Water radial distribution function within protein, and potential of mean force calculations

So after I produced MD simulations with a water within a protein, I needed both a quantification of whether the water stayed put, and if so how much time did it spend coordinated to important inner atoms.

The latter is easiest expressed as a Radial Distribution Function (RDF). This function is the radial distance between 2 particles. Although simple, this metric is connected to deep statistical mechanical properties of the system. One property that I was interested in is the free energy of binding of the water. This is the energy is that which is required to pull the bound particle into the bulk surroundings and is named the Potential of Mean Force (PMF).

One can see how the energy binding a particle in place would be correlated with how much time it spends near the thing it is bound to. And  in fact, the PMF free energy is calculateable from the RDF.

-RT ln (RDF) = PMF

Where R is the gas constant, and T is temp. The difference between the high and low point of this curves is the binding energy.

So, I exported the RDF for water about an interior atom the water was observed to locate near.  The output file was readable in the Linux plotting program, but I wanted to work the data more easily, so I had to write a little python script to extract the data, and turn it into a .csv form. This ended up with millions of data points, and both excel and the Linux excel replacement crashed when I tried to open it. I had to turn to R, which easily dispensed with the processing, and figure creation.

Pow.

A: The bound water, coordinated to flavin and two amino acids.

B: density (any oxygen in water, to be exact) VS distance (aka the Radial Distribution). For the wild type and an interesting mutant.

C: PMF versus distance. The difference between high and low is the binding energy. Also for the wild type and the interesting mutant.