Geometric confinement governs the rupture strength of H-bond assemblies at a critical length scale.

The ultrastructure of protein materials such as spider silk, muscle tissue, or amyloid fibers consists primarily of beta-sheets structures, composed of hierarchical assemblies of H-bonds. Despite the weakness of H-bond interactions, which have intermolecular bonds 100 to 1000 times weaker than those in ceramics or metals, these materials combine exceptional strength, robustness, and resilience. We discover that the rupture strength of H-bond assemblies is governed by geometric confinement effects, suggesting that clusters of at most 3-4 H-bonds break concurrently, even under uniform shear loading of a much larger number of H-bonds. This universally valid result leads to an intrinsic strength limitation that suggests that shorter strands with less H-bonds achieve the highest shear strength at a critical length scale. The hypothesis is confirmed by direct large-scale full-atomistic MD simulation studies of beta-sheet structures in explicit solvent. Our finding explains how the intrinsic strength limitation of H-bonds can be overcome by the formation of a nanocomposite structure of H-bond clusters, thereby enabling the formation of larger and much stronger beta-sheet structures. Our results explain recent experimental proteomics data, suggesting a correlation between the shear strength and the prevalence of beta-strand lengths in biology.