Are you as smart as the (inanimate) blind watchmaker

Here’s a problem the cell has solved. Can you? Figure out a way to send a protein to two different membranes in the cell (the membrane encoding it { aka the plasma membrane }, and the endoplasmic reticulum) in the proportions you wish.

The proteins must have exactly the same sequence and content of amino acids, ruling out alternative splicing of exons in the mRNA (if this is Greek to you have a look at the following post — https://luysii.wordpress.com/2012/01/09/molecular-biology-survival-guide-for-chemists-v-the-ribosome/ and the others collected under — https://luysii.wordpress.com/category/molecular-biology-survival-guide/).

The following article tells you how the cell does it. Recall that not all of the messenger RNA (mRNA) is translated into protein. The ribosome latches on to the 5′ end of the mRNA,  subsequently moving toward the 3′ end until it finds the initiator codon (AUG which codes for methionine). This means that there is a 5′ untranslated region (5′ UTR). It then continues moving 3′ ward stitching amino acids together.  Similarly after the ribosome reaches the last codon (one of 3 stop codons) there is a 3′ untranslated region (3′ UTR) of the mRNA. The 3′ UTR isn’t left alone but is cleaved and a polyAdenine tail added to it. The 3′ UTR is where most microRNAs bind controlling mRNA stability (hence the amount of protein produced from a given mRNA).

The trick used by the cell is described in [ Nature vol. 522 pp. 363 – 367 ’15 ]. The 3’UTR is alternatively processed producing a variety of short and long 3’UTRs. One such protein where this happens is CD47 — which is found on the surface of most cells where it stops the cell from being eaten by scavenger cells such as macrophages. The long 3′ UTR of CD47 allows efficient cell surface expression, while the short 3′ UTR localizes it to the endoplasmic reticulum.

How could this possibly work? Once the protein is translated by the ribosome, it leaves the ribosome and the mRNA doesn’t it? Not quite.

They say that the long 3′ UTR of CD47 acts as a scaffold to recruit a protein complex which contains HuR (aka ELAVL1), an RNA binding protein and SET to the site of translation. The allows interaction of SET with the newly translated cytoplasmic domains of CD47, resulting in subsequent translocation of CD47 to the plasma membrane via activated RAC1.

The short 3′ UTR of CD47 doesn’t have the sequence binding HuR and SET, so CD47 doesn’t get to the plasma membrane, rather to the endoplasmic reticulum.

The mechanism may be quite general as HuR binds to thousands of mRNAs. The paper gives two more examples of proteins where this happens.

It’s also worth noting that all this exquisite control, does NOT involve covalent bond formation and breakage (e.g. not what we consider classic chemical reactions). Instead it’s the dance of one large molecular object binding to another in other ways. The classic chemist isn’t smiling. The physical chemist is.

The twists and turns of topoisomerase (pun intended)

It is very sad that my late friend Nick Cozzarelli isn’t around to enjoy the latest exploits of the enzyme class he did so much great work on — the topoisomerases. For a social note about him see the end of the post.

We tend to be quite glib about just what goes on inside a nucleus when DNA is opened up and transcribed into mRNA by RNA polymerase II (Pol II). We think of DNA has a linear sequence of 4 different elements (which it is) and stop there. But DNA is a double helix, and the two strands of the helix wind around each other every 10 elements (nucleotides), meaning that within the confines of our nuclei this happens 320,000,000 times.

I’ve written a series of six posts on what we would see if our nuclei were enlarged  by a factor of 100,000 (which is the amount of compaction our DNA must undergo to fit inside the 10 micron (10 millionths of a meter) in diameter nucleus (since if fully extended our DNA would be 1 meter long. So if you compacted the distance from New York to Seattle (2840 miles or 14,995,200 feet) down by this factor you’d get a sphere 150 feet in diameter or half the length of a football (US) field. Now imagine blowing up the diameter and length of the DNA helix by 100,000 and you’d get something looking like a 2,840 mil long strand of linguini which twists on itself  320,000,000 times. The two strands are 3/8th of an inch thick. They twist around each other every 9/16ths of an inch.

For the gory details start at https://luysii.wordpress.com/2010/03/22/the-cell-nucleus-and-its-dna-on-a-human-scale-i/ and follow the links.

Well, we know that for DNA to be copied into mRNA it must be untwisted, the strands separated so RNA polymerase II (Pol II) can get to it.  Pol II is enormous — a mass of 500 kiloDaltons and 7 times thicker at 140 Angstroms than the DNA helix of 20 Angstrom thickness.

Consider the fos gene (which we’ll be talking about later). It contains 380 amino acids (meaning that the gene contains at least 1140 nucleotides ). The actual gene is longer because of introns (3,461 nucleotides), which means that the gene contains 346 complete turns of the double helix, all of which must be unwound to transcribe it into mRNA.

So it’s time for an experiment. Get about 3 feet of cord roughly 3/8 of an inch thick. Tie the ends together, loop one end around a hook in your closet, put a pencil in the other end and rotate it about 100 times (or until you get tired). Keeping everything the same, have a friend put another pencil between the two strands in the middle, separating them. Now pull on the strands to make the separation wider and move the middle pencil toward one end. In the direction of motion the stands will coil even tighter (supercoiling) and behind they’ll unwind.

