[gmx-users] alternative means of calculating PMF

[chris.neale at utoronto.ca]

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]

2. Define your unbound energy (E_ub) from your PMF and Boltzmann  
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.
I read something in the users'list about instead of using umbrella sampling
I would use constraints in order to separate my system's components. But I
was not able to find anything more specific about this type of calculation
on the manual.
Some help on the matter would be of great help
Thank you