# Re: Free Energy Calculation of a protein

From: Mert Gür (gurmert_at_gmail.com)
Date: Thu Dec 10 2009 - 03:48:22 CST

Dear Pu,
I have given the issue a second tought. I think it is not wrong to treat the
solvent as an T,P reservoir for the protein. So there shouldn't be anything
wrong in terms of the configurational sampling.
Best,
Mert

On Thu, Dec 10, 2009 at 11:14 AM, Mert Gür <gurmert_at_gmail.com> wrote:

> Dear Pu,
>
> Thank you for your response.
>
>
>
> I am comming from an mechanical enginnering background and it keeps
> bothering me how much work potential a protein has at a sepecific
> temperature, and pressure . I know that I just can take my protein to the
> reference state and that there are plenty of methods to evaluate the free
> energy difference.
>
> Additionally I am curious how long it will take for the entropy to
> converge.
>
> This procedure I am intending was supposed to be straightforward
>
>
>
> The expression I have provided evaluates the free energy relative to an
> ideal gas reference state E_i=0 .This is due to the fact that I am using the
> values of the energie vlaues directly . So I am not using any other specific
> reference (dead) state. As long as I am consistent with my formula in my
> work I believe I am thermodynamically right.
>
>
>
> So what you are saying is that it is impossible to evaluate the free energy
> of a protein only which was simulated in solvent? The only thing I can
> evaluated is the free energy of the whole ensemble am I right?
>
>
>
> Best,
>
> Mert
>
>
> On Wed, Dec 9, 2009 at 11:53 PM, Pu Tian <tianpu_at_mail.nih.gov> wrote:
>
>> 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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