Primate Noses, Genomic Classification, and Entropy-Driven Crystals

Today I Learned:
1) Order primate is commonly divided into “wet-nosed” primates and “dry-nosed” primates. Seriously?

2) A really strange way of classifying species by genomic structure, which seems to work better than it sounds like it should. Here’s what you do:

a) Start with a square labeled A, T, C, and G at the corners, and put a point at the center.
b) Start with the first nucleotide of some species’ genome. Move the point halfway from its current position to the corner of the square labeled with the first nucleotide. Repeat this for every nucleotide, giving you a heckabuncha points scattered on the square. This is called a “Chaos Game Representation” (CGR).
c) Use a measure of image dissimilarity (for instance, structural dissimilarity index, or DSSIM) to produce a matrix of distances between CGR representations of genomes (that is, a big matrix where the number on the i-th row and the j-th column is the distance between the i-th and j-th genome.
d) Plot the genomes using the dissimilarity matrix to determine how far apart each pair of dots are. Multi-dimensional scaling (MDS) is a good tool to do this.

If you do this on the mitochondrial genomes of creatures from a huge array of eukaryotes, it very nicely recapitulates much of known taxonomy. In fact, it is *better* than euclidean or manhattan distances at successfully classifying snippets of genomes into the correct species. This is quite surprising to me. More information at http://ift.tt/1UU4jsg (free article).

3) Entropy alone can drive crystallization! Imagine this experiment — you take a bunch of identical rigid polyhedra, say tetrahedrons (d4’s). Put them in a box. Shake the box. Continuing to shake the box, start adding more of your shape in until you are filling slightly more than 50% of the box (by total volume). Do you see it? Are your shapes making a crystal? Because that’s what happens, at least for a lot of shapes.

The key awesome thing about this is that you can get crystal structures even from bodies that have no interactions other than bouncing off of each other like billiard balls. There’s no electrostatic charges, no binding, no latching into place — just jiggling of solid polyhedra, which are driven *by entropy* to form ordered, structured, repeating (or non-repeating, depending on the shape) crystals. This is very much the opposite of how I usually think of entropy working — usually you think of high entropy as being more *disordered*, but in some cases, it’s more entropically favorable to have ordered structures that give the individual components more room to wiggle (thus increasing the total number of states they can occupy).

For more information, see http://ift.tt/1NwaKiQ. I think the “The Polyhedral Zoo” is probably a good one, but you’ll need Science access to read it (which I don’t currently have, thus the “I think”).