Why Extensile and Contractile Tissues Could be Hard to Tell Apart

Active nematic models explain the topological defects and flow patterns observed in epithelial tissues, but the nature of active stress-whether it is extensile or contractile, a key parameter of the theory-is not well established experimentally. Individual cells are contractile, yet tissue-level behavior often resembles extensile nematics. To address this discrepancy, we use a continuum theory with two-tensor order parameters that distinguishes cell shape from active stress. We show that correlating cell shape and flow, whether in coherent flows in channels, near topological defects, or at rigid boundaries, cannot unambiguously determine the type of active stress. Our results demonstrate that simultaneous measurements of stress and cell shape are essential to fully interpret experiments investigating the nature of the physical forces acting within epithelial cell layers.