This should make it harder for Pol II to do its work (or for enzymes which copy DNA to more DNA). This is where the various topoisomerase come in. They cut DNA allowing supercoils to unwind. They remain attached to the DNA they cut so that the DNA can be put back together. There are basically two classes of topoisomerase — Type I topoisomerase cuts one strand, leaving the other intact, type II cuts both.

Who would have thought that type II topoisomerase would be involved in the day to day function of our brain.

Neurons are extended things, with information flowing from dendrites on one side of the cell body to much longer axons on the other. The flow involves depolarization of the cell body as impulses travel toward the axon. We know that certain genes are turned on by this activity (e.g. the DNA coding for the protein is transcribed into mRNA which is translated into protein by the ribosome). They are called activity dependent genes.

This is where [ Cell vol. 1496 – 1498, 1592 – 1605 ’15 ] comes in. Prior to neuronal activity, when activity dependent genes are expressed at low levels, the genes still show the hallmarks of highly expressed genes (e.g. binding by transcription factors and RNA polymerase II, Histone H3 trimethylation of lysine #4 {H3K4Me3 } at promoters).

This work shows that such genes are highly negatively supercoiled (see above) preventing RNA polymerase II (Pol II) from extending into the gene body. On depolarization of the cell body in some way Topoisomerase IIB is activated, leading to double strand breaks (dsbs) within promoters allowing the DNA to unwind and Pol II to productively elongate through gene bodies.

There is evidence that neuronal stimulation leads to dsbs ( Nature NeuroScience vol. 16 pp. 613 – 621 ’13 ) throughout the transcription of immediate early genes (e.g. genes turned on by neural activity). The evidence is that there is phosphorylation of serine #139 on histone variant H2AX (gammaH2AX) which is a chromatin mark deposited on adjacent histones by the DNA damage response pathway immediately after DSBs are found.

Etoposide (a topoisomerase inhibitor) traps the enzyme in a state where it remains bound to the DNA of the dsb. On etoposide Rx, there is an increase in activity dependent genes (Fos, FosB, Npas4). Inhibition of topiosomerase IIB (the most prevalent topoisomerase in neurons) by RNA interference (RNAi) leads to blunted activity dependent induction of these genes. This implies that DNA cutting by topoisomerase IIB is required for gene activation in response to neuronal activity.  Other evidence is that knocking down topoisomerase  using RNA interference (RNAi) stops activity dependent gene transcription.

Further supporting this idea, the authors induced dsbs at promoters of activity dependent genes (Fos, fosB, Npas4) using the CRISPR system. A significant increase in transcription was found when the Fos promoter was targeted.

I frankly find this incredible. Double strand breaks are considered bad things for good reason and the cell mounts huge redundant machines to repair them, yet apparently neurons, the longest lived cells in our bodies are doing this day in and day out. The work is so fantastic that it needs to be replicated.

Social Note: Nick Cozzarelli is one of the reasons Princeton was such a great institution back in the 50s (and hopefully still is). Nick’s father was an immigrant shoemaker living in Jersey City, N. J. Princeton recognized his talent, took him in, allowing him to work his way through on scholarship, waiting tables in commons, etc. etc. He obtained a PhD in biochemistry from Harvard and later became a prof at Berkeley, where he edited the Proceedings of the National Academy of Sciences USA for 10 years. He passed away far too soon of Burkitt’s lymphoma in his late 60s. We were friends as undergraduates and in grad school.

I can only wonder what Nick would say about the latest twists of the topoisomerase story

The uses of disorder

There was a lot of shock and awe about a report showing how seemingly minor changes in an aliphatic group on benzene led to markedly different conformations in its protein target (lysozyme from bacteriophage T4) http://pipeline.corante.com/archives/2015/06/18/tiny_and_not_so_tiny_changes.php.

Our noses are being rubbed in just how floppy proteins are, in contrast to the first glimpses of protein structure obtained by Xray crystallography. Back then we knew so little about proteins, that seeing all the atoms laid out in alpha helices and beta sheets was incredibly compelling. We talked about the structure of a protein rather than a structure. Even back then, with hemoglobin (one of the first solved proteins) it was obvious that proteins had to have more than one structure. The porphyrin ring in heme that oxygen binds to is buried deep in hemoglobin, and the initial structure had to move in some way to allow oxygen to find its way in (because the initial structure showed no obvious channel for oxygen). So hemoglobin had to breathe.

We now know that many proteins have intrinsically disordered segments. Amazingly, the most recent estimate I could find in my notes (or in Wikipedia) is this — It is estimated that over 30% of eukaryotic proteins have stretches of over 30 amino acids that are intrinsically disordered [ J. Mol. Biol. vol. 337 pp. 635 – 645 ’04 ]. Does anyone out there know of more recent data?

We’re a lot smarter now — here’s a comment on Derek’s post — “I have always thought crystal structures of proteins/enzymes are more a guide than actually useful. You are crystallizing a protein first-proteins don’t pack like that in vivo. Then you are settling on the conformation that freezes out- is this the lowest energy form? Then you are ignoring hte fact that these are highly dynamic structures that are constantly moving, sliding, shaking, adjusting. Then if you put a ligand in there you get the lowest energy form-which is what it would look like after reaction and before ligand dissociation- this is quite different from what it can look like at other stages of the reaction.”

