Spicules and the Effect of Rigid Rods on Enclosing Membrane Tubes

Membrane tubes (spicules) arise in cells, or artificial membranes, in the nonlinear deformation regime due to, e.g., the growth of microtubules, actin filaments, or sickle hemoglobin fibers towards a membrane. We calculate the axial force $f$ exerted by the tube, and its average radius, taking into account steric interactions between the fluctuating membrane and the enclosed rod. We find a smooth crossover of the axial force between $f\sim \sqrt{\sigma }$ and $f\sim \sigma$ as the membrane tension $\sigma$ increases and the tube radius shrinks. This crossover occurs around the most physiologically relevant membrane tensions. Our work may be important in (i) interpreting experiments in which axial force is related to the tube radius or membrane tension, and (ii) constructing dynamical theories for biopolymer growth in narrow tubes where these fluctuation effects control the tube radius.

Figure 1

Sketch of an axial slice through a membrane tube (left) and a section of tube (right) of average radius $\overline{r}$ enclosing a cylindrical rod (of fixed radius $b$). The radial fluctuations are of amplitude $\delta r(z,\varphi )$ and have mean squared extent $⟨\delta r^2⟩$.