**From:** johan strumpfer (*johan.ks.uiuc_at_gmail.com*)

**Date:** Tue Jun 14 2011 - 09:51:22 CDT

**Next message:**johan strumpfer: "Re: Impropers in Charmm and OPLS"**Previous message:**Jérôme Hénin: "Re: A question on Jarkynski equation"**In reply to:**Jérôme Hénin: "Re: A question on Jarkynski equation"**Next in thread:**Jun Zhang: "Re: A question on Jarkynski equation"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

Hi Jun,

Following on a little from what Jerome and Yi nicely explained, you

can get a little more info on the effect of pulling speed and water

viscosity from Hsin and Schulten, Biophys, J., 100:L22-L24 (2011).

Also, although this doesn't really help that much with ligand

unbinding, but you can pull first from point A to point B, and then

from point B back to point A. If you are pulling in solution only

(i.e. not trying to reproduce a bound state) both trajectories should

give the same (positive) work values. You can then combine them using

the bi-directional sampling method (as in FEP - see Pohorille,

Jarzynski and Chipot, J. Phys. Chem B, 2010, 114, 10235â€“10253), which

should give a free energy difference of 0.

Cheers,

Johan

----------------------------------------------------------------

Johan Strumpfer (johanstr_at_ks.uiuc.edu)

Theoretical and Computational Biophysics Group

3115 Beckman Institute

University of Illinois at Urbana-Champaign

405 N. Mathews

Urbana, IL 61801, USA

On Tue, Jun 14, 2011 at 10:09 AM, JÃ©rÃ´me HÃ©nin <jhenin_at_ifr88.cnrs-mrs.fr> wrote:

*> Yi, thanks for your remark. This emphasizes one point that I should
*

*> have mentioned: the "rare event" problem is highly dependent on
*

*> pulling speed. At slow speeds in a low-viscosity solvent like water,
*

*> friction is small or comparable to Brownian forces, so-called 'second
*

*> law violations' become fairly frequent and the exponential estimator
*

*> can converge. Similarly, in a FEP calculation between very similar
*

*> states, convergence is much improved (hence the use of staged
*

*> transformations).
*

*>
*

*> Cheers,
*

*> Jerome
*

*>
*

*> On 14 June 2011 15:11, Wang Yi <dexterwy_at_gmail.com> wrote:
*

*>> Hi Jun,
*

*>> Dr.Â HÃ©nin has pointed out the general concerns regarding SMD and JE. ButÂ for
*

*>> processes like moving in water, you might not have to worry too much about
*

*>> that. What I mean is:
*

*>> The work done for dragging a ligand in a water box is mostly against the
*

*>> "friction" from solvent. Since water molecules move in all directions, the
*

*>> "frictions" the ligand is experiencing changes all the time. Thus, you will
*

*>> notice the SMD force fluctuating roughly around zero (albeit with large
*

*>> swings). Then after integrating the force curve, the positive work and
*

*>> negative work will mostly cancel each other. And after applying JE, although
*

*>> there exists the issue of "heavey-weight rare events", the final value would
*

*>> be pretty small (compared to thermo energy). That's especially true in a
*

*>> unbinding process simulation, where the unbinding part has a much larger
*

*>> magnitude than the "free moving in water" part.
*

*>> That is based on my understanding.
*

*>> Best,
*

*>> ___________________________
*

*>> Yi (Yves) Wang
*

*>> Duke University
*

*>>
*

*>>
*

*>>
*

*>>
*

*>> åœ¨ 2011-6-14ï¼Œä¸Šåˆ4:43ï¼Œ JÃ©rÃ´me HÃ©nin å†™é“ï¼š
*

*>>
*

*>> Hi,
*

*>>
*

*>> You put your finger on a very interesting question. The Jarzynski
*

*>> equality is formally exact, hence the estimator will converge towards
*

*>> zero, at least on paper. As you note, since the reversible work is
*

*>> zero, all measured work is irreversible: we expect it to be positive
*

*>> basically all the time. Then how can the average be zero?
*

*>>
*

*>> Actually, statistical mechanics dictates that a few trajectories will
*

*>> give negative work values, i.e. negative irreversible work, i.e. a net
*

*>> decrease in entropy. This is why such situations are sometimes called
*

*>> 'second law violations'. They are not really violations, just a
*

*>> reminder that the second law applies to macroscopic systems only (even
*

*>> if we in the molecular modeling community often stretch the notion of
*

*>> macroscopic a little far). In the case of a solute moving through a
*

*>> solvent, the 'negative work' case would be a trajectory where random
*

*>> fluctuations in the solvent happen to push the solute along its path,
*

*>> instead of slowing it down in a normal frictional behavior.
*

*>>
*

*>> Such negative work values will be exceedingly rare, but they have a
*

*>> huge weight in the exponential average of the Jarzynski formula. That
*

*>> is why a few negative values are enough to make the average zero even
*

*>> though almost all values are positive. Because these events are so
*

*>> rare, numerical convergence will be awful, so it is unlikely that you
*

*>> will manage to get a zero free energy value from a numerical
*

*>> simulation. To some extent, the same can be said of any application of
*

*>> the Jarzynski estimator, and is also true of FEP calculations with the
*

*>> exponential formula: these averages are dominated by rare events,
*

*>> which results in various degrees of convergence problems.
*

*>>
*

*>> For more details on 'second law violations', see for example:
*

*>> http://arxiv.org/abs/cond-mat/0401311
*

*>>
*

*>> Cheers,
*

*>> Jerome
*

*>>
*

*>>
*

*>> On 14 June 2011 05:01, Jun Zhang <coolrainbow_at_yahoo.cn> wrote:
*

*>>
*

*>> Hello Everyone:
*

*>>
*

*>> I want to use Jarkynski's equation combined with SMD to compute the binding
*

*>> free energy of a protein and its ligand (eg. JCP, 120, 5946). However, I was
*

*>> puzzled by some theoretical issues.
*

*>>
*

*>> For example, a system composed of water and a ligand. if we move a single
*

*>> ligand in aqueous for some distances, the work done cannot be zero, but the
*

*>> free energy change should be zero since the state of the ligand has not
*

*>> changed.
*

*>>
*

*>> It seems somewhat strange, and may be a naive question. But I am really
*

*>> puzzled by it, so I'm looking for help. Thank you in advance!
*

*>>
*

*>> Cheers up!
*

*>>
*

*>> Jun Zhang
*

*>>
*

*>> Nankai University
*

*>>
*

*>> coolrainbow_at_yahoo.cn
*

*>>
*

*>>
*

*>>
*

*>>
*

*>>
*

*>
*

*>
*

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