Has the great white whale of oncology finally been harpooned?

The ras oncogene is the great white whale of oncology. Mutations in 20 – 40% of cancer turn its activity on so that nothing can turn it off, resulting in cellular proliferation. People have been trying to turn mutated ras off for years with no success.

A current paper [ Cell vol. 165 pp. 643 – 655 ’16 ] describes a new and different way to attack it. Once  ras is turned on (either naturally or by mutation) many other proteins must bind to it, to produce their effects — they are called RAS effectors, among which are the uneuphoniously named RAF, RalGDS and PI3K. They bind to activated ras by the cleverly named Ras Binding Domain (RBD) which has 78 amino acids.

The paper describes rigosertib, a not that complicated molecule to the chemist, which inhibits the binding (by resembling the site on ras that the RBD binds to). It is a styryl benzyl sulfone and you can see the structure here — https://en.wikipedia.org/wiki/Rigosertib.

What’s good about it? Well it is in phase III trials for a fairly uncommon form of cancer (myelodysplastic syndrome). That means it isn’t horribly toxic or it wouldn’t have made it out of phase I.

Given the mechanism described, it is possible that Rigosertib will be useful in 20 – 40% of all cancer. Can you say blockbuster drug?

Do you have a speculative bent? Buy the company testing the drug and owning the patent — Oncova Therapeutics. It’s quite cheap — trading at $.40 (yes 40 cents !). It once traded as high as $30.00 — symbol ONTX. I don’t own any (yet), but for the price of a movie with a beer and some wings afterwards you could be the proud owner of 100 shares. If Rigosertib works, the stock will certainly increase more than a hundredfold.

Enough kidding around. This is serious business. In what follows you will find some hardcore molecular biology and cellular physiology showing just what we’re up against. Some of the following is quite old, and probably out of date (like yours truly), but it does give you the broad outlines of what is involved.

The pathway from Ras to the nucleus

The components of the pathway had been found in isolation (primarily because mutations in them were associated with malignancy). Ras was discovered as an oncogene in various sarcoma viruses. Mutations in ras found in tumors left it in a ‘turned on’ state, but just how ras (and everything else) fit into the chain of binding of a growth factor (such as platelet derived growth factor, epidermal growth factor, insulin, etc. etc.) to its receptor on the cell surface to alterations in gene expression wasn’t clear. It is certain to become more complicated, because anything as important as cellular proliferation is very likely to have a wide variety of control mechanisms superimposed on it. Although all sorts of protein kinases are involved in the pathway it is important to remember that ras is NOT a protein kinase.

l. The first step is binding of a growth factor to its receptor on the cell surface. The receptor is usually a tyrosine kinase. Binding of the factor to the receptor causes ‘activation’ of the receptor. Activation usually means increasing the enzymatic activity of the receptor in the tyrosine kinase reaction (most growth factor receptors are tyrosine kinases). The increase in activity is usually brought about by dimerization of the receptor (so it phosphorylates itself on tyrosine).

2. Most activated growth factor receptors phosphorylate themselves (as well as other proteins) on tyrosine. A variety of other proteins have domains known as SH2 (for src homology 2) which bind to phosphorylated tyrosine.

3. A protein called grb2 binds via its SH2 domain to a phosphorylated tyrosine on the receptor. Grb2 binds to the polyproline domain of another protein called sos1 via its SH3 domain. At this point, the unintiated must find the proceedings pretty hokey, but the pathway is so general (and fundamental) that proteins from yeast may be substituted into the human pathway and still have it work.

4. At last we get to ras. This protein is ‘active’ when it binds GTP, and inactive when it binds GDP. Ras is a GTPase (it can hydrolyze GTP to GDP). Most mutations which make ras an oncogene decrease the GTPase activity of RAS leaving it in a permanently ‘turned on’ state. It is important for the neurologist to know that the defective gene in type I neurofibromatosis activates the GTPase activity of ras, turning ras off. Deficiencies (in ras inactivation) lead to a variety of unusual tumors familiar to neurologists.

Once RAS has hydrolyzed GTP to GDP, the GDP remains bound to RAS inactivating it. This is the function of sos1. It catalyzes the exchange of GDP for GTP on ras, thus activating ras.

