Total external work calculation in SMD-PMF calculation

From: Rathinavelan, Thenmalarchelvi (
Date: Sat Sep 01 2007 - 17:53:55 CDT

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?


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