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Back in the 80s when artificial intelligence (AI) was going to make humans obsolete, LISP was the programming language of choice for AI. As a neurologist I was interested in intelligence in any form (machine or otherwise) so I tried to learn it. Most programs looked like gibberish. There was a great quote in a book "Let's Talk LISP" after a particularly convoluted piece of code — "Relax you, never understand anything, you just get used to it".

I think the same thing has happened with our understanding of biologically relevant proteins. We've just become used to the fact that biological proteins have a dominant shape. However, we also know that other polymers don't. DNA and RNA certainly don't have a single shape.

So why do biologically meaningful proteins have one? Consider enzymes. The amino acid side chains comprising the active site are found all over the protein rather than next to each other in the sequence. Chymotrypsin, one of the best studied enzymes, has a catalytic triad made from histidine #57, aspartic acid #102 and serine #195. To function, they must be brought near to each other and held there fixed (and in the proper orientation to boot). The same holds for structural proteins that make up muscle and the cytoskeleton.

Yet only 10 kcal/mole — 2 hydrogen bonds — is enough to denature them. Not much of an activation energy — not even close to a covalent bond. Once denatured, Anfinsen showed that ribonuclease found its way back to the original shape, implying that there were no other conformations of similarly low energy available to it.

It is remarkable that we only have 20,000 or so protein coding genes when you consider just how large possible protein space is. In this regard, proteins are like English words. There are very few of them when you calculate how many there could be. Sonnet #18 — "Shall I compare thee to a summer's day?" contains 114 words of which 17 are 7 or more letters long. The Oxford English dictionary contains 600,000 or so words of all lengths. There are 8 x 10^9 strings of 7 letters. Few of them have meaning.

Words are a lot shorter than proteins. There are 8 times as many strings of 4 amino acids (20^4 = 160,000) than we have proteins. My guess is that this isn't an accident, because I doubt that most strings of amino acids have a dominant shape (e.g., biological meaning), and even if they did, they couldn't find it quickly enough (the Levinthal paradox again).

How would you prove me wrong? Is the question even meaningful scientifically? I (of course) think it is quite meaningful in a philosophic sense, since it bears on just how probable or improbable life is. The next post will discuss some gedanken experiments which could settle the question (or show that it is unanswerable).

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Well of course they don't, but the proteins we know the most about (because they can be crystallized and their structure determined by X-ray diffraction) do have a shape. Sperm whale myoglobin, the first protein to have its 3-dimensional structure determined, showed that this couldn't be the whole story. Sperm whales (air breathing mammals after all) use their myoglobin to carry oxygen during their hour-long dives down to 1000 meters. Kendrew and Perutz's crystal structure showed no way for oxygen to find its way in to the embedded porphyrin ring. Amazingly, the 153 amino acids of myoglobin must themselves breathe to let the oxygen in.

All it takes to denature (seriously change its tertiary structure so it is no longer functional) a protein of 100 amino acids is 10 kcal/mole (Voet & Voet - Biochemistry 3rd Edition p. 258). That's two hydrogen bonds - not much.

Sight your eye at the alpha carbon of one of the amino acids of this protein, looking toward the carbonyl carbon. There are three conformational energy minima the carbonyl can adopt. That's potentially 3^99 = 10^48 conformations (clearly an overestimate because of self intersection, but still, a huge number). Yet to be crystallizable, this protein must choose just one of them, and it must be lower in energy by 2 hydrogen bonds than all the rest.

In addition, to get to this single structure, the protein can't possibly sample all the conformations available to it. The rotation barrier of ethane is 12 kJ/mole and a barrier of 73 kJ/mole allows a rotation rate of 1 per second, and every 6 kJ changes the barrier by a factor of 10 at 25 deg C (Clayden et al. Organic Chemistry pp. 450-1). So the maximum rate of rotation of ethane is 10^11 per second (at a body temperature of around 37 deg C) rather than 10^10 at 25 deg C. This is clearly an upper bound on the rotation rate as the mass attached to the alpha carbons of a protein will make the rotation far slower, but let it pass (that's why I chose ethane in the first place). That's 10^37 seconds to sample the conformations available, far longer than the age of the universe. This is the Levinthal paradox.

