Abstract
Recent experiments reveal that the volume of adhered cells is reduced as their basal area is increased. During spreading, the cell volume decreases by several thousand cubic micrometers, corresponding to large pressure changes of the order of megapascals. We show theoretically that the volume regulation of adhered cells is determined by two concurrent conditions: mechanical equilibrium with the extracellular environment and a generalization of Donnan (electrostatic) equilibrium that accounts for active ion transport. Spreading affects the structure and hence activity of ion channels and pumps, and indirectly changes the ionic content in the cell. We predict that more ions are released from the cell with increasing basal area, resulting in the observed volume-area dependence. Our theory is based on a minimal model and describes the experimental findings in terms of measurable, mesoscale quantities. We demonstrate that two independent experiments on adhered cells of different types fall on the same master volume-area curve. Our theory also captures the measured osmotic pressure of adhered cells, which is shown to depend on the number of proteins confined to the cell, their charge, and their volume, as well as the ionic content. This result can be used to predict the osmotic pressure of cells in suspension.