| Recent developments in nonequilibrium statistical mechanics, including Jarzynski's equality and the Crooks Fluctuation Theorem, have made the calculation of equilibrium free energy differences from irreversible processes possible. Building off these theorems, two approaches have been developed to calculate the free energy surface, or potential of mean force, along a continuous reaction coordinate: the stiff spring approximation and the Hummer-Szabo method. In this thesis, we extend the Hummer-Szabo method to encompass pulling experiments performed with different biasing protocols and to calculate multidimensional potentials of mean force. These extensions are tested on toy one-dimensional and two-dimensional systems. Next, we compare the efficacy of the stiff spring approximation and the Hummer-Szabo method in interpreting pulling experiments at different spring stiffnesses and using dynamic force spectroscopy on the model peptide deca-alanine. We find that analysis based on the stiff spring approximation fails when weaker springs are used. The Hummer-Szabo method is generally more effective for interpreting dynamic force spectroscopy. For both methods, the second cumulant expansion is found to be a good way to make the best of a limited sample. We anticipate that the methods and analysis presented in this thesis will be useful to experimentalists seeking to design and interpret irreversible single-molecule pulling experiments. |