So for the crystallizable proteins (all of biological interest so far) one conformation out of all those available must be more stable (but only by two hydrogen bonds) than all the rest, and the particular conformation must be findable quickly (or we'd all be dead).

How likely is this for a 'random' sequence of amino acids. We'll probably never know (but we might if we're lucky). This is the subject of the next post...

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The mass of the earth is given by my physics book (Halliday 6th Ed.) as 6 x 10^27 grams. If we made just one molecule of each protein containing n amino acids linked together, when would we run out of material? Make a guess. I found the results surprising.

Assume the earth is made of nothing but hydrogen, oxygen, nitrogen, carbon and sulfur. Clearly not true, but we're going for what mathematicians call an upper bound. If mathematicians can get away with things like "consider a spherical cow" I can get away with this. (The cognoscenti may wish to go for a least upper bound). Proteins are linear chains of 20 different amino acids ranging in mass from glycine at 79 Daltons to tryptophan at 204. When linked together by an amide (peptide) bond, 18 Daltons of mass is lost (water is split out). So figure the average amino acid at 100 Daltons (roughly).

So there are 20 x 20 = 400 distinct proteins of 2 amino acids, 8000 with 3, 160,000 with 4, 3,200,000 with just 5. Shorties like this are called peptides (or polypeptides) and just when you start calling them proteins seems to be a matter of taste.

We're figuring the mass of the typical amino acid at 100 Daltons, but a Dalton doesn't have much mass. It is 1/12 the mass of a single atom of carbon-12, Avogadro's number (about 6 x 10^23) of which have a mass of 12 grams. So one Dalton has a mass of 10^-24 grams (roughly).

The number of distinct proteins containing n amino acids is 20^n. The mass of each protein (in Daltons) is (roughly) 100 x n — depending on the amino acids chosen. The mass of the collection of distinct proteins of length n in grams is (20^n) x (100 x n) x (10^-24). It's clear that we're over 1 gram for the collection at only 24 amino acids (as 20^24 is much larger than 10^-24. How far over? 2^24 x 100 x 24 = 40,265,318,400 = 4 x 10^10 grams.

As noted, the mass of the earth is 6 x 10^27 grams. So we're not too far away at 24 amino acids. Certainly no farther away than another 17 amino acids as 20^17 is much greater than 10^17.

So, the mass of the earth (which isn't all carbon, hydrogen, etc... ) isn't enough to make just one molecule of each of the possible proteins 41 amino acids long. 41 amino acids is a very small protein (some would call it a polypeptide). Just about every protein of biological interest is much larger. The champ is a muscle protein called titin which has 27,000+ amino acids.

So what? It means that chemists will never be able to explore more than a tiny morsel of the space of possible proteins. Perhaps computationally we will (I doubt it), but that's the subject of a future post.

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This post is pretty philosophic, but it discusses some issues raised by the previous post that shouldn't be ignored. Future posts will be far more chemical.

Do we have any hope of constructing a nice chain of causality for what happens when we throw epidermal growth factor (EGF) at a Hela cell (described in the last post) — e.g., the EGF receptor activates kinases 1 through N, each of which phosphorylates substrates (some of which are other kinases) which eventually phosphorylate the 924 sites on the 2,244 proteins (and in the correct temporal order to boot). I don't think there are enough researchers to do it, or labs to hold them. Even worse, if the results were available, I don't think our minds are strong enough to grasp them.

A big stumbling block would be the multiple degrees of feedback present even with something as simple as phosphorylation and dephosphorylation. Simple ideas of causality and control vanish with feedback (see two posts back — "The Decline of Master Gland..."). Causality is inherently a linear, sequential idea. Even chaos theory is basically causal, although predictability goes out the window.

That's not to say our brains don't do incredibly complex things such as just recognizing people. You never see anyone at exactly the same angle, under the same light, with the same background. People are usually moving, attired differently, etc., etc... Yet our brains in some way compute an invariant that computer science can only dream about permitting instant recognition. As people move about and you interact with them, zillions of new sensory inputs must be absorbed, transformed and matched to the same invariant. Since we do all this unconsciously, we don't think anything of it.

