April 01, 2016 at 12:28AM

Today I Learned: 1) Willow trees* in Florida have an interesting relationship with American alligators. The willow tree grows at a very specific altitude of about a foot, where it has ready access to water without being actively waterlogged (which would presumably be a difficult position for a willow sprout). Most of the best places for willow trees to grow are on stone outcroppings of some sort, including limestone and sandstone. These rocks end up donut-shaped, with a pool in the center, thanks to alligators -- alligators really like to bask under the willows, and many years of many alligators shuffling around under the willow scrapes out a depression in the rock on which it sits. This makes a little pool of water... which is perfect for an alligator to sit and and wait for prey to come by. Today's tree fact brought to you by Mengsha Gong. * not the weeping kind, another species. 2) Those of you who design primers often, this one's for you. When you design primers, ever wonder what those "self 3' complementarity" and "self complementarity" scores are? I did. Today I learned what they are. "Self complementarity" is a somewhat abstract score that measures how well a primer will dimerize. The self complementarity score is calculated by finding the best alignment of the primer against another copy of the primer. Once an optimal alignment is found, the self complementarity score is calculated as the number of correctly-paired nucleotides minus the number of incorrectly-paired nucleotides, with an extra penalty for gaps and less penalty for a pair with an "N" in it. I'm pretty sure the algorithm doesn't allow scores less than 0. You can see the full description of the algorithm (which is pretty short) here: http://ift.tt/1M4WO1z "Self 3' complementarity" is a related measure of how likely primers are to prime off each other. It's the same as the self complementarity measure, except that the "best" local alignment is restricted to be one where the 3' end is anchored, which would allow amplification off that primer. Full algorithm details here: http://ift.tt/1SqIaOR 3) Why the Boltzmann distribution describes probabilities of states based on energy level! I'm not going to go into the full explanation here, because I don't think I can do a better job than this source: http://ift.tt/1M4WOyo (it's 6 pages at high-school level math, one of which is a table and one of which is totally skippable if you're not specifically interested in statistical QM (everything after BD-5) -- definitely worth a read if you want to see why thermodynamics works). I'll try to give a short preview, though. You can get to the Boltzmann distribution by considering a small, finite number of particles (or springs or coins or molecules or whatever) with discrete energy summing to some constant total (since energy is conserved in a closed system). You can enumerate out all the possible ways to distribute the discrete lumps of energy to the particles -- each assigment of a unique energy to each particle is a microstate, and every collection of microstates with the same overall distribution of energies (i.e., two particles with zero energy, five particles with one energy, and one particle with two energy) is a macrostate. You take the limit of that distribution as the number of particles gets really big and the difference between energy levels goes to zero, and you get a Boltzmann distribution. One thing that explanation *didn't* cover at all was how temperature gets into the equation -- the author just shows that the distribution of states has the form αe^(β-E(s)), where α and β are some constants, but they don't show why β ends up being 1/kT. Thanks to Dean Clamons for finding this wonderful little gem!

