# [gmx-users] Total potential energy: 1/2 protein-solvent interactions??

David van der Spoel spoel at xray.bmc.uu.se
Thu Mar 6 09:42:09 CET 2008

```Xavier Periole wrote:
> On Wed, 05 Mar 2008 20:38:59 +0100 (MET)
>  pascal.baillod at epfl.ch wrote:
>>
>> Dear developers,
>>
>> I would like to know the exact definition of the total potential
>> energy with
>> respect to protein-solvent interactions, in an explicit solvent
>> protein simulation.
> The definition of protein-solvent interaction is the sum of the
> pair-wise interaction (non-bonded) involving on one side the protein
> atoms and on the other side the solvent atoms.
>
>>
>> For protein atom Pm and solvent atom Wn, there are two interactions:
>>
>> Pm to Wn
>> Wn to Pm
> Those two terms are identical! You can not separate them! Here you just
> express them in two different ways which are totally identical.
> It is like A+B=B+A, can you differentiate the sum of B on A and the
> sum of A on B?
>>
>> Are both interaction energies counted in the total potential energy
>> given in the log file or by g_energy?
> As they are the same they are both counted but only one time!
>>
>> If I want to compute the total potential enery of the protein, plus
>> protein-solvent interactions, should I then only add half of the
>> protein-solvent terms given by g_energy? I am only interested in the
>> effect of solvent "felt" by the protein, and not in the effect of the
>> protein felt by the solvent.
> Again, how would you differentiate those two terms? Counting
> the interactions from protein to solvent or solvent to protein is
> exactly the same.
>

Still, if you want to partition the energy over molecules you have to
make some kind of division. For instance, if you calculate the potential
energy for 216 water molecules you will find that is is roughly -9000
kJ/mol at room T, and hence you can derive the potential energy per
molecule to be -42 kJ/mol, which agrees with heat of vaporization. If
you however would do as you suggest, and take one water molecule and
compute all its intermolecular interactions you would end up with an
energy of -84 kJ/mol, because all terms are counted double! Therefore it
is entirely reasonable (though this is not a rigorous derivation!) to
partition the Protein-Solvent energy equal between protein and solvent,
in order to get an estimate of the Protein energy. As an extra
indication that this is reasonable, the linear interaction energy method
by Aqvist (Prot. Eng. 7 (1994) p. 385-391) derives that the contribution
to the Gibbs energy of solvation involves 0.5 times the protein-solvent
Coulomb interaction.

A proper derivation would probably involving computing the heat of
solvation for the protein, and compare that to potential energies that
come directly from the simulation, (and obviously to experimental data).

Cheers,
--
David van der Spoel, Ph.D.
Molec. Biophys. group, Dept. of Cell & Molec. Biol., Uppsala University.
Box 596, 75124 Uppsala, Sweden. Phone:	+46184714205. Fax: +4618511755.
spoel at xray.bmc.uu.se	spoel at gromacs.org   http://folding.bmc.uu.se

```