5. What does activated ras do? It activates Raf-1 silly. Raf-1 is another oncogene. How does activated ras activate Raf-1 ?  Ras appears to activate raf by causing raf to bind to the cell membrane (this doesn’t happen in vitro as there is no membrane). Once ras has done its job of localizing raf to the plasma membrane, it is no longer required. How membrane localization activates raf is less than crystal clear. [ Proc. Natl. Acad. Sci. vol. 93 pp. 6924 – 6928 ’96 ] There is increasing evidence that Ras may mediate its actions by stimulating multiple downstream targets of which Raf-1 is only one.

6. Raf-1 is a protein kinase. Protein kinases work by adding phosphate groups to serine, threonine or tyrosine. In general protein kinases fall into two classes those phosphorylating on serine or threonine and those phosphorylating on tyrosine. Biochemistry has a well documented series of examples of enzymes being activated (or inhibited) by phosphorylation. The best worked out is the pathway from the binding of epinephrine to its cell surface receptor to glycogen breakdown. There is a whole sequence of one enzyme phosphorylating another which then phosphorylates a third. Something similar goes on between Raf-1 and a collection of protein kinases called MAPKs (mitogen activated protein kinases). These were discovered as kinases activated when mitogens bound to their extracellular receptors.There may be a kinase lurking about which activates Raf (it isn’t Ras which has no kinase activity). Removal of phosphate from Raf (by phosphatases) inactivates it.

7. Raf-1 activates members of the MAPK family by phosphorylating them. There may be several kinases in a row phosphorylating each other. [ Science vol. 262 pp. 1065 – 1067 ’93 ] There are at least three kinase reactions at present at this point. It isn’t known if some can be sidestepped. Raf-1 activates mitogen activated protein kinase kinase (MAPK-K) by phosphorylation (it is called MEK in the ras pathway). MAPK-K activates mitogen activation protein kinase (MAPK) by phosphorylation. Thus Raf-1 is actually mitogen activated protein kinase kinase kinase (sort of like the character in Catch-22 named Junior Junior Junior). (1/06 — I think that Raf-1 is now called BRAF)

8. The final step in the pathway is activation of transcription factors (which turn genes off or on) by MAP kinases by (what else) phosphorylation. Thus the pathway from cell surface is complete.

A new wrinkle in an old reaction

Just when you thought we knew everything there was to know about the Diels Alder reaction, cometh Nature vol. 532 pp. 484 – 488 ’16 in which triple bonds are used in both the diene and the dienophile. Naturally they are all put in the same molecule so they can’t get away from each other. I can’t draw the structure in this post, but it’s worth a look, particularly since a benzyne intermediate is formed in one, and an even more bizarre (and labile) intermediate (a diradical with the unpaired electrons, each on an atom, separated by two more carbons) is formed in the other. It’s sort of chemical bonsai. Enjoy

Carly ‘s Cancer

Today Senator Cruz said that Carly Fiorina would be his running mate, should he get the republican nomination. It’s worth reposting (with a few modifications) what I wrote last September about her cancer when it looked like she had a chance of getting the nomination. See the end for why the health problems of our leaders are problems for us all.

Carly Florina had breast cancer surgery (bilateral mastectomy) 2 March 2009 at Stanford University Hospital followed by chemotherapy and radiation. She was given an excellent prognosis for full recovery — https://en.wikipedia.org/wiki/Carly_Fiorina.

So far so good and it’s just over 7 years. But it is reasonable to ask just what her prognosis really is, particularly as she may be our next vice-president. I asked an old friend and colleague who has been involved in research on breast cancer and in many of the clinical trials of therapy over the past 35 years.

So I wrote the following — I’m writing you for some idea what the chances of someone with breast cancer being free for 6+ years (Carly’s surgery was 2/09) will be free for the next 5+? I know that there are all sorts of statistics on survival in breast cancer (because the cohort is so large). If anyone would know them, it would be you.

and got this back

Impossible to answer your question. Too many variables and NO DATA or info. Many people, docs and patients alike call ductal carcinoma in situ,” cancer” but cure rate is 99%. If she was one of those then, of course, she’s likely to be cured . Stage 1 ,luminal A tumors (even though real cancers) have excellent prognoses—probably > 90% cured. For other real cancers Lots depend on stage, hormone receptors ad infinitum. On thin ice lumping anyone into a broad statement without lots more info

just what you’d expect from an circumspect intelligent expert

So I dug a bit more and sent him this

I tried to find out just what type of breast cancer Carly had. No luck, but various newspaper articles show that she did receive postop chemo causing her hair to fall out as well as radiation. Would ductal carcinoma in situ (Dcis) be treated this way? Would stage 1 luminal A tumors be treated this way?

