Natural Axles, Dissociation Constants, and Occam's Razor, Bayes Style

Today I Learned:
1) It's a well-known quirk of natural design that nature doesn't feature a lot of wheels. Animals and plants and other creatures have implemented virtually every kind of simple machine you can think of, and probably some you can't. Wheels, however, or in fact any kind of freely-rotatly axle, are incredibly rare.

There are two known molecular-scale examples of freely-rotating axles in nature, and both are relatively ubiquitous. The first is ATP synthase, which is a protein that sits in the membranes of bacteria, archaea, and mitochondria. They're essentially molecular-scale water-sheels. Hydrogen traveling down a gradient across the membrane forces the protein to spin, the motion of which is used to forcibly jam phosphates onto ADT, turning it into ATP, which is used to power processes throughout the cell (ATP synthase can sometimes also be run in reverse -- ATP spins the motor backward, forcing hydrogen back out of the cell).

The other molecular axle is the flagellar motor, which is thought to be derived from ATP synthase but acts to spin a flagella, which works like a propeller to (typically) move a cell.

Today I learned that there's also a macro-scale example of a freely-rotating axle in animals, and that is the crystalline style of certain mollusks. The crystalline style is essentially a buffer of digestive enzymes in crystal form kept in the midgut. The mollusk spins the style against its abrasive stomach lining, wrapping it in mucus and dissolving or abrading off the digestive enzymes. Go mollusks!

2) A dissociation constant is just an equillibrium constant for the special case where you have chemicals that do something like A + B <=> C like breakdown/synthesis or binding and unbinding (as it's commonly encountered in biology)

3) ...how Bayes Theorem leads naturally to Occam's Razor, at least in some cases. I'm not going to go into the full details here (though I can if there's interest), but the basic idea is that if you compare the probability of two hypotheses, each hypotheses' likelihood term gets multiplied by one over a normalization term that's related to the plausible range of each parameter involved, and that term is multiplicative in parameters, so that a hypothesis with more parameters ends up with a larger normalization constant.