Yet we don't do very well predicting events where feedback is involved (like the stock market where most people lose). Perhaps the next step up in human intelligence is the ability to perceive the various forms of multiloop feedback, the way we recognize faces and people.

Could our brains change that fast? Possibly. Consider the man's best friend vs. the chimp. [Science vol. 298 pp. 1634–1636 (2002)] Chimpanzees are terrible at picking up human cues as to where food is hidden, even when the cues are as obvious as pointing to the food container. Even chimps that eventually perform well, take dozens of trials or more to learn what the cues mean. I find this surprising.

However, puppies (raised with no contact with humans) do much better at this than chimps — anyone owning a dog knows they can read us like a book. Wolf cubs don't do better than the chimps, even cubs raised by humans. This implies that during the process of domestication, dogs have been selected for a set of cognitive and social abilities that allow them to communicate with us. Domestication has only gone on for 10,000–15,000 years (the dawn of agriculture). I find it absolutely incredible that we could have changed the dog's brain in what is basically a microsecond in evolutionary time. Yet we did. Hopefully our brains are as plastic.

Not to be too depressed by this. There clearly are single chains of causality in the cell and chokepoints which we can find and modify. Consider Gleevec. Success stories like this provide employment for legions of chemists.

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So nat'ralists observe, a flea
Hath smaller fleas that on him prey,
And these have smaller fleas that bite 'em,
And so proceed ad infinitum.
– Jonathan Swift

Is anything like this going on in the cell? Consider mitogen activated protein kinase kinase kinase (abbreviated MAPKKK) — shades of Major Major Major in Catch-22. Recall that a kinase is an enzyme which attaches a phosphate group to (phosphorylates) one of the 3 amino acids with hydroxyls on their side chains — serine, threonine and tyrosine. A phosphate ester is formed in the process adding a significant amount of negative charge and some local bulk to the protein (and if the protein is an enzyme often significantly altering its activity).

And what is the target that MAPKKK phosphorylates? Why MAPKK, another kinase which itself phosphorylates MAPK (yet another kinase — I'm not making this up). MAPK phosphorylates a variety of proteins, among them transcription factors which turn on various genes.

All quite linear (sequential) and comprehensible. There is a nice chain of causality from the agent outside the cell (the mitogen) to the receptor for it, to MAPKKK and so on to a particular set of genes whose level of expression is altered with the net result being cellular proliferation (e.g., mitosis).

Discovering this pathway took a lot of hard work on the ras protein, which is mutated in 30% of all cancers. Just the steps from the mitogen binding to its receptor to ras and thence to MAPKKK are quite complex. It was a hard slog, one (linear) step at a time. But what if all this work was like the drunk looking under the street light for his key because that's where the light was. Suppose far more than that is going on.

Instead of teasing out pathways one protein at a time, suppose you just threw a mitogen (in this case epidermal growth factor — EGF ) at a cell (OK, a cancer cell — the Hela cell — the workhorse of cancer research) and looked at every protein to see what was phosphorylated and what was not. Using advanced mass spectroscopy and some other cutting edge techniques [Cell vol. 127 pp. 635–648, 2006] did just that. Some 6,600 distinct phosphorylation sites on 2,244 different proteins were found. 924/6,600 sites showed more than a twofold change in the phosphorylated to unphosphorylated ratio.

In addition, the work was repeated at several time points within 30 minutes of EGF application, allowing the time course of phosphorylation at each site to be determined. The time courses of phosphorylation varied from site to site. Many proteins had more than one site phosphorylation. Even on the same protein the time course of phosphorylation depended on the site studied. At least 46 distinct regulators of gene transcription showed a greater than twofold variation in phosphorylation. It doesn't take much imagination to see that adding a lot of negative charge would alter the ability of a transcription factor to approach DNA (which has one phosphate per nucleotide).

Where this leaves our notion of causality (which really is quite linear) and whether our minds are strong enough to comprehend these events is the subject of the next post.

