How protein materials balance strength, robustness and adaptability

We report a theoretical fracture mechanics framework for describing underlying physical mechanism of H-bond rupture events that control the strength of beta-sheet protein structures found in materials such as silk, muscle and amyloid fibers. Using large-scale atomistic simulation and theory, we show that rupture of H-bonds 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 large number of H-bonds. This universal result leads to an intrinsic size-dependent strength limit that suggests that shorter beta-strands with less H-bonds achieve the highest shear strength, which is comparable to theoretical values obtained for metals. The asymptotical near-equilibrium strength limit predicted by our theory agrees very well with single-biomolecule experiments on beta-proteins. Our results also explain recent experimental proteomics data, suggesting a correlation between strength and the prevalence of beta-strand lengths in biology.