Force Dependence of Proteins’ Transition State Position and the Bell–Evans Model

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Abstract
Single-molecule force spectroscopy has opened a new field of research in molecular biophysics and biochemistry. Pulling experiments on individual proteins permit us to monitor conformational transitions with high temporal resolution and measure their free energy landscape. The force–extension curves of single proteins often present large hysteresis, with unfolding forces that are higher than refolding ones. Therefore, the high energy of the transition state (TS) in these molecules precludes kinetic rates measurements in equilibrium hopping experiments. In irreversible pulling experiments, force-dependent kinetic rates measurements show a systematic discrepancy between the sum of the folding and unfolding TS distances derived by the kinetic Bell–Evans model and the full molecular extension predicted by elastic models. Here, we show that this discrepancy originates from the force-induced movement of TS. Specifically, we investigate the highly kinetically stable protein barnase, using pulling experiments and the Bell–Evans model to characterize the position of its kinetic barrier. Experimental results show that while the TS stays at a roughly constant distance relative to the native state, it shifts with force relative to the unfolded state. Interestingly, a conversion of the protein extension into amino acid units shows that the TS position follows the Leffler–Hammond postulate: the higher the force, the lower the number of unzipped amino acids relative to the native state. The results are compared with the quasi-reversible unfolding–folding of a short DNA hairpin.
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