Too funny to pass up

This is 95%+ a scientific blog, but the following is simply too funny to pass up. None of the people receiving it had heard of it, and liberals and conservatives alike think it’s a riot. I don’t know who wrote it, but it isn’t me. Would the real author step forward? I googled the title but came up with nothing similar.

Subject: Canadians on illegal immigrants

The flood of Trump-fearing American liberals sneaking across the border into Canada has intensified in the past week, sparking calls for increased patrols to stop the illegal immigration. The Republican Presidential primary campaign is prompting an exodus among left leaning citizens who fear they’ll soon be required to hunt, pray, and live according to conservative ideas about the Constitution.

Canadian border farmers say it’s not uncommon to see dozens of sociology professors, global warming activists, and “green” energy proponents crossing their fields at night. “I went out to milk the cows the other day, and there was a Hollywood producer huddled in the barn,” said Southern Manitoba farmer Red Greenfield, whose acreage borders North Dakota. “The producer was cold, exhausted and hungry. He asked me if I could spare a latte and some free-range chicken. When I said I didn’t have any, he left before I even got a chance to show him my screenplay, eh?” In an effort to stop the illegal aliens, Greenfield erected higher fences, but the liberals scaled them. He then installed loudspeakers that blared Rush Limbaugh across the fields, but they just keep coming.

Officials are particularly concerned about smugglers who meet liberals near the Canadian border, pack them into electric cars and drive them across the border where they are simply left to fend for themselves after the battery dies.

“A lot of these people are not prepared for our rugged conditions,” an Ontario border patrolman said. “I found one carload without a single bottle of Perrier drinking water. They did have a nice little Napa Valley cabernet, though, and some kale chips.”

When liberals are caught, they’re sent back across the border, often wailing loudly that they fear assassination from Trump high hairers. Rumors have been circulating about plans being made to build re-education camps where liberals will be forced to drink domestic beer and study the Constitution.

In recent days, liberals have turned to ingenious ways of crossing the border. Some have been disguised as senior citizens taking a bus trip to buy cheap Canadian prescription drugs. After catching a half- dozen young vegans in blue-hair wig disguises, Canadian immigration authorities began stopping buses and quizzing the supposed senior citizens about Perry Como and Rosemary Clooney to prove that they were alive in the ’50s. “If they can’t identify the accordion player on The Lawrence Welk Show, we become very suspicious about their age,” an official said.

Canadian citizens have complained that the illegal immigrants are creating an organic-broccoli shortage, buying up all the Barbara Streisand c.d.’s, and renting all the Michael Moore movies. “I really feel sorry for American liberals, but the Canadian economy just can’t support them,” an Ottawa resident said. “How many art-history majors does one country need?”

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The narrative rolls on

Let’s play spot the narrative and then, being scientific types, look at the numbers and see what they are telling us. The following is a direct quote of the headline and first few paragraphs of the following ‘news’ article appearing today followed a link to it.

Poll: Majority of American voters blame Donald Trump for violence at rallies

More than two-thirds of American voters hold Donald Trump responsible, in part, for the recent violence that has surrounded his Republican presidential campaign rallies, a new poll has found.

According to the Quinnipiac University national poll released this week, 37 percent of voters surveyed said they believe the GOP front-runner is “very responsible” for violent incidents involving supporters and protesters at his campaign rallies, while 27 percent said he’s “somewhat responsible.”

Less than a quarter said they believe he’s “not responsible.”

More than three-quarters of respondents, meanwhile, also blamed protesters at Trump rallies for being “very responsible” or “somewhat responsible” for such violence, while 70 percent said supporters of the businessman are very or somewhat responsible, the poll found.

Quinnipiac University Poll Assistant Director Tim Malloy contended that the results come somewhat in contrast to claims Trump has made about the origin of such incidents at his campaign events.

http://www.masslive.com/politics/index.ssf/2016/03/poll_majority_of_americans_bla.html#incart_most-comments

A Slanted headline at its best.

