Cooperativity governs the size and structure of biological interfaces

Interfaces, defined as the surface of interactions between two parts of a system at a discontinuity, are very widely found in nature. While it is known that the specific structure of an interface plays an important role in defining its properties, it is less clear whether or not there exist universal scaling laws that govern the structural evolution of a very broad range of natural interfaces. Here we show that cooperativity of interacting elements, leading to great strength at low material use, is a key concept that governs the structural evolution of many natural interfaces. We demonstrate this concept for the cases of β-sheet proteins in spider silk, gecko feet, legs of caterpillars, and self-assembling of penguins into huddles, which range in scales from the submolecular to the macroscopic level. A general model is proposed that explains the size and structure of biological interfaces from a fundamental point of view.