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Dwell-Time Distribution Analysis of Polyprotein Unfolding Using Force-Clamp Spectroscopy

Jasna Bruji, Rodolfo I. Z. Hermans, Sergi Garcia-Manyes, Kirstin A. Walther and Julio M. Fernandez

Department of Biological Sciences, Columbia University, New York, New York 10027

Correspondence: Address reprint requests to Jasna Bruji at her present address, Center for Soft Matter Research, Dept. of Physics, New York University, New York, NY 10003. E-mail: jb2929{at}nyu.edu; E-mail: jb2379{at}columbia.edu; or to J. M. Fernandez, E-mail: jfernandez{at}columbia.edu.

Using the recently developed single molecule force-clamp technique we quantitatively measure the kinetics of conformational changes of polyprotein molecules at a constant force. In response to an applied force of 110 pN, we measure the dwell times of 1647 unfolding events of individual ubiquitin modules within each protein chain. We then establish a rigorous method for analyzing force-clamp data using order statistics. This allows us to test the success of a history-independent, two-state model in describing the kinetics of the unfolding process. We find that the average unfolding trajectory is independent of the number of protein modules N in each trajectory, which varies between 3 and 12 (the engineered protein length), suggesting that the unfolding events in each chain are uncorrelated. We then derive a binomial distribution of dwell times to describe the stochastic dynamics of protein unfolding. This distribution successfully describes 81% of the data with a single rate constant of = 0.6 s^–1 for all N. The remainder of the data that cannot be accounted for suggests alternative unfolding barriers in the energy landscape of the protein. This method investigates the statistical features of unfolding beyond the average measurement of a single rate constant, thus providing an attractive alternative for measuring kinetics by force-clamp spectroscopy.

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