He replied

Dcis definitely no. luminal a probably shouldn’t be. Sounds like a significant cancer. Next issue is did she get antihormonal therapy. Estrogen receptor tumors are the ones that tend to relapse after 5 years. ER neg. tumors while more aggressive overall seldom recur >5 yrs after dx. The radiation part doesn’t mean much unless she had a mastectomy since all lumpectomy patients get radiation. – If she had mastectomy and chemo and radiation it was probably a poorer risk tumor. Even chemo might not be so bad—–we give chemo to node neg tumors which could end up with very good long term prognosis.AMONG RELAPSES in ER pos pts. 15% recur before year 5 and 17% recur after year 5. However overall likelihood of relapse depends on whether or not she had positive or negative nodes and was ER + or Neg. Sorry to be so wordy but prognosis has been improving steadily. I would guestimate that we’re curing about 70% of women with newly diagnosed breast cancer—excluding dcis who are virtually all cured.

I realized that I’d neglected to tell him that she’d had a bilateral mastectomy as well and got the following back after I did.

If she indeed had radiation after a mastectomy as well as chemo it speaks for a more aggressive presentation. Rule of thumb—-post mastectomy xrt reserved for patients with > 4 positive nodes or tumors >5 cm in size. Today, many are giving post mastectomy xrt to 1-3 positive nodes although that was very controversial for years . newer data impies benefit. So, just guessing, but she probably had positive nodes—a poorer prognostic sign for long term—but only if she was estrogen receptor pos. as noted in prior email.

So there you have it — she’s fortunately well presently, but the tumor and prognosis doesn’t sound that good. Still unknown are histologic type of the tumor, presence or absence of spread to lymph nodes (and if so how many), estrogen receptor positivity, which would certainly give us a better idea of her ultimate prognosis (and the country’s should she become president).

I take no pleasure in any of these posts. https://luysii.wordpress.com/2016/04/24/why-hillary-clinton-had-a-stroke-in-2012/ Both Carly and Hillary are brilliant women it would be an honor to know and I wish them both the best. FYI Hillary was valedictorian of her class at Wellesley.

So why write about their potential health problems? Look at the sad saga of Hugo Chavez who claimed he was cured in July elected in the fall with death before he could take office in March of the following year — see https://luysii.wordpress.com/2013/03/05/q-e-d/. Also consider the last months in office of Woodrow Wilson and Franklin Roosevelt and the results of the League of Nations and the Yalta conference when they were both impaired.

Why Hillary Clinton had a stroke in 2012

Hillary Clinton decimated Bernie Sanders in the New York primary and is the likely nominee. This makes the nature of her illness in December 2012 even more important. This retired board certified Neurologist and Neurology Board examiner thinks she had a stroke back then. Here’s why.

First: a timeline.

At some point in the week of 9 December 2012 Mrs. Clinton is said to have fainted suffering a concussion. The New York Times reported on this 13 December.

She remained at home until 30 December at which point she was admitted to New York-Presbyterian Hospital when a blood clot was found in a vein draining her brain.

Subsequently she had double vision due to her eye muscles not working together for a month or so and had to wear special glasses (Fresnel lenses) to correct this.

Second: The following explanation for these events was given by Lisa Bardach M. D, a board certified internist in a letter released by the Clinton campaign 31 July 2015.

You may read the entire letter at http://online.wsj.com/public/resources/documents/clintonhealth2015.pdf but the relevant paragraph is directly quoted below.

“In December of 2012, Mrs. Clinton suffered a stomach virus after traveling, became dehydrated, fainted and sustained a concussion. During follow up evaluations, Mrs. Clinton was found to have a transverse sinus venous thrombosis and began anticoagulation therapy to dissolve the clot. As a result of the concussion, Mrs. Clinton also experienced double vision for a period of time and benefited from wearing glasses with a Fresnel Prism. Her concussion including the double vision, resolved within two months and she discontinued the use of the prism. She had followup testing in 2013, which revealed complete resolution of the effects of the concussion as well as total dissolution of the thrombosis. Mrs. Clinton also tested negative for all clotting disorders. As a precaution, however, it was decided to continue her on daily anticoagulation.”