Here is an interesting example of the uses of protein disorder going on right now in just about every neuron in your body. Most neurons have long processes, far too long for diffusion to move a needed protein to their ends. For that purpose we have microtubules (aka neurotubules in neurons) stretching the length of the processes, onto which two types of motors attach (dyneins which moves things to negative end of the microtubule and kinesins which move things to the positive end).

The microtubule is built from a heterodimer of two proteins (alpha and beta tubulin). Each contains about 450 amino acids and forms a globule 40 Angstroms (4 nanoMeters) in diameter. The heterodimers pack end to end to form a protofilament. 13 protofilaments line up side by side to form the microtubule, a hollow structure about 250 Angstroms in diameter. In cells microtubules are 1 to 10 microns long, but in nerve process they can be ‘up to’ 100 microns in length. Even at 1 micron (1,000 nanoMeters) that’s 13 * 250 heterodimers in a microtubule.

Any protein structure this important has a lot of modifications imposed on it to alter structure and function. Examples include phosphorylation and the addition of glutamic acid chains (polyglutamylation). The carboxy terminal tails of alpha and beta tubulin are flexible and stick out from the tubulin rod (which is why they aren’t seen on Xray crystallography). The carboxy terminal tail is the site of post-translational glutamylation. The enzyme polyglutamylating the carboxy terminal tail of beta tubular is TTLL7 (you don’t want to know what the acronym stands for). It binds to the alpha/beta tubular heterodimer by an intrinsically disordered region of its own (becoming structured in the process), then it binds to the intrinsically disordered carboxyl terminal tails, structuring them and modifying them. It’s basically a mating dance. There is a precedent for this — see https://luysii.wordpress.com/2013/12/29/the-mating-dance-of-a-promiscuous-protein/

So disordered regions of proteins although structureless are far from functionless

Not physical organic chemistry but organic physical chemistry

This post is about physical chemistry with organic characteristics in the sense that capitalism in China is called socialism with Chinese characteristics. A lot of cell biology is also involved.

I remember the first time I heard about Irving Langmuir and the two dimensional gas he created. It even followed a modified perfect gas law (PA = nRT where A is area). He did this by making a monolayer of long chain fatty acids on water, with the carboxyl groups binding to the water, and the hydrocarbon side chain sticking up into the air. I thought this was incredibly neat. It was the first example of organic physical chemistry. He published his work in 1917 and won the Nobel in Chemistry for it in 1932.

Fast forward to our understanding of the membrane encasing our cells (the technical term is plasma membrane to distinguish from the myriad other membranes inside our cells. To a first approximation it’s just two Langmuir films back to back with the hydrocarbon chains of the lipids dissolving in each other, and the hydrophilic parts of the membrane lipids binding to the water on either side. This is why it’s called a lipid bilayer.

Most of the signals going into our cells must pass through the plasma membrane, using proteins spanning it. As a neurologist I spent a lot of time throwing drugs at them — examples include every known receptor for neurotransmitters, reuptake proteins for them (think the dopamine transporter), ion channels. The list goes on and on and includes the over 800 G protein coupled receptors (GPCRs) with their 7 transmembrane segments we have in our genome [ Proc. Natl. Acad. Sci. vol. 111 pp. 1825 – 1830 ’14 ].

Glypiated proteins (you heard right) also known as PIGtailed proteins (you heard that right too) don’t follow this pattern. They are proteins anchored in the outer leaflet of the plasma membrane lipid bilayer by covalently linked phosphatidyl inositol. https://en.wikipedia.org/wiki/Phosphatidylinositol — the picture shows you why — inositol is a sugar, hence crawling with hydroxyl groups, while the phosphatidic acid part has two long hydrocarbon chains which can embed in the outer leaflet. We have 150 of them as of 2009 (probably more now). Examples of PIGtailed proteins include alkaline phosphatase, Thy-1 antigen, acetyl cholinesterase, lipoprotein lipase, and decay accelerating factor. So most of them are enzymes working on stuff outside the cell, so they don’t need to signal.

Enter the lipid raft. [ Cell vol. 161 pp. 433 – 434, 581 – 594 ’15 ] It’s been 18 years since rafts were first proposed, and their existence is still controversial (with zillions of papers saying they exist and more zillions saying they don’t). What are they — definitions vary (particularly about how large they are). Here’s what Molecular Biology of the Cell 4th edition p. 589 had to say about them — Rafts are small (700 Angstroms in diameter). Rafts are rich in sphingolipids, glycolipids and cholesterol. The hydrocarbon chains are longer and straighter than those of most membrane lipids, rafts are thicker than other parts of bilayer. This allows them to better accomodate ‘certain’ membrane proteins, which accumulate there. [ Proc. Natl. Acad. Sci. vol. 100 p. 8055 – 7’03 ] These include glycosylphosphatidylinositol anchored proteins (glypiated proteins), cholesterol linked and palmitoylated proteins such as Hedgehog, Src family kinases and the alpha subunits of G proteins, cytokine receptors and integrins.

Biochemical analysis shows that rafts consist of cholesterol and sphingolipids in the exoplasmic leaflet (outer layer of the plasma membrane) of the lipid bilayer and cholesterol and phospholipids with saturated fatty acids in the endoplasmic leaflet (layer facing the cytoplasm). The raft is less fluid than surrounding areas of the membrane. So if they in fact exist, rafts contain a lot of important cellular players.

