Multicellular Rosettes Drive Fluid-solid Transition in Epithelial Tissues

Models for confluent biological tissues often describe the network formed by cells as a triple-junction network, similar to foams. However, higher-order vertices or multicellular rosettes are prevalent in developmental and in vitro processes and have been recognized as crucial in many important aspects of morphogenesis, disease, and physiology. In this work, we study the influence of rosettes on the mechanics of a confluent tissue. We find that the existence of rosettes in a tissue can greatly influence its rigidity. Using a generalized vertex model and the effective medium theory, we find a fluid-to-solid transition driven by rosette density and intracellular tensions. This transition exhibits several hallmarks of a second-order phase transition such as a growing correlation length and a universal critical scaling in the vicinity of a critical point. Furthermore, we elucidate the nature of rigidity transitions in dense biological tissues and other cellular structures using a generalized Maxwell constraint counting approach, which answers a long-standing puzzle of the origin of solidity in these systems.