| Many biological tissues behave like viscous fluids on long timescales and possess a macroscopic, measurable surface tension. A large body of evidence suggests that surface tension correlates with the density of adhesion molecules on a cell's surface, but recent AFM experiments and experiments reported in this study indicate that a cell's cortical tension helps to determine the macroscopic surface tension. We have developed a minimal model for surface tension that considers the mechanical contributions of cell adhesion and cortical tension. We solve this model exactly for 2D ordered structures, and use numerical methods to show that disordered cellular structures are related to the ordered solutions in a remarkably simple way. An open question is whether a similar relationship holds in 3D between ordered and disordered local minimum energy states. This model can successfully explain the available experimental data and differs from previous analyses because it considers the feedback between mechanical energy and geometry and makes novel predictions about the shapes of cells on the surface of an aggregate, which we verify experimentally. Interestingly, this model also describes a dry foam for a particular choice of parameters, and in 2D it predicts how the surface energy of bubble clusters scales with system size. |
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