Velocity convergence of free energy surfaces from single-molecule measurements using Jarzynski's equality.

We studied the velocity dependence of mechanical unfolding of single protein molecules with the atomic force microscope. We showed that with enough realizations, the free energy surfaces reconstructed from Jarzynski's equality converge with respect to pulling velocity, in good agreement with theory. Using the I27 domain of titin as an example, we estimated the required number of realizations for a given pulling velocity, and suggested the optimal range of velocities for single-molecule experiments. The results demonstrate that Jarzynski's equality is a powerful and practical tool for reconstructing free energy landscapes.

Experimental free energy surface reconstruction from single-molecule force spectroscopy using Jarzynski's equality.

We used the atomic force microscope to manipulate and unfold individual molecules of the titin I27 domain and reconstructed its free energy surface using Jarzynski's equality. The free energy surface for both stretching and unfolding was reconstructed using an exact formula that relates the nonequilibrium work fluctuations to the molecular free energy. In addition, the unfolding free energy barrier, i.e., the activation energy, was directly obtained from experimental data for the first time. This Letter demonstrates that Jarzynski's equality can be used to analyze nonequilibrium single-molecule experiments, and to obtain the free energy surfaces for molecular systems, including interactions for which only nonequilibrium work can be measured.