# 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: Thu Aug 26 2021 - 13:52:19 CDT

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 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?

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.

Best

René

On 8/26/2021 2:01 PM, Jérôme Hénin wrote:
> Hi René,
>
> *What is the correct way to sample non-independent variables with
> proper guesses?*
>
> *
> *
> I'm not sure I can add much to answer this question. What you did
> seems correct, as far as I can tell.
>
> The one concern I have is how you extract the "marginal" free energy
> profiles from the 3D profile. That is not very clear to me. A correct
> way would be to compute the integral of the Boltzmann factor
> (exp(-A(x,y,z)/RT)) over coordinates x and y.
>
> Best,
> Jérôme
>
>
> ----- On Aug 14, 2021, at 7:28 PM, René Hafner TUK
> <hamburge_at_physik.uni-kl.de> wrote:
>
> Hi Giacomo,
>
>     yes I can confirm from the writings in the logfile stating:
>
>     "Enabling the extended Lagrangian term for colvar .. " for
> every colvar.
>
>     I make use of the CZAR estimator.
>
> By the way: I am using NAMD 2.14.
>
> René
>
> On 8/14/2021 7:17 PM, Giacomo Fiorin wrote:
>
> Hello René, can you confirm that you are using extended ABF,
> and more specifically what estimator you used?  (CZAR or
> Zheng/Yang).
>
> Orthogonality between variables is only required for straight
> ABF, where the force on the variable is obtained by projecting
> the atomic total forces directly, rather than using the
> extended-mass trick.
>
> Giacomo
>
> On Sat, Aug 14, 2021 at 11:24 AM René Hafner TUK
> <hamburge_at_physik.uni-kl.de <mailto:hamburge_at_physik.uni-kl.de>>
> wrote:
>
> Hi,
>
> I am trying to use a distance like colvar to sample a
> surface with a ligand using extended ABF.
>
> In order to speed up the surface sampling process I turned
> the abf line into a 3D one where I also sample the X and Y
> direction.
>
>
> My colvar file roughly looks like:
>
> colvar { name X; distanceZ ... } #  Ligand distance
> from Membrane Center in X direction
>
> colvar { name Y; distanceZ ... }  # Ligand distance
> from Membrane Center in Y direction
>
> colvar { name distanceFromMembrane}  # Ligand local
> distance from Membrane Surface (selfdefined)
>
> abf { colvars X Y distanceFromMembrane;  ... }
>
>
> This means the third variable is not independent
> from/orthogonal to X and Y but that shouldn't be and issue
> when using eABF.
>
>
> Comparing 1D run and 3D run (averaged the 3D PMF over X,Y
> to get PMF(distMembrane) )
>
>
> * When I did 1D sampling ( only distanceFromMembrane) I
> obtained rougly 5.5kcal/mol as dG (difference from Minimum
> to a point far away from Membrane)
>
> * When I do *3D sampling* using "subtractAppliedForce
> *on*" *in all 3 colvars* I obtained dG ~ 4kcal/mol. (I
> used the term "subtractAppliedForce" because I initially
>
> * When I do *3D sampling* using "subtractAppliedForce
> *off*" *in all 3 colvars* I obtained dG ~ 1-2kcal/mol.
>
>
> *What is the correct way to sample non-independent
> variables with proper guesses?*
>
> (I expect the 3D to reconstruct the 1D sampling case when
> done correctly and just help improving the sampling of the
> whole surface)
>
>
> Kind regards
>
> René
>
>
> --
> --
> Dipl.-Phys. René Hafner
> TU Kaiserslautern
> Germany
>
> --
> --
> Dipl.-Phys. René Hafner
> TU Kaiserslautern
> Germany
>
>

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

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