RE: How to use a proper force constant to decrease computational cost while keeping calculation precision?

From: Radak, Brian K (
Date: Wed Apr 20 2016 - 16:22:09 CDT

This is slightly shameless self-promotion, but hopefully you will agree that it is relevant. We recently developed an alternative maximum likelihood approach to the traditional WHAM that can often compensate for sparse windows. The details can be found in a few papers:

Lee, et. al J Chem Theory Comput, 2013, 9, 513 - A new maximum likelihood approach for free energy profile construction from molecular simulations

Lee, et. al. Chem Theory Comput, 2014, 10, 24 - Roadmaps through free energy landscapes calculated using the multidimensional {vFEP} approach

The code is free/open source and accepts a format compatible with the popular WHAM implementation by Alan Grossfield.

Hope that helps,

P.S. A common mistake that first time users of umbrella sampling make is to forget that the force constants are usually specified in kcal/mol-rad^2 whereas angle coordinates are usually computed in degrees. You may spend some time until realizing that you are off by a factor or (pi/180)^2.

Brian Radak
Postdoctoral Appointee
Leadership Computing Facility
Argonne National Laboratory

9700 South Cass Avenue, Bldg. 240
Argonne, IL 60439-4854
(630) 252-8643
From: [] on behalf of Ana Celia Vila Verde []
Sent: Wednesday, April 20, 2016 3:03 AM
To:; wliu
Subject: Re: namd-l: How to use a proper force constant to decrease computational cost while keeping calculation precision?

Hi Wei,

The article by Roux, B., The calculation of the potential of mean force using computer simulations
Computer Physics Communications, 1995, 91, 275-282
is very useful.

In general, running more windows with a slightly larger k is more efficient than running fewer windows with lower k. Keep in mind that there is no single value of k which is correct; many values of k, coupled with different numbers of windows, will give you a good result, provided that all windows overlap. Your k=35 might work with windows that are 5, or even 10 degrees apart, for example. If you want to test, and given that your system does not appear to be very complicated, you can do a couple of other runs where you take the same k but use smaller and larger windows, and see how your PMF is affected. If you reach a point where two runs with different window sizes give the same PMF, despite different overlap between windows, then you know you have enough sampling.

Oh, you should always use WHAM to build your PMF from umbrella sampling...

I hope it helps,


On 20/04/16 09:18, wliu wrote:
Dear all,

  Recently, I am learning how to use umbrella sampling method to calculate the potential mean force of one torsion angle of a specific residue in a protein. I am curious about how to choose the force constant wisely.

If k is too large, to fulfill the overlap, we have to employ more windows. On the contrary, the center value of torsion we set will be displaced largely. So, is there any quantitative criterion to judge if the value of k is reasonable (small enough and can guarantee the PMF calculation precision)?

For example, if we set k=35, 0=110, after a short time's MD (such as 6 ns), I got the distribution of , then I calculation the mean of , <>=104.12, standard deviation =6.04. Then the displacement =5.88 (<). Thus, we consider k=35 to be confident (within 68% of Gaussian).

Any suggestions or relevant literatures will be appreciated.


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