[gmx-users] Is the PMF from "gmx wham" a free energy curve?

Alexander Björling alex.bjorling at gmail.com
Tue Jan 6 23:00:08 CET 2015

2015-01-06 0:13 GMT+01:00 Justin Lemkul <jalemkul at vt.edu>:

> On 1/5/15 8:52 AM, Alexander Björling wrote:
>> Dear users,
>> I have a question about how to interpret (rather than about how to
>> perform)
>> a GROMACS calculation.
>> I have calculated the Potential of Mean Force for separating two protein
>> chains, in order to estimate the free energy of monomerization for this
>> dimer, loosely following Justin Lemkul's tutorial. I have arrived at a PMF
>> which seems reasonable and robust according to the error estimates of "gmx
>> wham". The reaction coordinate is the distance in the Z-direction only,
>> nothing is position restrained, and there is good overlap between the 2 ns
>> windows.
>> My question: is the resulting PMF a correct estimate of the free energy of
>> monomerization, or are there missing entropic terms due to the
>> translational confinement?
>> Google turns up a JACS paper (dx.doi.org/10.1021/ja2060066), claiming
>> that
>> the missing entropy is as large as 15-30 kcal/mol, which seems very high
>> to
>> me:
>> "The PMF is expected to decrease after the monomers are completely
>> dissociated because of the gain in translational and rotational entropy.
>> According to previous reports, this entropy gain is anticipated to be on
>> the order of 50-100 cal/(mol K). Thus at 300 K the PMF is expected to
>> decrease 15-30 kcal/mol upon dissociation."
>> Is this true?
> Certainly plausible.  The output of gmx wham is indeed a free energy
> profile per the WHAM algorithm that is used ubiquitously.  Does it
> necessarily tell the whole story?  Not necessarily; but the entropy term is
> almost certainly system size-dependent.  I haven't read the JACS article,
> but dissociation of a protein dimer probably has a large entropy term.  For
> smaller peptides or protein-ligand complexes, the effect is likely far
> smaller.
> -Justin
Thanks, Justin, for your reply,

Although a science question and not a GROMACS issue, I think this deserves
attention as it is important for how umbrella sampling + gmx wham can
actually answer chemical questions. I know there are plenty of experts

Now, if there are missing free energy contributions because of confinement
to the umbrella potentials, couldn't we just correct the endpoints of the
PMF? In this case, protein dimerization, would it not be a good idea to
calculate (with a lambda approach) the free energy cost of applying the
umbrella potential in absolute coordinates to a free monomer (perhaps
significant) and also that of releasing the umbrella potential in relative
coordinates from a bound half-dimer (probably low), and including these


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