# [gmx-users] Entropy correction in PMF

Ángel Piñeiro fangel at usc.es
Mon Mar 31 00:19:27 CEST 2008

```Dear all,

My question is related to the calculation of absolute binding Gibbs energies
more than to the use of Gromacs but it is motivated by a paragraph of the
Gromacs manual version 3.3 (and also on several papers by Gilson, Karplus,
and others), so I hope someone can help me.

We have calculated the PMF curve along the distance between the center of
mass of a cyclodextrin (an oligosaccharide with a hydrophobic cavity
mimicking a pocket in a protein) and a surfactant of relatively short
aliphatic chain. Following the work of Gilson (several papers published
between 1997 and 2006 mainly in J Phys Chem B and Biophys. J.), we hope to
obtain a quantitative approach to the absolute binding Gibbs energy from the
integration of the Boltzmann factor for the pmf, but our problem is whether
or not we should perform before in this curve the so-called entropic
correction (also named by others volume correction term). The abovementioned
paragraph is in the page 111 (the first page of chapter 6):

“When a distance between two atoms or the centers of mass of two groups is
constrained or restrained, there will be a purely entropic contribution to
the pmf due to the rotation of the two groups. For a system of two
non-interacting masses the potential of mean force is:

Vpmf (r) = (nc-1)kBT log(r)           (6.1)

where nc is the number of dimensions in which the constraint works (i.e. nc
= 3 for a normal constraint and nc = 1 when only the z-direction is
constrained).”

I think that I understand the meaning and source of that term but the
paragraph follows:

“Whether one needs to correct for this contribution depends on what the pmf
should represent. When one wants to pull a substrate into a protein, this
entropic term indeed contributes to the work to get the substrate into the
protein. But when calculating a pmf between two solutes in a solvent, for
the purpose of simulating without solvent, the entropic contribution should
be removed. Note that this term can be significant; when at 300K the
distance is halved the contribution is 3.5 kJ mol-1.”

I assume that our case is very similar to a substrate-protein complex and
then we should not correct the pmf, but I do not understand exactly why not.

Angel Piñeiro.

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