# Re: ABF calculation - normalization of the PMF

From: Giovanni Bellesia (gbellesia_at_chem.ucsb.edu)
Date: Tue Sep 29 2009 - 10:40:01 CDT

Hi Jerome,
I am aware of the JACS paper and I will certainly use Equation 3 to
calculate the dimerization free energy.
However, my problem right now is with the larger values of the reaction
coordinate: the free energy profile is
flat but it does not "converge" to zero.
In more details, I have two free energy profiles calculated from two
independent simulations starting from two
different stable conformations of the peptide dimer (see Biophysical
Journal 96(3), 875-886 (2009)).
The idea is to compare the two curves and check the relative stability
of the two dimers.
As far as I understand, to make the comparison I should "normalize" the
two curves so that they both ==> 0 when
the reaction coordinate is large (and the profile is flat).
The normalization procedure in JCP 121(7), 2904 (2004) for some reason
"works" only for one of the two curves.

Alternatively I was thinking about simply calculate (for both curves)
the average value of the free energy within the flat (right) section of
the profile and then shift the curves accordingly.
Is this correct ?

Best

Giovanni

> Hi Giovanni,
> To get the dimerization free energy, you'll need an integral over the
> domain of the pmf corresponding to the dimer. There is an example
> there:
> http://pubs.acs.org/doi/abs/10.1021/ja050581y
> although Equation (3) in there is missing a factor 2 to account for
> the symmetry of the homodimer (see ref. 50 in that paper).
> Jerome
>
> 2009/9/19 Giovanni Bellesia <gbellesia_at_chem.ucsb.edu>:
>
>> Hi all,
>> I am trying to calculate the dimerization free energy of a short peptide
>> using the ABF method.
>> My 'reaction coordinate' is the COM-distance between the two peptides.
>>
>> I'm currently going through the JCP papers where the ABF method is
>> introduced and evaluated.
>> In particular, reading about the implementation of the method in JCP 121(7),
>> 2904 (2004) I found at
>> the end of Section IIB2 the comment about the normalization of the PMF via
>> subtraction of the
>> "Jacobian correction" from the free energy profile.
>>
>> Here's my question (just to be sure I understood correctly):
>> Shall I subtract from the free energy profile the quantity
>> k_B * T * ln |J|
>> with |J| defined as in formula (16) ?
>>
>>
>> Best
>>
>> Giovanni
>>
>>
>
>

```--
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Giovanni Bellesia
Department of Chemistry and Biochemistry
University of California, Santa Barbara
Santa Barbara, California 93106-9510, USA.
Email: gbellesia_at_chem.ucsb.edu
Phone: 805 893 2767
Web: http://www.chem.ucsb.edu/~gbellesia/
------------------------------------------
```

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