March 31, 2016 at 03:02AM

Today I Learned: 1) Thermodynamics! Specifically, why temperature plays the role it does in chemical reactions, as reasoned from the Boltzmann distribution. If you're well-versed in statistical mechanics, you probably aren't going to learn anything from this post. For the rest of y'all, I'm going to try to explain the role temperature plays in chemistry, using basic statistical mechanics. You'll need some high school algebra, internet access and a browser capable of using wolframalpha.com, and some patience (yeah, these thermodynamics TILs tend to end up pretty long). I'll also be writing out equations, and Facebook doesn't make writing out equations particularly easy. It should be pretty straightforward if you follow along on paper. First, let's define a state. That's pretty simple -- a state is an arrangement of atoms (and their momentums) of some collection of atoms. Actually, it doesn't have to be atoms -- you can apply statistical mechanics to anything where you can define states, energies over states, and temperatures, but atoms are the usual agents in thermodynamics. Let's consider a super-simple system consisting of a coin with the states "lying flat on a table" (I'll call it "FLAT") and "standing on its edge" (I'll call it "EDGE"). States are said to have an energy (or, more fomally, a Hamiltonian) that describes in a number how "stable" a state is (there are other ways to interpret what an energy is -- I don't have a way to explain it from first principles). The lower the energy of a state, the more stable it is. Let's assign some hypothetical energies to the coin states. The FLAT state is much more stable, so we'll give it a lower energy. Lets say FLAT has energy 1, while EDGE has energy 1,000. One of the more fundamental results of statistical mechanics (which I'm taking as brute fact) is the Boltzmann distribution. Statistical mechanics tells us (again, as I'm taking as brute fact) that systems with certain properties follow the Boltzmann distribution (basically, where you randomly sample states A LOT, which is generally true for chemistry and which we will assume is true for the coin example by assuming we either observe a hell of a lot of coins or we come back to the same one over and over again, with enough time in between that we can't predict the state of the coin from the last state it was observed in). What's does that mean? It means this -- the probability of a system being in a state x is proportional to e^-(E(x)/kT) where e is the number e, E(x) is the energy associated with state x, and T is the temperature. Oh, and there's k, the Boltzmann constant, which is an extremely important cosmologic constant and super-important for making units work out in this equation... but it's also just a number, so I'm going to drop it from here on out*. So, what does this say? It says that as the energy of a state gets higher, the probability of that state goes down essentially exponentially. I say the probability of a state is *proportional* to the thing above, but what's the *actual numeric probability* of a state? To find that, we use the fact that the sum of the probabilities of all of the states has to add up to 1, which means that if you divide the above thing by the sum-of-those-above-things-for-all-possible-states, you get the actual probability of that state. Written out, p(x) = e^-(E(x)/T) / Σ(e^-(E(s)/T)) where the sum is over all states s (this would be a good place to start following along on paper, if you aren't already). This is super-important, because it means the probability of each state is affected by the probabilities of all other states. Ok, so what's temperature doing in this equation? Let's consider the coin example again. What's the probability of the coin being on its edge, according to the Boltzmann distribution? There are only two possible states, so it's pretty easy to write out that equation above: p(EDGE) = e^-(E(EDGE)/T) / (e^-(E(EDGE)/T) + e^-(E(FLAT)/T)) There are a lot of terms with T in them up there. We can simplify things by dividing the numerator and denominator through by e^-(E(EDGE)/T), yielding: p(EDGE) = 1 / (1 + e^-(E(FLAT)-E(EDGE)/T)) That's much nicer. Lots more 1's, much fewer T's. Note that this is basically a simple function of two variables: there's T, the temperature; and there's E(FLAT) - E(EDGE), the difference between energies of the two states**. Let's call that difference X. To get an idea of what this function actually looks like, check it out on wolframalpha.com with T = 1 (http://ift.tt/1pMv7Qq). Positive values of X mean that FLAT has a higher energy (is less stable), while negative values of X mean that EDGE has a higher energy. If the two states have the same energy (X=0), then p(EDGE) is 0.5 -- the two states are equally likely. As X gets higher (FLAT has higher relative energy), the probability of EDGE gets higher pretty quickly, until it effectively saturates at 1. As X gets lower (EDGE has higher relative energy), the probability of EDGE drops dramatically until it bottoms out at 0. This matches intuition -- the more stable (lower-energy) state is much more likely. For our example, we said that E(FLAT) = 1, while E(EDGE) = 1000, so we're WAY off to the left -- FLAT is extremely unlikely. That's at temperature 1. What happens if we turn up the heat? Well, the only thing T does in the equation above is to modify X. Specifically, T acts to *scale* X -- as T increases, X/T gets closer to zero. It's kind of like the X-axix gets stretched out; or, equivalently, raising the temperature pushes you towards X = 0 in the plot I linked to above. As an example, let's try turning T up to 1000: http://ift.tt/1M2hA1D. Now you can see that 999 difference in energy isn't so much -- EDGE is now relatively likely. Raising the temperature *flattens out* the probabilities of different states by moving them from the edges of our probability graph toward the middle (http://ift.tt/1pMv5YT to see the probability of EDGE as a function of both X AND T). Conclusion: high temperature makes all states equally probable. Low temperature makes low-energy states much more likely. Now, at this point, if you're like me, you're thinking something's terribly wrong with this picture. After all, when you turn on your stovetop burner, your water doesn't start taking on random states. It does something very specific -- it heats up, then boils. What gives? To understand what's going on here, we have to think about the *microstates* of the pot of water vs its *macrostates*. The *microstates* of a system are really what I've been talking about above -- they're all of the possible arrangements of atoms in a system. That's too many atoms to individually track, so we usually talk about the *macrostate* of a system, which is a collection of techncially different but experimentally indistinguishable microstates. For instance "the water is liquid" is a macrostate -- there are bazillions of ways you can arrange the molecules in that pot of water that will still look liquid, so we call it a single macrostate. "The water is a vapor" is another macrostate. Some macrostates have a LOT MORE possible microstates than others. We say that those macrostates have high "entropy". That's all entropy is -- the number of microstates that look like a macrostate. What's happening when you boil water is that water vapor has MASSIVELY more states than liquid water, but microstates that look like water have much lower energy. When the temperature is low, the low-energy states are favored strongly, and your pot of water stays bound together as a liquid. When the temperature is raised enough, suddenly the probabilities of all of the states become more or less equal***. But! There are tons more "water is a gas" states than there are "water is a liquid" states, and when you add together all of the tiny-and-equal probabilities for the water-is-gas microstates, they collectively massively outweigh the sum of the probabilities for the tiny-and-equal water-is-liquid microstates. In other words, higher entropy macrostates are favored at high temperature. And there you have it -- the mathematics behind why low temperatures favor low energy and high temperatures favor high entropy. * If you're not comfortable with my dropping constants randomly, just pretend that for the rest of the TIL, T is actually the Boltzmann constant times temperature. ** You may have heard that there's no thing as absolute energy, only relative energy. Perhaps this gives some intuition into why -- if you add some constant amount to all of the energies of the states in a system, the resulting distribution of states is indistinuishable. *** I suspect, but have not yet convinced myself, that the exponential-looking shape of the plot of microstate probability around 0 energy difference are at least part of why you tend to see sharp phase transitions when you raise the temperature in a lot of setups -- changing the temperature mostly slides you around the flat tails of that distribution, where microstate probabilities aren't really affected much, until you suddenly hit a bit where microstate probabilities start exponentially moving away from 0 and 1. This produces a relatively sharp transition from an energy-dominated regime to an entropy-dominated one. The trouble is that temperature change doesn't move you linearly in that graph, and I don't have a good enough intuition for exactly how it does move you -- can anyone confirm or deny? Chris Lennox? Robert Johnson? Suzannah Fraker? Andrew Andy Halleran? Anders Knight? 2) Portable soup! Portable soup is the ancestor of modern boullion cubes. Portable soup was invented in the 18th century as a food for sailors. It's basically a soup, concentrated down to a thick gelatinous substance that can be stored apparently indefinitely. You can either dissolve it back into soup or just chew it. Portable soup was used as foodstuff in the Brittish Royal Navy until around 1815, at which point research suggested that it wasn't actually particularly good for sailor health, and was replaced by canned meats. Thanks to Tara Sullivan for enlightening me about portable soups. Many more juicy details on the portable soup wiki page (no joke: http://ift.tt/1SpBCRV) 3) ...how negative autoregulation can make genetic responses faster. See, the amount of a protein a cell has is determined by two factors: how quickly that protein is produced, and how quickly that protein is broken down (or diluted out). It turns out that the *speed at which a cell can change* the amount of protein in the cell is largely determined by the speed of degradation. Yes, if you're turning on a gene, you can make it respond faster by cranking up the production rate, but then you end up producing a lot *more* of that protein in the end, so you need to couple that with a higher degradation rate anyway to maintain the same steady-state protein level. ...unless the gene represses itself. Then you can have a high initial production rate when the gene is just turning on, which gives you a fast 'on' response, but the gene can regulate itself to whatever steady state you need. Note that this doesn't help at all with *deactivation* of a gene -- then you're still limited by how quickly the protein is degraded. * when a gene represses its own production Bonus fact, courtesy of Mengsha Gong: The cluster fig, though a beautiful tree, is an interesting kind of nusiance plant -- its roots are really, *really* good at finding water, and will happily search out pools, septic tanks, and sprinkler systems.

