Biology Reference
In-Depth Information
Fig. 2
Equilibrium distance of the centrosome from the cell center. Continuous three-dimensional
model (
Triangles
). Discrete model with 20 microtubules emanating in the directions of the vertices
of a dodecahedron (
Crosses
). Continuous two-dimensional model (positions reached spontane-
ously after a small perturbation of a fully symmetric cytoskeleton) (
Circles
). Slopes 1 and 2 for
reference (
Dashed
). Reproduced from Maly and Maly (
2010
) with permission from Elsevier
centrosome by all microtubules are zero, the entire microtubule cytoskeleton will be
in equilibrium inside the cell. It is such equilibrium forms of the microtubule cyto-
skeleton as a whole that are of interest to the theory of centrosome positioning and
cell body positioning within the cell boundary. The simplest cytoskeleton is charac-
terized by a uniform distribution of the unstressed directions at which the microtu-
bules are clamped at the centrosome. In this case, a displacement of the centrosome
from the center preserves one axis of symmetry, which coincides with the displace-
ment. This residual symmetry makes the total torque zero and the total force col-
linear with the centrosome displacement.
In three dimensions, as has been mentioned, any deviation of the centrosome
from the cell center specifies the direction of buckling for each microtubule, which
is convex in the direction of the centrosome displacement. Thus, any such deviation
generates a form of the cytoskeleton in which there is a non-zero total force on the
centrosome, and the direction of this force is away from the center. Calculations
show (Fig.
2
) that the equilibrium is reached when the centrosome is removed from
the cell center by a distance that is approximately twice as large as the difference
between the microtubule length and cell radius. Comparison of the numerical results
(Fig.
2
) shows that the simple continuous approximation for the microtubule aster is
already accurate when the number of microtubules is much lower than is typical in
mammalian cells. Figure
3
shows the shape of the three-dimensional cytoskeleton
at equilibrium.
The illustrated case of the spherical cell reproduces the salient features of the
internal structure of the quasi-spherical lymphocytes, namely the eccentric posi-
tion of the centrosome and the “combed” arrangement of the microtubules (Kuhn
and Poenie
2002
). This lends support to the model which is reviewed below in the
section devoted to the cell boundary dynamics and which asserts that the
