The stretching of single poly-ubiquitin molecules: static versus dynamic disorder in the non-exponential kinetics of...

Static disorder has recently been implicated in the non-exponential kinetics of the unfolding of single molecules of poly-ubiquitin under a constant force [Kuo, Garcia-Manyes, Li, Barel, Lu, Berne, Urbakh, Klafter, and Fernández, Proc. Natl. Acad. Sci. U.S.A. 107, 11336 (2010)]. In the present paper, it is suggested that dynamic disorder may provide a plausible, alternative description of the experimental observations. This suggestion is made on the basis of a model in which the barrier to chain unfolding is assumed to be modulated by a control parameter r that evolves in a parabolic potential under the action of fractional Gaussian noise according to a generalized Langevin equation. The treatment of dynamic disorder within this model is pursued using Zwanzig's indirect approach to noise averaging [Acc. Chem. Res. 23, 148 (1990)]. In conjunction with a self-consistent closure scheme developed by Wilemski and Fixman [J. Chem. Phys. 58, 4009 (1973); ibid. 60, 866 (1974)], this approach eventually leads to an expression for the chain unfolding probability that can be made to fit the corresponding experimental data very closely.