On the fluctuations of the force exerted by a lipid nanotubule

Abstract

After deriving the projected stress tensor in cylindrical geometry for a fluid membrane described by the Helfrich Hamiltonian, we calculate the average force f exerted by a thermally fluctuating nanotubule of radius R , and its standard deviation $\Delta$ f . We obtain f and $\Delta$ f in terms of the internal membrane tension $\sigma$ , the bending rigidity $\kappa$ , the temperature k _B T and a molecular cutoff $\Lambda$ . We find for f a shift ∼ 1/$\sqrt{{\sigma}}$ with respect to the mean field behavior ∼ $\sqrt{{\sigma}}$ . We obtain ($\Delta$ f )² ∼ R ln(R/b) where b is a molecular length, $\Delta$ f being typically small compared to f . Taking into account the difference between the internal tension $\sigma$ and the actual mechanical tension $\tau$ applied to the membrane from which the tubule is drawn, we discuss the amplitude of the fluctuation-induced corrections to the average force. Our results, obtained in the harmonic approximation, hold for tubules with aspect ratio not larger than $\approx$ 200 , of radius significantly smaller than 100nm, that are connected to a large membrane reservoir, e.g., a giant vesicle.