Free energy surfaces from single-molecule force spectroscopy

Single-molecule force spectroscopy has the potential to provide unprecedented insights into the mechanical properties of individual molecules. The unfolding of proteins and nucleic acids, the dissociation of molecular complexes, and other molecular transitions can be induced through mechanical forces exerted, for example, by laser optical tweezers or atomic force microscopes and monitored with subnanometer resolution. Can one obtain the equilibrium free energy of the molecular system along the pulling coordinate from such nonequilibrium force measurements? Jarzynski's remarkable identity does not immediately solve this problem because it relates the nonequilibrium work to free energy differences at different times, not positions. By surmounting this difficulty, we were able to express the free energy profile in terms of the integral of the force with respect to extension. Here we present the theory in a simple way and discuss various practical aspects in the context of pulling experiments. We illustrate our rigorous free energy reconstruction procedure by applying it to force-induced RNA unfolding experiments.