# Re: eABF 3D sampling using distance Colvars + X and Y: averaged PMF difference to 1D sampling

From: René Hafner TUK (hamburge_at_physik.uni-kl.de)
Date: Fri Aug 27 2021 - 08:47:26 CDT

Hi Jérôme,

alright, I'll try it like that!

Best

René

On 8/27/2021 2:05 PM, Jérôme Hénin wrote:
> Hi René,
>
> ----- On Aug 26, 2021, at 8:52 PM, René Hafner TUK
> <hamburge_at_physik.uni-kl.de> wrote:
>
> Hi Jérôme!
>
> The way I extract it was to run second abf instance with only
> the distanceFromMembrane colvar that is **not** applied.
>
> Which turned out to be the same as when just weighting the
> zgrad(x,y,z) by the respective counts and average over X,Y.
>
> But we were wondering whether this is the correct way.
>
> I don't think that is correct, because the simulation is biased in the
> directions X and Y, so you are not computing an unbiased average at
> each z value.
>
>
> I even tried an easier setup with an almost flat membrane
> surface where I can compare results to a simple distanceZ
> variable.
>
> Here the distanceMin 1D case returns 4.6 (+. 0.1) kcal/mol
> (same as distanceZ)
>
>                         the 3D case returns dG = 4.3 (+- 0.1)
> kcal/mol (with the above assumption)
>
>
> Though what you suggest is to calculate the marginal
> distribution via the following?
>
> Just an integral instead of an average:
>
> What I additionally needed to do in order to gain a smooth
> curve here was to weight every grid point by its counts (such
> that "bad" guesses with low counts get suppressed). But I am
> not yet the sure the scale is correct.
>
> With the expression above you won't need to worry about that.
>
> Jérôme

```--
--
Dipl.-Phys. René Hafner
TU Kaiserslautern
Germany
```

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