Active Biochemical Regulation of Cell Volume and a Simple Model of Cell Tension Response

Abstract

Active contractile forces exerted by eukaryotic cells play significant roles during embryonic development, tissue formation, and cell motility. At the molecular level, small GTPases in signaling pathways can regulate active cell contraction. Here, starting with mechanical force balance at the cell cortex, and the recent discovery that tension-sensitive membrane channels can catalyze the conversion of the inactive form of Rho to the active form, we show mathematically that this active regulation of cellular contractility together with osmotic regulation can robustly control the cell size and membrane tension against external mechanical or osmotic shocks. We find that the magnitude of active contraction depends on the rate of mechanical pulling, but the cell tension can recover. The model also predicts that the cell exerts stronger contractile forces against a stiffer external environment, and therefore exhibits features of mechanosensation. These results suggest that a simple system for maintaining homeostatic values of cell volume and membrane tension could explain cell tension response and mechanosensation in different environments.

Cell mechanics: a dialogue

“…The results are straightforward [116], and we find that the passive stress within the network is relatively small when compared with the contractile stress and hydrostatic pressure, and the normal component of the force balance obtained from dotting equation (12) with n becomes $$\mathrm{normal\Delta }P-false(T+{\sigma }_{a}hfalse)false(\nabla \cdot \mathrm{boldn}false)=0.$$The tangential component is also interesting, and depending on the spatial variations in σ , there could be membrane flow and tension gradients. Geometrically, ∇ · n = 2 H where H is the cell surface mean curvature [136].…”

“…Alternatively, if the deformation is slow, then water will flow, leading to cell volume change. It appears that the relevant deformation time scale is μ m s −1 [105, 116]. With this time scale or slower, cells can change volume significantly.…”

Cellular mechanosensing of the biophysical microenvironment: A review of mathematical models of biophysical regulation of cell responses

“…The mechanosensitive ion channels are regulated by the mechanical force balance at the cell membrane-cortex surface, and their action determines homeostatic values of cell volume and membrane tension (Fig. 3E–F) [71]. …”

“…To understand the pathways underlying this volumetric regulation, a chemomechanical model was proposed by Tao & Sun, which modeled activation of the Rho signaling pathway by the opening of mechanosensitive ion channels [71]. There are two main assumptions in this model.…”

“…(D) Myosin and α-actinin accumulation increase at the pipette tip and filamin increases in the neck region during micropipette aspiration [117]. (E) Steady state cellular volume increases with increasing extracellular osmotic pressure [71]. (F) Schematic of the model prediction of volumetric changes in response to osmotic shock.…”