4 research outputs found
Fluctuating Filaments I: Statistical Mechanics of Helices
We examine the effects of thermal fluctuations on thin elastic filaments with
non-circular cross-section and arbitrary spontaneous curvature and torsion.
Analytical expressions for orientational correlation functions and for the
persistence length of helices are derived, and it is found that this length
varies non-monotonically with the strength of thermal fluctuations. In the weak
fluctuation regime, the local helical structure is preserved and the
statistical properties are dominated by long wavelength bending and torsion
modes. As the amplitude of fluctuations is increased, the helix ``melts'' and
all memory of intrinsic helical structure is lost. Spontaneous twist of the
cross--section leads to resonant dependence of the persistence length on the
twist rate.Comment: 5 figure
Fluid-membrane tethers: minimal surfaces and elastic boundary layers
Thin cylindrical tethers are common lipid bilayer membrane structures,
arising in situations ranging from micromanipulation experiments on artificial
vesicles to the dynamic structure of the Golgi apparatus. We study the shape
and formation of a tether in terms of the classical soap-film problem, which is
applied to the case of a membrane disk under tension subject to a point force.
A tether forms from the elastic boundary layer near the point of application of
the force, for sufficiently large displacement. Analytic results for various
aspects of the membrane shape are given.Comment: 12 page
Modeling oscillatory Microtubule--Polymerization
Polymerization of microtubules is ubiquitous in biological cells and under
certain conditions it becomes oscillatory in time. Here simple reaction models
are analyzed that capture such oscillations as well as the length distribution
of microtubules. We assume reaction conditions that are stationary over many
oscillation periods, and it is a Hopf bifurcation that leads to a persistent
oscillatory microtubule polymerization in these models. Analytical expressions
are derived for the threshold of the bifurcation and the oscillation frequency
in terms of reaction rates as well as typical trends of their parameter
dependence are presented. Both, a catastrophe rate that depends on the density
of {\it guanosine triphosphate} (GTP) liganded tubulin dimers and a delay
reaction, such as the depolymerization of shrinking microtubules or the decay
of oligomers, support oscillations. For a tubulin dimer concentration below the
threshold oscillatory microtubule polymerization occurs transiently on the
route to a stationary state, as shown by numerical solutions of the model
equations. Close to threshold a so--called amplitude equation is derived and it
is shown that the bifurcation to microtubule oscillations is supercritical.Comment: 21 pages and 12 figure