An equation of state is something you hear about in introductory thermodynamics, for example, the Ideal gas equation. The ideal gas equation relates the pressure, volume, and the number of particles of the gas, to its temperature, uniquely defining its state. This description is possible in physics when the system under investigation is in equilibrium or near equilibrium. In biology, a tissue is modeled as a fluid composed of cells. These cells are constantly interacting with each other through mechanical and chemical signaling, driving them far from equilibrium. Can an equation of state exist for such a messy interacting system? In this talk, I show that the presence of strong cell-cell interaction in tissues gives rise to a novel non-equilibrium, size-dependent surface tension, something unheard of for classical fluids. This surface tension, in turn, modifies the packing of cells inside the tissue generating a size-dependent density and pressure. Finally, we show that a combination of these non-equilibrium pressure and densities can yield an equation of state for biological tissues arbitrarily far from equilibrium. In the end, I discuss how this new paradigm of size-dependent biological properties gives rise to novel modes of cellular motion in tissues

At small length-scales, capillary effects are significant, and thus the mechanics of soft material interfaces may be dominated by solid surface stresses or liquid surface tensions. The balance between surface and bulk properties is described by an elasto-capillary length-scale, in which equilibrium interfacial energies are constant. However, at small length-scales in biological materials, including living cells and tissues, interfacial energies are not constant but are actively regulated and driven far from equilibrium. Thus, the balance between surface and bulk properties depends upon the distance from equilibrium. Here, we model the spreading (wetting) of living cell aggregates as ‘active droplets’, with a non-equilibrium surface tension that depends upon internal stress generated by the actomyosin cytoskeleton. Depending upon the extent of activity, droplet surface properties adapt to the mechanics of their surroundings. The impact of this adaptation challenges contemporary models of interfacial mechanics, including extensively used models of contact mechanics and wetting.