Friday, April 29, 2016

April 30, 2016 at 12:40AM

Today I Learned: I've been reading Ron Milo and Rob Phillips' "Cell Biology by the Numbers", which has given me more than three TIL-worthy facts in the last twenty minutes... so today y'all get four facts! The book can be read for free here, I highly recommend picking some random chapters and reading through them if you're into cell biology stuff: http://ift.tt/1AvhcfE 1) The plasma membrane (the lipid bilayer that defines the outside of a cell) actually only contains less than 10% of the total membrane in a typical eukaryotic (i.e., human) cell. The rest is mostly bound up in mitochondria and the endoplasmid reticulum, though it varies quite a bit by cell type. 2) Mitochondria are usually pictured in textbooks as little pill-shaped organelles, roughly the size and shape of a bacteria. Which makes sense, given that mitochondria are descended from bacterial endosymbionts. However, if you look at mitochondria under a microscope, you'll see that they actually look more like a continuous net, like the outside of a morel mushroom (some example 3D reconstructions here: http://ift.tt/1Un6cPY). The reason mitochondria look like little pill-shaped things in all the EM pictures in textbooks is that those EM pictures are all 2D slices through that net. Well, today I learned that mitochondria sometimes *do* take on little separate pill-like shapes. Specifically, when yeast are grown in ethanol, their mitochondria split up and form little balls. I'm a little suspicious about this, though. Ethanol is a pretty stressful condition for yeast, and the blebbing of mitochondria reminds me (at least superficially) of what happens to cells when they apoptose. Perhaps that mitochondrial morphology is just a precursor to apoptosis? 3) Chloroplasts in a plant cell will often move away from light to avoid photodamage! How ironic, given how much effort plants put into moving towards light. 4) Speaking of chloroplasts (and mitochondria, for that matter), one of the most fascinating events in the history of life is the acquisition of cyanobacteria by some ancient Eukaryote, making the first chloroplast and the first photosynthetic Eukaryote (similar to what happened with the ancestor of all Eukaryotes when it first acquired a mitochondrion). One thing that's been seen repeatedly during endosymbiotic events like that is that the symbiont's genome slowly migrates to the nucleus, until the symbiont is left with a tiny little core genome of things that can't move for one reason or another. Here's a question -- how long should we expect that process to take? Some enterprising scientists performed an experiment to try to get at least some of the way towards an answer to that question. They engineered chloroplasts to hold a reporter gene (don't ask me how the heck they did that), then introduced those chloroplasts into hundreds of thousands of pollen grains (again, how?!?!), mated those pollens with plant eggs, and checked the resulting embryos for nuclear versions of the reporter. It turns out that the reporter was moved to the nucleus in about 1:10,000 mating events. That seems pretty darned fast! Of course, other events would also have to happen to make those genes *functional*, but it gives some hint about how long it should take to move a chloroplast's genome to the nucleus.

Thursday, April 28, 2016

April 29, 2016 at 12:27AM

Tody I Learned: 1) ...a little bit about how praying mantises eat. Like a lion, it seems they like to go for the throat, ripping off their prey's head before munching down the body. Unlike a lion, they're surprisingly not that good at actually *killing* their prey. It can take quite a while for the mantis to chew all the way through. They don't seem particularly concerned about holding a creature a significant fraction of their own size still struggling to get away. They're really scarily effective at holding insects. 2) ...how to cut RNA with Cas9! It turns out Cas9 is perfectly happy cutting RNA as long as you provide a little DNA oligo containing the PAM that binds to the PAM site on the RNA. In other words, Cas9 only requires DNA at the PAM sequence, and only on one strand -- it doesn't particularly care what kind of nucleic acid it binds to and cuts past that (though to be fair, cleavage of RNA isn't nearly as efficient as cleavage of dsDNA (though it should *also* be noted that the Cas9 does *bind* quite well to RNAs -- it just doesn't cleave them quite as well once attached, it seems)). More here (Nature, sorry abuot the paywall): http://ift.tt/1rDQDZr 3) ...a circuit architecture for exact tracking of a target (up to a factor). Say you want to detect molecule A, and you want a readout that follows the concentration of A -- for instance, you might want to produce GFP proportional to the amount of some hormone in the cell. You can do that with species B and C and the following regulatory relationships: A (linearly) turns on production of B B (linearly) turns on production of C C very strongly competitively inhibits B, or otherwise stops it from activating A And that's it! For certain parameter choices, at least. It's pretty robust, but not perfectly so. Thanks to Niles Pearce on this one!

Wednesday, April 27, 2016

April 27, 2016 at 11:28PM

Today I Learned: 1) ...how cells maintain nonzero finite steady-state populations! Well, at least how T-cells do it, at least according to a simplified model. For all of y'all who guess they were secreting some kind of inhibiting factor into their environment... close! Feedback *is* implemented by excreting something, in this case IL-2 (interleukin-2, a protein). Critically, though, IL-2 doesn't just inhibit cell growth -- it also activates cell growth. More specifically, IL-2 triggers cell death in a linear fashion (cell death ~ IL-2 * k, k is some constant) and enhances growth cooperatively, which is a fancy way of saying that the growth rate of cells against concentration of IL-2 looks something like this: http://ift.tt/1rjuv5X. This combination of feedbacks gives the population two steady states, one at no cells and one at some finite amount of cells*. The fact that IL-2 mediates *both* cell death and cell growth is critical! If it just modified one or the other, or if it modified both in a linear fashion, you would not get a non-zero steady state (you can try something similar to what I describe below to show this). Interestingly, there's reason to expect cells to only use one growth factor instead of two. You *can* get the same behavior with two growth factors, but if you use two growth factors, the system is more sensitive to parameters like production rate of the growth factors. * To see why, draw a plot of cell death vs IL-2 concentration and cell growth vs IL-2 concentration on the same plot. Remember that cell death is linearly dependent on IL-2 concentration, while cell growth is sigmoidal with IL-2 concentration. Now pick a "current" cell concentration, which should be proxied well by IL-2 concentration. This is a location on the x-axis. If cell death is higher than cell growth, then the cells are net dying out, and the population moves left, towards zero. If cell growth is higher than cell death, then the cells are net growing, and the population moves right, towards cancer. Anywhere that cell growth and cell death are equal, you have a steady state population that doesn't move. You should find three steady states -- two that populations will move towards, and one that populations move away from. 2) It takes about 25 minutes for a relatively normal-sized ice cube to melt on a plate, outside, in shade, on a relatively warm day. That's a lot longer than I expected! Thanks to Dawna Bagherian for donating an ice cube! 3) The promoter on the ColE1 origin of replication that produces RNAII (which is what primes the plasmid for replication) can be replaced by other, standard promoters, and the plasmid replicates just fine.