It should read

Poll: American voters think protesters at Trump rallies are more responsible for violence at his rallies than Trump.

This fits the facts as stated, if not the narrative. It’s right there in the numbers: 27 + 37 = 64% say it’s Trump’s fault while over 75% (why don’t they say just how far over) say it’s the fault of the protestors.

The higher drivel – II

From the obituary of a leading philosopher at an Ivy League institution. He proposed the following thought experiment to resolve the question of whether objects and relationship exist in the world independently of how we perceive them. This is what bothered Einstein about quantum mechanics, and he is said to have asked Bohr (I think) ” do you think the moon is not there if we don’t look at it”. The thought experiment is a brain placed in a vat by a mad scientist (I’m not making this up). So the brain in the vat — call him Oscar –could not formulate the sentence of “I am a brain in vat” because Oscar has no experience of a real brain or a real vat.

For this they’re currently paying 60K+ a year? It’s the higher drivel.

I read a book by Nozick with similar impossible situations he worried about after a rave review in the New York Times book review a few years ago. It had questions of the order ‘would bubblegum taste the same on the surface of the sun’.

The higher drivel series will appear from time to time — here’s the first one (published 5 years ago)

“The predicament of any tropological analysis of narrative always lies in its own effaced and circuitous recourse to a metaphoric mode of apprehending its object; the rigidity and insistence of its taxonomies and the facility with which it relegates each vagabond utterance to a strict regimen of possible enunciative formations testifies to a constitutive faith that its own interpretive meta-language will approximate or comply with the linguistic form it examines.”

From p. 35 of the NYTimes book review 16 October’11

You could actually major in this stuff (Semiotics) at an Ivy League university (Brown) in the 80’s. According to the article, Semiotics was the third most popular humanities major there at the time.  One son got in in ’86, but (fortunately) didn’t go there.  Nonetheless he was quite interested in Semiotics, hence the name of this blog.  Fortunately the author of the above quote recovered and notes “I now spend more time learning from the insights of science than deconstructing its truth claims.”

What a gigantic waste of time.  Think what Brown could have done by abolishing the department and using the funds for chemistry or mathematics.  The writer tries to salvage something from the experience noting that ‘a striking number of semiotics students have gone on to influential careers in the media and the creative arts.’  Unfortunately this explains a lot about the current media and ‘the creative arts’.

Students were being conned then, and they’re being conned now.  It might not have mattered what you majored in 50+ years ago at an Ivy League university, the world seemed to want us regardless.   A friend majored in Near Eastern studies, was hired by a bank, never saw the MidEast and did quite well.  Not so today.  The waitress serving us last Wednesday at a local bar was a graduate of one of the seven sisters in 2010.  She majored in Sociology and Psychology, is in debt for > 20K for the experience and is unable to find better work.   It isn’t clear what such a major prepares you for other than what she’s doing.  Finding out the distribution of majors of the jobless 20 somethings participating in OWS would be interesting

For a taste of the semiotics world of the 80’s, Google Alan Sokal and read about the fun he had with such a journal — “Social Text”.  Should you  still have the stomach for such things read “The Higher Superstition” by Gross and Levitt, which goes into more detail about Derrida, Foucault and a host of (mostly French) philosophes and what they tried to pull off.

When knowledge isn’t power

Here is a genetic disease, where we’ve known exactly what’s wrong with the causative gene for 23 years, over 10,000 papers have been written (a Google search comes up with about 418,000 results (0.45 seconds), but we don’t know how the mutation causes the problems it does or have a clue how to treat the disease. So much for finding the cause of a genetic disease leading to therapy. Imagine how much harder cancer is.

I speak of Huntington’s chorea, and the causative gene huntingtin. It’s a terrible neurologic disease characterized by progressive movement disorders, dementia and incapacitation over a decade or two. Woodie Guthrie had it; fortunately Arlo escaped. Like many people with the disorder Woodie was quite fertile, having 8 children.

It being a neurologic disorder, I’ve read a lot about it, and my jottings about my readings over the past few decades have consumed 83,635 characters (aren’t computers wonderful)? I’ve had a fair amount of experience with it, as an Indian agent in Montana had it, and produced many progeny with his women, leading to a good deal of devastation in one tribe.

Neuron vol. 89 pp. 910 – 926 ’16 is an excellent recent review (but not one for the fainthearted). Several mysteries are immediately apparent.

First huntingtin is expressed in nearly every neuron, but only a few die. It is expressed outside the brain in lung ovary and testes, but they work just fine.

Second Huntingtin interacts with over 350 different proteins. Figuring which are the important ones has provided steady employment.

Third it exists in many forms, so many that there aren’t enough scientists living to test them all. This is because huntingtin is subject to a variety of chemical modifications (phosphorylation, ubiquitination, acetylation, palmitoylation, sumoylation) at FORTY-EIGHT different sites (listed in the article). So this gives 2^48 possible modified forms of the protein (either modification being present or absent). 2^48 = 281,474,976,710,656 if you’re interested.

In addition to the modifications, the protein is huge — some 3,144 amino acids occurring in 67 exons forming two mRNAs of 10,366 and 13.711 nucleotides.

Fourth The protein can also be chopped up by at least 5 different enzymes at 6 different sites, and some fragments are biologically active (toxic in tissue culture).

Naturally, the region with the mutation (near the amino terminal end) of the protein has been studied most intensively.

Huntingtin has its fingers in many physiologic pies — the reference is excellent in this area — these include vesicular trafficking, cell division, cilia formation, endocytosis, autophagy, gene transcription. Abnormalities of which one causes the neurologic disease.

The mutant form forms protein aggregates. Like Alzheimer’s disease senile plaque or the Lewy body of Parkinson’s disease, we don’t know if the aggregates are toxic or protective.

Fifth: Despite all its known functions we don’t know if the mutation produces a loss of some vital function of Huntingtin, or a new and toxic function.

Even worse, compared to cancer, Huntington’s chorea is ‘simple’ because we know the cause.

An omen

An Omen. Since omens are inherently nonscientific, the cognoscenti can stop reading right here. Last night I bought some beer at the package store I always go to. It’s run by a seriously large Polish guy, an immigrant like my late grandmother. I’m always interested in his take on things. He said he thought Trump would be the next president. The store is in a heavily latino neighborhood (mostly Puerto Rican). Given what Trump has said about Mexicans, I pressed him on it, but he wouldn’t budge, and said the people in the neighborhood liked Trump.

Flashback to my late grandmother, running a drygoods store in a little New Jersey town in the 40s and 50s. Family lore has it that she was certain that Truman would win in 1948, despite every poll to the contrary. She said “they’re talking Dewey but they’ll vote Truman”.

People in retail (particularly those running the show) talk to anyone walking in the door. They see a far wider mass of humanity and interact with many more people in the course of a day than you and I.  Think about Pauline Kael’s remark that she didn’t know anyone who’d voted for Nixon.  Probably in upper Manhattan she didn’t.

 

An omen? Perhaps.

The chemical ingenuity of the cell

If you know a bit of molecular biology, you know that messenger RNA (mRNA) has a tail of consecutive adenines added at its 5′ end (sorry ! ! !  3′ end — oh well). If you don’t know that much all the background you need can be found in https://luysii.wordpress.com/2010/07/07/molecular-biology-survival-guide-for-chemists-i-dna-and-protein-coding-gene-structure/ — just follow the links.

