# [gmx-users] alternative means of calculating PMF

chris.neale at utoronto.ca chris.neale at utoronto.ca
Wed Oct 21 19:47:37 CEST 2009

```Hi Stefan,

If you know the bound state, you can use the double decoupling method
to decouple the bound state and then recouple into bulk solvent.

Note that both decoupling and umbrella sampling methods will require
that you make the appropriate corrections to standard state values and
that this correction may be what you are missing with your umbrella
sampling results.

I outline the way to get US standard state free energies, and this is
a very quick description so please refer to peer reviewed papers for
something that is more complete.

1. Boltzmann integrate your PMF (E_i values) over the bound state.

G_bound=-1/Bln*sum over i [exp(-BE_i)*delta_i]

integrate it over a distance, dist, such that the volume per monomer
will be 1.66 nm^3 (volume per molecule at 1 M concentration).

G_unbound=-1/Bln[exp(-BE_ub)*dist]

3. dG_binding = G_bound - G_unbound

Where I have here neglected any corrections for constraints (i.e. I
assumed that you reaction coordinate is a Center of Mass relation or
something similar).

Also, note that the form of equation 2 assumes that you have already
extracted the increasing volume portion of your PMF if you simply use
the distance between centers of mass. Therefore if you have not done
this then your equation 2 will be of a form like equation 1, except
that you integrate over an unbound region for a total of 1.66 nm^3.

Finally, make sure that you take both monomers into account in your
final calculations correctly so that your final concentration of
unbound monomer is really 1 M, not 0.5 M or 2 M.

And if your monomers are so big that the bound state occupies a volume
greater than 2*1.66 nm^3 just set your standard state to 0.1 M or
something and then make a final correction back to 1 M later.

Good luck,
Chris.

--- original message ---

Hello.
I have finished calculating the PMF of dimerization for my system using
umbrella sampling and WHAM. But came up with some free energy values that
are not compatible to the ones found in other works. I have alread had
several instrutions and tips from Justin in past email here in gms users'
list, and since now I believe there are no more variables to change in my
calculations, I believe another method (implemented in gromacs) would help
me compare results and justify my findings.