[gmx-developers] more on electrostatic decoupling

[Michel Cuendet]

Dear all,

Regarding the topic of hydration free energies in periodic systems vs. 
isolated, or lattice methods vs. cutoffs, a couple of papers just came 
out, which provide a very thorough study of the problem. Some of 
Michael's questions quoted below will certainly find an answer there.

Kastenholz, M.A. & Hunenberger, P.H.
Computation of methodology-independent ionic solvation free energies from
molecular simulations: I. The electrostatic potential in molecular liquids
J. Chem. Phys., 124, 124106 (2006) + Suppl mat

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).

In addition, Philippe Huneberger is really an electrostatics guru and also a very nice guy, so he would certainly be glad to answer more specific questions if needed...

Cheers,
Michel

Quoting Michael Shirts <mrshirts at gmail.com <http://www.gromacs.org/mailman/listinfo/gmx-developers>>:

>I thought I'd summarize a little more of what I see the issues are for
>some of the people who have not been in on the conversations offline.
>What we would LIKE to do calculate is the free energy of transferring
>an isolated assembly of partial charges called a "solute" into an
>infinite bath of classical water particles.  What we end up
>calculating with PME involves an infinite periodic lattices of both
>types of particles.
>
>"Charge annihilation"  corresponds to one end state being the periodic solute
>in periodic water, and the other end state being an uncharged periodic
>solute + periodic water (no solute-water interactions).  The free
>energy of uncharged periodic solute -> uncharged isolated solute is
>zero, as it takes no work to separate uncharged particles (neglecting
>vdW greater than the box length).  Assuming we can calculate the
>charging free energy of the molecule in isolation (not necessarily
>simple if it is flexible, might require a vacuum simulation that will
>be hard to with MD because of ergodicity issues with small systems,
>and if charged there are problems with the changing "charge jelly"
>used to yield cell neutrality) we then have one end state being the
>periodic solute in periodic water, and the other end state being
>isolated solute + periodic water.
>
>For "charge decoupling", the end states are the periodic solute in periodic
>water, and the other end state is periodic solute + periodic solvent
>(no interactions).   It seems it wouldn't be that difficult to compute
>the periodic solute -> isolated solute, but there may be complications
>(periodic space is not rotationally symmetrical, if they are not
>rigid, there is some polarization, etc). Certainly, if we are
>interested in ligand binding, with the same size systems in ligand
>binding for the complex and solvent decoupling simulations, this
>periodic -> isolated term is going to identically cancel.  Otherwise
>(only one simulation leg, different size boxes), things get more
>difficult . . .
>
>I think the general consensus in the field is that periodic PME pure
>water is the best approximation to bulk water that we can get right
>now with small simulations, and with a decent size system (even as
>small as 1 nm or so, but certainly at 2-3 nm), any difference is
>pretty small.
>
>But one thing that is unclear to me is the free energy to go from periodic
>solute in periodic water to isolated solute in infinite water.  My
>point (though I probably got my facts wrong) is that we don't really
>understand this transformation.  The proposition put forward seems to
>be (total dipole per box -> 0), therefore the free energy is zero.  But I don't
>know that we have really articulated well what this actually does
>consist.  It's even a little clear what process this transformation
>corresponds to.  Is it -inserting- other water molecules, increasing
>the box size further, until the periodic copies of the solute have no
>interaction?  The free energy of that process is nonobvious to me. 
>But somebody must have studied this at some point -- box size
>dependence of HF free energy solvation, perhaps?  Though you would
>need to do both the "decoupling" and "annihilation" approaches here,
>of course . . . although the same-cell HF Coulombic interaction is
>assumed to be zero in molecular mechanics models, the intercellular HF
>interaction changes depending on the treatment.
>
>Just brainstorming here, it seems like it would be possible to write a
>version of PME where the "mutated" version of the ligand NEVER (at
>either endpoint) has interactions with its self copies in other cells
>-- we just need to subtract out this term at all points.  It may
>require an extra Ewald calculation, but since it will involve a small
>number of atoms, it might not be a huge overhead.
>
>What would this imply . . . that we would have is one single solute
>floating in a sea of periodic water with an infinite series of small
>cavities.  But the solvent would be slightly polarized around these
>cavities, especially with a charged solute. . . . hmm.  This has
>complications as well. There might to be an endpoint polarization
>problem at the -coupled- end this time.  :)
>
-- 
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Michel Cuendet, Ph.D. student
Laboratory of Computational Biochemistry and Chemistry
Swiss Federal Institute of Technology in Lausanne (EPFL)
CH-1015 Lausanne						
Switzerland                            Phone : +41 44 633 4194
lcbcpc21.epfl.ch/Group_members/michel                        
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