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

From: Abhishek Acharya (
Date: Wed Nov 11 2020 - 13:04:29 CST


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 helpful.

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.

Abhishek Acharya

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