# Re: Umbrella sampling of AA and CNT dissociation, pmf doesn't flatten & reduces over large distances...

From: Giacomo Fiorin (giacomo.fiorin_at_gmail.com)
Date: Thu Apr 16 2020 - 09:13:14 CDT

Hi Zeynab, this is possibly due to the Jacobian term of the PMF, which
comes from the geometric definition of the variable. See e.g. the
appendices of the Colvars paper:
https://doi.org/10.1080/00268976.2013.813594
For a distance "r" there are increasingly more microscopic states as you go
to a larger r, because every spherical shell between r and (r + dr) carries
a number of angular states proportional to 4 pi r^2. The Jacobian term for
a distance can be calculated to be -kBT ln(r^2), or -2 kBT ln(r).

This term is physically correct: for exactly one amino acid molecule and
one nanotube in a macroscopic sample, one the amino acid leaves it will
never find its way back, as there is simply too much volume for it to
explore. You may think of this as an entropic term to the PMF.

The reason why you expect the PMF to flatten out is because PMFs are often
computed from a g(r), which is computed for a finite concentration of both
species (amino acid and nanotube). So even if one amino acid molecule
leaves for good, there are others ready to take its place to compensate.

Try adding 2 kB T ln(r) to your plots and see if the PMF flattens.

Giacomo

On Thu, Apr 16, 2020 at 12:17 AM zeynab hosseini <hosseinizeynab93_at_gmail.com>
wrote:

> Dear All,
>
> I'm new in the umbrella sampling (US) method. I followed the NAMD tutorial
> performing US technique to calculate the adsorption free energy of an amino
> acid (AA) on (infinite) single-walled carbon nanotube (SWCNT) surface. I
> used the weighted histogram analysis method (WHAM) to reconstruct the
> potential of mean force (PMF) from biased potential. The point is that we
> expect the pmf flatten when the AA distance from the CNT increases. But, as
> it is seen in the attached plot, the pmf reduces when the AA is getting
> close to the simulation box edges (around 30A). I wonder why this reduction
> happens. I reviewed namd-l following all related suggestions. Moreover, I‌
> plotted pmf every 6ns and I‌ need help to conclude whether the pmf is
> converging. The windows overlap is good... I also attached the colvars
> input file (US-base.in) and configuration file (win-base.conf)‌ if it is
> conjectured something is wrong with them...
>
> The CNT is fixed at the center of the 60A *60A *30A simulation box of
> water molecules and oriented along the z-axis. The reaction coordinate is
> the radial distance of the AA from the center of the CNT. The bounds of the
> reaction coordinate are 6.8A and 27.8A and the windows are spaced 1A apart,
> centered at 6.8A, 7.8A...27.8A. Each window is sampled for 38ns. The force
> constant is 2.5kcal/mol.
>
> Would be thankful if anybody guides me.
> All the best,
> Zeynab
>

```--
Giacomo Fiorin
Associate Professor of Research, Temple University, Philadelphia, PA
Research collaborator, National Institutes of Health, Bethesda, MD
http://goo.gl/Q3TBQU
https://github.com/giacomofiorin
```

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