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

Xavier Periole X.Periole at rug.nl
Thu Mar 6 11:59:13 CET 2008

>>> 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.
That is fine! It is just wrong to use this value to get the total energy
of the system, because then they are doubled. The factor of two in there
only because the water molecules are actually identical.
In the case of the protein-solvent interaction I don't see how you can
say that the interaction is doubled! There is only one protein!

>>> 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? 
Then what is the physical basis of the partitioning of the energy?
I can understand that for parametrisation and transferability of the
parameters one often uses this type partitioning. More than that, I don't
> We are actually working on testing something like this 
>systematically, i.e. how does the energy of a protein/water system changes 
>with the number of water molecules, no results yet though.
Well, as you increase the system size you'll see the interaction
energy increasing (if the cutoff follows the increase) bu the actual
effect on the system should not change: at long distances the forces
cancel each other on a spherical basis.
I am missing something?

> -- 
> 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
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XAvier Periole - PhD

NMR & Molecular Dynamics Group
University of Groningen
The Netherlands

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