Active Regulation of Pressure and Volume Defines an Energetic Constraint on the Size of Cell Aggregates.

We explore the relationship between the nonequilibrium generation of myosin-induced active stress within the F-actin cytoskeleton and the pressure-volume relationship of cellular aggregates as models of simple tissues. We find that due to active stress, aggregate surface tension depends upon its size. As a result, both pressure and cell number density depend on size and violate equilibrium assumptions. However, the relationship between them resembles an equilibrium equation of state with an effective temperature. This suggests that bulk and surface properties of aggregates balance to yield a constant average work performed by each cell on their environment in regulating tissue size. These results describe basic physical principles that govern the size of cell aggregates.