The Cell paper introduced synthetic fluorescent glypiated proteins into the outer plasma membrane leaflet of Chinese hamster ovary cells and was able to demonstrate nanoClustering on scales under 1,000 Angstroms (way too small to see with visible light, accounting for a lot of the controversy concerning their existence).

How can the authors make such a statement? The evidence was a decrease in fluorescence anisotropy due to Forster resonance energy transfer effects. Forster energy transfer is interesting in that it doesn’t involve molecule #1 losing energy by emitting a photon which is absorbed by molecule #2 increasing its energy. It works by molecule #1 inducing a dipole in molecule #2 (by a Van der Waals effect). Obviously, to do this, the molecules must be fairly close, and transfer efficiency falls off as the inverse 6th power of the distance between the two molecules.

In Fluorescence Resonance Energy Transfer (FRET), one fluorophore (the donor) transfers its excited state energy to a different fluorophore (the acceptor) which emits fluorescence of a different color. For more details see — https://en.wikipedia.org/wiki/Förster_resonance_energy_transfer — its interesting stuff. Again an example of physical chemistry with organic characteristics (and pretty good evidence for the existence of lipid rafts to boot).

Now it gets even more interesting. Nanoclustering is dependent on the length of the acyl chain forming the GPI anchor (at least 18 carbons must be present). NanoClustering diminishes on cholesterol depletion in actin depleted cell blebs and mutant cell lines deficient in the inner leaflet lipid — phosphatidylserine (PS) — which has two long chain fatty acids hanging off the glycerol. So it looks as if the saturated acyl chains of the glypiated proteins of the outer leaflet interdigitate with those of PS in inner leaflet. The effect is also enhanced on expression of proteins specifically linking PS to the actin cytoskeleton of the cortex. Binding of PS to the cortical actin cytoskeleton determines where and when the clusters will be stabilized. The coupling can work both ways — if something immobilizes and stabilizes the glypiated proteins extracellularly, than PS lipids can form correlated patches.

This might be a mechanism for information transfer across the plasma membrane (and acrossother membranes to boot). This could also serve as a way to couple many outer leaflet membrane lipids such as gangliosides and other sphingolipids with events internal to the cell. Cholesterol can stabilize the local liquid ordered domain over a length scale that is large than the size of the immobilized cluster. A variety of membrane associated proteins inside the cell (spectrin, talin, caldesmon) are able to bind actin. “The formation of the contractile actin clusters then determine when and where the domains may be stabilized, bringing the generation of membrane domains in live cells under control of the actomyosin signaling network.’

So just like the integrins which can signal from outside the cell to inside and from inside the cell to outside, glypiated proteins and the actin cytoskeleton may form a two way network for signaling. No one should have to tell you how important the actomyosin cytoskeleton is in just about everything the cell does. Truly fascinating stuff. Stay tuned.

The many ways the many tensor notations can confuse you

This post is for the hardy autodictats attempting to learn tensors on their own. If you use multiple sources, you’ll find that they define the same terms used to describe tensors in diametrically opposed ways, so that just when you thought you knew what terms like covariant and contravariant tensor meant,  another source defines them completely differently, leading you to wonder (1) about your intelligence (2) your sanity.

Tensors involve vector spaces and their bases. This post assumes you know what they are. If you don’t understand how a vector can be expressed in terms of coordinates relative to a basis, pick up any book on linear algebra.

Tensors can be defined by the way their elements transform under a change of coordinate basis. This is where the terms covariant and contravariant come from. By the way when Einstein says that physical quantities must transform covariantly, he means they transform like tensors do (even contravariant tensors).

True enough, but this approach doesn’t help you understand the term tensor product or the weird ® notation (where there is an x within the circle) used to describe it.

The best way to view tensors (from a notational point of view) is to look on them as functions which take finite Cartesian products (https://en.wikipedia.org/wiki/Cartesian_product) of vectors and covectors and produce a single real number.

To understand what a covector (aka dual vector) is, you must understand the inner product (aka dot product).

The definition of inner product (dot product) of a vector V with itself written < V | V >, probably came from the notion of vector length. Given the standard basis in two dimensional space E1 = (1,0) and E2 = (0,1) all vectors V can be written as x * E1 + y * E2 (x is known as the coefficient of E1). Vector length is given by the good old Pythagorean theorem as SQRT[ x^2 + y^2]. The dot product (inner product) is just x^2 + y^2 without the square root.

In 3 dimensions the distance of a point (x, y, z) from the origin is SQRT [x^2 + y^2 + z^2]. The definition of vector length (or distance) easily extends (by analogy) to n dimensions where the length of V is SQRT[x1^2 + x2^2 + . . . . + xn^2] and the dot product is x1^2 + x2^2 + . . . . + xn^2. Length is always a non-negative real number.

The definition of inner product also extends to the the dot product of two different vectors V and W where V = v1 * E1 + v2 * E2 + . … vn * En, W = w1 * E1 + . . + wn * En — e.g. < V | W >  = v1 * w1 + v2 * w2 + . . . + vn * wn. Again always a real number, but not always positive as any of the v’s and w’s can be negative.

