Free-energy calculations - Theoretical Biophysics Group

Free-energy perturbation calculations Measuring the error associated to an FEP calculation
The statistical error can be expressed in terms of the variance of the ensemble average,
viz. exp(−β∆A) = 〈exp(−β∆U)〉0, measured over the n samples accrued in a
single simulation.
Using the propagation of uncertainty, 41
σ 2 (1 + 2κ)
=
∆A nβ2 1
〈exp(−β∆U)〉 2 σ
0
2 〈exp(−β∆U)〉 0
where κ is the correlation length of the series and (1 + 2κ), the sampling ratio,
corresponds to the minimum number of samples found between two independent
observables. 42
A similar formula can be devised for the BAR 43 estimator,
σ 2 (1 + 2κ0)
=
∆A n0β2
〈f 2 (x)〉0
〈f (x)〉 2
− 1 +
0
(1 + 2κ1)
n1β2 where f (x) = 1/(1 + e x ) and x = β(∆U − C).
41 MEYER (1992)
42 STRAATSMA ET AL. (1986); FLYVBJERG, PETERSEN (1989)
43 BENNETT (1976); HAHN, THEN (2009); POHORILLE ET AL. (2010)
Chris Chipot Free-energy calculations
〈f 2 (−x)〉1
〈f (−x)〉 2
− 1
1