Re: statistical error in ABF calculations

From: Giacomo Fiorin (
Date: Thu Mar 15 2018 - 20:04:38 CDT

Hi Artur, have you tried looking at the considerations from this paper?

In a nutshell, it all boils down to finding out how many independent
samples you have for the total force in each bin, and applying the
central-limit theorem to them. Clearly, consecutive time steps are not
independent, and you need to find out the de-correlation time for the total

Also, keep in mind that it all works in the assumption of ergodicity, i.e.
that the variables you are not biasing are able to sample all their phase
space. If they are trapped in a local minimum, that's clearly not the case.

At the end of the day you'll find that most of the error comes from the
insufficient sampling in the slowest unbiased degrees of freedom, which is
generally underestimated by the above formula. Quantifying this error can
only be done by comparing multiple simulations, or by running a very long
simulation with multiple sweeps. Converging the orthogonal degrees of
freedom will require long times even in the best scenarios, and your
statistical error computed from the formula will be really tiny at that


On Wed, Mar 14, 2018 at 11:27 AM, Artur Hermano <>

> Hello NAMD users,
> I'm currently using ABF to measure the binding free energy of a
> protein-protein system. My simulations are divided into 2 angstroms windows
> and I am verifying convergence through progressively longer windows (5 ns,
> 10 ns, 15 ns and so on). I see convergence happening when I run 10
> ns/window simulations because the RMSE (calculated from the .grad files of
> this run) compared to longer windows runs is considerably small.
> My question is: how can I calculate the statistical error of an individual
> run? *Without having to compare it with other runs.*
> I aim at having the error bars for each window of my run, but I have not
> yet figured out how to do this with NAMD 2.12.
> Would someone please shed some light on how I can do this?
> Thank you so much!
> --
> Artur Hermano
> Mestrando em Biologia Computacional e Sistemas
> Instituto Oswaldo Cruz

Giacomo Fiorin
Associate Professor of Research, Temple University, Philadelphia, PA
Contractor, National Institutes of Health, Bethesda, MD

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