Monomer Depletion, Pressure Difference, and Membrane Tube Radius Reduction due to Fiber Polymerization in Microspikes

In many processes vital to life, the growth of biological fibers outwards from a membrane surface naturally produces membrane tube tethers or microspikes in biological cells. Here, we investigate the novel effect of pressure difference (due to monomer depletion) on the polymerization dynamics of biological fibers within long membrane tubes. We crucially find that fiber monomers become depleted close to the growing tip as the fiber polymerizes, thus reducing the local pressure, and hence decreasing the membrane tube radius at the tip. This process is found to slow the growth of the fiber, a process which becomes important when we go on to construct a dynamical theory for biopolymer growth in long, narrow tubes. Our result is interesting in that it emphasizes how “passive” biological transport mechanisms such as via pressure differences may play an important role in cell movements.

Figure 1

Diagram showing a typical biological microspike. A flux of monomers (dashed arrows) from a reservoir concentration of $\rho (0)$ at the base of a fiber bundle ($z=0$) feeds the growing bundle of $n$ fiber ends (at $z=L$), within an enclosing membrane tube. The cylindrical membrane radius $r(z)$ can be seen to decrease linearly (in the quasistatic regime) down the tube as the pressure is reduced due to monomers being used up at the fiber bundle tip of radius $b$.