Active elastic network: Cytoskeleton of the red blood cell

In red blood cells there is a cortical cytoskeleton; a two-dimensional elastic network of membrane-attached proteins. We describe, using a simple model, how the metabolic activity of the cell, through the consumption of ATP, controls the stiffness of this elastic network. The unusual mechanical property of active strain softening is described and compared to experimental data. As a by-product of this activity there is also an active contribution to the amplitude of membrane fluctuations. We model this membrane as a field of independent “curvature motors,” and calculate the spectrum of active fluctuations. We find that the active cytoskeleton contributes to the amplitude of the membrane height fluctuations at intermediate wavelengths, as observed experimentally.

Figure 1

A schematic illustration of our model of ATP-induced spectrin dissociation. The main parts of the figure show a side view of the RBC membrane, while the small parts show a schematic top view of the triangular cytoskeleton network. (a) The fully connected network, showing the balance between the stretched spectrin and curved bilayer. (b) The dissociated spectrin releases its stored tension. The phosphorylated node is indicated by the empty circle.

Figure 2

Calculated strain softening of the RBC network shear elasticity $\mu$ as a function of the local elongation $\lambda$ (solid line) from Eq. (2), compared to the experimental data (squares [24]). In the inset we plot the strain-stiffening of the fully connected network ${\mu }_0\left(\lambda \right)$, as calculated in Ref. 13.

Figure 3

Static fluctuation spectrum of the membrane of a normal RBC membrane $⟨h_q^2⟩$: stars and circles [29]. The solid line is the thermal component using Eq. (3), dashed and dash-dot lines are the active component of the curvature motor and direct force, respectively, using Eq. (5). A value of $\tau =50\mathrm{ms}$ was used in these calculations. Vertical dotted lines give $q_m$ (left) and $q_{\tau }$ (right), respectively.