**From:** Giacomo Fiorin (*giacomo.fiorin_at_gmail.com*)

**Date:** Fri Apr 23 2021 - 18:49:14 CDT

**Next message:**ROPÓN-PALACIOS G.: "Umbrella windows"**Previous message:**René Hafner TUK: "Re: Error Analysis in Metadynamics"**In reply to:**René Hafner TUK: "Re: Error Analysis in Metadynamics"**Next in thread:**Diship Srivastava: "Re: Error Analysis in Metadynamics"**Reply:**Diship Srivastava: "Re: Error Analysis in Metadynamics"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

Hi René, I think it all depends on how expensive is the system to simulate,

how complex the PMF (e.g. dimensionality, number of minima) and most

importantly, the intended use of the PMF: qualitative insight, or actual

quantification/measurement.

If the goal is to estimate the relative probabilities of different states,

the relevant scale is dictated by the thermal energy, i.e. ~0.6 kcal/mol in

most biological applications. An estimated PMF error of 1 kcal/mol, after

exponentiating, means that the corresponding probability can very easily be *a

factor of 5 larger or smaller*. On the other hand, 0.1 kcal/mol means that

the relative error on the corresponding probability is just ~15%.

Giacomo

On Fri, Apr 23, 2021 at 12:40 PM René Hafner TUK <hamburge_at_physik.uni-kl.de>

wrote:

*> 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
*

*>
*

*> René
*

*> 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 <miro.astore_at_gmail.com> wrote:
*

*>
*

*>> Hi Diship, you should be able to use the code/techniques in this
*

*>> tutorial. Good luck.
*

*>>
*

*>> https://urldefense.com/v3/__https://www.plumed.org/doc-v2.5/user-doc/html/trieste-4.html__;!!DZ3fjg!oO11QyWtHbxGT-WO97ohc55uoYoxSMDW2Mc608ODkfB0WTNQkU-dDTPob0qlhTn7fA$
*

*>> <https://urldefense.com/v3/__https://www.plumed.org/doc-v2.5/user-doc/html/trieste-4.html__;!!DZ3fjg!sp8OPR83ZO7SNR9X9YYdw-9CIV1DXCkkqKUva3mWJ5o6ou3SWvonbwVzjmecWx3n9w$>
*

*>>
*

*>> On Tue, Apr 20, 2021 at 4:41 PM Diship Srivastava <
*

*>> dishipsrivastava_at_gmail.com> 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
*

*>>> JRF
*

*>>> 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
*

*> Germany
*

*>
*

*>
*

**Next message:**ROPÓN-PALACIOS G.: "Umbrella windows"**Previous message:**René Hafner TUK: "Re: Error Analysis in Metadynamics"**In reply to:**René Hafner TUK: "Re: Error Analysis in Metadynamics"**Next in thread:**Diship Srivastava: "Re: Error Analysis in Metadynamics"**Reply:**Diship Srivastava: "Re: Error Analysis in Metadynamics"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

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