Probability of observing a number of unfolding events while stretching poly-proteins

Abstract

The mechanical stretching of single poly-proteins is an emerging tool for the study of protein (un)folding, chemical catalysis and polymer physics at the single molecule level. The observed processes i.e unfolding or reduction events, are typically considered to be stochastic and by its nature are susceptible to be censored by the finite duration of the experiment. Here we develop a formal analytical and experimental description on the number of observed events under various conditions of practical interest. We provide a rule of thumb to define the experiment protocol duration. Finally we provide a methodology to accurately estimate the number of stretched molecules based on the number of observed unfolding events. Using this analysis on experimental data we conclude for the first time that poly-ubiquitin binds at a random position both to the substrate and to the pulling probe and that observing all the existing modules is the less likely event.