In my opinion this letter essentially proves that Mrs. Clinton had a stroke.

Third: Why should you believe what yours truly, a neurologist and not a neurosurgeon says about the minimal likelihood of this clot being due to the head trauma she sustained when she fainted? Neurologists rarely deal with acute head trauma although when the smoke clears we see plenty of its long term side effects (post-traumatic epilepsy, cognitive and coordination problems etc. etc.). I saw plenty of it in soldiers when I was in the service ’68 – ’70, but this was after they’d been stabilized and shipped stateside. However, I had an intense 42 month experience managing acute head injuries.

To get my kids through college, I took a job working for two busy neurosurgeons. When I got there, I was informed that I’d be on call every other night and weekend, taking first call with one of the neurosurgeons backing me up. Fortunately, my neurosurgical backup was excellent, and I learned and now know far more about acute head trauma than any neurologist should. We admitted some of the head trauma cases to our service, but most cases had trauma to other parts of the body, so a general surgeon would run the show with our group as consultants. I was the initial consultant in half the cases. When I saw them initially, I followed the patients until discharge. On weekends I covered all our patients and all our consults, usually well over 20 people.

We are told that Hillary had a clot in one of the large draining veins in the back of her head (the transverse dural venous sinus). I’d guess that I saw over 300 cases of head trauma,but I never saw a clot develop in a dural sinus due to the trauma. I’ve spoken to two neuroradiologists still in practice, and they can’t recall seeing such a clot without a skull fracture over the sinus. Such a fracture has never been mentioned at any time about Hillary.

Fourth: Why does the letter essentially prove Hillary had a stroke back then ?

I find it impossible to believe that the double vision occurred when she fainted. No MD in their right mind would not immediately hospitalize for observation in a case of head trauma with a neurologic deficit such as double vision. This is just as true for the most indigent patient as for the Secretary of State. I suppose it’s possible that the double vision came up right away, and Dr. Bardach was talked into following her at home. Docs can be bent to the whims of the rich and powerful. Witness Michael Jackson talking his doc to giving him Diprivan at home, something that should never be given outside the OR or the ICU due to the need for minute to minute monitoring.

My guess was that the double vision came up later — probably after Christmas. Who gets admitted to the hospital the day before New Year’s Eve? Only those with symptoms requiring immediate attention.

Dr. Bardack’s letter states, “As a precaution,however, it was decided to continue her on daily anticoagulation.” I couldn’t agree more. However, this is essentially an admission that she is at significant risk to have more blood clots. While anticoagulation is not without its own risks, it’s a lot safer now than it used to be. Chronic anticoagulation is no walk in the park for the patient (or for the doctor). The most difficult cases of head trauma we had to treat were those on anticoagulants. They always bled more.

Dr. Bardack’s letter is quite clever. She never comes out and actually says that the head trauma caused the clot, but by the juxtaposition of the first two sentences, the reader is led to that conclusion. Suppose, Dr. Bardack was convinced that the trauma did cause the clot. Then there would be no reason for her to subject Mrs. Clinton to the risks of anticoagulation, given that the causative agent was no longer present. In all the cases of head trauma we saw, we never prescribed anticoagulants on discharge (unless we had to for non-neurosurgical reasons).

This is not a criticism of Dr. Bardach’s use of anticoagulation, spontaneous clots tend to recur and anticoagulation is standard treatment. I highly doubt that the trauma had anything at all to do with the blood clot in the transverse sinus. It is even possible that the clot was there all the time and caused the faint in early December.

Fifth: Isn’t this really speculation? Yes it is and this is typical of medical practice where docs do the best they can with the information they have while always wishing for more. The Clinton campaign has chosen to release precious little.

So what information would be useful? First Dr. Bardach’s office notes. I’m sure Mrs. Clinton was seen the day she fainted, and subsequently. They would tell us when the double vision came up. Second the admission history and physical and discharge summary from NY Pres. Her radiologic studies (not just the reports) — plain skull film, CT (if done), MRI (if done) should be available.

Sixth: why is this important.Fortunately, Mrs. Clinton has recovered. However, statistically a person who has had one stroke is far more likely to have another than a person who has never had one. This is particularly true when we don’t know what caused the first (as in this case).

