# Re: FEP: How check equilibration sufficiency? calculate dG?

From: Sebastian Stolzenberg (s.stolzenberg_at_gmail.com)
Date: Tue Oct 14 2008 - 11:44:51 CDT

Thank you Floris, Chris, and Jerome,

1.)
I followed Chris' suggestion and got:
delta_G=-kT*ln(1-<\delta H >_ref)
Is this the dG cum. average shown in the last column of the fep output file?
If yes, then I still don't understand how one can get delta_G, since the
<.>_ref term still contains unaccessible exp(-H) terms.

2.)
The way I understand how FEP works is that it runs two different systems
corresponding to lamda1 and lambda2 at the same time, collecting energy
values after the equilibration phase to obtain a cum. average of dG. I
have to make sure that both systems are well-equilibrated, and not just
"difference" observable between them.

I would love using dG (cum. aver.), but is it really a good measure for
convergence? Assume a system got stuck into a local minimum and only at
the very end of the equilibration phase, it leaves that local minimum.
This will not show up in a cum. average quantity. Are mere energy values
any better to check for convergence? (I doubt because these numbers are
soo large).

Thank you for your help again,
Sebastian

Chris Chipot wrote:
> Sebastian,
>
>
> one simply never calculates absolute free energies, which would
> the system -- this is never the case in practice. Instead, one
> defines a reference system and expresses the Hamiltonian of the
> target system as the sum of the reference Hamiltonian and some
> perturbation term. The free energy difference between the two
> systems can then be expressed as an ensemble average over the
> reference system. The latter average can be further expanded in
> a series, the first two terms of which are fairly easy to
> interpret -- the internal energy and a fluctuation term. Note
> that in a number of instances, this second-order interpretation
> is enough to understand the physics of the problem. The confusion
> between the vocabularies absolute and relative free energies comes
> from inappropriate usage of the former when measuring for instance
> binding constants or hydration free energies. Even if, in the first
> example, one deals with a single ligand bound to a protein, one
> still measures a relative quantity -- the difference between a
> bound state and a free state.
>
>
> Chris Chipot
>
>
> Floris Buelens a écrit :
>> Hi Sebastian,
>>
>> It's not feasible to compute the absolute value of G for a system of
>> any relevant size - you can only realistically sample over small
>> differences dG on the order of kT. To check convergence you're best
>> off monitoring the cumulative dG average which is calculated as your
>> simulation progresses (the last column in the FEP output file).
>>
>> Best regards,
>>
>> Floris
>>
>>
>> ----- Original Message ----
>> From: Sebastian Stolzenberg <s.stolzenberg_at_gmail.com>
>> To: Jerome Henin <jhenin_at_cmm.chem.upenn.edu>
>> Cc: namd-l_at_ks.uiuc.edu
>> Sent: Tuesday, 14 October, 2008 5:50:43
>> Subject: namd-l: FEP: How check equilibration sufficiency? calculate dG?
>>
>> Dear Jerome,
>>
>> I would like to to check, if for a step lambda1->lamba2, the FEP
>> equilibration time was sufficiently long.
>> One criterion I was thinking of was checking convergence of G_1 and
>> G_2 (corresponding to lambda1 and lambda2 respectively)- are these
>> quantities possible to calculate from the FEP output?
>> I tried using the energy values, but immediately saw that the numbers
>> are so large that they will cause overflow in the exponentials of the
>> partition functions.
>>
>> Is there a special trick to calculate G_1 or G_2? How did you
>> calculate dG?
>>
>> Thank you,
>> Best,
>> Sebastian
>>
>>
>>
>>
>

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