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!