Retread

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Endocrinology was pretty simple in med school back in the 60s. All the target endocrine glands (ovary, adrenal, thyroid, etc.) were controlled by the pituitary; a gland about the size of a marble sitting an inch or so directly behind the bridge of your nose. The pituitary released a variety of hormones into the blood (one or more for each target gland) telling the target glands to secrete, and secrete they did. The master gland ruled.

Things became a bit more complicated when it was found that a small (4 grams or so out of 1500) part of the brain called the hypothalamus sitting just above the pituitary was really in control, telling the pituitary what and when to secrete. Subsequently it was found that the hormones secreted by the target glands (ovary, etc.) were getting into the hypothalamus and altering its effects on the pituitary. Estrogen is one example. Any notion of simple control vanished into an ambiguous miasma of setpoints, influences and equilibria. Goodbye linearity and simple notions of causation.

As soon as feedback (or simultaneous influence) enters the picture it becomes like the three body problem in physics, where 3 objects influence each other's motion at the same time by the gravitational force. As John Gribbin (former science writer at Nature and now prolific author) said in his book ‘Deep Simplicity’, "It's important to appreciate, though, that the lack of solutions to the three-body problem is not caused by our human deficiencies as mathematicians; it is built into the laws of mathematics." The physics problem is actually much easier than endocrinology, because we know the exact strength and form of the gravitational force.

Organic chemists dearly love linearity. Nothing is more linear and causal than a multistep synthesis. We always search for conditions producing just what we want in high yield with as few unwanted products as possible, thank you. Le Chatelier's principle is used again and again to force reactions to go just the way we want. It is a type of thinking that will not help us understand what is going on within our cells.

At one time it was thought that we had about 100,000 genes coding for proteins. The best current estimates are around 20,000. These genes code for structural proteins (like those of muscle and bone) and enzymes which do things like metabolize sugar or build the components of structural proteins (amino acids) or of DNA and RNA (nucleotides). We are gradually finding out that a lot of our genes function as controlling elements.

For instance, we have 478 genes for enzymes called kinases which form phosphate esters on the hydroxyls of threonine, serine and tyrosine of proteins, radically altering their function usually (the phosphate group adds a lot of negative charge). We have 107 genes for enzymes (called phosphatases) just for removing the phosphate from tyrosine (never mind serine and threonine). Another 600 or so genes code for enzymes which add (or remove) a small protein called ubiquitin from other proteins. Again feedback, control and nonlinearity.

Where this leaves the notion of causality in the cell, and worse, our ability to comprehend it -- we do think linearly after all -- will be the subject of the next post.

Retread

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The Scandinavian Goddess I had a crush on all through high school could pick up any instrument and play it — piano, clarinet, guitar, saxophone, etc... She didn't think it was a big deal, it was just the way she was. The Hungarian uprising of '56 occurred while I was a freshman in college. A friend who already knew 12 or so languages picked up Hungarian in a week or two and went up to Camp Kilmer in New Jersey to act as a translator for the refugees. It was just something he could do. 50+ years later, the 16 year old high school student auditing an upper level college course in abstract algebra I was taking looked up occasionally from his German homework when the lecturer made an obscure point. He blitzed the course and later went on to college.

I don't think there is anything remotely like that in organic chemistry, although the rumor back then was that Woodward knew all of Beilstein before he hit puberty. Learning organic chemistry always seemed pretty easy and intuitive to me (even now when revisiting it years later). Perhaps it was playing with TinkerToys as a kid. I've found math much, much harder.

In organic chemistry you come to know carbon inside out and at least one atom of it is always present, so you can bring everything you already know (which is quite a bit) to the problem at hand. Math isn't like that at all. You are always bumping up against new definitions, concepts and theorems. Once you get past the plug and chug part of math (use the chain rule n times, integrate by parts m times to find an integral, look for a recursion formula by repeatedly differentiating) you are proving theorems. Here, you must bring everything you know about math to proving the theorem or problem at hand. You may have to create a function, a group, an ideal to solve it, reason by contradiction, think of a counterexample etc., etc...