So, if you hold W constant you can regard it as a function on the vector space in which V and W reside which takes any V and produces a real number. You can regard V the same way if you hold it constant.

Now with some of the complications which mathematicians love, you can regard the set of functions { W } operating on a vector space, as a vector space itself. Functions can be added (by their results) and can be multiplied by a real number (a scalar). The set of functions { W } regarded as a vector space is called the dual vector space.

Well if { W } along with function addition and scalar multiplication is a vector space, it must have a basis. Everything I’ve every read about tensors  involves finite dimensional vector spaces. So assume the vector space A is n dimensional where n is an positive integer, and call its basis vectors the ordered set a1, . . . , an. The dual vector space (call it B) is also n dimensional with another basis the ordered set b1, . . . , bn.

The bi are chosen so that their dot product with elements of A’s basis = Kronecker delta, e.g. if i = j then  < bi | aj >
= 1. If i doesn’t equal j  then < bi | aj >  = 0. This can be done by a long and horrible process (back in the day before computer algebra systems) called Gram Schmidt orthonormalization. Assume this can be done. If you’re a true masochist have a look at https://en.wikipedia.org/wiki/Gram–Schmidt_process.

Notice what we have here. Any particular element of the dual space B (a real valued function operating on A) call it f can be written down as f1 * b1 + . . . + fn * bn. It will take any vector in A (written g1 * a1 + . . . + gn * an) and give you f1 * g1 + . . . + fn * gn which is a real number. Basically any element ( say bj) of the basis of dual space B just looks at a vector in A and picks out the coefficient of aj (when it forms the dot product with the vector in A.

Now (at long last) we can begin to look at the contrary way tensors are described. The most fruitful way is to look at them as the product of individual dot products between a vector and a dual vector.

Have a look at — https://luysii.wordpress.com/2014/12/08/tensors/. To summarize  — the whole point of tensor use in physics is that they describe physical quantities which are ‘out there’ independently of the coordinates used to describe them. A hot dog has a certain length independently of its description in inches or centimeters. Change your viewpoint and the its coordinates in space will change as well (the hot dog doesn’t care about this). Tensors are a way to accomplish this.

It’s to good to pass up, but the length of the hot dog stays the same no matter how many times you (non invasively) measure it.  This is completely different than the situations in quantum mechanics, and is one of the reasons that quantum mechanics has never been unified with general relativity (which is a theory of gravity based on tensors).

Remember the dot product concerns  < dual vector — V | vector — W > . If you change the basis of vector  W (so vector W has different coordinates) the basis of dual vector   V must also change (to keep the dot product the same). A choice must be made as to which of the two concurrent basis changes is fundamental (actually neither is as they both are).

Mathematics has chosen the basis of vector W in as fundamental.

When you change the basis of W, the coefficients of W must change in the opposite way (to keep the vector length constant). The coefficients of W are said to change contravariantly. What about the coefficients of V? The basis of V changes oppositely to the basis of W (e.g. contravariantly), so the coefficients of V must change differently from this e.g. the same way the basis of W changes — e.g. covariantly. Confused?  Nonetheless, that’s the way they are named

Vectors and convectors and other mathematical entities such differentials, metrics and gradients are labelled as covariant or contravariant by the way their numerical coefficients change with a change in basis.

So the coefficients of vector W transform contravariantly, and the coefficients of dual vector V transform covariantly. This is true even though the coefficients of V and W always transform contravariantly (e. g. oppositely) to the way their basis transforms.

An immense source of confusion.

As mentioned above, one can regard vectors and dual vectors as real valued functions on elements of a vector space. So (adding to the confusion) vectors and dual vectors are both tensors. Vectors are contravariant tensors, and dual vectors are covariant tensors.

Now we form Cartesian products of vectors W (now called V) and convectors V (hereafter called V* to keep them straight).

We get something like this V x V x V x V* x V*, a cartesian product of 3 contravariant vectors and 2 dual vectors.

To get a real number out of them we form the tensor product V* ® V* ® V* ® V ® V, where the first V* operates on the first V to produce a real number, the second operates . . . and the last V* operates on the last V to produce a real number. All real numbers produced are multiplied together to produce the result.

Why not just call  V* ® V* ® V* ® V ® V a product? Well each V and V* is an n dimensional vector space, and the tensor V ® V is a n^2 dimensional space (and  V* ® V* ® V* ® V ® V is an n^5 dimensional vector space). When we form the product of two numbers (real or complex) we just get another number of the same species (real or complex). The tensor product of two n dimensional vector spaces is not another n dimensional space, hence the need for the adjective modifying the name product. The dot product nomenclature is much the same, the dot product of two vectors is not another vector, but a real number.

Here is yet another source of confusion. What we really have is a tensor product V* ® V* ® V* ® V ® V operating on a Cartesian product of vectors and covectors (tensors themselves) V x V x V x V* x V* to produce a real number.

Tensors can either be named by their operands making this a 3 contravariant 2 covariant tensor — (3, 2) tensor.

Other books name them by their operator (e.g. the tensor product) making it a 3 covariant 3 contravariant tensor (a 2, 3) tensor.

If you don’t get this settled when you switch books you’ll think you don’t really understand what contravariant and covariant mean (when in fact you do). Mercifully, one constancy in notation (thankfully) is that the contravariant number always comes first (or on top) and the covariant number second (or on bottom).

