Biology Reference
In-Depth Information
Fig. 3 Equilibrium
conformation of the
microtubule cytoskeleton in a
spherical cell. Sample
microtubule forms that lie in
the plane passing through the
centrosome and the cell
center are shown.
Reproduced from Maly and
Maly ( 2010 ) with permission
from Elsevier
microtubule cytoskeleton in these cells adopts the minimum-energy conforma-
tion, while the antigen-mediated conjugation with another cell provides the exter-
nal reference frame with respect to which the other forces may orient the
constitutively asymmetric microtubule aster (Arkhipov and Maly 2006a ; Baratt
et al. 2008 ).
As an example with real numbers, consider an experiment in which an aster of
N = 20 microtubules, each L = 12 μm long, is assembled inside an approximately
spherical chamber of radius R = 10 μm, with a bead replacing the centrosome (Holy
1997 ). The model predicts (Fig. 2 ) that when L / R = 12 μm/10 μm = 1.2, the normal-
ized equilibrium distance of the centrosome from the center of the chamber will be
Δ e / R ≈ 0.4. In the chamber of the assumed size, therefore, the distance of the centro-
some from the center will be Δ e = 0.4 R = 4 μm. This example demonstrates how the
unit-invariant form in which the model results are presented can be applied to any
specific situation in a quantitative experiment.
It was assumed in the above that all microtubules in the cell have the same length.
A generalization of the model to a distribution of lengths is straightforward. To
preserve the intrinsic symmetry of the cytoskeleton, the distribution characterized
by a density function q ( L ) should be the same for each orientation of unstressed
emanation from the centrosome. The only modification to the model will be to inte-
grate with respect to L in addition to integrating with respect to the emanation angle
when finding the total force F . The formula for the total force in the three-
dimensional case becomes
=
Ff
(,)()
q 0
LpqL
L
Let for example q ( L ) be the density function of a uniform distribution between
1.05 R and 1.15 R . Following the same computational strategy, Maly and Maly
( 2010 ) find in this case that Δ eq = 0.220 R . In the model with the constant length,
when its value was equal to the mean of this distribution ( L = 1.1 R ), the equilibrium
Search WWH ::




Custom Search