We present force-clamp data on the collapse of ubiquitin polyproteins from a highly extended state to the folded length, in response to a quench in the force from 110 pN to 5 or 10 pN. Using a recent method for free-energy reconstruction from the observed nonequilibrium trajectories, we find that their statistics is captured by simple diffusion along the end-to-end length. The estimated diffusion coefficient of ∼ 100 nm(2) s(-1) is significantly slower than expected from viscous effects alone, possibly because of the internal degrees of freedom of the protein. The free-energy profiles give validity to a physical model in which the multiple protein domains collapse all at once and the role of the force is approximately captured by the Bell model.

Force-clamp spectroscopy reveals the unfolding and disulfide bond rupture times of single protein molecules as a function of the stretching force, point mutations, and solvent conditions. The statistics of these times reveal whether the protein domains are independent of one another, the mechanical hierarchy in the polyprotein chain, and the functional form of the probability distribution from which they originate. It is therefore important to use robust statistical tests to decipher the correct theoretical model underlying the process. Here, we develop multiple techniques to compare the well-established experimental data set on ubiquitin with existing theoretical models as a case study. We show that robustness against filtering, agreement with a maximum likelihood function that takes into account experimental artifacts, the Kuiper statistic test, and alignment with synthetic data all identify the Weibull or stretched exponential distribution as the best fitting model. Our results are inconsistent with recently proposed models of Gaussian disorder in the energy landscape or noise in the applied force as explanations for the observed nonexponential kinetics. Because the physical model in the fit affects the characteristic unfolding time, these results have important implications on our understanding of the biological function of proteins.

Marine-gel biopolymers were recently visualized at the molecular level using atomic force microscopy (AFM) to reveal fine fibril-forming networks with low to high degrees of cross-linking. In this work, we use force spectroscopy to quantify the intra- and intermolecular forces within the marine-gel network. Combining force measurements, AFM imaging, and the known chemical composition of marine gels allows us to identify the microscopic origins of distinct mechanical responses. At the single-fibril level, we uncover force-extension curves that resemble those of individual polysaccharide fibrils. They exhibit entropic elasticity followed by extensions associated with chair-to-boat transitions specific to the type of polysaccharide at high forces. Surprisingly, a low degree of cross-linking leads to sawtooth patterns that we attribute to the unraveling of polysaccharide entanglements. At a high degree of cross-linking, we observe force plateaus that arise from unzipping, as well as unwinding, of helical bundles. Finally, the complex 3D network structure gives rise to force staircases of increasing height that correspond to the hierarchical peeling of fibrils away from the junction zones. In addition, we show that these diverse mechanical responses also arise in reconstituted polysaccharide gels, which highlights their dominant role in the mechanical architecture of marine gels.

The quaternary structure of Filamin A (FLNa) 16-23 was recently shown to exhibit multiple domain-domain interactions that lead to a propeller-like construction. Here we present single-molecule force spectroscopy experiments to show a wide variety of mechanical responses of this molecule and compare it with its linear counterpart FLNa 1-8. The compact structure of FLNa 16-23 leads to a broad distribution of rupture forces and end-to-end lengths in the force-extension mode and multiple unraveling timescales in the force-clamp mode. Moreover, a subset of force-extension trajectories reveals a mechanical hierarchy in which the rupture of domain-domain interactions at high forces (>200 pN) liberates the unfolding of individual domains at low forces (∼100 pN). This mechanism may also explain the order-of-magnitude difference in the rates of the biexponential fits to the distribution of unfolding dwell times under force-clamp. Overall, FLNa 16-23 under a force of 100 pN is more compliant than the linear FLNa 1-8. Because a physiological role of FLNa is to crosslink actin filaments, this range of responses allows it to accommodate a broad spectrum of forces exerted by the cell and its environment.

We present force-clamp data on the collapse of ubiquitin polyproteins in response to a quench in the force. These nonequilibrium trajectories are analyzed using a general method based on a diffusive assumption of the end-to-end length to reconstruct a downhill free energy profile at 5pN and an energy plateau at 10pN with a slow diffusion coefficient on the order of 100nm 2 s −1 . The shape of the free energy and its linear scaling with the protein length give validity to a physical model for the collapse. However, the length independent diffusion coefficient suggests that internal rather than viscous friction dominates and thermal noise is needed to capture the variability in the measured times to collapse.