Quantifying the shape of cells - from Minkowski tensors to p-atic order

P-atic liquid crystal theories offer new perspectives on how cells self-organize and respond to mechanical cues. Understanding and quantifying the underlying orientational orders is therefore essential for unraveling the physical mechanisms that govern tissue dynamics. Due to the deformability of cells this requires quantifying their shape. We introduce rigorous mathematical tools and a reliable framework for such shape analysis. Applying this to segmented cells in MDCK monolayers and computational approaches for active vertex models and multiphase field models challenges previous findings and opens new pathways for understanding the role of orientational symmetries andp-atic liquid crystal theories in tissue mechanics and development.