Xavier Periole wrote:
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!
Look at it this way: the total energy is a double sum over all
particles. For efficiency one only computes half the matrix, i.e.
E = sum_{i=1}^N sum_{j=i+1}^N E_{ij}
however one can also compute it like this:
E = 1/2 sum_{i=1}^N sum_{j=1}^N E_{ij}
Now if you define
E_i = 1/2 sum_{j=1}^N E_{ij}
then you still have
E = sum_{i=1}^N E_i
So that's fine isn't it?
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
know.
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?
I think the interaction energy will level off, even without cutoff (i.e.
PME). More later when we've done the work.
XAvier
--
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.
[EMAIL PROTECTED] [EMAIL PROTECTED] http://folding.bmc.uu.se
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-----------------------------------------------------
XAvier Periole - PhD
NMR & Molecular Dynamics Group
University of Groningen
The Netherlands
http://md.chem.rug.nl/~periole
-----------------------------------------------------
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--
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.
[EMAIL PROTECTED] [EMAIL PROTECTED] http://folding.bmc.uu.se
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