Nonkinetic Modeling of the Mechanical Unfolding of Multimodular Proteins: Theory and Experiments

We introduce and discuss a novel approach called back-calculation for analyzing force spectroscopy experiments on multimodular proteins. The relationship between the histograms of the unfolding forces for different peaks, corresponding to a different number of not-yet-unfolded protein modules, is exploited in such a manner that the sole distribution of the forces for one unfolding peak can be used to predict the unfolding forces for other peaks. The scheme is based on a bootstrap prediction method and does not rely on any specific kinetic model for multimodular unfolding. It is tested and validated in both theoretical/computational contexts (based on stochastic simulations) and atomic force microscopy experiments on (GB1)(8) multimodular protein constructs. The prediction accuracy is so high that the predicted average unfolding forces corresponding to each peak for the GB1 construct are within only 5 pN of the averaged directly-measured values. Experimental data are also used to illustrate how the limitations of standard kinetic models can be aptly circumvented by the proposed approach.