Re: Error Analysis in Metadynamics

From: René Hafner TUK (
Date: Fri Apr 23 2021 - 11:40:05 CDT

Dear Giacomo,

a question upon this:

     What would you call "long enough for today's review standards":

     Having convergence over serveral runs in the PMF within <1kcal/mol
or rather on the order of (maybe a few) 0.1 kcal/mol?

Kind regards


On 4/23/2021 5:57 PM, Giacomo Fiorin wrote:
> Hi Diship, it highly depends on what error analysis you plan on
> doing.  The approach that I and others use with metadynamics has very
> few assumptions: after estimating that the systems has explored all
> relevant states at least once, start collecting the PMF at regular
> intervals and simulate for additional time such that all states are
> visited a few more times, i.e. a few more layers of Gaussian hills are
> added on top of the converged PMF.  Then just compute the average and
> SD of the free-energy over the sample of multiple PMFs, which are only
> text files, so you can do the following:
> all_pmfs = np.zeros(shape=(n_files, n_points))
> for i_file in range(n_files):
>     _, pmf = np.loadtxt(pmf_file_names[i_file], unpack=True)
>     all_pmfs[i_file,:] = pmf[:]
> pmf_mean = all_pmfs.mean(axis=0)
> pmf_SD = all_pmfs.std(axis=0)
> The tutorial that Miro has linked uses block averages, where the
> additional difference is that the length of the blocks is also varied
> to converge the SD.  You should see for yourself that the dependence
> of the SD on the block length is rather slow (in theory, it should
> follow a square root).
> Having said all that, here you're not simulating something trivial
> like dialanine isomerization: any meaningful error estimate will
> require that the CV has already visited all states repeatedly during
> the simulation.  If you can see such trajectory, then you're in good
> shape and any PMF method including metadynamics will give you unbiased
> results.  If you ran long enough for today's review standards, your
> statistical error bars will be comparable or smaller than the size of
> the marker used in the plot :-)  You ought to be able to explain how
> you computed the statistical error bars, but these ought to be very
> small or downright negligible.
> On the other hand, if the CV is not a good reaction coordinate any
> error analysis will be uninformative: you need to analyze the atomic
> trajectory and show that at any given frame the structural properties
> (e.g. coordination with water or lipids) depend only on the value of
> the CV, but not on the simulation history.  Any inconsistency that you
> may see there may not easily be solved with longer simulation times.
> In short, statistical sampling is less of an issue than it used to be
> (the most common PMF methods are now at least two decades old!), but
> /picking a good CV/ has always been "the big deal", where your insight
> into the specific problem matters the most.
> Giacomo
> On Tue, Apr 20, 2021 at 3:37 AM Miro Astore <
> <>> wrote:
> Hi Diship, you should be able to use the code/techniques in this
> tutorial. Good luck.
> <;!!DZ3fjg!sp8OPR83ZO7SNR9X9YYdw-9CIV1DXCkkqKUva3mWJ5o6ou3SWvonbwVzjmecWx3n9w$>
> On Tue, Apr 20, 2021 at 4:41 PM Diship Srivastava
> < <>>
> wrote:
> Hi,
> I have done well tempered metadynamics for a system consisting
> of a molecule insertion into a bilayer using the colvars
> module. I am interested in doing an error analysis for
> obtained free energy preferably using colvars.
> Any help would be most appreciated.
> Thanks in advance
> --
> Diship Srivastava
> Department of Chemistry
> IIT(ISM) - Dhanbad
> India
> --
> Miro A. Astore   (he/him)
> PhD Candidate | Computational Biophysics
> Office 434 A28 School of Physics
> University of Sydney

Dipl.-Phys. René Hafner
TU Kaiserslautern

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