Active volume regulation in adhered cells

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.

Keywords: adhered cells; cell electrostatics; cell mechanics; cell volume; ion channels and ion pumps.

Fig. 1.

Sketch of an adhered cell. The nucleus occupies a fixed volume fraction $\alpha$. The cell contains proteins with localized ions (circled with dashed lines) as well as free cations and anions. While the proteins are confined to the cells, free ions exchange with the buffer through ion channels and pumps (not drawn). For simplicity, the proteins are assumed to have an average, effective charge of $-e/2\hspace{0.17em}\left(z=1/2\right)$. Electroneutrality is satisfied in the nucleus, in the cell, and in the buffer.

Fig. 2.

Measurements of cell volume as a function of their basal area from ref. (blue circles) and ref. (red squares), compared with the theoretical prediction of Eq. 7 for $z=0.26$ and ${\delta }_1=-0.14$. (A) Results in their original units. (B) Results in terms of the dimensionless area, $\stackrel{\sim }{A}$, and volume, $\stackrel{\sim }{V}$. The two experiments fall on the same curve.

Fig. 3.

Measurements from ref. of cell volume as a function of the external buffer pressure, compared with the theoretical prediction of Eq. 3. The curve corresponds to the same values of Fig. 2, $z=0.26$ and ${\delta }_1=-0.14$, used to fit the volume area measurements in Fig. 2, and a constant area of $A=\mathrm{1,500}\hspace{0.17em}\mathrm{\mu }{\mathrm{m}}^2$, in accordance with the experiment.