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

From: wliu (wliu_at_itcs.ecnu.edu.cn)
Date: Wed Apr 20 2016 - 02:18:01 CDT

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, χ0=110, after a short time's MD (such as 6
ns), I got the distribution of χ, then I calculation the mean of χ,
<χ>=104.12, standard deviation σχ=6.04. Then the displacement Δχ=5.88
(<σχ). Thus, we consider k=35 to be confident (within 68% of Gaussian).

Any suggestions or relevant literatures will be appreciated.

Wei

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