# Re: Calculating 2D PMF from 1D eABF simulations using CZAR estimator.

From: Abhishek Acharya (abhi117acharya_at_gmail.com)
Date: Thu Nov 19 2020 - 00:02:49 CST

Dear Jerome,

I had performed some initial test runs for about 25 ns per walker. The
artefacts were observed in both .pmf and .czar.pmf files.

Yes I am writing the zgrad files that I hope to use for constructing the
final pmf.

Thank you very much for your help.

Abhishek

On Mon, Nov 16, 2020 at 9:10 PM Jérôme Hénin <jerome.henin_at_ibpc.fr> wrote:

> Hi Abhishek,
>
>
> ----- On 11 Nov 20, at 23:13, Abhishek Acharya abhi117acharya_at_gmail.com
> wrote:
>
> > Hello Jerome,
> >
> > Thank you for your quick response.
> >
> > Well it does look simpler that I thought. Pardon my ignorance; I am a
> > biologist by training, so mathematics is not a strong suit (how I wish it
> > was).
> >
> > I have another follow up question. Looks like I can collect the joint
> > histogram for all the walkers using the histogram method. Easiest way is
> to
> > combine all of these to obtain the full joint histogram, calculate the
> > marginal and use the final full 1D PMF to obtain the 2D distribution.
> But I
> > am concerned that sampling artefacts at the window edges may cause
> > problems.
>
> Do you see artefacts in both the "regular" PMF and CZAR PMF?
>
> > A better way would be to calculate the 2D PMF separately for each
> > window, drop the values at the edges and perform an interpolation to
> obtain
> > the complete 2D PMF.
> > A third way I thought is to define slightly broader (and overlapping)
> > window ranges. This way I can simply combine the data across windows (for
> > both 1D and 2D cases) after dropping the problematic bins at both ends.
> > This would be slightly expensive but perhaps a bit cleaner.
>
> Yes, overlapping windows always work as well.
>
> At any rate, you are going to need the writeCZARwindowFile at some point
> to combine the windows.
>
> Cheers
> Jerome
>
>
> > On Wed, Nov 11, 2020 at 8:53 PM Jérôme Hénin <jerome.henin_at_ibpc.fr>
> wrote:
> >
> >> Hello Abhishek,
> >>
> >> you're almost there, but it's simpler than you think. If you can collect
> >> the joint histogram P(z1, z2), biased along z1, then you can obtain the
> 2d
> >> PMF by reweighting using the 1d CZAR PMF:
> >> A(z1, z2) = -kT ln( P(z1, z2) / P(z1) ) + A_CZAR(z1)
> >>
> >> where P(z1) is the observed (biased) histogram in z1 (aka the z1
> marginal
> >> of the 2d histogram).
> >>
> >> Best,
> >> Jerome
> >>
> >>
> >> ----- On 11 Nov 20, at 20:04, Abhishek Acharya abhi117acharya_at_gmail.com
> >> wrote:
> >>
> >> > Hello,
> >> >
> >> > We are trying to run 1D eABF simulations on our system of interest.
> >> > Specifically, the simulation is divided into 3 windows and we use 5
> >> walkers
> >> > per window for sampling.
> >> >
> >> > Obtaining the 1D PMF looks straightforward to do. Just to be sure we,
> >> > 1) Combine data for walkers using the inputPrefix directive of ABF to
> get
> >> > combined outputs for each window.
> >> > 2) Combine the gradients for each window to obtain the full gradient,
> >> > taking care of the edge values.
> >> > 3) Integrate the gradient to obtain 1D PMF.
> >> >
> >> > However for better insights and comparison with methods used
> previously,
> >> we
> >> > would like to obtain a PMF projected along an additional CV to obtain
> a
> >> 2D
> >> > picture. So, the idea is to apply ABF bias along, say z1 CV, but also
> >> > obtain samples along z2 (unbiased and defined without the Extended
> >> > Largrangian directive) and somehow combine these to obtain the 2D PMF.
> >> > Naively, I thought that maybe we can do a post-hoc estimation using
> the
> >> > CZAR estimator; essentially obtain the biased 2D histogram, P(z1, z2)
> and
> >> > the z1-averaged forces from the CV values and total forces printed
> out to
> >> > the colvar traj file, and finally using the 1D CZAR expression to
> obtain
> >> > the 2D PMF.
> >> >
> >> > 1. Is this at all a correct strategy? If not, some hints would be
> >> >
> >> > 2. Fu et al, *J. Chem. Theory Comput.* 2016 indicates that accurate
> >> > post-hoc analysis would require printing out the CV and force values
> >> every
> >> > timestep. For the aforesaid procedure, I thought that maybe we can use
> >> the
> >> > histogram directive to obtain the final 2D counts and combine it with
> the
> >> > 1D averaged forces.
> >> >
> >> > Any suggestions would be highly appreciated.
> >> >
> >> > Thanks in advance.
> >> >
> >> > Sincerely,
> >> > Abhishek Acharya
>

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