Heating Water in Molecular Dynamics

At parties, when people ask me what I, I tell them I simulate protein molecules. So what do I mean by that?

Simulating a very small peptide in water

Probably the simplest type of protein simulation you can do, is to simulate met-enkephalin. This is because:

  1. it is a peptide, or a very small protein; it is made up of amino acids, which most simulation packages handle
  2. it is small - only 6 amino acids, it's chemical name is H2N-Tyr-Gly-Gly-Phe-Met; the typical protein is ~300 amino acids
  3. it is important - these babies are neuro peptides; they are released by the brain to stimulate opiod receptors in the rest of your body, say, when you accidentally shoot a nail into your forearm.

It is now de riguer to simulate peptides in a box of water molecules because inside the biological cell, there's lots of water. And during th simulation, periodic boundary condition apply: a water at the edge of the box will feel the effects of a water from the other side of the box. Otherwise the water molecules will just float off into space.

In the beginning of the simulation, the water molecules are arranged in some kind of auto-generated starting position. There will be gaps near the molecule. You will see these gaps fill up.

This following is a movie of a molecular dynamics simulation of met-enkephalin.

  • grey molecule is the met-enkephalin
  • red balls are the water molecules
  • the movie shows a cross section of the box of water
  • runs for 100 ps, or 0.0000001 of normal second
  • where the water molecules are moving around at a temperature of 300K

Molecular dynamics use Newtown's equations to integrate the equations of motion, and pretends that quantum mechanics doesn't exist so chemical bonds never break. A key ingredient in such a simulation is to choose the smallest step to take, also known as the integration step size. The integration step of molecular dynamics depends on the smallest kinds of motions allowed using this level of approximation. It depends on a bond vibration. Typically, the step size for the integrating step of the equations is 1 fs (10-12s), or about 1/10th the time it takes for a bond to vibrate.

The previous movie showed the water molecules as single red balls denoting the position of the oxygen atom of the water molecules. As such, you won't be able to see the hydrogen atoms and the fluctuations of the hydrogen-bonding network. When heating from static structures at absolute zero to 300K (in steps of 50K chunks), you can see how the water molecules move:

The result is rather hypnotic as the water goes from a wobbly jelly to an swarm of angry molecules. However, these waters are rather unphysical since below ~250K, the water really should be frozen in any number of crystal states. I'll leave this for the force-field mavens to explain.

Heating a Larger protein: formation of water shells

When you scale up to larger proteins, subtle water effects appear. As an example, I was working on simulations of histones - the proteins that are used as scaffolds for DNA inside the nucles, and I found that heating the water up to 300K had to be done really carefully.

Now, all the tutorials recommend that you first apply positional constraints on the static structure during the heating. This is because the water effects could ruin the starting conformation of your protein. Well, I have indeed found this to be the case. When I don't restrain the protein, the histone distorts severely due to water effects during the heating. I don't want this.

So now I heat the water using positional constraints. And you can see exactly why this is necessary. Here's a movie of a cross-section of my histone in a 100 ps equilibration at 300K where all the heavy atoms of the DNA and protein have been fixed:

What you see is that initially regular density of the water molecules around the protein changing quickly to regions of low density water. You are seeing the water around the protein geting expelled, i.e. the effective formation of the transient water shells around the protein. It's awfully difficult to characterize these water shells analytically and quantitatively, but surprisingly, it's quite easy to eyeball it.