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

From: L. Michel Espinoza-Fonseca (mef_at_ddt.biochem.umn.edu)
Date: Tue Oct 14 2008 - 15:11:50 CDT

In this case, why not applying an external (biased) force to overcome
energy barriers? I'm not sure what problem you're trying to tackle,
but perhaps umbrella sampling or ABF can help you.

Michel

On Tue, Oct 14, 2008 at 6:44 PM, Sebastian Stolzenberg
<s.stolzenberg_at_gmail.com> wrote:
> 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.)
> Please correct me:
> 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
>> translate to having access to the complete partition function of
>> 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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