Tuesday, April 26, 2016

April 27, 2016 at 02:28AM

Tody I Learned: 1) By far the majority of magnesium ions in a bacterial cell (and, I think, most eukaryotic cells, too) are bound to something at any given time. Only something like 10% of a cell's magnesium ions are actually floating around in solution. 2) In Arch Linux (or any other systemd-based Linux), you can see what services/units are running by simply running "systemctl". 3) ...a new debugging rule to go in my Linux-user debugging toolkit -- if a secondary package manager (in my case, pacaur, which is like pacman (which is like apt-get or homebrew but for Arch Linux) but for unofficial repositories as well as official ones) isn't downloading anything, and your database list is synchronized, then try reinstalling the package manager. You may have to do a manual install, since the package manager isn't working....

Monday, April 25, 2016

April 26, 2016 at 02:05AM

Tody I Learned: 1) ...that it's possible to debug the Windows kernel, live. This is a process known as "kernel debugging", appropriately enough, and it's done by using one computer as a debugger and one as a test machine. There's some built-in Windows software that makes it relatively easy to set up and run. Pretty cool, Microsoft! Pretty cool! 2) There's an inherent instability in maintaining cell populations that pops up above and beyond what you see in, say protein populations in a cell. See, a cell can keep a protein at a constant (steady state) concentration very easily, by producing at a constant rate and letting the protein degrade at a constant rate *per protein molecule*. Because the total amount of protein degradation increases when there's more *total* protein in the cell, degradation becomes stronger relative to production as the concentration of protein increases. As the cell produces more protein, degradation and production eventually balance out, and the cell reaches a steady-state protein concentration. This doesn't work for cell populations (i.e., the population of white blood cells in the blood), at least not naively. The problem is the way you get "constant production" of a cell population. In the protein case, absolute production is fixed beacuse there's exactly one genome (well, probably two copies of any particular chromosome, but you get the idea) and it produces at some fixed rate. For that to work with cells, they would have to come from a fixed population of progenitor ("stem") cells... but then you have to have some way to maintain *that* population at a fixed size, so that solution really begs the question of how you maintain a constant population. You could also just have each cell in the population divide at a fixed rate, but unfortunately that gives you growth that's proportional to the size of your population. If that growth is *just perfect*, you can get perfect balance and have a constant population, but that's an unstable situation. If the growth rate is just a little too low, then the cells will die off too quickly and the population will crash to zero. If the growth rate is just a little too high, then the population explodes and probably gives you a tumor. How does the body handle this dynamic instability? Tune in on Wednesday to find out. In the meantime, care to take a guess? 3) ...about "The Next Rembrandt". The Next Rembrandt (which I will abbreviate TNR) is a rather complex piece of software deisgned to produce novel paintings in the style of Rembrandt. By which I don't just mean "kind of like Rembrandt's paintings" -- TNR was built to mimic Rembrandt in exquisite detail, from his overall composition to the size and shape of his figures' eyes to the technique and order of his brush strokes. TNR's debut painting was created by instructing it to paint a white man with certain facial features, in a black outfit, facing to the right. TNR designed a painting, then 3D-printed it, presumably out of paint, to give it the full texture of a Rembrandt painting. Go Google Image search "the next rembrandt" to see the result.

Friday, April 22, 2016

April 23, 2016 at 02:28AM

Today I Learned: 1) Apparently much of Chicago was built on swampland and straight-up water. This was accomplished largely by importing vast swaths of nearby dune-sand and filling in the land until it could support buildings. Also, the swampy ground of Chicago forced architects to come up with more sturdy building methods like steel framing, which is how we got skyscrapers. Go building-in-swamps! Cred to Mengsha Gong!!!!! 2) The poodle was originally bred for helping waterfowel hunters collect their catches. The traditional poodle haircut is descended from a style designed to keep the poor dog's joints when wet. Also, the word "poodle" probably comes from a german name "Pudelhound", which translates quite directly to "splashing-about-dog". ALSO, there are some ridiculous old drawings/paintings/engravings of old poodles on the Wiki poodle page. 3) Old thermal cyclers are ridiculous. For one thing, their interfaces suck, but I knew that already. Also, they tend not to have terribly many spots for tubes, and many don't have heated lids (which normally keep water from condensing on top of the sample tube -- without it, you have to cover your sample with mineral oil to prevent evaporation). But I kind of knew those problems, too. What I was *not* expecting was a thermal cycler designed for 0.6 mL tubes instead of the usual 0.2 mL tubes (formally known as "PCR tubes", as they're SPECIFICALLY DESIGNED FOR PCR IN THERMAL CYCLERS). Also, you can get a thermal cycler for less than $150 on ebay if you don't care how much space it takes and you're willing to be limited to 24 samples at a time. For a nice (non-gradient) thermal cycler, you're looking at between $500 and $1,200, and for anything with all the bells and whistles, you're looking at dropping more than $1,000. a

April 23, 2016 at 01:18AM

Tody I Learned: 1) Apparently much of Chicago was built on swampland and straight-up water. This was accomplished largely by importing vast swaths of nearby dune-sand and filling in the land until it could support buildings. Also, the swampy ground of Chicago forced architects to come up with more sturdy building methods like steel framing, which is how we got skyscrapers. Go building-in-swamps! Cred to Mengsha Gong. 2) The poodle was originally bred for helping waterfowel hunters collect their catches. The traditional poodle haircut is descended from a style designed to keep the poor dog's joints when wet. Also, the word "poodle" probably comes from a german name "Pudelhound", which translates quite directly to "splashing-about-dog". ALSO, there are some ridiculous old drawings/paintings/engravings of old poodles on the Wiki poodle page. 3) Old thermal cyclers are ridiculous. For one thing, their interfaces suck, but I knew that already. Also, they tend not to have terribly many spots for tubes, and many don't have heated lids (which normally keep water from condensing on top of the sample tube -- without it, you have to cover your sample with mineral oil to prevent evaporation). But I kind of knew those problems, too. What I was *not* expecting was a thermal cycler designed for 0.6 mL tubes instead of the usual 0.2 mL tubes (formally known as "PCR tubes", as they're SPECIFICALLY DESIGNED FOR PCR IN THERMAL CYCLERS). Also, you can get a thermal cycler for less than $150 on ebay if you don't care how much space it takes and you're willing to be limited to 24 samples at a time. For a nice (non-gradient) thermal cycler, you're looking at between $500 and $1,200, and for anything with all the bells and whistles, you're looking at dropping more than $1,000.

Thursday, April 21, 2016

April 22 2016 at 02:24AM

Today I Learned: 1) Here's a fun paleontology story, courtesy of Mengsha Gong. There are a lot of fossils of giant clams from the Mesozoic era. Berkeley has one such specimen, which happened to have a pair of holes in it. For a while, it was simply assumed that it had been crushed or fallen on by a rock or something similar. Then someone realized that it looked an awful lot like a pair of tooth holes, and there happened to be another fish with teeth just the right distance apart from the same time period.... Another fun anecdote: check out this thing. What do you think it is? http://ift.tt/23NhYsS Did you guess a pair of shrimp? That's what it looks like to me. The trouble is, they always come in pairs. That's because they belong to this guy, Anomalocaris (who was, by the way, about human-sized. Have a nightmare.): http://ift.tt/1SV39Js 2) The "turnover number" of an enzyme (or other catalyst) is the number of reactions the catalyst will perform, on average, before degrading, mis-reacting, or otherwise becoming unable to do its thing. Typical turnover numbers for enzymes are between 10 (at the *very* lowest) and several tens of thousands. Typical turnover numbers for man-made catalysts are less than 50. Unless they're manmade enzyme catalysts -- go Bioengineering! Kudos to Anders Knight on this one. 3) Cajil Bodies are sub-organelles of the nucleus, and are basically clumps of protein about the size of a smallish bacteria. Cajil bodies are involved in RNA processing, and are mostly found in cells that are either actively dividing (gametes, tumors) or doing a lot of metabolizing (neurons), presumably because these cells are pumping out tons of RNA to get processed. Relatedly, I learned that the nucleolis isn't really a separate compartment of the nucleus -- it's just a very dense cluster of coiled chromosome and its associated machinery, along with a bunch of nuclear ribosomes. Though given how dense that bit of the nucleus is, it might be wise to consider it as a separate compartment for many purposes.

Wednesday, April 20, 2016

April 21 2016 at 02:08AM

Today I Learned: 1) There are some super-useful, really intuitive rules for representing chemical reactions with differential equations, that let you take, say, the reaction system A + B -> C and write down some differential equations that describe the change of number of each species over time (in this case, dA/dt = -AB, dB/dt = -AB, and dC/dt = AB, up to a (rate) constant). Today I learned that you can derive these rules as the mean time values of the chemical master equation for the system, which is a more detailed, more-correct, stochastic description of the chemistry. 2) There's a new version of Cas9 on the market (metaphorically speaking). This one is a fusion of cas to cytidine deaminase, which converts C nucleotides into T nucleotides and G nucleotides into A nucleotides. As with most Cas fusions, the Cas bit of the enzyme targets the enzyme to specific sequences. The cytidine deaminase converts nucleotides, making this fusion a one-protein single-base pair editor! It's still rather restricted in some ways -- it can only convert C->T and G->A, for instance, and it doesn't actually have single-nucleotide precision (it affects everything in a 5bp window). Still, it's an awesome enzyme, as perhaps we might expect from a joint team of authors out of Harvard and MIT. Paper here (sadly, it's Nature, so you'll probably need a university connection to read it): http://ift.tt/1ScybRd Thanks to reddit and to Asher Rubin for alerting me to this article! 3) How the ColE1 plasmid origin* works. I've heard bits and pieces of how it functions before now, but I think I really more or less get it now...? So here's the basic idea -- ColE1 has a binding site for DNA polymerase, but it can't be replicated without an RNA primer. The origin provides this primer in the form of RNAII (kind of a dumb name, for multiple reasons), which is a 500-ish base pair RNA that folds up as it's transcribed, forming a secondary structure that places the end of itself right at the origin, where it acts as a primer. RNAII gets transcribed --> plasmid replicates. Importantly, the processing of RNAII is co-transcriptional -- there's never RNAII floating around in the cell, it just immediately gets turned into a primer. ...unless RNAI shows up, that is. RNAI is a cool little RNA species that sits entirely inside RNAII, and I do mean "entirely" -- its promoter, sequence, and terminator are all part of the RNAII sequence, but in reverse. Anyway, RNAI inhibits RNAII by binding to it, changing its secondary structure, and messing it up as a primer. I'm not *exactly* sure how this mechanism controls copy number... but I think it has to do with polymerases (or some other protein critical for plasmid replication to start) being really limiting. When there's only one plasmid, the polymerase/other molecule finds it and binds to it relatively quickly, but if there are a bunch of plasmids, the per-plasmid rate of replication slows way down as polymerase becomes limiting, but the rate of RNAI production (and inactivation of the plasmid's replication) remains the same. I don't find this totally satisfying, though, because on the surface it sounds like there should still be *some* replication, just not any faster than there would be with a lower copy number. *for those unfamiliar in the ways of molecular biology, a plasmid origin is the part of a plasmid that allows it to replicate. Part of an origin's job is to provide a place for the cell's replication machinery to sit down and start replicating the plasmid. The other part of the origin's job is to eventually *stop* replication so that the plasmid reaches some steady state concentration. Anybody have a more satisfying explanation? Thanks to Andrey Shur for teaching me more about ColE1

Tuesday, April 19, 2016

April 20 2016 at 01:06AM

Today I Learned: 1) What an opal looks like. It's a lot less creamy and a lot more scintillating than I thought. 2) There are live streams on Youtube. Here's one of an albatross nest: https://www.youtube.com/watch?v=KMdKKpXSMVU 3) The "principal-agent dilemma" is the economic term for the problem when one person/party (the agent) makes decisions for another person/party (the principal), even though the agent's incentives might not be completely aligned with that of the principal. This problem is, as you might imagine, everywhere. Examples include a politician making decisions on behalf of his or her constituents; an employee negotiating a contract on behalf of a company; and a parent making a decision for a child.

Monday, April 18, 2016

April 19 2016 at 02:37AM

Tody I Learned: 1) In bacteria, the ratio of number of transcription factor to the number of its binding sites in the cell ranges from about 1/10 to about 10,000, trending around 10. That means that for a typical promoter, there are only about ten times as many copies of each transcription factor that can bind to it as there are places for them to bind. 2) Fountain pen nibs have a hole in the middle, kind of reminiscent of the sound holes in string instruments. These holes hold a film of ink, which is channeled through a slit down the nib to the point, which is how the pen deploys ink. If you press harder on the pen, the slit opens wider and lets more ink out, which is how you can vary the thickness of your stroke with a fountain pen. Thanks on this one to Mengsha Gong! 3) Ethidium bromide (EtBr, a DNA stain commonly used in laboratories and famed for its low cost, high sensitivity, and mutagenicity) is commonly injected into cattle to treat African Sleeping Sickness (trypanosomiasis). These cattle are injected at MUCH higher concentrations than are used in the lab (as in, 1000 times the concentration), and the cattle don't seem to show any ill effects. There is no reported carcenogenicity in ethidium-bromide-treated cows. Why are we lab scientists afraid of EtBr, then? Well, lab studies *have* shown that EtBr is a mutagen in cells in cell culture. And... that's about it. Chris Lennox gets the credit for this one!

Sunday, April 17, 2016

April 18, 2016 at 01:21AM

Today I Learned: 1) It turns out it's a bad sign if fish open their mouths a lot when breathing. Apparently it's something they only do if they're having difficulty getting enough oxygen, which happens normally after exercising or if frightened. If they do it *all the time*, it probably means their water is low in dissolved O2. This calls for a bubbler, more volume per fish, or potentially cooler water if the fish can tolerate it. Another sign of low oxygen -- if a fish spends an inordinate amount of time near the surface. 2) More good numbers to know: the smallest human cells, sperm, are about the size of a yeast cell -- between 4 and 6 micrometers across, with a volume of about 40 cubic micrometers. A HeLa cell*, in comparison, is something like 20-40 microns across and has a volume of around 1,000 cubic micrometers. Can you guess what the largest human cell is? I know you'll be tempted to just keep reading until you get to the answer, but I suggest you take a moment to stop and think about it before you hit the end of all this buffer text that's really supposed to keep your eyes off the answer until you've made a guess or two. Anyway. The answer is: the oocyte, or egg cell, which is a sphere something like 150 micrometers across, totalling 4 million cubic micrometers. * HeLa = a particularly famous immortalized cancer line used in research. HeLa cells are heavily mutated, but generically similar to skin cells. 3) More good numbers to know: less than two percent of terrorist attacks in Europe over the last five years. Most of the terrorist attacks in Europe are carried out with nationalist or political motivations, not religious ones. The numbers in the US are similar. Oh, another fun fact: In 2013, More people were killed in the US by toddlers than by terrorist attacks. Of course, that's only by one reckoning -- there are always differences in how "deaths by terrorist attacks" are defined. Also, 2013 was a pretty good year for the US in terms of deaths from terrorist attacks. But I hope the point is clear anyway. If you are motivated by fear of terrorist attack, please stop. There are many, many things that deserve your attention more. Terrorism is not a threat to your life in any meaningful sense, not if you live in the US or Europe*. * Unless you're, say, a Muslim in Europe right now. Then terrorism might, *might* show up on the list of things-likely-to-kill-you.

Saturday, April 16, 2016

April 17, 2016 at 02:01AM

Today I Learned: 1) Here's a (questionably) useful random order-of-magnitude number: Cambodia has exactly three airports with regularly-scheduled international flights, and approximately ten other airports that don't. 2) For some reason, it turns out that bacterial mass (cell size) increases roughly exponentially with growth rate. That is, faster-growing cells are also consistently bigger. This result, as far as I know, only holds within-species, so if you take a bunch of bacteria from the same species and sort them by size and growth rate, the fastest-growing ones are also the biggest. 3) From Science Friday, via Mengsha Gong: There's a thing called an orchid mantis, and it's possibly the most beautiful land animal. Juvenile orchid mantises *look like orchids* -- they hide in plain sight around orchids and other flowers, and wait for insects to come check them out. To a human eye, they're pretty obviously insects, but they look like praying mantises *made out of orchids*, which I find a really moving sight. Perhaps surprisingly, orchid mantises don't seem to emulate any actual species of orchid -- they just look generically orchid-like.

April 16, 2016 at 05:22AM

Today I Learned: 1) ...how to grow Chlamydomonas reinhardtii, a common model photosynthetic protist. According to Carolina Biological, they just need water between pH 8. and 8.7 and a 12-hour-a-day supply of light at 100 watts/m^2. 2) Frozen custard and frozen yogurt are *not* the same things. Ask Sarah Seid for details. 3) Earth isn't the only planet with auroras -- any planet with a strong enough magnetic field can have aurora. You know what planet has a really big magnetic field? Jupiter. Yes, auroras on Jupiter are a thing, and they're amazing.

Friday, April 15, 2016

April 15, 2016 at 03:28AM

Today I Learned: 1) Rain drops are shaped roughly like flattened spheres. Actually, it's a bit more complex, as this video explains between 1:10 and 2:10: http://ift.tt/1qtLRMW. In any case, raindrops are decidedly NOT teardrop-shaped. What things *are* naturally shaped like teardrops, other than Rupert's drops and similarly-viscous things? Thanks to Chigozie Nri for this delightful surprise! 2) ...how to design primers for Gibson assembly! In theory, I already knew how to do this, but knowing intellectually how to design a primer is always different than having done it before. Thanks to Andrey Shur for his putting up with my stubbornness and helping plan out some Gibson cloning! 3) ...the difference between Bio-Rad's digital PCR and RainDance Technology's digital PCR. I think RainDance entered the dPCR market first, and they seem to treat dPCR as a Big Thing, like flow cytometry or mass-spec or confocal microscopy. Their machines are super-accurate, even for digital PCR, which they achieve by making on the order of 10 million individual reaction drops (as opposed to Bio-Rad's ~20,000 drops) and recommending that you load so that only about 1% of those drops get DNA. That way, the number of drops with *more* than 1 piece of DNA is really, really, really small, which gives you a better estimate of the actual concentration of your sample. Unfortunately, making 10 million drops of anything is pretty hard, which makes RainDance machines expensive and slow. Bio-Rad, in contrast, seems to be aiming to make dPCR more of a Routine Thing, more on par with qPCR or plate assaying. Bio-Rad's machine only makes about 20,000 drops per experiment, which can be done with much simpler, cheaper (~1/2 the capital cost) technology than RainDance's. It's also much faster to make and analyze 20,000 drops than to make 10 million -- the full RainDance pipeline takes on the order of 8 hours, while most of the time for a Bio-Rad run is the ~2 hour PCR incubation time. Bio-Rad also has packaged and marketed their dPCR machines and reagents in a more user-friendly, black-box, plug-and-play sort of way, which is both good and bad. On the one hand, everything's ready to go right out of the box, and it's pretty simple to use. On the other hand, RainDance also sells nice kits, and their machines are a bit more flexible in terms of substituting your own PCR chemistry in the droplets. All in all, sounds like Bio-Rad is by far the better system for most applications. Bonus fact: It's "digital PCR" or "dPCR", not "digital qPCR" or "dqPCR". Thanks Erik Jue!