March 30, 2016 at 02:57AM

Today I Learned: 1) Mangrove trees live in brackish water. They're one of the few species of trees that can. But mangrove trees use the same intracellular concentration of salt ions as other plants (or at least a concentration closer to other plants than to the water they live in). How do they deal with the excess salt they soak up? According to Mengsha Gong, mangrove trees deal with salt by selecting certain leaves to be salt sinks. They load up the leaf with tons of salt, then drop it. Kind of a waste of a leaf, IMHO, but I guess it's worth it! 2) Baobab trees are awesome. The most notable feature of a baobab tree is its giant, waterlogged trunk -- baobabs live in climates where it only rains about one month of the year, and in that month it rains torrentially. Baobabs take full advantage of this rainstorm by soaking up TONS of water in their giant, sponge-like trunks. The interior of a baobab tree, therefore, is basically sopping wet. Among other things, this is very attractive to elephants, who will mow down smaller baobabs and carve chunks out of older baobabs for the water. The second most notable feature of a baobab tree is its quickly-regenerating bark. Because elephants really like taking chunks out of the sides of baobabs, the trees have evolved to grow back quickly relative to other trees. They can also survive being ringed, so humans living in areas with baobabs will cut large swaths of bark off the tree to make clothing. This fact also courtesy of Mengsha Gong. 3) My feet are a half (US) shoe size smaller than I thought.

