[gmx-users] Long range interaction energy of charged particles with PME - GMX 3.3.1

[Ran Friedman]

Dear David, GMX users,

David Mobley wrote:

> Ran,
>
>> I previously asked how to calculate the long range interactions between
>> charged particles simulated with PME:
>> http://www.gromacs.org/pipermail/gmx-users/2004-October/012627.html
>>
>> I repeat the question here. If I want to calculate the LR Coulomb
>> interaction energy between say a protein and a ligand the normal
>> procedure would involve several mdrun -rerun runs: (1) with atoms
>> charged (2) with the charges on the protein neutralised (3) with the
>> charges on the ligand neutralised (4) with the charges on the solvent
>> neutralised. When the protein is charged, there will be a net charge in
>> the simulation shell in case (2). This net charged is corrected in PME
>> as implemented in GMX. In GMX 3.2.1, I could not account for the
>> correction, so the calculation wouldn't be exact (see the message
>> above). What's the situation in GMX 3.3.1?
>
>
> Systems with net charge are run with a uniform neutralizing background
> charge sincce they need to be neutral for PME. I don't have any idea
> how to properly account for this, although I would like to. This isn't
> just an issue for calculating interaction energies between, say, two
> molecules -- one also has to deal with similar issues if one wants to
> compute, say, the free energy of inserting or removing an ion.
>
> The problem, as I see it, is that I can't figure out any way to
> calculate the contribution to the energy (or free energy) of turning
> on the neutralizing background charge, which one would need to
> subtract off to get this right.
>
> I guess what makes this tricky is that you are really talking about
> the same problem I would have if I want to get an ion hydration free
> energy: You want to be able to evaluate the long range electrostatic
> interactions in a system that has net charge (a protein+ligand, where
> the protein+ligand isn't neutral; it's only neutral when you add the
> ions), so you really need to be able to do this with the neutralizing
> background charge (which will let you do the sum) and then somehow
> subtract off the energy of turning on the neutralizing background
> charge, which you can't compute directly since your sum won't converge
> if you turn it off.

Right.

>
> Maybe there is some way to get this out of the right combination of
> mdrun -rerun options. Can you be a bit more explicit about how you are
> thinking you would get this if you did (1) through (4)? And what do
> you mean by saying that this is the "normal procedure"? (Do you have a
> reference on it?)

I was not accurate. E(LR) is the total PME energy, and the rest can be 
extracted by neutralising selected groups. So the binding energy can 
calculated from: E(LR)-E(sol-sol)- E(ligand-ligand)- 
E(protein-protein)-E(solvent-ligand)-E(solvent-protein), where e.g. 
E(sol-sol) can be calculated when the protein and the ligand are both 
made uncharged. This still leaves us with the PME correction.

I think that deltaG calculations with charged particles and periodic 
systems are much more difficult than the interaction energy, and I do 
not deal with them.

Ran.

>
> Please continue the discussion. I'm happy to help in any way I can,
> but I just need to understand what you're thinking a bit better, and
> I'm also not sure anyone knows how to do this yet (at least, I'm not
> aware of anything that explains this).
>
> One reference that seems useful that I don't completely understand yet
> is this one:
>
> Kastenholz, M. & Hunenberger, P.H.
> Computation of methodology-independent ionic solvation free energies from
> molecular simulations: II. The hydration free energy of the sodium 
> cation.
> J. Chem. Phys., 124, 224501 (2006).
>
> David Mobley
> UCSF
>
>
>>
>> Thanks,
>> Ran.
>>
>> -- 
>> ------------------------------------------------------
>> Ran Friedman
>> http://bioinfo.tau.ac.il/~ran
>> Laser Laboratory for Fast Reactions in Biology
>> Department of Biochemistry
>> Faculty of Life Sciences
>> Tel-Aviv University
>> Tel. +972-3-6409824
>> Fax. +972-3-6409875
>> ------------------------------------------------------
>>
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-- 
------------------------------------------------------
Ran Friedman
http://bioinfo.tau.ac.il/~ran
Laser Laboratory for Fast Reactions in Biology
Department of Biochemistry
Faculty of Life Sciences
Tel-Aviv University
Tel. +972-3-6409824
Fax. +972-3-6409875
------------------------------------------------------