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Determining dynamics from statics in living tissue

There are numerous examples where living tissues reshape and remodel themselves, from the early stages of organism development to the onset of metastasis and tumor formation in cancer. A consensus is emerging that such processes are controlled not only by genetics, but also by interand intra-cellular stresses. Understanding how tissues generate and respond to stress is important, but difficult to study in bulk living tissue. Thus, identifying structural signatures of the mechanical properties of tissue would be extremely valuable to researchers, as one could analyze static images of tissue samples to extract cellular forces and mobility. Recent theoretical studies of the vertex model for confluent tissues [1] suggest that the asphericity of cell shapes can be used to extract dynamics and mechanical properties of tissue from static images. Briefly, the vertex model treats a two-dimensional (2D) tissue of confluent cells as a tessellation of N polygons with perimeter p and area a with total energy: