Evidence of robust, universal conformal invariance in living biological matter

Abstract

Collective cellular movement plays a crucial role in many processes fundamental to health, including development, reproduction, infection, wound healing, and cancer. The emergent dynamics that arise in these systems are typically thought to depend on how cells interact with one another and the mechanisms used to drive motility, both of which exhibit remarkable diversity across different biological systems. Here, we report experimental evidence of a universal feature in the patterns of flow that spontaneously emerges in groups of collectively moving cells. Specifically, we demonstrate that the flows generated by collectively moving dog kidney cells, human breast cancer cells, and by two different strains of pathogenic bacteria, all exhibit conformal invariance. Remarkably, not only do our results show that all of these very different systems display robust conformal invariance, but we also discovered that the precise form of the invariance in all four systems is described by the Schramm-Loewner Evolution (SLE), and belongs to the percolation universality class. A continuum model of active matter can recapitulate both the observed conformal invariance and SLE form found in experiments. The presence of universal conformal invariance reveals that the macroscopic features of living biological matter exhibit universal translational, rotational, and scale symmetries that are independent of the microscopic properties of its constituents. Our results show that the patterns of flows generated by diverse cellular systems are highly conserved and that biological systems can unexpectedly be used to experimentally test predictions from the theories for conformally invariant structures