The adenines are not coded in the genome. Why? I’ve always thought of it as something preventing the mRNA from being broken down before the ribosome translates it into protein. Gradually the adenines are nibbled off by cytoplasmic nucleases. The literature seems to agree — from my notes on various sources

Most mRNAs in mammalian cells are quite stable and have a half life measured in hours, but others turn over within 10 to 30 minutes. The 5′ cap structure in mRNA prevents attack by 5′ exonucleases and the polyadenine (polyA) tail prohibits the action of 3′ exonucleases. The absence of a polyA tail is associated with rapid degradation of mRNA. Histone mRNAs lack a polyA tail but have near their 3′ terminus a sequence which can form a stem loop structure this appears to confer resistance to exonucleolytic attack.

polyA — the polyAdenine tail found on most mRNAs must be removed before mRNA degradation can occur. Anything longer than 10 adenines in a row seems to protect mRNA. The polyA tail is homogenous in length in most species ( 70 – 90 in yeast, 220 – 250 nucleotides in mammalian cells). PolyA shortening can be separated into two phases, the first being the shortening of the tail down to 12 – 25 residues, and the second terminal deadenylation being the removal of some or all of them.

Molecular Biology of the Cell 4th Edition p. 449 — Once a critical threshold of tail shortening has been reached (about 30 As) the 5′ cap is removed (decapping) and the RNA is rapidly degraded. The proteins that carry out tail shortening compete directly with the machinery that catalyzes translation; therefore any factors increasing translation initiation efficiency increase mRNA stability. Many RNAs carry in the 3′ UTR sequences binding sites for specific proteins that increase or decrease the rate of polyA shortening.

But why polyAdenine? Why not polyCytosine or PolyGuanine or polyUridine? Here’s were the chemical ingenuity comes in. Of the 64 possible codons for amino acids only 3 tell the ribosome to stop. These are called various — termination codons, stop codons,and (idiotically) nonsense codons — they aren’t nonsense at all, and are  functionally vital for the following reason. Stop codons cause the ribosome to separate into two parts releasing the mRNA and the protein. Suppose a given mRNA doesn’t have a stop codon? Then the ribosome and the mRNA remain stuck together, and future protein synthesis by that particular ribosome becomes impossible. Not good.

This is probably why the codons for stop are so similar UAA, UAG and UGA — mutating a G to an A gives another one, and mutating either A in UAA to a G gives another stop codon. So the coding chosen for stop codons is somewhat resistant to mutation, because mRNAs with stop codons are disastrous for reasons shown above.

Well, randomness happens and suppose that the termination codon has been mutated to another amino acid. These are called nonStop RNAs which code for nonStop proteins. So the poor ribosome then translates the mRNA right to its 3′ end. Well what does AAA translate into — lysine. Lysine is quite basic and quickly becomes protonated on its epsilon lysine (even within the confines of the ribosome). The exit tunnel for the ribosome is strongly negatively charged, and so coulomb interaction grinds things to a halt. What other basic amino acids are there? There’s arginine, and perhaps histidine, but no codons for them is CCC or GGG or UUU.

Then the Ribosomal Quality Control system (RQC) then springs into action. I didn’t realize this until reading the following paper this year. Did you? Amazing cleverness on the part of the cell.

[ Nature vol. 531 pp. 191 – 195 ’16 ] Translation of an mRNA lacking a stop codon (nonStop mRNA) in eukaryotes results in a polyLysine protein (AAA codes for lysine). The positively charged lysine cause stalling in the negatively charged ribosomal exit tunnel. The Ribosomal Quality Control complex (RQC complex) recognizes nonStop proteins and mediates their ubiquitination and proteasomal degradation.

The eukaryotic RQC comprises Listerin (Ltn1) an E3 ubiquitin ligase, Rqc1, Rqc2 and the AAA+ protein CDC48. On dissociation of the stalled ribosome, Rqc binds to the peptidyl tRNA of the 60S sunit and recruits Ltn1 which curves around the 60S ribosome, positioning its ligase domain near the nascent chain exit. R2c2 is a nucleotide binding protein that recruits tRNA^Ala and tRNA^Thr to the 60S peptidyl tRNA complex. This results in the addition of a Carboxy terminal Ala/Thr sequence (a CAT tail) to the stalled nascent chain.

Mutation of Listerin causes neurodegeneration in mice.