March 29, 2016 at 01:50AM

Today I Learned: 1) ...that there's no direct linkage between the brain and lymphatic system. EXCEPT THAT THERE IS! UVA researchers have just discovered previously unknown lymphatic vessels entwined in the membranes surrounding the brain. This is big news for understanding neurological disorders with possible immune components, like Alzheimer's Disease. Got this information here: http://ift.tt/1USeccq Thanks Sarah Seid for pointing me to this! 2) ...a bit more about Kalman filters. In brief, a Kalman filter is an algorithm you used to guess at the state of a changing system (example -- the temperature of a pot of water, or the position of a moving car) from a potentially noisy set of measurements (example -- a bunch of inaccurate thermometer readings, or noisy GPS locations). In particular, a Kalman filter is the *optimal* algorithm for finding the maximum-likelihood solution for a particular Bayesian inference problem roughly equivalent to a hidden markov model with continuous state values and Gaussian noise. I knew that Kalman filters were supposedly "optimal", but I didn't know what that meant, exactly. Until today! 3) Not really a Thing I Learned as a Number I Crunched, but I thought this was a kind of interesting number -- a typical table is, order of magnitude, several tens of billions of atoms across. That's WAY smaller than I would have naively predicted, but I guess that's because when I think of Numbers of Molecules in things, I'm usually thinking about volume, and volume is, in some sense, much bigger than length.

March 28, 2016 at 01:55AM

Today I Learned: 1) ...a bit more about loop-mediated isothermal amplification, or LAMP (don't ask me how it got that acronym). LAMP is a specific, complicated form of PCR, which means it uses a polymerase to quickly and massively amplify a DNA target. Exactly how LAMP works is a bit much for me to explain here -- if you feel you're equipped to nerd out over PCR methods, check out NEB's video primer* here: http://ift.tt/1UR04jt. The gist is this: LAMP is more complex than the usual method of PCR, requires more primers, and makes a variety of multimeric chains of the target sequence instead of clean individual copies, BUT it can be performed entirely at room temperature just by mixing the primers, polymerase, buffer, and target, and only takes 10-20 minutes to run. This makes LAMP potentially really awesome for diagnostic applications, where a) the targets are more or less fixed, so you don't have to re-design primers all the time; b) you need super-fast results; and c) you don't want to have to be able to use a thermal cycler to use the diagnostic. * I couldn't help myself 2) There is a nice little stall in Pike Place, Seattle, that sells homemade pastas with incredible flavors. They well a habañero pasta which they warn is quite spicy. Today I learned to take that warning seriously. It did not need to be put in a spicy dish to work. 3) ...how to use the printers in SFL. Apparently when you print to them from a computer, they're put in a queue until you physically go to a printer, log or swipe yourself in, and tell it to print the job. I didn't have to do this last time I was in SFL, so this must be a new thing....

March 27, 2016 at 02:24AM

Today I Learned: 1) Estivation and hibernation are not the same thing. Hibernation is slowing down metabolism to survive cold; estivation is slowing down metabolism to survive heat. Ants hibernate, not estivate. Thanks to Dorothy Fontaine for setting me straight on this one! 2) So you know how the US legally abolished slavery in the 1860s? Well, Britain beat us to it -- the Slavery Abolition Act of 1833 legally emancipated slaves under the age of 6, and reclassified slaves over the age of 6 as apprentices, who would be phased out of apprenticeships over the next seven years. Slave owners were compensated for their losses, to a staggering tune of about £20 million, which is roughly equivalent to £70 billion today, and was 40% of Britain's expenditures for that year! 3) The ancient Greeks (and, therefore, much of Europe for most of known European history) apparently believed that the uterus was a sort of "animal within an animal", capable of moving around the body, and that wombs wandering into the wrong places could cause a number of illnesses and disorders.

March 26, 2016 at 03:37AM

Today I Learned: 1) Apparently banana plants are really difficult to kill (unless, you know, you're a banana blight). The reason is that banana trees form rhizomes, which are bulbous little root balls that can grow back an entire tree if the rest of the plant is killed. In fact, when bananas are harvested from their trees, the trees die off and are re-grown next season somewhere else in the root system. Also, regarding bananas, there are "variegated" banana varieties, which are striped in different shades of green. And yes, the fruit is striped too: http://ift.tt/1PwqmzG Thanks to Mengsha Gong for today's banana facts! 2) Ants have a surprisingly large range of eyesight-ability. Some are essentialy blind, and can only distinguish between large differences in illumination. Other species have great visual acuity for a creature of their size, and can distinguish motion from a meter away (!). Most ants fall somewhere in the middle -- they can detect ambient light pretty well, can see at very close ranges just fine, but can't see much detail at range. More importantly for my purposes, apparently most ants can't see well in red, so you can illuminate an ant nest with red light without freaking out the ants. (this may actually just be because humans can see better in low-light conditions when that light is red, so you can see without using as much light. I'd have to find some actual ant research to tell) 3) Apparently insurance companies make razor-thin margins when it comes strictly to payments and payouts, and some even pay out more than they receive in premiums. Where they actually make their money is in *investment*, which they can do very efficiently because they've lumped together lots of peoples' money in one pot. Thanks to Asher Rubin on this one!