Hopefully this is helpful.  I wish I’d had this spelled out when I started.

How little we know

Well it’s basic biochem 101, but enzymes only allow equilibrium to be reached faster (by lowering activation energy), they never change it. This came as a shock to the authors of [ Proc. Natl. Acad. Sci. vol. 112 pp. 6601 – 6606 ’15 ] when Cytosolic Nonspecific DiPeptidase 2 (CNDP2), a proteolytic enzyme, was found to tack the carboxyl group of lactic acid onto the amino group of a variety of amino acids, essentially running the proteolytic reaction in reverse. Why? Because intracellular levels of lactic acid and amino acids are in the high microMolar to milliMolar range. It’s Le Chatelier’s principle in action.

The compounds are called N-Lactoyl amino acids. No one had ever seen them before. They are part of the ‘metabolome’ — small molecules found in our bodies. God knows what they do. The paper was really shocking to me for another reason, because I had no idea how many members the metabolome has.

How large is the metabolome? Make a guess.

Well METLIN (https://metlin.scripps.edu/index.php has 240,000, and Human Metabolome DataBase http://www.hmdb.ca/metabolites?c=hmdb_id&d=up&page=1676 has 42,000. I doubt that we know what they are all doing. Undoubtedly some of them are binding to proteins producing physiologic effects. Drug chemists may be mimicking some of them unknowingly, producing untoward and unexpected side effects.

What’s even more shocking to me is the following statement from the paper. State of the art untargeted metabolomics studies still report ‘up to’ 40% unidentified, but potentially important metabolitcs which can be detected reproducibly. The unknown metabolites are only rarely characterized because of the extensive work required for de novo structure determination..

So we really don’t know everything that’s out there in our bodies, and even if we did, we don’t know what they are doing. Drug discovery is hard because we only dimly understand the system we are trying to manipulate. Until I read this paper, I had no idea just how dim this is.

At the 55th

This is a mostly nonscientific post concerning the 55th reunion of the Princeton Class of 1960 last weekend. First the Science. Nick Cozzarelli was one of the most distinguished members of our class — great work on Topoisomerase, editor of PNAS for 10 years which established a prize named for him for the best paper each year. No one I’ve ever talked to in the class knew of him or his work. Shirley Tilghman, president of Princeton certainly did, and was shocked to hear of his untimely passing from Burkitt’s lymphoma when I told her of it at our 50th, saying he was a great scientist. However, he’s one of the reasons Princeton back then was a great institution (and hopefully still is). The son of an immigrant shoemaker in Newark NJ, he was taken in, given a scholarship, and worked his way through, serving meals in commons etc. etc. I made sure the undergraduates picking up a little cash by pouring drinks and serving meals at reunions heard about him. He was a good friend.  R. I. P. Nick.

Another friend, an emeritus prof of chemical engineering, referees a lot of papers. He estimates that 80% of the papers in his field, quantum chemistry, coming from China are absolute trash. According to him China gives bonuses to people getting published in high impact journals. What he finds particularly appalling is that he writes up a detailed list of corrections and improvements for the paper, and then finds it published totally unchanged in another journal.

He and I reminisced about our great undergraduate advisor Paul Schleyer with the department chair (who of course knew of him since he is one of the most cited and prolific (1,400 papers) chemists of the 20th century). He’s another reason Princeton was such a great institution back then (and hopefully still is). For details please see https://luysii.wordpress.com/2014/12/15/paul-schleyer-1930-2014-a-remembrance/ and https://luysii.wordpress.com/2014/12/14/paul-schleyer-1930-2014-r-i-p/

I finally saw the new Chemistry building (under construction at the 50th) and it is gorgeous. The NMR set up is particularly impressive, with the megaHertz of the machinery a factor of 15 greater than those we first started using in the 60s. Alas Varian is no more. It was bought a few years ago by another company which terminated the business. For where the money came from see https://luysii.wordpress.com/2011/05/16/princeton-chemistry-department-the-new-oberlin/.

In a remarkable coincidence, my wife an I were able to chat with the son of a neurologist in my call group, just finishing up his PhD in Chemistry there. How improbable is that?

Now for the nonScientific part.

For those undergraduates reading this at similar institutions, some advice — get to know as many of your classmates as you can. Premeds at Princeton back then had to take a lot of the same courses — biology, basic chemistry, organic chemistry, calculus, physics etc. etc. So we got to know each other. The rest of the class, not so much unless we were in other organizations (in my case, the marching band, Triangle club, and the eating club). At reunions I always meet classmates that I wish I knew back then and form new friendships.

Sometimes that isn’t always easy, with everyone working out the various important issues present from 18 to 22. A classmate’s wife described the men of the class at their 25th reunion as ‘roosters’, crowing and impressing each other. Not the case 30 years later. Everyone glad just to be there and catch up.

Princeton was all male back then. The current wives (some being #2, #3, #5) are an impressive bunch. They were uniformly intelligent and interesting. Not a bimbo in the lot of them, although most were very attractive physically. So the class may have slept with bimbos, but they were no longer in evidence.

