[gmx-users] Re: Umbrella sampling- force vs time plots

Thomas Schlesier schlesi at uni-mainz.de
Wed Jul 10 12:18:00 CEST 2013

Using a higher force constant and / or pulling velocity drives the 
system faster out of equilibrium, which results in higher rupture forces.
Varying the force constant has two effects. The softer the potential is, 
the larger are the fluctuations in the coordinates but the lower are the 
fluctuations in the force (see Paper: Biophysical Journal Volume 72 
April 1997 1568-1581). So a lower force constant gives 'nicer looking' 
force-extension curves.
Problem with a low force constant is that it's harder to detect 
intermediates in the system (especially if they have small energy 
barriers). I think the was a paper from Grubmüller which showed this in 
a picture. But i don't remember the title and only believe it was from 
Grubmüller. But one this effect also in the PMF obtained from 
Jarzynski's equality - here a too low force constant (lower than the 
curvature of the PMF) gives deviations from the exact result (G. Hummer, 
A. Szabo; PNAS 107 (50): 21441-21446, 2010).

> Hello all,
> I am trying to understand the force vs time plots using Gromacs' umbrella
> sampling method. I am trying to pull a short polymer chain from the interior
> of a micelle and see what the PMF looks like. I use the following parameters
> to run the pulling simulation for 500ps to pull the polymer over a distance
> of 5nm:
> pull=umbrella
> pull_geometry=direction
> pull_vec1=1 0 0
> pull_start=yes
> pull_ngroups=1
> pull_group0=surf
> pull_group1=poly
> pull_rate1=0.01
> pull_k1=1000
> After the simulation, pullf.xvg plot I obtained is a linearly increasing
> plot with time and similar result when pull_rate1=0.001 nm per ps. I am not

The slope and the shape of the force-extension curve (extension = v*t) 
depends on the underlying potential surface. A linear increasing force 
corresponds (in first approximation) to an harmonic potential. In 
experiments where they use sometimes long linker molecules, one observes 
a force which increases steeper with increasing extension -> this 
corresponds to a Worm-Like-Chain.

> sure if this is right. My question is, on what basis do we select the
> optimum pull_rate1 and pull_k1 for a particular system? Or is it just a
> choice of parameters as long as the system does not deform? How does an
> ideal force-time plot look like and does the choice of pull_k1 affect the
> histogram?  It appears, the entire procedure depends on the choice of input
> of these two variables. I would greatly appreciate if someone can explain
> this concept.
> Thanks a lot.
> Andy


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