Maximum likelihood estimation of protein kinetic parameters under weak assumptions from unfolding force spectroscopy experiments

Worm-like Ising model for protein mechanical unfolding under the effect of osmolytes

We show via single-molecule mechanical unfolding experiments that the osmolyte glycerol stabilizes the native state of the human cardiac I27 titin module against unfolding without shifting its unfolding transition state on the mechanical reaction coordinate. Taken together with similar findings on the immunoglobulin-binding domain of streptococcal protein G (GB1), these experimental results suggest that osmolytes act on proteins through a common mechanism that does not entail a shift of their unfolding transition state. We investigate the above common mechanism via an Ising-like model for protein mechanical unfolding that adds worm-like-chain behavior to a recent generalization of the Wako-Saitô-Muñoz-Eaton model with support for group-transfer free energies. The thermodynamics of the model are exactly solvable, while protein kinetics under mechanical tension can be simulated via Monte Carlo algorithms. Notably, our force-clamp and velocity-clamp simulations exhibit no shift in the position of the unfolding transition state of GB1 and I27 under the effect of various osmolytes. The excellent agreement between experiment and simulation strongly suggests that osmolytes do not assume a structural role at the mechanical unfolding transition state of proteins, acting instead by adjusting the solvent quality for the protein chain analyte.

Unfolding proteins with an atomic force microscope: force-fluctuation-induced nonexponential kinetics

We show that in experimental atomic force microscopy studies of the lifetime distribution of mechanically stressed folded proteins the effects of externally applied fluctuations cannot be distinguished from those of internally present fluctuations. In certain circumstances this leads to artificially nonexponential lifetime distributions, which can be misinterpreted as a signature of protein complexity. This work highlights the importance of fully characterizing and controlling external sources of fluctuation in mechanical studies of proteins before drawing conclusions on the physics at play on the molecular level.

Nonkinetic modeling of the mechanical unfolding of multimodular proteins: theory and experiments

We introduce and discuss a novel approach called back-calculation for analyzing force spectroscopy experiments on multimodular proteins. The relationship between the histograms of the unfolding forces for different peaks, corresponding to a different number of not-yet-unfolded protein modules, is exploited in such a manner that the sole distribution of the forces for one unfolding peak can be used to predict the unfolding forces for other peaks. The scheme is based on a bootstrap prediction method and does not rely on any specific kinetic model for multimodular unfolding. It is tested and validated in both theoretical/computational contexts (based on stochastic simulations) and atomic force microscopy experiments on (GB1)(8) multimodular protein constructs. The prediction accuracy is so high that the predicted average unfolding forces corresponding to each peak for the GB1 construct are within only 5 pN of the averaged directly-measured values. Experimental data are also used to illustrate how the limitations of standard kinetic models can be aptly circumvented by the proposed approach.