Recent advances in non-equilibrium statistical mechanics and single-molecule technologies have made it possible to use irreversible work measurements to extract free-energy differences associated with the mechanical (un)folding of molecules. To date, free-energy recovery has been focused on native (or equilibrium) molecular states, but free-energy measurements of kinetic states have remained unexplored. Kinetic states are metastable, finite-lifetime states that are generated dynamically, and play important roles in diverse physical processes. In biophysics, there are many examples in which these states determine the fate of molecular reactions, including protein binding, enzymatic reactions, as well as the formation of transient intermediate states during molecular-folding processes. Here we demonstrate that it is possible to obtain free energies of kinetic states by applying extended fluctuation relations, using optical tweezers to mechanically unfold and refold deoxyribonucleic acid (DNA) structures exhibiting intermediate and misfolded kinetic states.
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