16 research outputs found
Axially symmetric membranes with polar tethers
Axially symmetric equilibrium configurations of the conformally invariant
Willmore energy are shown to satisfy an equation that is two orders lower in
derivatives of the embedding functions than the equilibrium shape equation, not
one as would be expected on the basis of axial symmetry. Modulo a translation
along the axis, this equation involves a single free parameter c.If c\ne 0, a
geometry with spherical topology will possess curvature singularities at its
poles. The physical origin of the singularity is identified by examining the
Noether charge associated with the translational invariance of the energy; it
is consistent with an external axial force acting at the poles. A one-parameter
family of exact solutions displaying a discocyte to stomatocyte transition is
described.Comment: 13 pages, extended and revised version of Non-local sine-Gordon
equation for the shape of axi-symmetric membrane
Formation and Interaction of Membrane Tubes
We show that the formation of membrane tubes (or membrane tethers), which is
a crucial step in many biological processes, is highly non-trivial and involves
first order shape transitions. The force exerted by an emerging tube is a
non-monotonic function of its length. We point out that tubes attract each
other, which eventually leads to their coalescence. We also show that detached
tubes behave like semiflexible filaments with a rather short persistence
length. We suggest that these properties play an important role in the
formation and structure of tubular organelles.Comment: 4 pages, 3 figure