# Re: Total external work calculation in SMD-PMF calculation

From: JC Gumbart (gumbart_at_ks.uiuc.edu)
Date: Tue Sep 04 2007 - 13:30:41 CDT

Looking at the Jensen et al. (2002) PNAS paper, the external work,
script-W(t) in Eq. 8, is calculated from Eq. 4. I think you are
(sort of) right in assuming it is only calculated for each window as
the PMF is reconstructed independently for each window. However, the
windows are not time slices of a single simulation; they are all
separate SMD simulations, each starting effectively at t=0. The
purpose is to minimize the accumulation of error over longer
trajectories.

On Sep 1, 2007, at 5:53 PM, Rathinavelan, Thenmalarchelvi wrote:

>
> Dear users,
> I would greatly appreciate if anyone help me to understand the
> total work calculation of the SMD-PMF reconstruction that is given
> in Jensen et al., PNAS,2002 & Amaro et al., PNAS, 2003. It has
> been given in the paper that in each time slice the average total
> external work over all the SMD generated trajectories is calculated
> by,
>
> <W(j)avg>traj = 1/N Sum N{integral over time slice(j) dt/
> deltaT * W(t)-
> 0.5k(<z(j)avg> -z0 –vt(j)avg)
> **2}
>
> (Sorry for the bad representation of the
> mathematical symbols)
>
> ‘Sum N’ – summation over N trajectories
> ‘< >traj’ - average over trajectory
> ‘(j)avg’ - average over the time slice
>
> Here is my question:
> I like to know how the total work W(t) is calculated.
> According to my understanding from the papers, it is calculated for
> each time slice, for instance, in the case of the time slice
> between 200-400ps (deltaT=200ps), the total work is the summation
> of work carried out over this time slice (200-400ps) at a given
> interval (for example, 2ps). Can anyone please tell me is this
> correct?
>
> Thanks,
> Thenmalar
>

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