Wednesday, April 13, 2016

April 14, 2016 at 02:26AM

Today I Learned: 1) Repressor proteins work best on weak promoters. In retrospect, the reason why is pretty obvious -- if the promoter is strong, it's because polymerases bind to it a lot, which makes it hard for a molecule to get in the way. This goes against my intuition, though, which is that if a promoter is weak, it doesn't have much room to go down in expression, so a strong promoter would be easier to repress. 2) One molar concentration (1 mole/liter) is approximately equivalent to 1 molecule in a box 1 nanometer on a side. My benchmark for stuff-that's-about-a-nanometer is the spacing between base pairs in a DNA helix, which is... 2 or 3 nanometers? Just a couple of nanometers. Anyway, that tells me that something at one molar would be concentrated enough to be peppered all over a strand of DNA just from randomly bumping into it -- that's pretty darned concentrated. Thanks Andy Halleran! Now I need to read the rest of "Cell Biology by the Numbers (http://ift.tt/1AvhcfE). 3) A colony of YFP*-positive bacteria glows quite nicely under a DNA gel light and filter. Also, cell-concentration GFP is pretty easy to visualize with a cell phone by taping the right filters over the flash and the camera. * YFP = Yellow Fluorescent Protein, which does exactly what it sounds like.

Tuesday, April 12, 2016

April 12, 2016 at 11:52PM

Today I Learned: 1) The list of games Buddha would not play: http://ift.tt/1TQkicg This list is fascinating on many levels. On one level, it's an interesting historical glimpse into what kinds of games may have been played in ancient India. It's interesting how familiar most of these games are -- there seem to be some more-or-less universals in the human condition regarding games. On another level, it's fascinating that Buddha would choose to write about not playing certain games, and there are a lot of possible impliciations for the list. Is this Buddha saying that he refuses to play games, a la Green Eggs and Ham? "I will not play them in a house, I will not play them with a mouse. I will not play them here or there -- I will not play them anywhere!" Or perhaps these are games the Buddha would not play because they specifically care about things the Buddha doesn't care about. I can think of possible reasons to not play most or all of the games on the list -- games on boards with rows and columns tend to be all about strategizing under man-made rules; ball-games are all about physicality; playing with toy versions of real things is kind of ignoring the reality of the real thing; imitating deformities is not a good way to cultivate compassion. Finally, there's #6 -- "Dipping the hand with the fingers stretched out in lac, or red dye, or flour-water, and striking the wet hand on the ground or on a wall, calling out 'What shall it be?' and showing the form required--elephants, horses, &c." Really? I mean, who wouldn't! 2) ...how to digital qPCR! It's remarkably easy, actually, given how much better it seems to be than old-fashioned qPCR. Chemically speaking, it basically *is* qPCR, except the master mix is different, and it's much more robust. The biggest difference is that there are a couple of extra mechanical steps. For the uninitiated, digital qPCR is a technique for quantifying amounts of DNA in a sample with very high accuracy. You basically make a qPCR mix (Taq polymerase, buffers, probes, and some sort of DNA-binding dye), use a microfluidic device to split the mix into about 20,000 microbubbles in oil (much, much, much easier than it sounds, using a disposable microfluidic device) and thermal cycle the whole thing to completion. The goal is to have the sample so dilute that you get approximately one copy of DNA per bubble. That way, some bubbles will randomly get one copy, some will get zero, and some will get a bit more. When you run the PCR reaction, each bubble will act as its own little PCR sample, and will amplify up a ton of DNA if there was one or more copies of the target in that bubble. Then you use a special bubble-imaging machine to count the bubbles with and without amplified product -- anything with amplified product will be brightly fluorescent (from the DNA-binding dye), and anything without amplified product will be essentially blank. From the counts of bubbles-with-no-product and bubbles-with-product, you can back-calculate the starting concentration of DNA. The nice thing about digital qPCR is that it uses binary endpoint-PCR results -- if there's product, you get a hit, and if there isn't, you don't, hence "digital". This makes it super insensitive to stuff like primer binding, salt conditions, inhibitors, and other kinds of things that could mess up traditional qPCR results. Another nice thing is that the readout you get at the end is an absolute quantity, not a relative quantitation, so you don't have to run every sample with a ladder to quantify how much stuff you have. Thanks to Erik Jue for getting me in on some dqPCR training! 3) When using pip (or conda) on a UNIX-like machine, make sure you have superuser priviliges (i.e., sudo) any time you use it to upgrade itself! Otherwise, it will uninstall the old pip(/conda), download the new one, and fail when it tries to install without superuser priviliges, leaving you without a working pip(/conda). Fortunately, pip is pretty easy to install with a bootstrap script (http://ift.tt/1mn7OFn), so if you *do* screw yourself over this way, it's relatively easy to recover from.

Monday, April 11, 2016

April 12, 2016 at 12:42AM

Today I Learned: 1) Tip for working with dynamical system models of gene networks -- if your output doesn't look right, check your parameters. Then think about what your parameters should be. Then check them again. 2) Apparently if you steep tea in less-than-boiling water, it doesn't come out quite so bitter. I'd heard you were supposed to do this, and now I know why. 3) It is surprisingly difficult to find sequences for origins of replication. For the life of me, I can't find any repositories that will just give you the sequence, aside from a few that are on the iGEM biobricks origins of replication page. The best I've been able to do so far is BLAST a sequence that I *think* is the origin, and hope it works. Biology sucks. *sigh*

April 11, 2016 at 05:25AM

Tody I Learned: 1) Technically, I learned this on Friday (thanks Mengsha Gong!), but today I *tested* the idea of cooking pasta in its sauce. It worked really well, except that a) it takes longer than boiling in water, and b) it burns the pot really easily. Definitely worth it for the extra flavor, perfect finish, and deliciously al dente texture. 2) Our University's little turtle ponds have at least one soft-shelled turtle! I eyed it sneaking off into the murk. 3) Speaking of our Unviersity's little turtle pond, the kinetic sculpture in the pool outside the library is gone! Where did it go?!