Various seminars were held. I went to one about America’s relation to food. The panelists were 6 trim females with a fair amount of pseudoscience and touchy feely crap emitted, but at least the cautionary tale of the trash in the popular press about diet was mentioned (e.g. the paper about eat chocolate lose weight). What was fascinating was that the incidence of obesity (BMI over 29) in the group of several hundred listeners was at most 5%, proving, once again, that obesity in the USA is largely a class phenomenon. Also noted, is that I only saw one or two undergraduates and graduates smoking, again a class phenomenon, something Americans don’t like to talk about, but there nonetheless.

A memorial service for classmates was held in the chapel (built in 1929 but designed to appear that it was built in 1299). The organ is magnificent as were the acoustics, the sound surrounding you rather than coming at you. Bach and Vidor were performed by the organist. Apparently there was quite a battle about which to do first — refurbish the organ or the chapel acoustics. The stone had roughened distorting the sound so it didn’t echo properly. Clear plastic was applied to smooth the stone and then the organ was fixed. If you can hear a concert there please do so. Great composers write for the space their music will be performed in as well as the instruments it will be performed on, certainly true of Gabrielli, Bach and Vidor.

On a sadder note. I know of 4 suicides of class members (we started with around 725). Probably there are more. Also a good friend and classmate’s wife and daughter appeared to accept an award in his name. Although still alive he is incontinent, unable to walk and demented from Alzheimer’s. Despite degrees from Princeton, Harvard and Penn, Board examiner in Neurology blah blah blah, I was totally unable to help him. All I could do was offer emotional chicken soup to his wife, something my immigrant grandmother did with her 4th grade education in the dry goods store she ran. That’s why it’s good to be retired from neurology and not see this day after day.

Finally the P-rade. It is a great emotional lift for the psyche to march a mile or so to the reviewing stand being cheered by probably 1,000 – 2,000 younger graduates the whole time. The younger they got the louder the cheers and the drunker they were. It’s pretty hard not to feel good after that. I have heard that the only weekend event where more beer is consumed than Princeton reunions is the Indianapolis 500.  Along those lines, I only saw one truly drunk individuals among the 250 or so classmates and significant others although just about everyone had alcohol.  The alcoholics are no longer around for the 55th.

What is schizophrenia really like ?

The recent tragic death of John Nash and his wife warrants reposting the following written 11 October 2009

“I feel that writing to you there I am writing to the source of a ray of light from within a pit of semi-darkness. It is a strange place where you live, where administration is heaped upon administration, and all tremble with fear or abhorrence (in spite of pious phrases) at symptoms of actual non-local thinking. Up the river, slightly better, but still very strange in a certain area with which we are both familiar. And yet, to see this strangeness, the viewer must be strange.”

“I observed the local Romans show a considerable interest in getting into telephone booths and talking on the telephone and one of their favorite words was pronto. So it’s like ping-pong, pinging back again the bell pinged to me.”

Could you paraphrase this? Neither can I, and when, as a neurologist I had occasion to see schizophrenics, the only way to capture their speech was to transcribe it verbatim. It can’t be paraphrased, because it makes no sense, even though it’s reasonably gramatical.

What is a neurologist doing seeing schizophrenics? That’s for shrinks isn’t it? Sometimes in the early stages, the symptoms suggest something neurological. Epilepsy for example. One lady with funny spells was sent to me with her husband. Family history is important in just about all neurological disorders, particularly epilepsy. I asked if anyone in her family had epilepsy. She thought her nephew might have it. Her husband looked puzzled and asked her why. She said she thought so because they had the same birthday.

It’s time for a little history. The board which certifies neurologists, is called the American Board of Psychiatry and Neurology. This is not an accident as the two fields are joined at the hip. Freud himself started out as a neurologist, wrote papers on cerebral palsy, and studied with a great neurologist of the time, Charcot at la Salpetriere in Paris. 6 months of my 3 year residency were spent in Psychiatry, just as psychiatrists spend time learning neurology (and are tested on it when they take their Boards).

Once a month, a psychiatrist friend and I would go to lunch, discussing cases that were neither psychiatric nor neurologic but a mixture of both. We never lacked for new material.

Mental illness is scary as hell. Society deals with it the same way that kids deal with their fears, by romanticizing it, making it somehow more human and less horrible in the process. My kids were always talking about good monsters and bad monsters when they were little. Look at Sesame street. There are some fairly horrible looking characters on it which turn out actually to be pretty nice. Adults have books like “One flew over the Cuckoo’s nest” etc. etc.

The first quote above is from a letter John Nash wrote to Norbert Weiner in 1959. All this, and much much more, can be found in “A Beatiful Mind” by Sylvia Nasar. It is absolutely the best description of schizophrenia I’ve ever come across. No, I haven’t seen the movie, but there’s no way it can be more accurate than the book.

Unfortunately, the book is about a mathematician, which immediately turns off 95% of the populace. But that is exactly its strength. Nash became ill much later than most schizophrenics — around 30 when he had already done great work. So people saved what he wrote, and could describe what went on decades later. Even better, the mathematicians had no theoretical axe to grind (Freudian or otherwise). So there’s no ego, id, superego or penis envy in the book, just page after page of description from well over 100 people interviewed for the book, who just talked about what they saw. The description of Nash at his sickest covers 120 pages or so in the middle of the book. It’s extremely depressing reading, but you’ll never find a better description of what schizophrenia is actually like — e.g. (p. 242) She recalled that “he kept shifting from station to station. We thought he was just being pesky. But he thought that they were broadcasting messages to him. The things he did were mad, but we didn’t really know it.”

