Re: Free Energy Calculation of a protein

From: Pu Tian (tianpu_at_mail.nih.gov)
Date: Wed Dec 09 2009 - 15:53:35 CST

Hi Mert,

I am wondering why do you want to know the "free energy" of a
particular state. For any system, it is the free energy landscape,
which describe the free energy as a function of its position in phase
space (or some real metrics) that determines its property. The
absolute free energy is arbitrary, what you have in you formula lacks
a constant, which is the free energy of the reference state. So I
think your question itself is not thermodynamically right.

In addition, you should not attempt to evaluate the "free energy" of
your protein without water as your conformational sampling was
performed in water. In other words, without water, you will have a
different ensemble of protein structures/configurations.

Best,

Pu

On Dec 9, 2009, at 3:19 PM, Mert Gür wrote:

> Dear all,
> To start with I am familliar with SMD,WHAM, ABF,FE . So my problem
> is not regarding the evaluation of a PMF or free energy change.
> I am interested in evaluating the free energy of a protein at
> specified temperature and pressure.
>
> Let assume that I have a very long simulation so that I have enough
> sampling in the phase space.(I know this is a hard job)
>
> For an T,V,N simulation I should be able to evaluate the Helmholtz
> Free Energy as
>
> F=-kT ln[ <exp(b E_i)> ]
>
> What I do here is to simply evaluate exp(b E_i) for every
> snapshot(i) and then take the average of them.
>
> Now when I perform an T,P,N ensemble I got stucked. Because I have
> to evaluate the Gibbs Free energy with the same methodology as
>
> G=-kT ln[ <exp( b [E_i+P V_i] )> ]
>
> But what is the volume of the protein at the ith snapshot in Namd? I
> know that the volume of the water box fluctuate, but how about the
> volume of the protein?
> Or is the fluctuation in the proteins volume so small that we can
> ignore it.
> Best,
> Mert
>
>

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