| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
Biophys J, September 1998, p. 1141-1142, Vol. 75, No. 3
Max-Planck-Institut für Kolloid und Grenzflächenforschung, Teltow, Germany
The remarkable elasticity of red cells shows up
under a variety of conditions both in vivo and in controlled
experiments on single cells. Squeezed through narrow capillaries with
diameters significantly smaller than the cells themselves, they
perfectly recover their biconcave resting shape countless times during
their life cycle of about 100 days in the circulatory system. Likewise, this normal biconcave shape undergoes drastic transformations if the
physiochemical conditions are changed by, for example, cholesterol
depletion, which causes a transition from discocytes to cup-shaped
stomatocytes. All these deformations imply both nonlinearity and
anisotropy, because the intermediate or final shapes differ
substantially from the initial biconcave rest shape. Micropipet
aspiration has become the paradigmatic method for the controlled study
of strong deformation.
How can the elastic behavior of the red blood cell in these conditions
be understood quantitatively on the basis of the molecular architecture
of its compound membrane? This question has intrigued biophysicists for
nearly 30 years. Based on a body of earlier work, Discher, Boal and
Boey have now made big progress in modeling the erythrocyte membrane,
as reported in two companion papers in this issue (Boey et al., 1998 The structural duality resides in the membrane's two-component
structure consisting of the lipid bilayer to which a protein network is
attached. Clearly the influence of the spectrin net on elasticity is
profound, in particular because it endows the cell with some shear
resistance. Investigators pursuing a reductionist approach have
systematically studied the bare fluid membrane elasticity during the
last ten years both theoretically and experimentally by using giant
vesicles. These studies have shown that a large variety of shapes and
shape transformations can be explained simply on the basis of curvature
elasticity and constraints on area and volume (Seifert, 1997 Network elasticity is much harder to model for strong deformations such
as those encountered in aspiration. Continuum models have two related
weaknesses (Elgsaeter and Mikkelsen, 1991 Exploiting the dichotomy of scales between the mesh size of about 70 nm
and the scale of the cell about 100 times larger, Discher and
co-workers have successfully modeled a whole cell undergoing
strong deformation using a two-step simulation approach. First, they
simulated an almost planar two-dimensional network modeling each
spectrin strand between the junctions as a polymer with about 10 to 20 monomers. Such simulations yield area-pressure characteristics and
elastic parameters even for the nonlinear regime where steric
interactions between the strands (for strong compression) and finite
extendability (for strong stretching) become important. Although it
would be desirable to use this model for the whole cell, the
computational cost of such a full-scale simulation is still
prohibitive. The clever idea of Discher and co-workers is to use these
small-scale simulations to calibrate parameter values of a
coarse-grained model for the network, keeping only the junctions which
interact through two and three body potentials. The functional form of
these potentials is chosen to reproduce the elasticity of the more
detailed model. In the second step, the network of junctions is put on
a closed fluid bilayer membrane with rigidity, thus modeling the
compound membrane. Simulation of the whole cell, e.g., in an aspiration
experiment, is made possible through this significant reduction in the
number of degrees of freedom.
Discher et al. have thus been able to bridge the gap between the mesh
size scale and that of the whole cell. As a first illustration, they
demonstrate the power of this quantitative approach by comparing the
calculated network density profile in the aspirated tongue with that
obtained from fluorescence imaging experiments. Such a comparison
reveals that the cytoskeleton seems to be prestressed, i.e., the
junctions are closer together than they would be in an isolated
cytoskeleton. A possible origin of this effect could be the loss of
bilayer material in the early stages of cell maturation.
In the future, Discher and colleagues' model (and ramifications still
to be developed) can be applied to several interesting problems
highlighted in the following incomplete list. First, even though
breaking of axisymmetry has not been crucial in the aspiration
experiment, this model can be used to investigate distinctly nonaxisymmetric shapes such as echinocytes that would be difficult to
study with continuum models. In such a study one should allow for the
expected partial separation between network and bilayer. Second, in
this model both the bilayer and the network are still homogeneous,
whereas the bilayer membrane of real cells consists of various lipids
and integrated proteins and the real network has a significant number
of defects. How does this inhomogeneity affect and how is it affected
by strong deformations? Such a question can be addressed by decorating
this model with additional particles modeling the proteins and by
introducing network defects. Depending on the interactions of proteins
with both the membrane and the network, enrichment or depletion will
occur in a manner sensitive to local curvature and network distortion.
Finally, an outstanding challenge will be to extend this approach to
study of the dynamics of shape changes induced by external hydrodynamic
fields such as shear or capillary flow. This will require incorporating
long-range hydrodynamic interactions into the model, a task recently
achieved in the simpler model system of fluid bilayer vesicles (Kraus
et al., 1996
ARTICLE
;
Discher et al., 1998). Their success consists in exploiting and finally
resolving both the structural duality and the dichotomy of scales
of the red cell.
). On the
other hand, the same studies have also revealed that this simple
one-component model membrane lacking the network does not form anything
like the spicules of echinocytes.
). First, nonlinear elasticity
is difficult to implement without introducing some arbitrariness.
Second, the contribution of thermal fluctuations to the configurations
of the network can be incorporated easily only on the linear level. On
the other hand, computer simulations of discrete networks have been
devoted to almost planar configurations with a few exceptions
concerning polymerized vesicles (Gompper and Kroll, 1997).
). Discher and colleagues' model and its future
refinements can take us closer to a quantitative understanding of the
remarkable mechanochemical properties of the red blood cell.
| |
FOOTNOTES |
|---|
Received for publication 16 June 1998.
Address reprint requests to Udo Seifert, Max-Planck-Institut für Kolloid und Grenzflächenforschung, Kantstrasse 55, D-14513 Teltow, Germany. Tel.: 49-3328-46594; Fax: 49-3328-46212; E-mail: useifert{at}menkar.mpikg-teltow.mpg.de.
| |
REFERENCES |
|---|
Biophys J, September 1998, p. 1141-1142, Vol. 75, No. 3
© 1998 by the Biophysical Society 0006-3495/98/09/1141/02 $2.00
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||
| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