Trump

Too late to start an enormous post on huntingtin, the protein mutated in Huntington’s chorea. Coming soon. Sorry. But consider this: If Trump wins the presidency it will be a remarkable demonstration of the the lack of power of the press. When have the following agreed on an issue — New York Times, Wall Street Journal, National Review, The Nation, Weekly Standard, etc. etc. They all hate Trump editorially and by their selection of articles and phraseology. I’ve never seen anything like it.

Remarkable times. There is tremendous dissatisfaction with the way things are going. Bernie taps into it as well.

Is a rational treatment for Multiple Sclerosis in our future?

Two very recent papers taken together point the way to a rational treatment of multiple sclerosis (and probably all autoimmune disease). The short story:
Paper #1 found a way to find the antigen or antigens patients with MS are reacting to
Paper #2 found a way to selectively impair the response to an inciting antigen without clobbering the whole immune system

Some history: Some evening in 1966 or 1967 a fellow neurology resident and I were sitting on the ward having dealt with the complications of high doses corticosteroids for a case of optic neuritis (often the first sign of MS). I said, some day they’ll look at what we’re doing the way we look at docs of 200 years ago using leeches (and bloodletting). As a kid, I remember my parents driving into Philly. Shortly after getting over the Ben Franklin bridge we’d pass a pharmacy offering leeches on its sign.

It was obvious even back then that MS in some way was an attack by the immune system on the brain. Finding the particular antigen the system was reacting to would lead us to the cause and hopefully less simplistic treatment than clobbering the immune system. We didn’t know all the proteins we had or even how many, so people would look for antibodies to a variety causes (which they’d arrived at by reasoning, not data). Increased antibody titers to a variety of viruses were found, but that led nowhere. No one ever isolated a virus from MS brain, although sightings on electron microscopy were eagerly reported. Eventually it became obvious that the immune system was on high alert with increased antibodies to lots of things.

This leads to paper #1 [ Proc. Natl. Acad. Sci. vol. 113 pp. 2188 – 2193 ’16 ] To make a long story short they used something called the Human Protein Atlas Program to find what proteins the antibodies in MS patients were reacting to. So rather than having a theory about what MS patients might be reacting to and testing it, they looked at all proteins and watched. It’s the difference between being a Greek philosopher reasoning things out from first principles and collecting data. Only when the technology is available can you stop a priori theorizing and just look. Don’t be too hard on the earlier researchers, they didn’t have the tools.

The found that MS patients were reacting to a protein called anoctamin2, which actually showed increased expression near and inside the demyelinating plaques of MS.

For the gory details keep reading, otherwise skip to **** where I’ll discuss paper #2

Gory details — The Human Protein Atlas produces human protein fragments, selected on the basis of their low similarity to other proteins in the proteome. [ Science vol. 347 1260419 (23 Jan) ’15 ] The atlas hopes to find out where and how much of each our proteins is at the tissue and cellular level. It is based on antibody based profiling on tissue microarrays (of proteins?). This based on transcript expression (RNA-Seq), and immunohistochemistry (24,028 antibodies coresponding to 16,975 protein coding genes). 44 tissues were studied. The antibodies produced more than 13 million tissue based mmunohistochemistry images. They also report subproteomes (secreted proteins n = 3,171, and membrane bound proteins n = 5,570). Interstingly there was an overall concurrence between mRNA and protein levels for a given gene product across various tissues.

The PNAS paper profiled 2,169 plasma samples from MS cases and population based controls (with neurologic disease) using bead arrays built with 384 human protein fragments seleted from an initial screening with 11,520 antigens. There was increased reactivity to anoctamin2 (aka TMEM16B) in MS vs. controls (by how much?). This was corroborated in independent assay with alternative protein constructs and by epitope mapping with peptides covering the identified region of anoctamin 2.

ImmunoFLuorescence in human MS brain tissue showed increased anoctamin2 expression as small cellular aggregates near and inside MS lesions. The controls had other neurologic disease. There was a 5.3 fold change in fluorescence intensity in the MS group. The antibodies are directed against the amino terminal region.

