Re: About pmf

From: JC Gumbart (
Date: Tue Jun 26 2007 - 15:24:01 CDT

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
follows a similar procedure, might have more information.

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?
> Thank your for your time again! I really need your help.
>         Sting
>           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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