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.Folding-landscape formalisms have broad applications in biophysics, from improving predictive structural models and protein engineering 10,11 to providing crucial insights into biomolecular structure, dynamics, function and disease 12,13 . Specific characteristics of folding landscapes, such as the roughness of the free-energy surface 14 or the properties of partially folded intermediate 15 and transition states 16 , including how they are altered by temperature changes, solvent substitutions or mutations 17 , have been widely studied by experiment and theory. However, it has proven remarkably challenging to go beyond such isolated features and measure the entire profile of the free-energy landscape along the reaction coordinate.Single-molecule force spectroscopy provides a unique window into folding reactions because of its ability to measure properties of the free-energy landscape. In single-molecule force spectroscopy, a single molecule is held under mechanical tension by a spring-like force probe such as an optical trap or atomic force microscope, and the end-to-end extension of the molecule is recorded while the molecule folds/unfolds under the influence of the denaturing force (Fig. 1a). By this means, the folding energies and rates, partially folded intermediates and similar characteristics may be explored 18 . Measurements can be made either in the equilibrium regime (for example, by maintaining a constant force using an active 19 1 Department of Physics, University of Alberta, 11322-89 Ave, Edmonton AB, T6G 2G7, Canada, 2 National Institute for Nanotechnology, 11421 Saskatchewan Dr, Edmonton AB, T6G 2M9, Canada. † These authors contributed equally to this work. *e-mail: Michael.woodside@nrc-cnrc.gc.ca. or passive 20 force clamp) or in the non-equilibrium regime (for example, by ramping the ...

Porous silica coatings were prepared by acid- and base-catalyzed sol−gel method. Surface morphology studies by atomic force microscopy showed smooth surface for acid-catalyzed coatings while base catalysis resulted in coarse particle morphology. On increasing the tetraethyl orthosilicate to base molar ratio from 1:1 to 1:3, the mean particle size of the coating shifted from 30 to 100 nm while the pore size varied from 4.7 to 14 nm. Infrared spectral analysis exhibited a change in the ratio of integrated peak intensities of Si−O−Si to Si−OH in acid-and base-catalyzed silica coatings. Textural studies showed an increase in particle size and porosity with base concentration. Optical transmission and surface roughness of base-catalyzed samples were found to be higher than that of acid-catalyzed silica coatings.

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