Is anything like that in organic chemistry? Of course there is. The theorems of organic chemistry are its syntheses. Every reaction you ever heard of comes into play, new ones must be invented, mechanistic pitfalls considered, conditions carefully adjusted etc., etc... You are not asked to synthesize strychnine as a college junior but you start proving theorems in math at that point and never stop. That's why math is harder (to learn).

So math is harder to learn, but organic chemistry and math are equally hard to do. If we really understood mechanism and reactivity, we could just write out the steps and have a robot perform them. We don't because our knowledge is very incomplete. In this sense, organic synthesis is actually harder than math, because in math you are starting with a huge background of solidly proven results which are at your disposal. In chemistry you have a similarly huge background, but there is no guarantee that any of it will work on your particular problem. It's your job to figure out why something which should have worked didn't do so and a way around it as well. That's not easy at all.

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Much of the training of budding neurologists in the 60s was concerned with how to perform a good neurological exam and interpret the results. Various constellations of abnormalities pointed to different regions of the nervous system and the history often told us what sort of trouble was present there. Essentially we were inferring abnormalities of structure from abnormalities of function.

Why not just look? We had only two ways to do so back then (1) sticking a needle in an artery and injecting a dye which X-rays couldn't pass through (radio-opaque dyes – if you don't already know what they are, think of what you'd want to synthesize) – this had a 1–5 % stroke rate at the time (2) injecting air via a spinal tap and taking X-rays subsequently (I'm not kidding).

The advent of computerized axial tomography (CAT scans) and MRIs (magnetic resonance imaging) changed all that. We were able to directly look at structure without a decent exam. Not only that – problems could be picked up before they produced changes in function (e.g., earlier).

Naturally, neurologists were panicked, thinking that we would soon become the buggy whip manufacturers of medicine. Somehow, telling my colleagues that MRIs showed the essential correctness of quantum mechanics didn't help, producing only blank stares and decreased referrals.

Telling the man in the street that spectroscopy alone shows the correctness of quantum mechanics (sharp absorption and emission lines show that only certain energies of molecules and transitions between them are permissible) just doesn't cut it. But everybody knows what an MRI is.

Forget the wave nature of light (for today). Think of photons as baseballs travelling at various speeds (I know, light has but one speed and its frequency determines its energy just as the speed of a baseball determines its kinetic energy). Throw the baseball at a window. If you throw it fast enough (high kinetic energy) it goes through, if you throw it slowly it doesn't. Everybody knows that.

Not so with the light used for MRI. They are radiowaves and contain around one millionth of the energy of visible light, yet they go right through our skull and brain rather than bouncing back. Why? The only way we can get them absorbed by our brains is to place ourselves in a strong magnetic field in the scanner. The magnetic field essentially creates two new energy levels so close together in energy that the tiny energy difference between them matches the energy of the radiowave permitting it to be absorbed. Without absorption, no pictures. Certainly counterintuitive, but used every day all over the world. Quantum mechanics rules (but weirdly).

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An incredible article appeared last month in the journal Science. If it can be verified and if it applies generally, our conception of just how genes coding for protein are turned on will be radically changed (yes, there are many other kinds of genes other than those coding for proteins). If DNA compaction, nucleosomes, histones, lysine methylation and demethylation, the histone code, nuclear hormone receptors (particularly the estrogen receptor), DNA glycosylase and topoisomerase aren't old friends have a look at the first comment on this post for the background you need. Don't worry, there is plenty of chemistry to follow.

Some histone code modifications are reversible, particularly acetylation of the epsilon amino group of lysine. Enzymes acetylating histone lysines are called histone acetylases, those removing it are called histone deacetylatases (HDACs). However, lysine methylation was thought to be permanent until '04 when several enzymes able to demethylate lysine were found. One such enzyme is called LSD1 (it has nothing to do with the hallucinogen). It removes the two methyl groups from lysine #9 of histone #3 (H3K9me2). If this modification is present on a nucleosome near a gene, the gene is silenced, so the methyls must be removed so the protein it codes for can be made.

