From: Sterling Paramore (gnilrets_at_gmail.com)
Date: Tue Jun 26 2007 - 16:58:01 CDT

Another good paper on obtaining a PMF without invoking the stiff
spring approximation is Hummer and Szabo (2001) PNAS v98 p3658

On 6/26/07, JC Gumbart <gumbart_at_ks.uiuc.edu> wrote:
> 1. Your point is well-taken; I also am worried from looking at that
> pmf that it is starting-point dependent. I do not know how they
> chose the points, although the paper by Wang, Tajkhorshid, and
> Schulten on AqpZ (I think) in Structure a couple years ago, which
>
> 2. I'm looking in the sixth window of figure 2c; it looks to me like
> the work peaks in that window.
>
> 3. Eq. 4 is not subtracting the energy in the spring. Eq. 4 is
> actually, I believe, exactly what you're proposing where dt*v is
> replaced by dx (because v = dx/dt) and f(t) by f(x). The energy in
> the spring is subtracting when going from the script W (eq. 4) to W,
> what's used in eq. 5, 6, 7, and 8.
>
> Here's the thing: that procedure gives you the PMF for the perturbed
> system, not the system without external forces which is what you
> want; this is pointed out in Eq. 3 of the Jensen paper. These two
> are usually equated by use of the "stiff spring" approximation where
> the ligand follows the imaginary point very closely. Since that
> wasn't the case for yours, it becomes more difficult to connect the
> PMF you calculate to the one you want. Please see the following two
> papers for more discussion on this point:
>
> 1) Park, Khalili-Araghi, Tajkhorshid, and Schulten. (2003) Free
> energy calculation from steered molecular dynamics simulations using
> Jarzynski's equality. JCP. 119: 3559-3566.
>
> 2) Park and Schulten. (2004) Calculating potentials of mean force
> from steered molecular dynamics simulations. JCP. 120: 5946-5961.
>
> In any case, I am pretty sure still that one simulation cannot give
> you an accurate pmf, I'm afraid. Using ABF (adaptive biasing forces)
> may work, although I've never tried it myself; see the NAMD manual
> for more on this.
>
> On Jun 25, 2007, at 9:38 PM, Sting wrote:
>
> > Hi JC Gumbart,
> > Thank you for your help!
> > But still there some question in my head.
> > 1. Can one just pull the ligand out only in one direction? How
> > they choose the start point for each SMD? I think the choosing for
> > the start point will eventually effect the profile of the external
> > work in fig2.C.
> > 2. I havn't see the highest point occurs in one of the reverse
> > direction. Since the forces in reverse directions is negative , the
> > work from cumulant will fall down accordingly.
> > 3. When computing the external work on ligand, the result from
> > formula 4 will substract the energy store in the 'spring'. Since in
> > our simulation, the center of mass of ligand deviates from the
> > pulling direction signicantly,can we just get the external work on
> > ligand by computing the inner product between the expulsion force
> > and the displacement vector of the center of the coordinates of the
> > ligand, and then employed the formula 6? If not, how can I get the
> > PMF correctly?
> >
> >
> >
> > Sting
> > stg1979_at_emails.bjut.edu.cn
> > 2007-06-26
> >
> > ==============
> >
> >> 1) Each SMD simulation started from an equilibrated point. To
> >> minimize the number of equilibration simulations needed, they pulled
> >> in opposite directions from each starting point.
> >>
> >> 2) I think so. I wouldn't say they had reduced work though; the
> >> highest point occurs in one of the reverse directions.
> >>
> >> 3) The procedure in the deca-alanine tutorial is the same as that in
> >> the paper in Eq. 7, both using the cumulant expansion of the average
> >> work. Eq. 8 is just a more complicated way of calculating <W> and
> >> <W^2>.
> >>
> >> On Jun 23, 2007, at 9:23 PM, Sting wrote:
> >>
> >>> Hi JC Gumbart,
> >>> sorry to disturb you again. As your suggestion, I read the paper
> >>> of Jensen et al.carefully, and in this paper I still have some
> >>> confusion:
> >>> 1. Why they performed SMD in two directions?
> >>> 2. It seems the most forces obtained from the inverse direction
> >>> are negative and these had reduced the works computed in Fig 2.b.
> >>> Do the negative values derive from the 'negative' direction?
> >>> 3. In this paper, a formula 8 was used, but I can not have any clue
> >>> from the tutorial 10Ala_tutor.
> >>> Since both the papers are from your group, they really puzzle me.
> >>>
> >>>
> >>> Thank you a lot!
> >>> ======= =======
> >>>
> >>>> I can attempt to answer but someone may correct me:
> >>>>
> >>>> 1) I'm pretty sure it would be the former, although it seems at
> >>>> least
> >>>> in our group that people calculate it slightly differently (but
> >>>> I am
> >>>> pretty sure both ways are equivalent). Please see some papers from
> >>>> our group for more specifics on this point (I'm looking at right
> >>>> now
> >>>> for instance Jensen et al. "Energetics of glycerol conduction
> >>>> through
> >>>> aquaglyceroporin GlpF").
> >>>>
> >>>> 2) The PMF is a force profile where as the activation energy is the
> >>>> amount of energy required to overcome the initial barrier. I do
> >>>> not
> >>>> know if the free energy of activation is different or not. I have
> >>>> never calculated a PMF myself, but one way to judge would be the
> >>>> size
> >>>> of the activation energy. 100 kJ/mol (~25 kcal/mol) does seem a
> >>>> bit
> >>>> large however and would likely only proceed if something else
> >>>> provided the energy or a conformational change took place (for
> >>>> comparison, thermal energy is only about 0.6 kcal/mol). One
> >>>> point I
> >>>> will make is that calculating accurate PMFs requires good sampling,
> >>>> so if you only ran one trajectory, it probably accumulated a large
> >>>> amount of irreversible work. Additional trajectories,
> >>>> appropriately
> >>>> averaged using Jarzynki's equality (again, papers from our group
> >>>> would be most helpful), may yield a lower number.
> >>>>
> >>>> More experienced people may feel free to chime in here. In any
> >>>> case,
> >>>> good luck!
> >>>>
> >>>>
> >>>> On Jun 18, 2007, at 11:00 PM, Sting wrote:
> >>>>
> >>>>> Hi all:
> >>>>>
> >>>>> I have performed a series of SMD with a constant velocity of 10
> >>>>> Å/
> >>>>> ns to force a ligand release from the binding pocket and try to
> >>>>> reconstruct the PMF, and I have some problem as follow:
> >>>>>
> >>>>> 1. How to compute the works done during the process? Should it be:
> >>>>> The displacement of ligand*applied Force or The displacement of
> >>>>> the
> >>>>> moving point which drag the ligand ?
> >>>>>
> >>>>> 2. What is the diffrence between the PMF and the Activation Energy
> >>>>> as well as that between it and the Free Energy of Activation, and
> >>>>> how to verify a reasonable PMF?
> >>>>>
> >>>>>
> >>>>> I really need someone to help me. Thank you in advance!
> >>
> > = = = = = = = = = = = = = = = = = = = =
> >
> >
> >
>
>
>

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