We’ve had two presidents neurologically impaired by stroke in the past century (Woodrow Wilson after World War I and Franklin Delano Roosevelt at Yalta). The decision they made in that state were not happy for the USA or the world.

NonAlgorithmic Intelligence

Penrose was right. Human intelligence is nonAlgorithmic. But that doesn’t mean that our physical brains produce consciousness and intelligence using quantum mechanics (although all matter is what it is because of quantum mechanics). The parts (even small ones like neurotubules) contain so much mass that their associated wavefunction is too small to exhibit quantum mechanical effects. Here Penrose got roped in by Kauffman thinking that neurotubules were the carriers of the quantum mechanical indeterminacy. They aren’t, they are just too big. The dimer of alpha and beta tubulin contains 900 amino acids — a mass of around 90,000 Daltons (or 90,000 hydrogen atoms — which are small enough to show quantum mechanical effects).

So why was Penrose right? Because neural nets which are inherently nonAlgorithmic are showing intelligent behavior. AlphaGo which beat the world champion is the most recent example, but others include facial recognition and image classification [ Nature vol. 529 pp. 484 – 489 ’16 ].

Nets are trained on real world images and told whether they are right or wrong. I suppose this is programming of a sort, but it is certainly nonAlgorithmic. As the net learns from experience it adjusts the strength of the connections between its neurons (synapses if you will).

So it should be a simple matter to find out just how AlphaGo did it — just get a list of the neurons it contains, and the number and strengths of the synapses between them. I can’t find out just how many neurons and connections there are, but I do know that thousands of CPUs and graphics processors were used. I doubt that there were 80 billion neurons or a trillion connections between them (which is what our brains are currently thought to have).

Just print out the above list (assuming you have enough paper) and look at it. Will you understand how AlphaGo won? I seriously doubt it. You will understand it less well than looking at a list of the positions and momenta of 80 billion gas molecules will tell you its pressure and temperature. Why? Because in statistical mechanics you assume that the particles making up an ideal gas are featureless, identical and do not interact with each other. This isn’t true for neural nets.

It also isn’t true for the brain. Efforts are underway to find a wiring diagram of a small area of the cerebral cortex. The following will get you started — https://www.quantamagazine.org/20160406-brain-maps-micron-program-iarpa/

Here’s a quote from the article to whet your appetite.

“By the end of the five-year IARPA project, dubbed Machine Intelligence from Cortical Networks (Microns), researchers aim to map a cubic millimeter of cortex. That tiny portion houses about 100,000 neurons, 3 to 15 million neuronal connections, or synapses, and enough neural wiring to span the width of Manhattan, were it all untangled and laid end-to-end.”

I don’t think this will help us understand how the brain works any more than the above list of neurons and connections from AlphaGo. There are even more problems with such a list. Connections (synapses) between neurons come and go (and they increase and decrease in strength as in the neural net). Some connections turn on the receiving neuron, some turn it off. I don’t think there is a good way to tell what a given connection is doing just by looking a a slice of it under the electron microscope. Lastly, some of our most human attributes (emotion) are due not to connections between neurons but due to release of neurotransmitters generally into the brain, not at the very localized synapse, so it won’t show up on a wiring diagram. This is called volume neurotransmission, and the transmitters are serotonin, norepinephrine and dopamine. Not convinced? Among agents modifying volume neurotransmission are cocaine, amphetamine, antidepressants, antipsychotics. Fairly important.

So I don’t think we’ll ever truly understand how the neural net inside our head does what it does.

Is that mutation significant?

Face it, our genomes are a real mess. A study of just the parts of the genome coding for amino acids (2% at most) in about 2,500 people found an average of 205 variants which change the amino acid coded for IN EACH PERSON. Each person also had an average of 3 termination codons in the 15,000+ protein coding sequences they studied. So they are wandering around with 3 abnormally short proteins. You can read more about it in this old post –https://luysii.wordpress.com/2012/07/31/how-badly-are-thy-genomes-oh-humanity/

Here’s the problem — these people were healthy. Obviously, not a problem for them, but a big problem for physicians attempting to do genetic counseling. For how it affected epilepsy counseling see — https://luysii.wordpress.com/2011/07/17/weve-found-the-mutation-causing-your-disease-not-so-fast-says-this-paper/.

This brings us to Lynch syndrome (aka Hereditary NonPolyposis Colorectal Cancer — HNPCC). It is a familial cancer syndrome, and we now know what the problem is — mutations in any of four genes involved in a type of DNA mutation repair (there are many). The genes are called MSH2, MSH6, MLH1 and PMS2 (acronyms all whose names you don’t need to know) and the type of repair is called MisMatch Repair (MMR).

This isn’t academic at all. Suppose your aunt comes down with colon cancer and you get tested for mutations in one of the four, and a mutation is found. You’re fine now. The question before the house is — should you have your colon out? Colonoscopy won’t help because this kind of colon cancer doesn’t arise from polyps (which is what colonoscopy is looking for).

The problem is that the 4 genes are ‘peppered’ with missense variants (change the amino acid coded for). They are called VUS (Variants of Unknown Significance). The following paper [ Proc. Natl. Acad. Sci. vol. 113 pp. 3918 – 3820, 4128 – 4133 ’16 ] used a clever way to test a VUS for significance. This would have been impossible 5 years ago. What they did was use CRISPR to introduce the variant into the appropriate protein in mouse Embryonic Stem cells. Then they tested the manipulated stem cells for defects in MisMatch Repair. They tested 59 (yes fifty-nine) such VUSs and found that about 1/3 (19) produced MMR defects.

Fascinating time to be alive and reading about all this stuff.

Activating a proto-oncogene without mutating it

Many proto-oncogenes have to be mutated to cause cancer. Not so the TAL1, LMO2 genes. They drive blood formation, and are aberrantly activated (e.g. more proteins made from them is expressed) in T cell Acute Lymphoblastic Leukemia (TALL). [ Science vol. 351 pp. 1298- 1299, 1454 – 1458 ’16 ] activated them experimentally using the CRISPR technique, and therein hangs a tale.

Addendum 11 April — LMO2 is well known to gene therapists as early work (2002) using retroviruses inserted randomly in the genome to cure SCID (Severe Combined Immunodeficiency) resulted in TALL in 4kids.  The problem was that the vector integrated in multiple sites all over the genome and one such random site  turned on expression of LMO2.

I’ve written a series of six posts trying to imagine the incredible mass of DNA in a 10 micron nucleus on a human scale — we take it for granted, but it’s far from obvious how this is accomplished — here’s the link to the first — https://luysii.wordpress.com/2010/03/22/the-cell-nucleus-and-its-dna-on-a-human-scale-i/. — just follow the links to the rest.

[ Cell vol. 153 pp. 1187 – 1189, 1281 – 1295 ’13 ] Hi-C and 5C (Carbon Copy Chromosome Conformation Capture) allow determination of chromatin organization and long range chromatin interactions in an unbiased genome wide manner at the megaBase scale. Topologically associated domains (TADs) are the way the genome in the nucleus is organized into megabase to submegaBase sized interacting domains. TADs are conserved between species and are invariant across cell types. [ Call vol. 156 p. 19 ’14 ] They average 700 – 800 kiloBases and are said to contain 5 – 10 protein coding genes and a few hundred enhancers. The expression of genes within a TAD is ‘somewhat correlated’. Some TADs have active genes, while others have repressed genes. Genomic interactions are strong within a domain, but are sharply depleted on crossing the boundary between two TADs.

Well TADs have to be separated from each other. The current thinking is that the boundaries are formed by sites in the DNA which bind the CTCF protein, and possibly cohesin proteins as well. CTCF is a large protein (although maddeningly I can’t seem to find out how many amino acids it has) with a molecular mass of 80 kiloDaltons. It’s DNA binding is quite specific as it contains 11 zinc fingers (each of which can specifically bind a 3 nucleotide stretch of DNA). In addition to binding to DNA it can bind to itself, forming a perfect way to form loops of DNA.

All the Science paper did was to delete a few CTCF binding sites using the CRISPR technique around the two oncogenes and bang — expression increased. Why?  Because the insulation between the TAD containing the genes and adjacent TADs was broken, allowing control of the genes by enhancers in the new and larger TAD that had been previously sequestered in an adjacent TAD.  The deletions were thousands of basepairs away from the coding sequence of the genes themselves.  All very nice, but it’s fairly artificial.

However the paper notes that across a large pan-cancer cohort, there was a 2 fold enrichment for boundary CTCF site mutations.

