Rigidity and mechanical response in biological structures

Rigidity is an emergent property of materials - it is not a feature of individual components that comprise the structure, but instead arises from interactions between many constituent parts. Recently, it has been recognized that floppy-rigid or fluid-solid transitions are harnessed by biological systems at all scales to drive form and function. This review focuses on the different mechanisms that can drive emergent rigidity transitions in biomechanical networks, and describes how they arise in mathematical formalisms and how they are observed in practice in experiments. The goal is to aid researchers in identifying mechanisms governing rigidity in their biological systems of interest, highlight mechanical features that are universal across different systems, and help drive new scientific hypotheses for observed mechanical phenomena in biology. Looking forward, we also discuss how biological systems might tune themselves towards or away from such transitions over developmental or evolutionary timescales.