Free energy reconstruction from nonequilibrium single-molecule pulling experiments Hummer Gerhard Szabo Attila Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, MD 20892-0520 Copyright © 2001, The National Academy of Sciences 2001 See commentary on page 3636.

Laser tweezers and atomic force microscopes are increasingly used to probe the interactions and mechanical properties of individual molecules. Unfortunately, using such time-dependent perturbations to force rare molecular events also drives the system away from equilibrium. Nevertheless, we show how equilibrium free energy profiles can be extracted rigorously from repeated nonequilibrium force measurements on the basis of an extension of Jarzynski's remarkable identity between free energies and the irreversible work.

This can be seen in the following summation: ∑ m p ˙ m = 0

Sample 1: G over Σ and Σ¯

Sample 2: N , with Σ¯ being a disjoint copy of Σ

Sample 3: Σ = a 1 , ⋯ , a n

Sample 4: X a 1 , ⋯ , X a n

Sample 5: X a i → a i ⁢ X a 1 | ⋯ | X a n * ⁢ a¯ i    1 ≤ i < n .

Sample 6: X a 1 | ⋯ | X a n *

Sample 7: X a → a ⁢ L X , a ⁢a¯

Sample 8: X → a ⁢ X 1 ⋯ X n ⁢a¯

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