**From:** Chris Chipot (*Christophe.Chipot_at_edam.uhp-nancy.fr*)

**Date:** Sun Oct 29 2006 - 09:51:43 CST

**Next message:**Neelanjana Sengupta: "Re: Using NBFIX"**Previous message:**sukesh shenoy: "Using NBFIX"**In reply to:**jz7_at_duke.edu: "error estimate in FEP calculation"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

Jeny,

When is your trajectory long enough to assume safely that the free

energy calculation has converged? Sources of errors likely to be at

play are diverse, and, hence, will modulate the results differently.

The choice of the force field parameters, which correspond to a

systematic error, undoubtedly affects the results of the simulation,

but this contribution can be largely concealed by the statistical

error arising from insufficient sampling. Paradoxically, exceedingly

short free energy calculations employing inadequate force field

parameters may, nonetheless, yield the correct answer. Under the

hypothetical assumption of an optimally designed potential energy

function, quasi non-ergodicity scenarios constitute a common pitfall

towards fully converged simulations.

Appreciation of the statistical error has been devised following

different schemes. Historically, the free energy changes for the

lambda -> lambda + delta lambda and the lambda -> lambda - delta

lambda perturbations were computed simultaneously to provide the

hysteresis between the forward and the reverse transformations. In

practice, it can be shown that when delta lambda is sufficiently

small, the hysteresis of such "double-wide sampling" (Jorgensen,

1985) simulation becomes negligible, irrespective of the amount of

sampling generated in each window - as would be the case in a

"slow-growth" calculation. A somewhat less arguable point of view

consists in performing the transformation in the forward, a -> b,

and in the reverse, b -> a, directions. Micro-reversibility imposes

that, in principle, Delta A(b -> a) = -Delta A(a -> b). Unfortunately,

forward and reverse transformations do not necessarily share the

same convergence properties. Case in point, the Widom's insertion

and deletion of a particle: Whereas the former simulation converges

rapidly towards the expected excess chemical potential, the latter

never does. This shortcoming can be ascribed to the fact that

configurations in which a cavity does not exist where a real atom

is present are never sampled. In terms of density of states, this

scenario would translate into the distribution of a embracing that

of b entirely, thereby ensuring a proper convergence of the forward

simulation, whereas the same cannot be said for the reciprocal,

reverse transformation. Estimation of errors based on forward and

reverse simulations should, therefore, be considered with great

care. In fact, appropriate combination of the two can be used

profitably to improve the accuracy of free energy calculations

(Bennett's acceptance ratio, simple overlap sampling, etc... - Lu,

2003).

In FEP, convergence may be probed by monitoring the time-evolution

of the ensemble average. This is, however, a necessary, but not

sufficient condition for convergence, because apparent plateaus of

the ensemble average often conceal anomalous overlap of the density

of states characterizing the initial and the final states. The latter

should be the key-criterion to ascertain the local convergence of the

simulation for those degrees of freedom that are effectively sampled.

Statistical errors in FEP calculations may be estimated by means of

a first-order expansion of the free energy, which involves an

estimation of the sampling ratio of the latter of the calculation

(Straatsma, 1986).

In the idealistic cases where a thermodynamic cycle can be defined,

closure of the latter imposes that the sum of individual free energy

contributions sum up to zero. In principle, any deviation from this

target should provide a valuable guidance to improve sampling

efficiency. In practice, discrimination of the faulty transformation,

or transformations, is cumbersome on account of possible mutual

compensation or cancellation of errors.

As I mentioned it previously, visual inspection of the density of

states indicates whether the free energy calculation has converged.

Deficiencies in the overlap of the two distributions is also

suggestive of possible errors, but it should be kept in mind that

approximations like a first-order expansion of the free energy only

reflect the statistical precision of the computation, and evidently

do not account for fluctuations in the system occurring over long

time scales. In sharp contrast, the statistical accuracy is expected

o yield a more faithful picture of the degrees of freedom that have

been actually sampled. The safest route to estimate this quantity

consists in performing the same free energy calculation, starting

from different regions of the phase space - the error is defined as

the root mean square deviation over the different simulations.

Semantically speaking, the error measured from one individual run

yields the statistical precision of the free energy calculation,

whereas that derived from the ensemble of simulations provides its

statistical accuracy.

Chris Chipot

jz7_at_duke.edu a écrit :

*> Dear all,
*

*>
*

*> Can someone please recommend references for the estimate of error
*

*> (including sampling error) for the free energy perturbation calculation?
*

*> I want to know how reliable my delt_delt_G is.
*

*>
*

*> Thanks so much!
*

*>
*

*> Jeny
*

_______________________________________________________________________

Chris Chipot, Ph.D.

Equipe de dynamique des assemblages membranaires

Unité mixte de recherche CNRS/UHP No 7565

Université Henri Poincaré - Nancy 1 Phone: (33) 3-83-68-40-97

B.P. 239 Fax: (33) 3-83-68-43-87

54506 Vandœuvre-lès-Nancy Cedex, France

E-mail: Christophe.Chipot_at_edam.uhp-nancy.fr

http://www.edam.uhp-nancy.fr

To sin by silence when we should protest makes cowards out of men

Ella Wheeler Wilcox

_______________________________________________________________________

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