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

From: zeynab hosseini (
Date: Tue Sep 01 2020 - 12:52:30 CDT

Dear Giacomo,

I have spend almost a lot of time to go through the journal articles to
understand what you were explained to me and I forgot to thank you for the
comprehensive answer. It indeed was true and worked for me. Thanks you so

On Thu, Apr 16, 2020 at 10:36 PM Giacomo Fiorin <>

> Hi Zeynab, one small correction. I just noticed that you are using
> distanceXY, i.e. the distance in cylindrical rather than polar
> coordinates. The Jacobian term of the PMF in that case would be just -kB T
> ln(r).
> Giacomo
> On Thu, Apr 16, 2020 at 10:13 AM Giacomo Fiorin <>
> wrote:
>> 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:
>> 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 <
>>> 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 ( 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
> --
> Giacomo Fiorin
> Associate Professor of Research, Temple University, Philadelphia, PA
> Research collaborator, National Institutes of Health, Bethesda, MD

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