Equlibration in Molecular Dynamics

An explanation by Dan Ensign
A lot of molecular dynamics simulations -- in fact, many of them using explicit solvent models, and at least some that use implicit solvent -- have an initial "equilibration" step. This step can allow water molecules to find more natural positions with respect to one another, and to solutes like protein molecules, than might have been provided by the GROMACS software.

The issue is roughly as follows. The oxygen atom of a water molecule has a slight negative charge, and the hydrogen atoms have slight positive charges (water is neutral, so it must be that q[O] + 2*q[H] = 0, of course). This means that the oxygen end of a water molecule likes to hang out near the hydrogen atoms of other water molecules, or other stuff with positive charges, like arginine or lysine residues in a protein, or the hydrogen atom of an alcohol molecule. Conversely, the hydrogen atoms of water like to get jiggy with negatively charged stuff, like the oxygens on other waters, glutamate and aspartate residues in a protein, and so on.

Not everyone gets what they want, however: because there is thermal energy (means, stuff is moving around a lot), sometimes oxygen atoms don't get to be near positive charges. So, say that typically a water oxygen is near a positive charge 90 % of the time (we statistical mechanics nerds would say, "Water oxygen is near a positive charge 90 % of the time at equilibrium). The equilibration step will allow this "normal" water behavior to come about in the system before the protein folding starts. After the equilibration step is accomplished, we then allow the protein to start moving around.

But water is small (we statistical mechanics nerds would say, "It's itty bitty") and it moves around really fast. Then, it probably doesn't take a more than 100 picoseconds (a picosecond is ten-to-the-minus-twelve seconds; a typical game show lasts 1.26e15 picoseconds) for the water to come to equilibrium. And here's the rub: if we have a FAH project which simulates 5 nanoseconds (5,000 picoseconds), and the GENeration 0 WUs are meant for the equilibration step, then we equilibrate 50 times longer than we have to.

One solution would be to run equilibration on a local cluster, but that gets unreasonable for projects of the kind that I'm doing now; if a two-day WU simulates 5 ns, and I need to equilibrate 32,000 WUs for 100 ps each, then that's (1 day/2500 ps) * 100 ps * 32,000 WUs = 1,280 days just to get the project started. That's 3.5 years, and with all my debauchery, underhanded goofingaroundness, and general partying, I might not even be alive let alone sane enough to put that 3.5-year, equilibrated project step onto FAH. I'd be lucky to remember where I work.

So if I want to equilibrate a project of the scale of p2106 or p2107, I have no choice but to use the FAH machines directly! This gets me past the equilibration step in about a week, depending of course on how fast people typically return data. (By the way, p2106 and 2107 don't contain an equilibration step since there are no water molecules, but I mention them because they each consist of 32,000 independent trajectories. That's beeeg.)

Another solution would be to allow different-length WUs, so that the equilibration, GEN0 WUs, would be shorter by some amount than subsequent GENerations. But there are two considerations, here: 1. We want WUs to take a couple of days; doing 100 ps / 5,000 ps * 100 % = 2 % of a WU for equilibration is a waste of the FAH resource; it's much more efficient to use your computer for a couple of days before talking to the Stanford servers. 2. If WUs from the project are worth 220 points, then you'd get 229 PPH for the equilibration WU. Like candy! Maybe they'd just be a nice treat, but it would probably turn out that some lucky b*****d would get a bunch of these, report on the forum, "Nyah, nyah, I just broke 1,000,000,003 points so I'm the best." Then a mob would assemble and tear that poor person to pieces.

So, in the interest of public safety, equilibration runs have to be 50 times too long!

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