Sunday, April 10, 2016

April 10, 2016 at 05:06AM

Today I Learned: 1) ... how to pickle/jar things! Most saliently, the key to pickling successfully (i.e., without killing yourself or letting your food spoil) is keeping the pH of your picklees below 4.6, or ideally below 4.2. The only real danger in pickled stuff is C. botulinum, which grows well in the kinds of anoxic environment that pickling produces, *but* which can't survive below pH 4.6 (it's fairly heat-resistant, so even pasteurizing by boiling won't completely kill it). pH 4.2 is even better, because then you won't get random fluctuations bringing you into the danger zone. 2) Another pickling tip I learned today -- when you cap a jar to be pickled (leaving a bit of air on the top!), don't tighten the jar too much. The trick to getting it exactly tight enough is to screw the lid using the tips of your fingers. Without the leverage of your whole hand, your fingers apply just enough force to seal to the right level of tightness. I think what's going on is that if you do seal your jar too tightly, then air won't be able to escape as the jar heats, so when you take it back out, you have exactly as much air as you started with. That won't form a vacuum-seal, it will just be 1 atm air. 3) Apparently pine needles are edible, and can be used to make flavored water, tincture-style, or flavored sugar or syrup, mead-style. They don't all *taste good*, but some do, and rumor has it that many have a nice lemon-like flavor.

Friday, April 8, 2016

April 09, 2016 at 02:21AM

Tody I Learned: 1) Something really cool about working with TX-TL that I can't actually talk about (IP stuff). Sorry, but it really is TIL-worthy, I swear! 2) A little tiny bit about how diatoms* and radiolarians** make their shells. It all comes down to vesicles, perhaps unsurprisingly -- many microorganisms appear to be capable of causing silica-based mineralization on the surfaces of specialized vesicles. The cell will pull a vesicle into roughly the right shape, often an oblong "plate" or tubular "pole", using microfilaments and microtubules as a kind of guy wire, or by stretching them across the surface of some other, larger vesicle. Once in place, the vesicle is triggered to mineralize, making a hard plate, scale, or other structural component that can be guided to the outside of the shell. The above process seems to be the primary means of construction of diatom shells. Radiolarians (and I think, to some degree, diatoms as well) use a different variation on this technique to make net-like, porous coverings. This is accomplished by making a vesicle "foam" around the nucleus or cell exterior. Mineralization is tuned to only occur where two vesicles touch. So what you see in a radiolarian shell is actually a network of intersections in a foam of vesicles. More information in section 7.3 of "Biomineralization: Principles and Concepts in Bioinorganic Materials Chemistry" (http://ift.tt/25QzpaF). Thanks to Mengsha Gong for teaching me about this! * http://ift.tt/20oD8rL ** http://ift.tt/25QzpaH 3) ...about a rather contentious molecule among vegans -- cysteine. Yeah, the amino acid. Turns out most cysteine is derived from hydrolized animal hair and feathers, which makes it a no-go for vegans. This also explains some of my confusion about Einstein Bagel Bros bagels, as sources differ drastically about which of their bagels are vegan. It seems that all or almost all of their bagels contain industrial cysteine, which has led them to label their bagels as non-vegan... but less strict vegans may be ok eating pretty much all of their bagels.

Thursday, April 7, 2016

April 07, 2016 at 11:10PM

Today I Learned: Today's TIL brought to you by a special talk by representatives from Industrial Light and Magic. 1) You know that really cool remote-control BB-8 robot that J. J. Abrams took onstage with himself a while back? That model was, sadly, built after the movie was finished. What you see on screen is mostly a puppeteered model, mixed in with a wheelable "trike" model, a stationary wobbleable model, and CGI. 2) One of the novel features of Star Wars: The Force Awakens' CGI was their shader palette. Usually shader palattes, which determine the color and spectral response of materials on a CGI model, are designed by an artist. ILM made theirs by actually measuring spectral responses of reference materials in the field. So if you ever caught yourself thinking "huh, the Millennium Falcon's hull has awfully realistic specular reflection", now you know why. 3) Speaking of the Millennium Falcon, the CGI model of the Millennium Falcon is technically a character. In fact, all (most?) of the CGI ships in The Force Awakens were designed using the same software and animation model as their CGI aliens and characters. Bonus fact: Tentales are apparently notoriously difficult to animate. In particular, the longer the tentacles, the more difficult they are to animate realistically (and the more likely they are to accidentally clip through each other).

Wednesday, April 6, 2016

April 07, 2016 at 01:59AM

Tody I Learned: 1) Today I have some super cool facts about B. subtilis, a commonly-studied sporulating bacteria. B. subtilis (or B. sub, as it is affectionately known) grows into colonies on surfaces, just like most studied bacteria. The colony displays an interesting growth pattern. It grows quickly at first, but slows down as it becomes too big for nutrients to diffuse easily into the middle of the colony. Then, at somewhere around 50 or 100 microns, the colony starts growing in regular pulses. Apparently what happens is that bacteria near the center of the colony become nutrient limited by gluatamate, which is the primary nitrogen source for B. sub (and therefore more or less absolutely required for growth). When the colony gets big enough that glutamate can't diffuse easily to the center past the mass of growing bacteria on the perimeter, the whole colony will periodically stop growing for a bit to let glutamate through. This lets the colony keep growing while keeping the cells in the interior alive. Now, how does a population of bacteria communicate their pulse across a colony that could be hundreds of microns across? The answer's a doozy -- they use propagating electrochemical signals that are functionally reminiscent of (and possibly the ancestral basis for) neuronal communication. Here's how it works. B. sub, like pretty much all cells, keeps a ton of (positively charged) potassium ions in its interior. This potassium, among other things, maintains an electrical potential of about -150 mV across the cell membrane. B. sub has a membrane channel that, when activated, lets out potassium ions, depolarizing the cell and causing the electrical potential to go away, and spewing tons of potassium into the surrounding environment. The channel is thought to be held closed by glutamate. When intracellular glutamate is low, the channels open. B. sub also has membrane channels that actively pump glutamate into the cell, BUT these channels rely on the membrane potential to function. So when a neighboring cell fires, the efflux of potassium ions depolarizes a B. sub's membrane, turning off its glutamate channels. The cell pretty quickly runs out of glutamate, which triggers its potassium channels, spewing out more potassium to trigger the next cell to fire. Using this active firing mechanism, B. sub can communicate across a hundreds-of-micron-diameter colony in a few minutes, which is *way* faster than it could communicate by diffusion. These spikes also look uncannily like neuronal firing, and honestly, the mechanism is rather similar. 2) When bacterial biofilms reach a certain size, they undergo complex patterns of (programmed?) cell death. This causes the biofilm to buckle*, forming ridge-like "veins", like you can see in this colony of Pseudomonas aeruginosa: http://ift.tt/1RQqWdV. Apparently scientists have recently observed fluid movement through these channels, suggesting that they *may* serve to move nutrients around the colony, which at this point has a lot of difficulty getting nutrients to its center. * This is because the whole surface of the colony is under a lot of physical strain -- it's full of bacteria that are actively growing and pushing on their neighbors. When a hole opens up, the whole thing expands into it, which causes things like buckling. 3) ...how to calculate Ct in qPCR (the cycle at which an amplified sample crosses a threshold, which is used to back-calculate the starting concentration of the sample). In particular, I learned that the threshold value is basically arbitrary, as long as it isn't in the noise range or the plateau. The rest is just linear interpolation.

