On the fluctuations of the force exerted by a lipid nanotubule
Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS & Université Paris Diderot-Paris 7, Bât. Condorcet, CC 7056, 75205, Paris, France
Revised: 6 April 2009
Accepted: 30 April 2009
Published online: 12 June 2009
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 f . We obtain f and f in terms of the internal membrane tension , the bending rigidity , the temperature k B T and a molecular cutoff . We find for f a shift ∼ 1/ with respect to the mean field behavior ∼ . We obtain ( f )2 ∼ R ln(R/b) where b is a molecular length, f being typically small compared to f . Taking into account the difference between the internal tension and the actual mechanical tension 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 200 , of radius significantly smaller than 100nm, that are connected to a large membrane reservoir, e.g., a giant vesicle.
PACS: 87.10.-e Biological and medical physics: general theory and mathematical aspects – / 87.16.dj Membranes, bilayers, and vesicles: dynamics and fluctuations –
© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg, 2009