multiple HILLS file, aveage FES with error estimate

[Dániel Szöllősi]

Dear All,

I'm testing sodium binding to a fixed transporter and therefore using welltempered metadynamics in 5 repeat per system setup. The distance components (X,Y,Z simultaneously)  to the center of the protein were biased. I would like to generate an average free energy estimation from the repeats with an error estimation. A single repeat converges relatively slowly therefore I want to use all repeats in one go. The sum_hills allows me to plug in all the HILLS file at once but then I obtain free energies five time as deep, is that correct?

I am aware of the block averaging, but that happens over time and not over repeats.

Could you give me a suggestion how to shuffle the data to be statistically sane?

Thank you!

Daniel

p.s. attached is an example of the obtained 3D map (single repeat) with sodium stating position as one of the orange spheremesh. The darker blue the volume is the deeper the FES is.

[Giovanni Bussi]

Hello,

I am not sure there is a theoretical justification, but something that could work is to take the average rather than the sum.

A quick hack would be to concatenate the HILLS file and then divide by 5 the height of each Gaussian (should be the second-to-the-last column, but check the header)

Giovanni

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[Massimiliano Bonomi]

Would you be possible to merge statistics with WHAM?

Max

Sent from my iPhone

On 15 Jun 2021, at 15:09, Giovanni Bussi <giovann...@gmail.com> wrote:



Hello,

I am not sure there is a theoretical justification, but something that could work is to take the average rather than the sum.

A quick hack would be to concatenate the HILLS file and then divide by 5 the height of each Gaussian (should be the second-to-the-last column, but check the header)

Giovanni

On Tue, Jun 15, 2021 at 1:57 PM Dániel Szöllősi <d.szo...@gmail.com> wrote:

Dear All,

I'm testing sodium binding to a fixed transporter and therefore using welltempered metadynamics in 5 repeat per system setup. The distance components (X,Y,Z simultaneously)  to the center of the protein were biased. I would like to generate an average free energy estimation from the repeats with an error estimation. A single repeat converges relatively slowly therefore I want to use all repeats in one go. The sum_hills allows me to plug in all the HILLS file at once but then I obtain free energies five time as deep, is that correct?

I am aware of the block averaging, but that happens over time and not over repeats.

Could you give me a suggestion how to shuffle the data to be statistically sane?

Thank you!

Daniel

p.s. attached is an example of the obtained 3D map (single repeat) with sodium stating position as one of the orange spheremesh. The darker blue the volume is the deeper the FES is.

<Na1_noNa2_3D_rep1.png>

<Na1_3D_rep2.png>

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[Giovanni Bussi]

In theory yes (I was tempted to propose so). However, I never tested it.

In principle, one of the requirements of WHAM is that each simulation is ergodic in the respective ensemble. If they are visibly different this may not hold. On the other hand, with well-tempered metad, the bias changes less and less and could be trapped to a different profile in each replica. If so, WHAM would optimally combine the simulations that were performed with different biases taking this factor into account.

So, I would use it with a lot of care. 

Giovanni

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[Billy Noonan]

Hi Giovanni and Max,

What you have both said is interesting.
Because the bias history is shared between replicate simulations of multiple walkers, can you not just use the HILLS files as is with sum_hills?
You would assume the ensemble is sufficiently sampled.

Can you also use the COLVAR files with sum_hills to generate the FES for PB-MetaD?

Any help with my related question here would be greatly appreciated:

https://groups.google.com/g/plumed-users/c/x-83N3To44A

Hope you're all well,
Billy

[Giovanni Bussi]

The question asked here was, as far as I understood, related to separate simulations, and not multiple walkers.

In case of multiple walkers sharing the same bias, since the bias is identical doing WHAM would give you exactly the same result as averaging the histograms

Giovanni

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[Dániel Szöllősi]

Yes, these are all independent simulations with different length and also some parts of the collective variable space is sampled only by a few repeats. However, these partially covered areas are less of importance.

The application of the WHAM in this case is not obvious to me, especially how that would give me an error estimate.

The scaling of the hill height is straight forward, but can I do an averaging on the 3D FES maps (taking the mean of the identical voxels)? If so, then a standard deviation could be also calculated by the same means and the partially covered areas highlighted as under sampled regions.

Thanks for your ideas!

Daniel