Re: collective variable space PMF, including biasing potential terms?

From: Giacomo Fiorin (gfiorin_at_seas.upenn.edu)
Date: Wed May 13 2009 - 16:38:56 CDT

Hi Sebastian, two answers:

1) We haven't yet found an example where one method has clear
advantages. The best method is the one that gives the best results in
your case, and you're the judge. There can be an advantage with
respect to methods like umbrella sampling, where you sample a big
interval that you impose from the start, not knowing what their
relevance would be in the free energy plot. ABF and metadynamics
start instead from the lowest free energy regions, and then work their
way up until the maximum free energy that you decide to sample (20
kcal/mol? 50?). Other than that, it's very hard to say something
general, regardless of the system size.

2) It depends whether your Tcl forces are applied on the same atoms
you want to compute the PMF on. For instance, if you apply them on a
dihedral and then compute the PMF, the effect should be trivial: the
new PMF would be a sum of the "regular" one and your biasing
potential.

Technically, ABF measures the average forces from the system acting on
the collective variables, and by the way NAMD is designed they do not
include the user-defined restraints. Metadynamics doesn't the forces
at all, but looks instead at the resulting histogram in the collective
variable space, so implicitly it does take your external potential
into account. Then, there are three cases:

1. tcl forces and PMF calculation on the same atoms: sum your biasing
potential to the ABF-derived PMF, or take the metadynamics one as it
is; or even better, just compute one "unperturbed" PMF with either
method and sum the different biasing potentials to it to obtained the
"perturbed" PMFs :-P

2. tcl forces applied only on a subset of the "PMF" atoms: in this
case, ABF would miss some of the forces, but not homogeneously and you
can't simply sum your bias to the PMF. Metadynamics may be more
appropriate in this case.

3. tcl forces applied on different atoms from the "PMF" ones: ABF and
metadynamics should give you the exact same PMFs (minus sampling
errors).

Giacomo
---- ----
 Giacomo Fiorin
   Center for Molecular Modeling at
     University of Pennsylvania
     231 S 34th Street, Philadelphia, PA 19104-6323
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On Wed, May 13, 2009 at 3:48 PM, Sebastian Stolzenberg
<s.stolzenberg_at_gmail.com> wrote:
> Dear All,
>
> as far as I understand (with NAMD 2.7b1), there are two ways I can measure
> potential of mean forces in collective variable space: ABF and metadynamics.
>
> 1.)
> For small systems like the alanine dipeptide, does one PMF method have any
> performance advantages over the other?
>
> 2.)
> Eventually, I want to add a few biasing dihedral energy terms and measure
> the effect on its free energy surface.
> Thus, I also need to include the biasing dihedral terms into the PMF
> calculations.
> One way to do this I see is using tclForces with the "addenergy" command
> (adding the dihedral energy terms into the "MISC" bin).
> Which method, ABF or metadynamics, takes into the account the MISC energies
> for the PMF calculation?
>
> Thank you,
> Best,
> Sebasitan
>
>

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