*****

*****

Paper #2 — [ Nature vol. 530 pp. 422 – 423, 434 – 440 ’16 ] basically found a way to knock out the immune system’s response to a single antigen — not all of them. The point is that just an antigen by itself isn’t enough to turn the immune system on. A costimulatory molecule must also be present on the antigen presenting cell. If it isn’t there the immune system is actually turned off by forming regulatory T cells (which even though they are part of the immune system they actually turn it off).

One can form models of human autoimmune disease in mice. Two such are EAE (Experimental Allergic Encephalomyelitis) formed by giving the animal myelin basic protein (a constituent of myelin which is attacked in MS), and rheumatoid arthritis (formed by giving collagen to the animals). What is so great about this paper is that MHC II carrying peptides from collagen suppress disease in a mouse model of rheumatoid arthritis, but NOT in mice with EAE. MHC-II carrying CNS antigen peptides control EAE but not collagen induced arthritis.. In addition neither treatment impaired the immune response to infection — something that almost always happens when you clobber the immune system.

Well it’s a long way from the lab to the bedside, but imagine finding what the immune system is reacting to and stopping it (without stopping the immune system). That’s what these two papers portend. Exciting times.

Threading the ribosomal needle

What do you do when you to try to thread a needle? You straighten out the thread. This is exactly what a newly discovered RNA modification (1 methyl adenosine) is doing. If you look at the of adenine pairing with thymine in the following link, the hydrogen sitting between the adenine and thymine is replaced with a much bulkier methyl group in 1 methyl adenosine. Watson-Crick base pairing is impossible.

http://users.rcn.com/jkimball.ma.ultranet/BiologyPages/B/BasePairing.html

Not much 1 methyl adenosine is found in a given mRNA (usually one or less). The authors note that it is usually found near a transcription start site (and in a highly structured region — based on the PARS score — whatever that is). In particular it is found at alternative initiation sites in the second or third exon of a gene. Unsurprisingly, when it is present more protein is expressed from the mRNA.

The work is described in Nature vol. 530 pp. 422 – 423, 441 – 446 ’16. The authors wonder how many mRNA modifications are out there waiting to be discovered. Let’s hope they look. Other mRNA modifications are known (pseudouridine, 6 methyl adenine and 5 methyl cytosine). The modification is dynamic, the amount changing with cellular conditions. This isn’t a flash in the pan as 1/3 of the same sites are methylated in mouse mRNA.

Numerology – I

It’s time to put some numbers on the formulas of statistical mechanics to bring home just how fantastic the goings on inside our cells actually are.

To start — we live at temperatures of 300 Kelvin (27 Centigrade, 80 Fahrenheit). If you’ve studied statistical mechanics you know that the kinetic energy of a molecule is 3/2 k * T — where k is the Boltzmann constant and T is the temperature in Kelvin. The Boltzmann constant is the gas constant R divided by Avogadro’s number. R is to be found in the perfect gas law familiar from elementary PChem or physics — PV – nRT, where P is Pressure, V is volume, and n is the number of moles.

If you’re a bit foggy on this look at https://luysii.wordpress.com/2016/01/10/the-road-to-the-boltzmann-constant/ where you’ll find an explanation of why the dimensional units of R are energy divided by temperature times the number of moles.

This is all very nice but how fast are things moving at room temperature? We need to choose some units and stick to them. We’ve got Kelvin already. We can get from k (the Boltzmann constant) to R (the gas constant) easily by multiplying k by Avogadro’s number.

So now we have kinetic energy per mole (not molecule) is 3/2 R * T

You now need a choice of units for expressing the gas constant. The first part of every course in grad school was consumed with units. Don Voet used to say he preferred the hand stone fortnight system, but that isn’t used much anymore. We’ll use the MKS (Meter KiloGram Second) system. This gives kinetic energy in Joules.

