Hierarchies, multiple energy barriers, and robustness govern the fracture mechanics of α-helical and β-sheet protein domains

The fundamental fracture mechanisms of biological protein materials remain largely unknown, in part, because of a lack of understanding of how individual protein building blocks respond to mechanical load. For instance, it remains controversial whether the free energy landscape of the unfolding behavior of proteins consists of multiple, discrete transition states or the location of the transition state changes continuously with the pulling velocity. This lack in understanding has thus far prevented us from developing predictive strength models of protein materials. Here, we report direct atomistic simulation that over four orders of magnitude in time scales of the unfolding behavior of a-helical (AH) and beta-sheet (BS) domains, the key building blocks of hair, hoof, and wool as well as spider silk, amyloids, and titin. We find that two discrete transition states corresponding to two fracture mechanisms exist. Whereas the unfolding mechanism at fast pulling rates is sequential rupture of individual hydrogen bonds (HBs), unfolding at slow pulling rates proceeds by simultaneous rupture of several HBs. We derive the hierarchical Bell model, a theory that explicitly considers the hierarchical architecture of proteins, providing a rigorous structure-property relationship. We exemplify our model in a study of AHs, and show that 3-4 parallel HBs per turn are favorable in light of the protein's mechanical and thermodynamical stability, in agreement with experimental findings that AHs feature 3.6 HBs per turn. Our results provide evidence that the molecular structure of AHs maximizes its robustness at minimal use of building materials.