Experimental validation of free-energy-landscape reconstruction from non-equilibrium single-molecule force spectroscopy measurements

The energy-landscape theory is an important tool for investigating how proteins fold. Hummer and Szabo conceived a simple method for constructing folding-energy landscapes from single-molecule pulling experiments. But are these non-equilibrium measurements a valid approach to equilibrium landscapes? The Hummer–Szabo formalism is now experimentally validated for the first time. Free-energy-landscape formalisms provide the fundamental conceptual framework for physical descriptions of how proteins and nucleic acids fold into specific three-dimensional structures 1 , 2 . Although folding landscapes are difficult to measure experimentally, recent theoretical work by Hummer and Szabo 3 has shown that landscape profiles can be reconstructed from non-equilibrium single-molecule force spectroscopy measurements using an extension of the Jarzynski equality 4 . This method has been applied to simulations 5 , 6 and experiments 7 , 8 but never validated experimentally. We tested it using force–extension measurements on DNA hairpins with distinct, sequence-dependent folding landscapes. Quantitative agreement was found between the landscape profiles obtained from the non-equilibrium reconstruction and those from equilibrium probability distributions 9 . We also tested the method on a riboswitch aptamer with three partially folded intermediate states, successfully reconstructing the landscape but finding some states difficult to resolve owing to low occupancy or overlap of the potential wells. These measurements validate the landscape-reconstruction method and provide a new test of non-equilibrium work relations.