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

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.

Molten globule–like transition state of protein barnase measured with calorimetric force spectroscopy

“…This fact precludes us from determining the coexistence force and the folding free energy at zero force using (1). To circumvent this problem, we have determined the force dependence of the unfolding and folding kinetic rates beyond the Bell-Evans model, where distances of N and U to the TS are taken as force independent [62,63]. To do so, we have used the detailed balance condition,…”

Protein Nanomechanics

“…Experimental data obtained from single-molecule force spectroscopy contain enormous amounts of unique information, which is otherwise highly difficult to obtain using any other methods [18]. When a protein folds and unfolds at different force ranges, an underlying 1D free-energy landscape can be recovered after careful analysis due to Hammond-Leffler transition state movements [19]. In addition to studies regarding functional folded proteins, the mechanical properties of peptides on water/solid interfaces can be quantified using force spectroscopy [20].…”

“…Non-equilibrium pulling data and derived force-dependent kinetic rates measurements show a systematic discrepancy between the total distance between the native (N) and the unfolded state (U) from elastic models and the sum of the measured distances for folding and unfolding kinetics. Rico-Pasto et al [19] performed single-molecule force spectroscopy for highly kinetically stable protein barnase to explain the observed discrepancy. The authors observed that the transition state (TS) shifts with force relative to the unfolded state, which provides a plausible explanation for the discrepancy.…”