Tuesday, April 5, 2016

April 05, 2016 at 11:49PM

Tody I Learned: 1) There is a scientific definition of a pebble, as a shape -- it's a 3D solid for which the curvature* of points around the surface has a normal (Gaussian) distribution. That is, if you sample random points on the outside of a pebble and measure the curvature of each point, and make a histogram of those curvatures, you get a normal distribution (bell curve). *Also, today I learned the definition of curvature, at least on a plane. The curvature of a point on a plane is one divided by the radius of a circle you could make that would snugly hug the plane at that point. The idea is that as the radius of the circle gets bigger (and the curvature gets smaller), the edge of the circle gets flatter and flatter. Credit for these two facts goes to Mengsha Gong. Thanks Mengsha! 2) Ants get their pheromonal boquets from the queen, especially in a young colony. The ants that attend to the queen pick up her scent, and as they share food and grooming, they spread it around the colony. This means that you can take pupae from another colony, and if you can get them to survive and be groomed in the nest for long enough, they pick up the queen's scent and are treated as members of the colony. Conversely, if you take those ants and reintroduce them to their mothers' colony, they will be rejected as foreign. This suggests a somewhat risky tactic for supplementing young queens' retinues if you have a breeding hive of the same species. Getting new workers in a young colony is critical for the colony's stability. I'm not sure if any special treatment would be required to keep the larvae safe, but it seems worth a try. 3) Polytetrafluoroethylene (PTFE, also known by the brand names Teflon and Goretex) is ridiculously safe stuff. Item 1: PTFE is used to coat stents, and is not obviously toxic or dangerous (http://ift.tt/1V8eBra and http://ift.tt/1SOGQYA for a couple of different perspectives -- it's not clear whether or not they're better than bare-metal stents, but they're ceratinly not overtly toxic). Item 2: Rats fed a diet of 25% PTFE for 90 days showed no signs of toxicity or damage (http://ift.tt/1V8eEmN). That's ridiculous. What about Teflon cookware? Well, PTFE itself is pertty damned stable at cooking temperatures, but there are chemicals in old teflon cookware involved in sticking the teflon to the actual pan that could volatilize and potentially cause some respiratory damage. Bonus: A dialectic, in the classical, Socratic sense (as opposed to the Hegelian sense) is a discussion in which two people with different opinions argue in order to figure out the truth. I really, really should have already known this, and now I do thanks to Eliza Dickinson Urban!

Monday, April 4, 2016

April 05, 2016 at 01:54AM

Today I Learned: 1) ...a trick for bounding the possible number of real roots of a polynomial with relatively few terms (but possibly very high-order). In short (I'll give a specific example in a second) you want to look for the number inflection points in the function, which you do by taking the second derivative... and finding roots. If taking the second derivative gives you something that's easy to determine the root number for, then you're done. If not, then you recursively apply the same trick to figure out the number of roots of *that* polynomial.... Example: How many real roots does the equation ax^100 + bx + c = 0have? In general, figuring out how many real roots a high-order polynomial has is difficult. Here, though, you can put a bound on it pretty quickly. The key is that for the equation to have lots of roots, it has to squiggle up and down a lot so it crosses the y-axis a bunch. Each squiggle potentially gives you a new root, but it also requires an additional inflection point in the function, which is a location where the second derivative is zero. So, how many inflection points does ax^100 + bx + c have? To figure that out, take the second derivative and find its roots -- that gives you something like ax^98 = 0 (the constant becomes a new constant, but who cares what that constant is?). Now *that* equation is easy to solve -- x = 0. That means that the function ax^100 + bx + c has exactly one inflection point, which means it has at most three roots (try drawing out a polynomial with only one inflection point and it will pretty quickly become apparent why). What about ax^100 + bx^37 + cx^2 + dx + e = 0? When you take the second derivative, you get ax^98 + bx^35 + c = 0 -- not so easy to figure out how many inflection points this function has. But! You can use the same procedure on the new function, taking the second derivative and ending up with ax^96 + bx^33 = 0, or x^33(ax^63 + b) = 0. 0 is a root, as are the two 63rd roots of ax^63 + b = 0, so the original function can't have more than three inflection points, therefore the polynomial ax^100 + bx^37 + cx^2 + dx + e = 0 can't have more than 5 roots. This only puts an upper limit on the number of roots -- depending on the constants involved, you might or might not actually get y-axis crossings for those extra inflection points. But it's a nice way of bounding high-order polynomials with very few terms. Even better, you can use this technique to bound polynomials with known form but unknown order. As an example exercise for the reader, can you put an upper bound on the number of real roots in the polynomial ax^N + bx^(N-1) + cx + d = 0, for unknown whole number N>3? Also, for those real math majors out there, is this something I should have learned back in college or high school as a matter of course? It feels like the kind of thing that I might have just missed somewhere.... 2) PCR plates for qPCR don't have to be clear. Probably. Which makes sense, really -- both sample excitation and scanning is done from the top, so who cares what the sides are made out of? 3) It looks like Tesla Motors is now profitable! Sort of. Over the last couple of years*, Tesla has operated on revenues in the single-digit billions of dollars and still managed to lose between a few and a bunch of hundreds of millions each year. But! As of a few days ago, Tesla as about 276,000 reservations (!!!) for their Tesla 3, most of which were placed within the last week. That's almost $10 billion in sales on its own, which represents a couple years' worth of operation *on its own* at their current rate of spending. Of course, they don't actually *have that money* yet -- it's just promises to buy -- but it's still a lot of value that Tesla can pretty well count on seeing. Thanks to Andy Halleran for alerting me to this. Also, apologies for misinterpreting some of their financial numbers in an earlier conversation today -- it's not quite so ridiculously rosy as I thought for Tesla. * Tesla's a young enough and fast-growing enough company that looking back farther than "a few years" doesn't make sense to me.

