Cooperativity governs the size and structure of biological interfaces

Abstract

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.

Introduction

An interface facilitates interactions between two systems with a discontinuity and covers a very broad range of applications including natural materials, biological tissues and social units (Granovet, 1973, Gao and Ji, 2003, Gao and Yao, 2006, Buehler and Yung, 2009, Nel and Madler, 2009, Keten and Xu, 2010). One function of those interactions is to connect two distinct systems so that they can act together, through either physical forces or communication. A tissue or organ can reach its physiological functions only with physical connections to other units that enable them to act as a larger system, the organism. For example, the enthesis in our body is formed from collagen fibers that act as a junction to connect tendon and bone (Resnick and Niwayama, 1983), and through this interface the forces generated by muscles enable the movements of the body that are structurally supported by the bone tissue. Sociological interfaces are often more abstract, as they include the interactions between individuals or groups of social units with differences in values, interests, knowledge and power (Granovet, 1973). The structure of biological interfaces is often hierarchical, and intriguing examples include the structure on a gecko's toe with geometrical features from the nano- to the micrometer length scale and remarkable adhesion strength (Autumn and Peattie, 2002, Gao and Ji, 2003, Gao and Wang, 2005, Wei and Naraghi, 2012, Irschick and Austin, 1996).

While it has been shown that the function of specific biological interfaces is sensitive to their structural morphology, what is less clear is whether or not there exist universal scaling laws that govern the evolution of structures of very different natural interfaces. Adaption of structure in biology is a process that enables species and populations to effectively deal with their environment, and the goal of this process is to utilize limited material, volume, mass, energy, etc. to reach a level of performance that is sufficient for survival. In this context, adhesion strength can be seen as an overarching objective function of many mechanically relevant biological interfaces. An overview of different interfaces is shown in Fig. 1, where the key question is how to enhance the adhesion strength and minimize the use of adhesive materials. To achieve this goal, the interface geometry is important to maximize cooperativity, as is defined as the uniform nature of the interfacial material to respond to loading. We hypothesize that natural morphologies of mechanically relevant biological interfaces are solutions to maximize cooperativity that lead to enhanced adhesion strength under these constraints.