Table 1. Role and mechanism of individual levels of structural hierarchies for overall system behavior, illustrating that each hierarchical level plays a key role in achieving the overall system performance.

Hierarchy level Hn	Description	Key mechanism(s)
H0	Level of chemistry; Intrabackbone H-bond; Basic chemical bonding, enabled by particular polypeptide structure	H-bonds form at moderate temperatures; Drive self-assembly of alpha-helices
H1	Alpha-helix turn defined by cluster of 3–4 H-bonds; Basic building block of alpha-helix filament	Clusters of 3–4 H-bonds provide optimal resistance against mechanical failure [25] (3–4 H-bonds break concurrently, providing maximum possible mechanical strength at minimal material cost)
H2	Alpha-helix filament; Basic building block of square lattice	Particular geometry with linear array of turns provides structural basis for large extensibility of >150% strain via repeated rupture of turns (see Figure 1D)
H3	Square lattice unit cell; Microstructural geometry of network level	Distance between filaments provides structural basis to independently stretch without affecting neighboring bonds, since there are no immediate interactions between individual filaments in the network that prevent microscopic rotations and shear (see Figure 7C); Facilitates extreme strain gradients at low energy cost (≈2×1011 %/Å)
H4	Network; Macroscopic functional scale (e.g. nuclear envelope for mechanical integrity)	Structural transformation of crack-like defects (see Figure 6C and 8) to mitigate stress concentrations