Sunday, April 3, 2016

April 04, 2016 at 02:07AM

Tody I Learned: 1) Ant boquets (the blend of pheromonal hydrocarbons unique to an ant colony) are, at least in some cases, dependent on the food source of the ants. For instance, ants that live in twiggish soil have different hydrocarbon ratios depending on the species of tree whose twigs they live in. 2) Today I watched my first (partial) game of Warhammer 40k, and learned some of the rules (there are a lot). It's a game that requires way, WAY more time and money and effort than I want to put into anything new right now, but boy it's cool to watch a couple of experienced players with big armies duke it out. 3) Sweden has one of the highest tax rates in the world (swapping regularly with Denmark for first and second place) clocking in between 45% and 50% of GFP collected as taxes! Sweden also has a nice tax return system where you receive a tax form filled out by the government, which you can modify if anything's incorrect or you want to add anything. This makes a lot of sense to me -- the IRS in the US already has most of the information required to tell you how much you owe in taxes. Making you figure it out yourself just adds a step where you can get it wrong (or lie).

Saturday, April 2, 2016

April 03, 2016 at 02:43AM

Tody I Learned: 1) So I knew that ants carry their dead to special graveyard recepticles, but today I learned a bit more about that behavior, called necrophoria. When an ant comes upon a dead nestmate, she will scan it briefly with her antennae (solid rule of thumb when it comes to ants -- the first thing an ants does to *anything* is to scan it with her antennae), pick it up, and carry it directly to a graveyard location, usually quite far from the nest. If you house ants in a container smaller than the ideal graveyard radius (as is common in captivity), then the ant will carry her fallen sister to the edge of the container, then wander around the perimeter for several (many?) minutes before dropping it at random. Furthermore, if a dead body is dropped this way, and another ant comes across it, *she* will then pick up the dead ant again and random-walk it around the perimeter some more. Here's the fun part. It turns out that necrophoria is triggered by one very specific class of molecules, specifically olefins produced by the decaying body. If you clean the corpse of olefins and re-introduce it to the nest, workers will eat it or treat it as any other refuse instead of disposing of it properly. Furthermore, if you paint or spray pretty much any other object with the olefins, you can get workers to treat that object as an ant corpse. You can even paint other nestmates as dead ants. If you do, nestmates will carry the painted sister (without resistance) to the graveyard and set her down. The painted sister will vigorously clean herself and wander right back to the nest, where she will usually be picked up and carried right back. 2) My showerhead has multiple action modes! 3) Watched some showcased ballroom dancing today. I learned a few little things (like what a cha-cha looks like), but the thing that really stood out to me was the rhythm of ballroom waltzes. Fair warning, I'm talking from a sample size of about N=3, so it may be too early to generalize, but it looked to me like ballroom waltzes are quite... loose with their rhythm. About half the time, I saw moderately strong "one-two-three" rhythm. The other half of the time was mixed rhythms that kind of sort of fit into the beat. In particular, one of the waltzes looked like it spent a fair amount of time in a one-two-threepausefour rhythm, where the third beat was split into a triplet with steps on the first and third sub-beat, presumably to make the balance or footwork (foot-fingering? footing? what's the word for this?) work out. Ironically, one of the waltzes with the strongest one-two-three rhythm wasn't actually performed to a waltz -- the piece they danced to was 4/4 or 2/4 rhythm, and they just danced three-against-four. Thanks to Mengsha Gong for suggesting I come out to see some dancing, and for a beautiful performance. Also, Sean Chen was awesome, and it was a pleasure to see him perform. Bonus: Bonus ant fact! Today I learned a bit more about how ant identification works. All ants produce a hydrocarbon mix that's unique to the species (or to a few related species), usually with some sub-blend that's unique to the colony and further specifying blends that sometimes identify individuals. The ants produce these hyrdocarbons in specialized internal organs (ants have a LOT of organs for producing chemicals). The hydrocarbons are then distributed internally, and go into cuticle production. Ants also are thought to spit out hydrocarbons and "wash" themselves with them -- in fact, the fastideous self-cleaning demonstrated by ants may be as much to distribute hydrocarbons as it is for hygenic purposes. Also, ants will clean nestmates who have been away from the nest for a long time with extra vigorousness. Second Bonus: Second bonus ant fact! Apparently if an ant finds an offending object in the nest and can't carry it away, it will instead bury it with some dirt. So maybe my pogonomyrmex keep burying their water cap because they find it an offending object?

Friday, April 1, 2016

April 02, 2016 at 02:05AM

Today I Learned: 1) ...a bit more about the evolution of trophallaxis, or sharing of food by regurgitation, in ants. The most evolutionarily-basal ant clades (ponerine and one I forget) don't regurgitate food -- they can only carry droplets back to the nest and offer them to other nestmates. They can't perform trophallaxis, in fact, because they lack a specialized trophallaxic gut (not the real name) that holds food without digesting it. Fun trophallaxis fact -- some species of ants will regurgitate and offer food during combat with ants from other colonies, particularly when they take submissive stances. This is thought to be a kind of surrender gesture, though it may just be accidental firing of the trophallaxis behavior reflex, which is triggered by a friendly ant tapping the offerer's antannae. 2) There is no solid evidence that ants communicate with each other through any kind of visual means, and not for lack of trying. Ants just don't communicate by visual signals. 3) Ok, so I still don't understand why temperature does what it does in the Boltzmann equation, but I've at least found a more concrete nugget of not-understanding to try to hack apart. In statistical mechanics, where Boltzmann's equation reigns supreme, it seems that temperature has a really funny definition. Specifically, the temperature T of a system is defined as 1/T = dS/dE, where S is the entropy of the system (the log of the number of microstates possible in that system) and E is the energy of the system. That is, temperature is a measure of the change in the number of states accessible by the system as the energy of the system is raised. Actually, it's 1 over that rate of change. I find this really frustrating, because this is where every text I can find on statistical mechanics starts, when it comes to temperature, but this gives me no intuition of how temperature is related to either the thermodynamic definition (average kinetic energy of the molecules) or the everyday experience of temeperature. Chris Lennox, I know you've worked with definition before -- why the hell is that what temperature is?!