Cooperativity is a hallmark of proteins, many of which show a modulararchitecture comprising discrete structural domains. Detecting and describingdynamic couplings between structural regions is difficult in view of themany-body nature of protein-protein interactions. By utilizing the GPU-basedcomputational acceleration, we carried out simulations of the protein forcedunfolding for the dimer WW-WW of the all-beta-sheet WW domains used as a modelmultidomain protein. We found that while the physically non-interactingidentical protein domains (WW) show nearly symmetric mechanical properties atlow tension, reflected, e.g., in the similarity of their distributions ofunfolding times, these properties become distinctly different when tension isincreased. Moreover, the uncorrelated unfolding transitions at a low pullingforce become increasingly more correlated (dependent) at higher forces. Hence,the applied force not only breaks "the mechanical symmetry" but also couplesthe physically non-interacting protein domains forming a multi-domain protein.We call this effect "the topological coupling". We developed a new theory,inspired by Order statistics, to characterize protein-protein interactions inmulti-domain proteins. The method utilizes the squared-Gaussian model, but itcan also be used in conjunction with other parametric models for thedistribution of unfolding times. The formalism can be taken to thesingle-molecule experimental lab to probe mechanical cooperativity and domaincommunication in multi-domain proteins.
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