The estrogen receptor + estrogen complex bound to the ERE (the estrogen response element – a 15 nucleotide DNA sequence) triggers H3K9me2 removal. The process of demethylation is oxidative (how else would you split a nitrogen to hydrocarbon bond?). Hydrogen peroxide is produced, a loose cannon which oxidizes the juicy electron-rich bases of DNA nearby, forming in particular 8 oxo-guanine, as guanine is the most easily oxidized DNA base. Since 21% of the DNA bases in our genome are guanine, H₂O₂ doesn't have far to look. This calls in some fairly heavy artillery (DNA glycosylase to remove the 8 oxo-guanine, topoisomerase IIbeta to unwind the DNA so it can be repaired, the repair enzymes, etc, etc...). Naturally this opens up the compacted DNA structure around the gene allowing RNA polymerase II to do its work transcribing the estrogen responsive gene into mRNA (once the damage is repaired).

So according to this paper, estrogen turns on gene transcription by damaging DNA. This is fantastic (if true). There's more. The estrogen receptor is but one member of a group of proteins called nuclear hormone receptors. The name comes from the fact that other hormones (progesterone, androgen, thyroid, glucocorticoids, mineralocorticoids) have their own proteins that turn on (or turn off) genes the same way. Subsequently it was found that some vitamin metabolites (vitamin D3, vitamin A) have similar receptors even though they aren't hormones. The human genome contains 48 such proteins. Less than half of them have known ligands. Those with known ligands have their finger in just about every metabolic pie in the cell.

One final point. It has been estimated that 8-oxoguanine is formed 100,000 times each day in every cell. Perhaps its formation is physiologic rather than pathologic. Where does that leave antioxidant therapy, which has been touted to do everything but cure hemorrhoids? Well, one such trial was done on 29,000 Finnish men at high risk for lung cancer (they were smokers) [New England J. Med. vol. 330 pp. 1029-1035 (1994)] Alpha tocopherol (one antioxidant used in the study) didn't decrease the incidence of lung cancer, and there was an 18% higher incidence of lung cancer among the men receiving beta carotene (another antioxidant). In medicine, theory is great but data trumps it every time.

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[Editor’s note – a new guest contributor, Retread, has joined the team, and should be familiar to some of our readers...]

Feb 13, 2008

"Everything in Chemistry turns blue or explodes". Only a philosophy major in full hubristic cry could say that to his pre-med chemistry-major ex-roommate. There was some reality to it as the teacher of Chem 101, Dr Hubert N. Alyea, was really a small boy trapped in a professor suit, and usually blew something up in every lecture. Chemistry is still the Rodney Dangerfield of the sciences, important when the demand for taxol for breast cancer threatened to destroy every yew tree in sight, yet largely ignored by its progeny, biochemistry and molecular biology and the press.

Probably every nascent chemist suffers through things like this, but I got more than most, rooming with two philosophy majors as an undergraduate (one of whom was later a Rhodes). It definitely gives you both a thick skin and a more abstract cast of mind.

For who I am and my background go to ChemBark, scroll down the Categories section until you get to Rip Van Winkle open it up and start reading. This where I would have stayed, happily posting now and then and reading and responding to comments. However Paul has other fish to fry (probably his thesis) and ChemBark has developed a definite funereal cast in the 3 months since Paul's last post. Anyway, Paul got me started and gave me a forum, encouragement and advice, so I owe him at least a good dinner. Thanks Paul.

If contact with budding philosophers didn't make me somewhat reflective, then following the development of molecular biology from '62 to the present with the eye and background of a Woodward grad student and medical practice as a neurologist from '67 to '00 certainly was enough to do so. This is why future posts will be on things like:

1. Is there really such a thing as causality in cellular biochemistry and physiology?

2. Is organic chemistry easy or hard?
2a. If it's hard, is math harder?

3. Are there important chemical experiments which we can't do because the earth isn't big enough?

4. Is there really such a thing as control in chemical systems with feedback on every component (including the elements providing the feedback)?

5. Does the complexity of cellular chemistry and biochemistry raise questions about the adequacy of chance to bring it about?

That's for the future. The next post (probably a very long one because of the background required) will be on a recent spectacular paper which, if replicated and generally applicable, will revolutionize the way we think of the control of gene transcription. Thomas Kuhn where are you when we need you?

Stay tuned

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