimpse of incredible and unseen power. For me it was like seeing the face of God.

The second and third examples occurred this year as I was going through Tony Zee’s book “Group Theory in a Nutshell for Physicists”

The second example occurs with the rotation group in 3 dimensions, which is a 3 x 3 invertible matrix, such that multiplying it by its transpose gives the identity, and such that is determinant is +1.  It is called SO(3)

Then he tensors 2 rotation matrices together to get a 9 x 9 matrix.  Zee than looks for the irreducible matrices of which it is composed and finds that there is a 3×3, a 1×1 and a 5×5.  The 5×5 matrix is both traceless and symmetric.  Note that 5 = 2(2) + 1.  If you tensor 3 of them together you get (among other things 3(2) + 1)   = 7;   a 7 x 7 matrix.

If you’re a chemist this is beginning to look like the famous 2 L + 1 formula for the number of the number of magnetic quantum numbers given an orbital quantum number of L.   The application of a magnetic field to an atom causes the orbital momentum L to split in 2L + 1 magnetic eigenvalues.    And you get this from the dimension of a particular irreducible representation from a group.  Incredible.  How did abstract math know this.  

The third example also occurs a bit farther along in Zee’s book, starting with the basis vectors (Jx, Jy, Jz) of the Lie algebra of the rotation group SO(3).   These are then combined to form J+ and J-, which raise and lower the eigenvalues of Jz.  A fairly long way from chemistry you might think.  

All state vectors in quantum mechanics have absolute value +1 in Hilbert space, this means the eigenvectors must be normalized to one using complex constants.  Simply by assuming that the number of eigenvalues is finite, there must be a highest one (call it j) . This leads to a recursion relation for the normalization constants, and you wind up with the fact that they are all complex integers.  You get the simple equation s = 2j where s is a positive integer.  The 2j + 1 formula arises again, but that isn’t what is so marvelous. 

j doesn’t have to be an integer.  It could be 1/2, purely by the math.  The 1/2 gives 2 (1/2) + 1 e.g two numbers.  These turn out to be the spin quantum numbers for the electron.  Something completely out of left field, and yet purely mathematical in origin. It wasn’t introduced until 1924 by Pauli — long after the math had been worked out.  

Incredible.  

The science behind Cassava Sciences (SAVA)

I certainly hope Cassava Sciences new drug Simufilam for Alzheimer’s disease works for several reasons

l. It represents a new approach to Alzheimer’s not involving getting rid of the plaque which has failed miserably

2. The disease is terrible and I’ve watched it destroy patients, family members and friends

3. I’ve known one of the principals (Lindsay Burns) of Cassava since she was a teenager and success couldn’t happen to a nicer person. For details please see https://luysii.wordpress.com/2021/02/02/montana-girl-does-good-real-good/.

Unfortunately even if Sumifilam works I doubt that it will be widely used because of the side effects (unknown at present) it is very likely to cause.  I certainly hope I’m wrong.

Here is the science behind the drug.  We’ll start with the protein the drug is supposed to affect — filamin A, a very large protein (2,603 amino acids to be exact).  I’ve known about it for years because it crosslinks actin in muscle, and I read everything I could about it, starting back in the day when I ran a muscular dystrophy clinic in Montana.  

Filamin binds actin by its amino terminal domain.  It forms a dimerization domain at its carboxy terminal end.  In between are 23 repeats of 96 amino acids which resemble immunoglobulin — forming a rod 800 Angstroms long.  The dimer forms a V with the actin binding domain at the two tips of the V, making it clear how it could link actin filaments together. 

Immunoglobulins are good at binding things and Lindsay knows of 90 different proteins filamin A binds to.  This is an enormous potential source of trouble.  

As one might imagine, filamin A could have a lot of conformations in addition to the V, and the pictures shown in https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2099194/.

One such altered (from the V) conformation binds to the alpha7 nicotinic cholinergic receptor on the surface of neurons and Toll-Like Receptor 4 (TLR4) inside the cell.

Abeta42, the toxic peptide, has been known for years to bind tightly to the alpha7 nicotinic receptor — they say in the femtoMolar (10^-15 Molar) range, although I have my doubts as to whether such tiny concentration values are meaningful.  Let’s just say the binding is tight. 

The altered conformation of filamin A makes the binding of Abeta to alpha7even tighter. 

In some way, the tight binding causes signaling inside the cell (mechanism unspecified) to hyperphosphorylate the tau protein, which is more directly correlated with dementia in Alzheimer’s disease than the number of senile plaques. 

So what does Sumifilam actually do — it changes the ‘altered’ conformation of filamin A back to normal, decreasing Abeta signaling inside the cell.  

How do they know the conformation of filamin A has changed?  They haven’t done cryoEM or Xray crystallography on the protein.  The only evidence for a change in conformation, is a change in the electrophoretic mobility (which is pretty good evidence, but I’d like to know what conformation is changed to what).

Notice just how radical this proposed mechanism of action actually is.  The nicotinic cholinergic receptor is an ion channel, yet somehow the effect of Sumifilam is on how the channel binds to another protein, rather than how it conducts ions. 

However they have obtained some decent results with the drug in a very carefully done (though small — 13 patients) study in J. Prev Alz. Dis. 2020 (http://dx.doi.org/10.14283/ipad2020.6) and the FDA this year has given the company the go ahead for a larger phase III trial.

Addendum 26 March: The above link didn’t work.  This one should — it’s from Lindsay herself

https://link.springer.com/article/10.14283/jpad.2020.6

Why, despite rooting for the company and Lindsay am I doubtful that the drug will find wide use.  We are altering the conformation of a protein which interacts with at least 90 other proteins (Lindsay Burns, Personal Communication).  It seems inconceivable that there won’t be other effects in the neuron (or elsewhere in the body) due to changes in the interaction with the other 89 proteins filaminA interacts with.  Some of them are likely to be toxic.