  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 exerted by the cylindrical membrane tube, and its average radius,
by taking into account steric interactions between the fluctuating membrane and
the enclosed rod. The force required to confine a fluctuating membrane near the
surface of the enclosed rod diverges as the separation approaches zero. This
results in a smooth crossover of the axial force between a square root and a
linear dependence on the membrane tension as the tension increases and the tube
radius shrinks. This crossover can occur at 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 (ii)
dynamical theories for biopolymer growth in narrow tubes where these
fluctuation effects control the tube radius.
