Stress tensor field and mesoscopic stresses in the vertex model for tissues

Mechanical stresses are fundamental regulators in biological tissues, where the vertex model (VM) is pivotal for theoretical and force-inference studies. Yet, no uniform expression for the stress tensor exists for the VM. Here we provide a microscopic derivation of it, linking mesoscopic stresses to the VM forces. The stress field presents a freedom on how tensions are distributed across cells, which allows previous expressions to emerge as particular realizations of the field and suggests a link between mesoscopic stresses and cytoskeletal force-transmission architectures in real cells.