211 research outputs found
Aggregation of Red Blood Cells: From Rouleaux to Clot Formation
Red blood cells are known to form aggregates in the form of rouleaux. This
aggregation process is believed to be reversible, but there is still no full
understanding on the binding mechanism. There are at least two competing
models, based either on bridging or on depletion. We review recent experimental
results on the single cell level and theoretical analyses of the depletion
model and of the influence of the cell shape on the binding strength. Another
important aggregation mechanism is caused by activation of platelets. This
leads to clot formation which is life saving in the case of wound healing but
also a major cause of death in the case of a thrombus induced stroke. We review
historical and recent results on the participation of red blood cells in clot
formation
Parameterization invariance and shape equations of elastic axisymmetric vesicles
The issue of different parameterizations of the axisymmetric vesicle shape
addressed by Hu Jian-Guo and Ou-Yang Zhong-Can [ Phys.Rev. E {\bf 47} (1993)
461 ] is reassesed, especially as it transpires through the corresponding Euler
- Lagrange equations of the associated elastic energy functional. It is argued
that for regular, smooth contours of vesicles with spherical topology,
different parameterizations of the surface are equivalent and that the
corresponding Euler - Lagrange equations are in essence the same. If, however,
one allows for discontinuous (higher) derivatives of the contour line at the
pole, the differently parameterized Euler - Lagrange equations cease to be
equivalent and describe different physical problems. It nevertheless appears to
be true that the elastic energy corresponding to smooth contours remains a
global minimum.Comment: 10 pages, latex, one figure include
Second variation of the Helfrich-Canham Hamiltonian and reparametrization invariance
A covariant approach towards a theory of deformations is developed to examine
both the first and second variation of the Helfrich-Canham Hamiltonian --
quadratic in the extrinsic curvature -- which describes fluid vesicles at
mesoscopic scales. Deformations are decomposed into tangential and normal
components; At first order, tangential deformations may always be identified
with a reparametrization; at second order, they differ. The relationship
between tangential deformations and reparametrizations, as well as the coupling
between tangential and normal deformations, is examined at this order for both
the metric and the extrinsic curvature tensors. Expressions for the expansion
to second order in deformations of geometrical invariants constructed with
these tensors are obtained; in particular, the expansion of the Hamiltonian to
this order about an equilibrium is considered. Our approach applies as well to
any geometrical model for membranes.Comment: 20 page
Viscous regularization and r-adaptive remeshing for finite element analysis of lipid membrane mechanics
As two-dimensional fluid shells, lipid bilayer membranes resist bending and
stretching but are unable to sustain shear stresses. This property gives
membranes the ability to adopt dramatic shape changes. In this paper, a finite
element model is developed to study static equilibrium mechanics of membranes.
In particular, a viscous regularization method is proposed to stabilize
tangential mesh deformations and improve the convergence rate of nonlinear
solvers. The Augmented Lagrangian method is used to enforce global constraints
on area and volume during membrane deformations. As a validation of the method,
equilibrium shapes for a shape-phase diagram of lipid bilayer vesicle are
calculated. These numerical techniques are also shown to be useful for
simulations of three-dimensional large-deformation problems: the formation of
tethers (long tube-like exetensions); and Ginzburg-Landau phase separation of a
two-lipid-component vesicle. To deal with the large mesh distortions of the
two-phase model, modification of vicous regularization is explored to achieve
r-adaptive mesh optimization
Electrical Double Layer and Phospholipid Membranes. Aspects of Interface Water Structure
It is inferred that the formation of an electrical double layer in phospholipid membranes is affected by the modified water. structure at the membrane/water interface. Theoretical evidence is presented indicating a decrease in the number density of water hydrogen bonds and the appearance of a layer of spontaneously polarized water at the solid/water interface which are the consequence of the orientational properties of the water structure and the asymmetric structure of the water molecule respectively. Consequences of such modifications of water structure are discussed on the basis of simple models regarding ion distribution at the interface, effect on the phospholipid chain melting phase transition temperature and the membrane-membrane interaction
Vesicle shape, molecular tilt, and the suppression of necks
Can the presence of molecular-tilt order significantly affect the shapes of
lipid bilayer membranes, particularly membrane shapes with narrow necks?
Motivated by the propensity for tilt order and the common occurrence of narrow
necks in the intermediate stages of biological processes such as endocytosis
and vesicle trafficking, we examine how tilt order inhibits the formation of
necks in the equilibrium shapes of vesicles. For vesicles with a spherical
topology, point defects in the molecular order with a total strength of
are required. We study axisymmetric shapes and suppose that there is a
unit-strength defect at each pole of the vesicle. The model is further
simplified by the assumption of tilt isotropy: invariance of the energy with
respect to rotations of the molecules about the local membrane normal. This
isotropy condition leads to a minimal coupling of tilt order and curvature,
giving a high energetic cost to regions with Gaussian curvature and tilt order.
Minimizing the elastic free energy with constraints of fixed area and fixed
enclosed volume determines the allowed shapes. Using numerical calculations, we
find several branches of solutions and identify them with the branches
previously known for fluid membranes. We find that tilt order changes the
relative energy of the branches, suppressing thin necks by making them costly,
leading to elongated prolate vesicles as a generic family of tilt-ordered
membrane shapes.Comment: 10 pages, 7 figures, submitted to Phy. Rew.
Budding transition for bilayer fluid vesicles with area-difference elasticity
We consider a curvature model for bilayer vesicles with an area-difference elasticity or non-local bending-energy term. Such a model interpolates between the bilayer-couple and spontaneous-curvature models. We report preliminary results for the budding transition. The shape transformation between the dumbbell and the pear phases can be continuous or discontinuous depending on the ratio of the non-local to the local bending rigidities
Thermodynamics of vesicle growth and instability
We describe the growth of vesicles, due to the accretion of lipid molecules
to their surface, in terms of linear irreversible thermodynamics. Our treatment
differs from those previously put forward by consistently including the energy
of the membrane in the thermodynamic description. We calculate the critical
radius at which the spherical vesicle becomes unstable to a change of shape in
terms of the parameters of the model. The analysis is carried out both for the
case when the increase in volume is due to the absorption of water and when a
solute is also absorbed through the walls of the vesicle.Comment: To be published in Phys. Rev.
Stresses in lipid membranes
The stresses in a closed lipid membrane described by the Helfrich
hamiltonian, quadratic in the extrinsic curvature, are identified using
Noether's theorem. Three equations describe the conservation of the stress
tensor: the normal projection is identified as the shape equation describing
equilibrium configurations; the tangential projections are consistency
conditions on the stresses which capture the fluid character of such membranes.
The corresponding torque tensor is also identified. The use of the stress
tensor as a basis for perturbation theory is discussed. The conservation laws
are cast in terms of the forces and torques on closed curves. As an
application, the first integral of the shape equation for axially symmetric
configurations is derived by examining the forces which are balanced along
circles of constant latitude.Comment: 16 pages, introduction rewritten, other minor changes, new references
added, version to appear in Journal of Physics
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