**From:** Jérôme Hénin (*jhenin_at_ifr88.cnrs-mrs.fr*)

**Date:** Tue Jun 14 2011 - 09:09:13 CDT

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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
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*> processes like moving in water, you might not have to worry too much about
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*> that. What I mean is:
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*> The work done for dragging a ligand in a water box is mostly against the
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*> "friction" from solvent. Since water molecules move in all directions, the
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*> "frictions" the ligand is experiencing changes all the time. Thus, you will
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*> notice the SMD force fluctuating roughly around zero (albeit with large
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*> swings). Then after integrating the force curve, the positive work and
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*> negative work will mostly cancel each other. And after applying JE, although
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*> there exists the issue of "heavey-weight rare events", the final value would
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*> be pretty small (compared to thermo energy). That's especially true in a
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*> unbinding process simulation, where the unbinding part has a much larger
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*> magnitude than the "free moving in water" part.
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*> That is based on my understanding.
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*> Best,
*

*> ___________________________
*

*> Yi (Yves) Wang
*

*> Duke University
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*>
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*>
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*>
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*>
*

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

*> Hi,
*

*>
*

*> You put your finger on a very interesting question. The Jarzynski
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*> equality is formally exact, hence the estimator will converge towards
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*> zero, at least on paper. As you note, since the reversible work is
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*> zero, all measured work is irreversible: we expect it to be positive
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*> basically all the time. Then how can the average be zero?
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*>
*

*> Actually, statistical mechanics dictates that a few trajectories will
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*> give negative work values, i.e. negative irreversible work, i.e. a net
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*> decrease in entropy. This is why such situations are sometimes called
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*> 'second law violations'. They are not really violations, just a
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*> reminder that the second law applies to macroscopic systems only (even
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*> if we in the molecular modeling community often stretch the notion of
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*> macroscopic a little far). In the case of a solute moving through a
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*> solvent, the 'negative work' case would be a trajectory where random
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*> fluctuations in the solvent happen to push the solute along its path,
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*> instead of slowing it down in a normal frictional behavior.
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*>
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*> Such negative work values will be exceedingly rare, but they have a
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*> huge weight in the exponential average of the Jarzynski formula. That
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*> is why a few negative values are enough to make the average zero even
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*> though almost all values are positive. Because these events are so
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*> rare, numerical convergence will be awful, so it is unlikely that you
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*> will manage to get a zero free energy value from a numerical
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*> simulation. To some extent, the same can be said of any application of
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*> the Jarzynski estimator, and is also true of FEP calculations with the
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*> exponential formula: these averages are dominated by rare events,
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*> which results in various degrees of convergence problems.
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*>
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*> For more details on 'second law violations', see for example:
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*> http://arxiv.org/abs/cond-mat/0401311
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*>
*

*> Cheers,
*

*> Jerome
*

*>
*

*>
*

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

*> Hello Everyone:
*

*>
*

*> I want to use Jarkynski's equation combined with SMD to compute the binding
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*> free energy of a protein and its ligand (eg. JCP, 120, 5946). However, I was
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*> puzzled by some theoretical issues.
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*>
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*> For example, a system composed of water and a ligand. if we move a single
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*> ligand in aqueous for some distances, the work done cannot be zero, but the
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*> free energy change should be zero since the state of the ligand has not
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*> changed.
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*>
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*> It seems somewhat strange, and may be a naive question. But I am really
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*> puzzled by it, so I'm looking for help. Thank you in advance!
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*>
*

*> Cheers up!
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*>
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*> Jun Zhang
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*>
*

*> Nankai University
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*>
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*> coolrainbow_at_yahoo.cn
*

*>
*

*>
*

*>
*

*>
*

*>
*

**Next message:**johan strumpfer: "Re: A question on Jarkynski equation"**Previous message:**Henriette Elisabeth Autzen: "Impropers in Charmm and OPLS"**In reply to:**Wang Yi: "Re: A question on Jarkynski equation"**Next in thread:**johan strumpfer: "Re: A question on Jarkynski equation"**Reply:**johan strumpfer: "Re: A question on Jarkynski equation"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

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