7 research outputs found
Cylindrical equilibrium shapes of fluid membranes
Within the framework of the well-known curvature models, a fluid lipid
bilayer membrane is regarded as a surface embedded in the three-dimensional
Euclidean space whose equilibrium shapes are described in terms of its mean and
Gaussian curvatures by the so-called membrane shape equation. In the present
paper, all solutions to this equation determining cylindrical membrane shapes
are found and presented, together with the expressions for the corresponding
position vectors, in explicit analytic form. The necessary and sufficient
conditions for such a surface to be closed are derived and several sufficient
conditions for its directrix to be simple or self-intersecting are given.Comment: 17 pages, 4 figures. Published in J. Phys. A: Math. Theore
Contour models of cellular adhesion
The development of traction-force microscopy, in the past two decades, has
created the unprecedented opportunity of performing direct mechanical
measurements on living cells as they adhere or crawl on uniform or
micro-patterned substrates. Simultaneously, this has created the demand for a
theoretical framework able to decipher the experimental observations, shed
light on the complex biomechanical processes that govern the interaction
between the cell and the extracellular matrix and offer testable predictions.
Contour models of cellular adhesion, represent one of the simplest and yet most
insightful approach in this problem. Rooted in the paradigm of active matter,
these models allow to explicitly determine the shape of the cell edge and
calculate the traction forces experienced by the substrate, starting from the
internal and peripheral contractile stresses as well as the passive restoring
forces and bending moments arising within the actin cortex and the plasma
membrane. In this chapter I provide a general overview of contour models of
cellular adhesion and review the specific cases of cells equipped with
isotropic and anisotropic actin cytoskeleton as well as the role of bending
elasticity.Comment: 24 pages, 9 figures. arXiv admin note: text overlap with
arXiv:1304.107