https://doi.org/10.1140/epje/i2009-10468-8
Regular Article
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
* e-mail: jean-baptiste.fournier@univ-paris-diderot.fr
Received:
23
January
2009
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