High level mathematicians look like normal people

Have you ever had the pleasure of taking a course from someone who wrote the book? I did. I audited a course at Amherst from Prof. David Cox who was one of three authors of “Ideals, Varieties and Algorithms” It was uncanny to listen to him lecture (with any notes) as if he were reading from the book. It was also rather humbling to have a full professor correcting your homework. We had Dr. Cox for several hours each weak (all 11 or 12 of us). This is why Amherst is such an elite school. Ditto for Princeton back in the day, when Physics 103 was taught by John Wheeler 3 hours a week. Physics 103 wasn’t for the high powered among us who were going to be professional physicists (Heinz Pagels, Jim Hartle), it was for preMeds and engineers.

Dr. Cox had one very useful pedagogical device — everyone had to ask a question at the beginning of class, Cox being of the opinion that there is no such thing as a dumb question in math.

Well Dr. Cox and his co-authors (Little and O’Shea) got an award from the American Mathematical sociecty for their book. There’s an excerpt below. You should follow the link to the review to see what the three look like along with two other awardees. http://www.ams.org/publications/journals/notices/201604/rnoti-p417.pdf. Go to any midsize American city at lunchtime, and you’d be hard pressed to pick four of the five out of the crowd of middle aged men walking around. Well almost — one guy would be hard to pick out of the noonday crowd in Williamsburg Brooklyn or Tel Aviv. Four are extremely normal looking guys, not flamboyant or bizarre in any way. This is certainly true of the way Dr. Cox comports himself. The exception proving the rule however, is Raymond Smullyan who was my instructor in a complex variables course back in the day– quite an unusual and otherworldly individual — there’s now a book about him.

Here’s part of the citation. The link also contains bios of all.

“Even more impressive than its clarity of exposition is the impact it has had on mathematics. CLO, as it is fondly known, has not only introduced many to algebraic geometry, it has actually broadened how the subject could be taught and who could use it. One supporter of the nomination writes, “This book, more than any text in this field, has moved computational algebra and algebraic geometry into the mathematical mainstream. I, and others, have used it successfully as a text book for courses, an introductory text for summer programs, and a reference book.”
Another writer, who first met the book in an REU two years before it was published, says, “Without this grounding, I would have never survived my first graduate course in algebraic geometry.” This theme is echoed in many other accounts: “I first read CLO at the start of my second semester of graduate school…. Almost twenty years later I can still remember the relief after the first hour of reading. This was a math book you could actually read! It wasn’t just easy to read but the material also grabbed me.”
For those with a taste for statistics, we note that CLO has sold more than 20,000 copies, it has been cited more than 850 times in MathSciNet, and it has 5,000 citations recorded by Google Scholar. However, these numbers do not really tell the story. Ideals, Varieties, and Algorithms was chosen for the Leroy P. Steele Prize for Mathematical Exposition because it is a rare book that does it all. It is accessible to undergraduates. It has been a source of inspiration for thousands of students of all levels and backgrounds. Moreover, its presentation of the theory of Groebner bases has done more than any other book to popularize this topic, to show the powerful interaction of theory and computation in algebraic geometry, and to illustrate the utility of this theory as a tool in other sciences.”

State functions, state equations, graphs of them and reversibility

Thermodynamic States are all considered to be continuous variables (the fact that Internal Energy (U) is a state variable is half of the first law).

A continuous function of state_function_1 in terms of state_function_2, . . . . state_function_n produces a graph which is an n dimensional surface in n + 1 dimensional space. If this seems rather abstract, we’ll get concrete shortly. Consider the classic calculus 101 function y = x^2. Write it like this

f : R^1 –> R^1
f : x |–> x^2

This does seem a bit stuffy, but the clarity it provides is useful, as you’ll see. R^1 is the set of real numbers. The first line tells you that f goes from the real numbers to the real numbers. The second like gives you what f does to a point in the domain. What about the graph of f? It is the parabola, which lives in the x – y plane, a 2 dimensional space. The graph of f is just a curved line with dimension 1, living in a space one dimension higher (e.g. dimension 2).

