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

David van der Spoel spoel at xray.bmc.uu.se
Thu Mar 6 10:57:37 CET 2008

```Xavier Periole wrote:
> On Thu, 06 Mar 2008 09:42:09 +0100
>  David van der Spoel <spoel at xray.bmc.uu.se> wrote:
>> 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.
> Agreed.
>> 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!
> There no terms counted 2 times in this calculation!? They become doubled if
> you use this number x 216 H2O to obtain the total potential energy. The
> average interaction energy of one molecule with 215 others is still -84
> kJ/mol!
> Isn't it?

There are no terms calculated double in the MD simulation. But the
average interaction energy is indeed -84 kJ/mol.

>> 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.
> I totally miss the concept of partitioning the interaction energy between
> two parts into each one!

Hm, what can I say? We are actually working on testing something like
this systematically, i.e. how does the energy of a protein/water system