# Re: Error Analysis in Metadynamics

From: Diship Srivastava (dishipsrivastava_at_gmail.com)
Date: Sun Apr 25 2021 - 12:39:05 CDT

Thanks for the answer. I have one more question - since I am doing 2D well
tempered metadynamics will the error analysis be done for both cv's
separately or is there a method to combine the error analysis for both cv
into one?

On Sat, 24 Apr 2021, 05:22 Giacomo Fiorin, <giacomo.fiorin_at_gmail.com> wrote:

> 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!rkoiprliWDa4dAvZ_C6kcdRq2hsiZJ7UaAfB8ieuMj3_8IqnfaG19QfOwKmL2BTbPw\$
>>> <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.
>>>>
>>>>
>>>>
>>>>
>>>> --
>>>> Diship Srivastava
>>>> JRF
>>>> Department of Chemistry
>>>> 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
>>
>>

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