Because of his previous mathematical achievments, people saved what he wrote — the second quote above being from a letter written in 1971 and kept by the recipient for decades, the first quote from a letter written in 12 years before that.

There are a few heartening aspects of the book. His wife Alicia is a true saint, and stood by him and tried to help as best she could. The mathematicians also come off very well, in their attempts to shelter him and to get him treatment (they even took up a collection for this at one point).

I was also very pleased to see rather sympathetic portraits of the docs who took care of him. No 20/20 hindsight is to be found. They are described as doing the best for him that they could given the limited knowledge (and therapies) of the time. This is the way medicine has been and always will be practiced — we never really know enough about the diseases we’re treating, and the therapies are almost never optimal. We just try to do our best with what we know and what we have.

I actually ran into Nash shortly after the book came out. The Princeton University Store had a fabulous collection of math books back then — several hundred at least, most of them over $50, so it was a great place to browse, which I did whenever I was in the area. Afterwards, I stopped in a coffee shop in Nassau Square and there he was, carrying a large disheveled bunch of papers with what appeared to be scribbling on them. I couldn’t bring myself to speak to him. He had the eyes of a hunted animal.

Why making money in the stock market is as stressful than a missile attack (for me)

I made a ton of money in stock market in the past 7 weeks. I hated every minute of it. I found the stress very hard to take, particularly the anxiety and the inability to think of little else. As wives often do, my wife told me I’m nuts. “Don’t you remember how hard you worked for those neurosurgeons? This is the easiest money you’ve ever made”. I made probably more than half a year’s salary from them in absolute amount, and I was well paid.

But that was 25 years ago. For details see https://luysii.wordpress.com/2015/04/19/hilarys-stroke/. Yes, I was on every other night and probably was out between midnight and 8 AM every third night on call with a full day’s work to follow before sleep. It was physically demanding, but not particularly stressful mentally. “All you could lose was money, but in practice you could lose a life”. True, but I knew that I’d never make a mistake of omission, or commission or due to lack of knowledge (fairly arrogant but true, I really kept up with the literature in practice). Decisions didn’t always work out, initial diagnoses weren’t always correct, untoward reactions ensued (particularly to drugs), but I always knew that I given it my best shot. The stress came from doing everything right but still being unable to help, watching helplessly as patients deteriorated.

Thinking this over, after what my wife said, I realized that I was very much like a patient who really educated me.

Neurologists see headaches, lots of headaches. This young man came to see me about them, complete with his own (correct) diagnosis of their cause — a divorce in progress. Taking the history always starts things off, and a standard question is “When did the headaches start?” Oh, just after I got back from Riyadh. (This was during the Gulf War). Riyadh? Wasn’t there a missile attack that killed people while you were over there? Yes. Didn’t you have headaches then? No, but this divorce is killing me, doc. He was right.

So just like the shrinks say, it isn’t the situation itself, but how you perceive it.

Don’t get your hopes up — but

Amyotrophic lateral sclerosis (ALS) is a God-awful disease, where patients progressively weaken and die because they aren’t strong enough to breathe, remaining mentally intact the entire time. A recent paper [ Science vol. 348 pp. 239 – 242 ‘ 15 ] showed that a drug already released by the FDA for treating hypertension — Wytensin (Guanabenz) was of benefit in a mouse model of the disease. So the drug is out there. If I were still in practice, I’d certainly give it a shot in my patients — off-label use be damned. Even better, enterprising organic chemists synthesized an analogue of Wytensin (Sephin1) which doesn’t lower blood pressure, but which still works in the mouse model.

Here’s why you shouldn’t get your hopes up too high. [ Nature vol. 4564 pp. 682 – 685 ’08 ] The work using SOD1 mutant mice (the mouse model of ALS mentioned above) is quite sloppy and nearly 12 drugs with benefit in mouse models have had no benefit in clinical trials. Minocycline which was effective in 4 studies in mice actually made things worse in a clinical trial of over 400 patients .

Now for a bit of background. Most cases of ALS aren’t familial, but a few are. One protein Superoxide Dismutase 1 (SOD1) was found to mutated in about 20% of familial ALS. It’s been studied out the gazoo, and some 140 different mutations have been found in its 153 amino acids in familial cases.

It’s hard to conceive of them all acting the same way, and literally thousands of papers have been written on the subject. It does seem clear that aggregated proteins occur in the dying neurons of ALS patients, but whether they are made mostly of SOD1 remains controversial (although it is present in the inclusions to some extent). Mature SOD1 is a 32 kiloDalton homodimeric metalloenzyme, in which each monomer contains Cu and Zn and one intrasubunit disulfide bond. It is one of the most abundant cellular proteins. It has a tendency to aggregate when overexposed.

The mouse results are impressive, as it improved established disease. In vivo, Sephin1 prevented the motor morphological and molecular defects of two unrelated protein misfolding diseases in mice (Charcot Marie Tooth 1B and ALS ! ! !). The mice had a mutant SOD1 (G93A). SOD1 mutants bind to Derlin1 on the the cytosolic side of the endoplasmic reticulum (ER) membrane blocking degradation of ER proteins causing ER stress. Very impressive ! ! ! !

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