Different state functions apply to different physical systems at which point they are called equations of state, with every point on their graph representing a collection of state variables at which the system is at equilibrium (e.g. not changing with time)

The simplest state function comes from the ideal gas law PV = nRT, which was promulgated in 1834 by Claperyon. You may regard it as

T : R^2 –> R^1
T : (P, V) |–> P*V/R == T

This is Temperature (statefunction1) in terms of P (statefunction2) and V (statefunction3). What is its graph — something 2 dimensional living in 3 dimensional space — e. g. a surface.

If you’ve studied PChem, you’ve probably met the Carnot cycle. Here’s a link https://en.wikipedia.org/wiki/Carnot_cycle.  It is represented by  a bunch of curved lines in the PV plane, but each line in the diagramreally represents a line on the 3 dimensional graph of T. You can think of this like a topographic map of a mountain, but not quite. The top and bottom lines represent constant temperature (altitude) but the (semi)vertical lines are paths up and down the mountain. Just looking at the flat PV diagram is pretty misleading.

Any combination of P, V, T not satisfying PV = RT is not on the surface, and is not in equilibrium.  You won’t see any of them on the diagram of the PV plane, which is why it’s so misleading. 

P, V and T will change so they approach the surface (either by minimizing internal energy or maximizing entropy or a combination of both — these are the driving forces of Dill’s book — Molecular Driving Forces.

The definition of surface given above is quite general and applies to more complicated situations — which is why I went to the trouble to go through it. For instance, in some systems Internal Energy (U) is a function of 3 variables Entropy (S), Volume (V) and the number of molecules (N). This is a 3 dimensional surface living in 4 dimensions. It’s just as much of a surface as that for T in terms of P and V, but I can’t visualize it (perhaps you can) Note also that when you go to higher magnification N is not a continuous variable, any more than concentration is.

Any point on the surface can be reached reversibly from any other — what does reversibility actually mean?

Berry Physical Chemistry 2nd Ed 2000 p. 377. Reversibility of changes in equilibrium means 3 things.

l. The change occurs almost infinitesmally slowly (a very large class of real processes have work and heat values very close to reversible processes)

2. Changes remain infinitesmally close to equilibrium (e.g. they stay on the surface. At equilibrium, thermodynamic variables still fluctuate. If movement on the surface is slow enough that the thermodynamic variables are within 1 standard deviation of the average values of the thermodynamic state variables, no observation can show that the stat eof the system has changed

3. Intensive variables corresponding to work being done (e.g. pressure, surface tension, voltage) are continuous across the boundary of the system on which work is being done.

Objects off the surface aren’t in equilibrium and maximization of entropy or minimization of internal energy drive them toward the surface. This implies that the surface is is an attractor. Now that chaos is well known, are there thermodynamic attractors — I’ve written Dill to ask about this.

Hopefully this will be helpful to some of you. Putting it together was to me. As always, the best way to learn something is trying to explain it to someone else.

Sn2 — It’s a gas

Sn2 reactions are a lot more complicated than as taught in orgo 101 (at least in the gas phase). The classic mechanism is very easy to teach to students, it’s just an umbrella turning inside out in the wind. A current article in Science (vol. 352 pp. 32 – 33 1 April ’16) shows how complicated things can be when the reaction is carried out in the gas phase. Mechanisms illustrated include rebound stripping, frontside attack, ion-dipole complex, roundabout, hydrogen bond complex, frontside complex and double inversion.

Why study Sn2 in the gas phase? One reason is to sharpen computational and theoretical methods to be able to predict reaction rates (in gas phase reactions). I was surprised on looking up Rice-Ramsperger-Kassel-Marcus theory to find out how old it was. Back in the 60’s it was taught to us without any names attached. One assumes that before and after reaction the ion molecule complexes are trapped in potential wells. It is assumed that vibrational energies in the complex are quickly distributed to ‘equilibrium’ in the complexes so that detailed computation of rates can be carried out.

Is this of any use to the chemist actually reacting molecules in solution? Other than by sharpening computational tools, I don’t see how it can be given the present state of the art.

Gas phase kineticists are starting to try, but they’ve got a very long way to go. “Stepwise addition of solvent molecules to the bare reactant anion offers a bottom up approach to learn more about the transition of chemical reactions from the gas to liquid phase. To investigate the role of solvation in Sn2 reactions Otto et al. have performed crossed molecular beam studies of the microsolvated” Sn2 reaction (e.g. the approaching anion solvated with all of one or two waters). “The results show that “the dynamics differ dramatically from the unsolved anion.”

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