[gmx-users] Re: Re: Which/What is the adequate overlap using g_BAR

[Mike Nemec]

>> Dear Gromacs People,
>>
>> I want to calculate free energy differences between two states A and B
>> using g_BAR.
>>
>> For this I read many papers concerning the overlap between neighboring
>> sample windows (Delta H) but I am still wondering about the following 
>> issue:
>>
>> I know, that there has to be an adequate overlap to get accurate free
>> energy differences, but I am not sure, which neighboring sample
>> distributions have to overlap in the gromacs nomenclature.
>>
>> Do the neighboring distributions N(Delta H(lambda=0.05) | lambda=0) AND
>> N(Delta H(lambda=0) | lambda=0.05) have to overlap? Or shall there be an
>> overlap between neighboring distributions calculated from the left side
>>
>> N(Delta H(lambda=0.05) | lambda=0) ; N(Delta H(lambda=0.10) |
>> lambda=0.05) ; N(Delta H(lambda=0.15) | lambda=0.10) ...
>>
>> and then neighboring from the right side
>>
>> N(Delta H(lambda=0) | lambda=0.05) ; N(Delta H(lambda=0.05) |
>> lambda=0.10) ; N(Delta H(lambda=0.10) | lambda=0.15) ... ?
>>
>> I am puzzled, because if one takes a hypothetic stepsize of "1", then
>> one only gets two distributions
>>
>> N(Delta H(lambda=1) | lambda=0) AND N(Delta H(lambda=0) | lambda=1)
>>
>> which then should overlap to get a right free energy difference
>> estimation. Am I right?
>
> Perhaps I'm a bit confused on how you're presenting the question. Are you
> asking about "forward" and "reverse" transformations giving an equivalent
> result?  Keep in mind that there is no such directionality in these 
> types of
> transformations, as long as you're not using a slow-growth method.  
> Otherwise, I
> don't see how one can have left-handed overlap but not right-handed 
> overlap in
> adjacent distributions. 
Sorry for the misunderstanding. What I was asking is the following:

 From the histogram, one gets distributions, e.g. N(Delta H(lambda=0.15) 
| lambda=0.10), where it is calculated at foreign lambda = 0.15 in the 
lambda=0.1 trajectory. This I called "right-side" neighbor 
distributions, because the foreign lambda is larger then the native 
lambda. The same I called the "left-side" distributions.

> Either the neighboring lambda windows overlap or don't.
>

My problem is, that I am not sure, what "neighboring lambda windows" 
means in the nomenclature of
N(Delta H(lambda=0.15) | lambda=0.10) .
As I already mentioned, if one takes a hypothetical step size equal to 
1, one gets from the histogram only the two distributions
N(Delta H(lambda=1) | lambda=0) AND N(Delta H(lambda=0) | lambda=1) ,
which then should overlap, to get an adequate free energy estimation, is 
that right? If they do not overlap, one has to simulate more alchemical 
states inbetween. But that would result, that e.g.  N(Delta 
H(lambda=0.15) | lambda=0.10) AND N(Delta H(lambda=0.10) | lambda=0.15) 
have to overlap.

>> So, concluding this, the last two cases should be right, but refering 
>> to the
>> "mailing-list-question" of Fabian Casteblanco
>> http://gromacs.5086.x6.nabble.com/Free-energy-sampling-using-G-bar-td4455419.html#a4455420 
>>
>> Justin Lemkul replies, that "the histograms look fine [...]. Lots of
>> overlap.", which would result, that all the "left-side" and all the
>> "right-side" neighbor distributions have to overlap, I think
>>

According to the Post of Fabian Casteblanco, you (Justin Lemkul) said, 
that the histogram looks o.k., so the overlap should be large enough. 
But if I am looking for example at the first eight distributions of him
https://www.dropbox.com/s/dzyva125yrw8ap3/From_FabianCasteblanco.png ,
one can see the large gap between the two groups of distributions. 
Concluding this, it is enough that the following distributions have to 
overlap:
N(Delta H(lambda=0) | lambda=0.05) AND N(Delta H(lambda=0.05) | 
lambda=0.10)
N(Delta H(lambda=0.05) | lambda=0.10) AND N(Delta H(lambda=0.10) | 
lambda=0.15)
...
and the same if the foreign lambda is smaller than the current one.
Why is this true? Which distributions in detail have to overlap? And why 
should not e.g.  N(Delta H(lambda=0.05) | lambda=0.10) AND N(Delta 
H(lambda=0.05) | lambda=0) overlap, as they are distributions at 
lambda=0.05 calculated from an arbitrary state A (lambda=0) and an 
arbitrary state B (lambda=0.10)? Maybe there is a simple point I just do 
not see or do not understand... I would be really glad, if someone could 
clarify this for me, because it is an important point for validating the 
method.

>> Depending on your answer, can you please explain, why thedistributions
>> of your answer have to overlap, and not the others?
>>
>>
>> For this case I calculated the free energy difference with g_BAR of one
>> tripeptide Valine-Leucine-Valine where thepartial charges of the Leucine
>> are turned to "0" from state A to B in steps of "0.02" (see attachement,

At the following URLs
https://www.dropbox.com/s/crwucp7uwutisly/Overlap.png
https://www.dropbox.com/s/17jouggywkwm1fi/Overlap_VLV_L2V_DTA1_OFF_Histo.xvg.pdf
you see at the distributions I get from decharging the partial charges 
of Leucine. For me, it looks very similar to the histogram generated by 
Fabian Casteblanco. So is that overlap accurate respectively good?


>> representative 4 neighboring distributions). In the case, that all the
>> "left side calculated" and all the "right side calculated" neighbor
>> distributions have to overlap, the overlap in the attached file is 
>> great,
>> isn't it?
>> But is that really the correct overlap?
>>
> The list does not accept attachments.  Please provide a URL to share 
> the file.
>
> -Justin
>
> -- ================================================== Justin A. 
> Lemkul, Ph.D. Postdoctoral Associate Department of Pharmaceutical 
> Sciences School of Pharmacy Health Sciences Facility II, Room 601 
> University of Maryland, Baltimore 20 Penn St. Baltimore, MD 21201 
> jalemkul at outerbanks.umaryland.edu | (410) 706-7441
>
>

thank you for any help.

   Mike