# [gmx-users] pulling force vs free energy

Justin A. Lemkul jalemkul at vt.edu
Wed Nov 16 16:25:26 CET 2011

```
Vijayaraj wrote:
>
>
>     Message: 4
>     Date: Wed, 16 Nov 2011 09:34:02 -0500
>     From: "Justin A. Lemkul" <jalemkul at vt.edu <mailto:jalemkul at vt.edu>>
>     Subject: Re: [gmx-users] pulling force vs free energy
>     To: Discussion list for GROMACS users <gmx-users at gromacs.org
>     <mailto:gmx-users at gromacs.org>>
>     Message-ID: <4EC3C9DA.7040400 at vt.edu <mailto:4EC3C9DA.7040400 at vt.edu>>
>     Content-Type: text/plain; charset=ISO-8859-1; format=flowed
>
>
>
>     Vijayaraj wrote:
>      > Hi,
>      >
>      > What is the relation between pulling force and free energy of
>     binding.
>      > can we relate the maximum pulling force with the free energy. for
>      > example, 2 systems has the maximum pulling force and free energy as
>      > below from umbrella sampling and g_wham analysis,
>      >
>      >                       max. force        free energy
>      > system 1          1470                42
>      > system 2          1647                32
>      >
>      > system 2 has higher pulling force than system 1 and the free energy
>      > result is different from this trend.
>      >
>
>     How did you obtain the maximum force, just a single SMD trajectory?
>      If so, I
>     wouldn't put a lot of faith in it necessarily.  Umbrella sampling is
>     a more
>     robust method than a single pull.  You can use large numbers of pulling
>     simulations and apply Jarzynski's equation to calculate free energy,
>     but there
>     are distinct caveats (although I suppose there are caveats with any
>     method).
>
>     -Justin
>
>
> yes. the max force is obtained from single SMD trajectory. So in this
> case we dont have to worry about the correction between max. force and
> free energy. I found one of my free energy result is 2 times larger than
> the previous result, where they have applied Jarzynski's equation.
>

SMD is path-dependent, while a true DeltaG is a path-independent quantity.
Hence why you cannot easily connect the two.  Convergence in sampling and
limitations in each technique make it sometimes hard to compare the results that
others have obtained with other methods.  Proper data collection for Jarzynski's
method requires exhaustive sampling, which is often hard to obtain (not a blind
criticism of others' work, just a fact).

-Justin

--
========================================

Justin A. Lemkul
Ph.D. Candidate
ICTAS Doctoral Scholar
MILES-IGERT Trainee
Department of Biochemistry
Virginia Tech
Blacksburg, VA
jalemkul[at]vt.edu | (540) 231-9080
http://www.bevanlab.biochem.vt.edu/Pages/Personal/justin

========================================

```