Two-State Folding Energy Determination Based on Transition Points in Nonequilibrium Single-Molecule Experiments

Many small protein domains or nucleic acid structures undergo two-state unfolding-refolding transitions during mechanical stretching using single-molecule techniques. Here, by applying the Jarzynski equality (JE), we analytically express the folding energy of a molecule as a function of the experimentally measured transition points xi* obtained with two typical time-varying mechanical constraints: the force constraints F(t) and the position constraints R(t) of a Hookian spring attached to one end of the molecule. Compared to previous applications of JE based on the integration of accurately measured force extension curves of a tether that typically contains the molecule of interest and handles, our approach just needs to accurately measure a single data point. In the case of the F(t) process, the calculation is handle-independent. The broad applications of the theory are demonstrated by measuring the folding energies of a DNA hairpin, a DNA G-quadruplex, and the titin 127 domain based on transition forces using magnetic tweezers.