Force-clamp analysis techniques reveal stretched exponential unfolding kinetics in ubiquitin

TL;DR

This study uses force-clamp spectroscopy and advanced statistical analysis to demonstrate that ubiquitin unfolding follows a stretched exponential (Weibull) distribution, challenging previous models and impacting our understanding of protein mechanics.

Contribution

The paper develops robust statistical techniques to identify the stretched exponential distribution as the best model for protein unfolding times, providing new insights into protein mechanics.

Findings

Unfolding times follow a Weibull distribution.

Robust statistical tests favor the stretched exponential model.

Results challenge Gaussian disorder models.

Abstract

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 non-exponential kinetics. Since 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.