Continuous time random walk approach to analyze unfolding of Poly-I91 using single molecule force spectroscopy

Einat Chetrit, Department of Chemical Engineering, Ben-Gurion University of the Negev, Beer Sheva, Israel
Yasmine Meroz, School Of Plant Science And Food Security, Tel Aviv University, Tel-aviv, Israel
Ronen Berkovich, Department Of Chemical Engineering, Ben-gurion University Of The Negev, Beer Sheva, Israel

Single molecule force spectroscopy (SMFS) has emerged as a powerful new tool to explore the mechanical stability and folding pathways of individual proteins. In such SMFS experiment, a single protein or poly-protein is tethered at both ends between a surface and a cantilever tip within an Atomic Force Microscope (AFM). The protein conformational unfolding dynamics of the protein is recorded as a response to the application of a calibrated force. Protein unfolding is commonly depicted as a two state process, where the protein unfolds from its native state to some unfolded conformation by crossing an activation barrier. This dynamics is expected to give rise to Arrhenius kinetics, described by an exponential decay with a Poisson distribution. However, in practice, unfolding of proteins under the application of a mechanical load was reported to deviate from such exponential dependency. As a result, alternative approaches were proposed to explain this discrepancy such as maximum likelihood, and using heuristic log-normal and stretched exponential (Weibull) distributions. Here we measure the unfolding dwell times and step-size trajectories of individual poly-(I91) protein, displaying a non-exponential unfolding time dependency. We suggest a different approach, which is based on the statistical and physical nature of the unfolding process, within the framework of continuous time random walk (CTRW), described by a power-law behavior. Our results showed that this process display sub-diffusive features with a fitted exponent α = 0.85 ± 0.14, which can give raise to the possible interpretation that these process may not be Markovian, i.e., possess some memory. Analysis of the temporal and spatial averaged mean square displacement (TA-MSD) confirmed the same exponent α, indicating that the unfolding process is non-ergodic.