A Joule is the kinetic energy of a mass of 1 kiloGram moving at a velocity of 1 meter/second — or in units — kilogram (meter/second)^2.

Now we’re getting somewhere. The next step is to get molar mass in kiloGrams. Chemists use the Dalton, where the mass of 1 mole of hydrogen is 1 Dalton (1 gram — not kilogram).

Kinetic energy = 1/2 *mass * velocity^2 = mass * (meter/second)^2 == 3/2 R*T

So velocity (in meters/second) = Sqrt ( 3 * R * T / molar mass in kilograms).

To keep things simple I’m going to assume that we’re dealing with hydrogen atoms — so its molar mass is 1 gram (10^-3 kiloGrams)

Putting it all together — the velocity of a hydrogen atom at 300 Kelvin is Sqrt ( 3 *8.314 * 300 / 10^-3 ) == 2,735 meters second

Pretty fast. To convert this to kilometers per hour multiple by 3600 and divide by 1000 == 9,846 Kilometers/hour

In Miles per hour this is 9846 (miles/kilometer) = 6,113 miles per hour.

Recall the number 2735. All you have to do to find out how fast ANY molecular species is moving at room temperature is divide this by the square root of the molecules mass (in Daltons not kiloGrams). So that of water is 2735/ sqrt (18) = 644 meters/second.

I never could be sure that some of the energy of a molecule wasn’t sucked up in vibrations and conformation change. Multiple attempts at understanding the equipartition of energy theorem didn’t help. Finally one of authors of one of 3 biophysics books I’m reading said that “the speed just depends on mass. That’s the translational part. Other degrees of Freedom (like vibrations) can absorb potential energy. But it doesn’t affect velocity.

The velocity formula works even for something as large as RNA polymerase II (500 kilodaltons). To make things really easy lets work with a molecular complex of mass 1,000,000 daltons (1 megaDalton) — there are plenty of such protein complexes of this size (and more) in the cell. A 1 megaDalton mass has a velocity of 2.7 meters a second.

Cells are small. The 3 polymerases transcribed DNA into RNA have masses in the megaDalton range. So how long should it take them to traverse a nucleus 10 microns (10^-5 meters) in diameter. It’s going at 2.7 meters/second so it will traverse 270,000 in a second or one every 4 microSeconds.

Clearly I’ve left something out — nothing in the cell moves in a straight line. It is very crowded, so that even though things are moving very quickly their trajectory isn’t straight (although the numbers I’ve given are correct for the total length of the trajectory when straightened out.  I’ll be writing about diffusion constants etc. etc. in the future, but here’s one more numerological example.

Consider pure water. How many moles of water are in a liter (1 kilogram) of water. 1000/18 – 55.5 moles. How many molecules is that

55.5 * 6.023 * 10^23. How big is water — I found a source that water can be considered a squashed sphere of maximum diameter 2.82 Angstroms. Now Angstroms are something chemist’s deal with — the hydrogen atom is about 1 Angstrom in diameter, and the carbon carbon single bond is 1.54 Angstroms.

So what is the volume of a water molecule — its (4/3) * pi * (2.82/2)^3 == 11.7 cubic Angstroms.

What is the volume of a liter in cubic Angstroms? An Angstrom is 10^-10 meters and a liter is a cube .1 meter on a side — so there are 10^27 cubic Angstroms in a liter. How many cubic Angstroms do the 55.5 moles of water in a liter take up

11.7 * 55.5 * 6.023 ^ 10^23  == 3.9 * 10^26 cubic Angstroms — 40% of the volume of a liter. So water molecule1 is likely to hit another one in 2.5 * 2.28 Angstroms or in about 7 Angstroms. How long will that take ? It’s moving at 6.44 * 10^2 meters/second and 7 Angstroms is a distance of 7 * 10^-10 meters, so it’s like to meet another water in (roughly) 10^-12 seconds (1 picoSecond).

There’s all sorts of hell breaking loose with the water inside our cells. That’s enough for now.

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