[gmx-users] Deviations in free energies with slow growth (single and 3-step process)

[Maik Goette]

David

Thanks for your answer.
I'm aware of that problem, but the idea was, that such a small system is 
very close to equilibrium on a 10ns timescale (maybe to optimistic).
Actually, the thought behind it was to compare the results of the 
different free energy calculation methods. Now, if I assume slow growth 
has a systematic error of X because of non-equilibrium, I expect this 
error to occur more or less in the 1_step and in the 3_step calculation.
However, I didn't mention, but I also did non-equilibrium tests (e.g. 
BAR) with this system and the deviation is exactly the same; means:
BAR gives a difference of 7 kJ/mol for the ethane to methanol in 1_step 
hardcore and 3_step hc/sc/hc for the first and third being coulomb and 
the second being Lennard Jones.
This actually puzzles me a bit, cause in the case of some tripeptide 
sidechain morphing (SER to ALA), the results of 1_step and 3_step 
perfectly match. I don't have to tell you, that the cycle together with 
the sim in gas phase gives a difference in free energy of solvation 
which is somewhat 15 kJ/mol away from the experiment, though. ;)

For me the question arises, how to publish such "shitty" results.
Do you think, 7 kJ/mol lies within the usual error of free energy 
calculations? If, one could never resolve reliably smaller free energy 
differences and the whole method won't be applicable for say drug 
screening or so.

Regards

Maik Goette, Dipl. Biol.
Max Planck Institute for Biophysical Chemistry
Theoretical & computational biophysics department
Am Fassberg 11
37077 Goettingen
Germany
Tel.  : ++49 551 201 2310
Fax   : ++49 551 201 2302
Email : mgoette[at]mpi-bpc.mpg.de
         mgoette2[at]gwdg.de
WWW   : http://www.mpibpc.gwdg.de/groups/grubmueller/


David Mobley wrote:
> Maik,
> 
>> I simulated a switching process (slow growth TI) over 10ns of ethane to
>> methanol with hardcore slow-growth in water (365 TIP4P waters,PME) and
>> in vacuum. The thermodynamic cycle of this calculation yields a DeltaG,
>> which is in perfect agreement with the experiment and other calculations.
> 
> Slow growth is notoriously problematic, because it only gives the true
> free energy in the limit that you do it infinitely slowly. Otherwise
> you're really measuring nonequilibrium work values, which are
> connected to free energies but only in an average way (see the
> Jarzynski relationship for a more recent discussion of this).
> 
> This could be a classic example of "just because a method gives
> perfect agreement with experiment, you can't be sure it's giving the
> correct value for the force field." In other words, since force fields
> have their own limitations, we can't necessarily expect that when we
> do things right, we'll get optimal agreement with experiment. In some
> cases one may get better agreement with experiment by doing things
> *wrong* than by doing them right. i.e., suppose the correct value for
> the force field is actually off by 2 kJ/mol from the experimental
> value. If you make a protocol mistake, there's roughly a 50% chance
> (assuming the errors are randomly distributed!) that it will give you
> a value that's closer to the experimental value than your original
> value was.
> 
>> Now, when splitting this simulation into 3 steps (3x 3.2ns), where I
>> switch the charges to zero in the first step (hardcore), morph the LJ
>> and bonded in the second (softcore or hardcore) and switch the charges
>> back on from zero in the third step (hardcore), all in solvent, the sum
>> of the single contributions does NOT yield the same number as the
>> "single-step switching".
>> In vacuum, the work values I get from the single step process and from
>> adding up the values from the 3-step process perfectly match.
>>
>> The topologies for all systems are the same (except +/- water) for the
>> 1-step and the 3-step simulations.
>>
>> Now I'm a bit puzzled and can't get an idea, where this difference in
>> the solvated system may come from. I exclude a problem due to softcore,
>> cause I also simulated the 3-step process all hardcore...
>>
>> Any ideas?
> 
> I'm betting your problems are largely due to the fact you're doing
> slow growth. Again, see the Jarzynski relationship; I especially
> recommend his Phys. Rev. E. paper on convergence (2001?). It's also
> worth noting that slow growth transformations in different directions
> have different convergence properties, and with slow growth
> (interestingly enough) particle insertion actually converges more
> quickly than particle deletion. So you could try reversing the
> direction of the transformations and see what happens. But again, slow
> growth isn't recommended these days -- you should probably make sure
> you have a very good reason for doing it and are aware of the
> limitations.
> 
> Best,
> David
> 
> 
>> Regards
>>
>> --
>> Maik Goette, Dipl. Biol.
>> Max Planck Institute for Biophysical Chemistry
>> Theoretical & computational biophysics department
>> Am Fassberg 11
>> 37077 Goettingen
>> Germany
>> Tel.  : ++49 551 201 2310
>> Fax   : ++49 551 201 2302
>> Email : mgoette[at]mpi-bpc.mpg.de
>>          mgoette2[at]gwdg.de
>> WWW   : http://www.mpibpc.gwdg.de/groups/grubmueller/
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