Biology Reference
In-Depth Information
fundamental problem of equal vs. unequal cell division, i.e., of symmetric vs. asym-
metric position of the dividing, bipolar cell body within the still undivided cell
boundary along their common axis of symmetry.
The developed theory of the spindle (Maly
2012
, and the nonaxisymmetric calcu-
lations presented here) derives the static equilibria from the considerations of bend-
ing of the astral microtubules against the cell boundary, and assesses the stability of
the equilibria. In this respect, it is an extension of the pioneering spindle model by
Bjerknes (
1986
). The distinctive new method is explicit computation of the bent
microtubule forms and stability analysis, like in the application to the interphase
cytoskeleton (last section). The chief general prediction obtained with this method is
that an intrinsically symmetric mitotic microtubule cytoskeleton may spontaneously
adopt asymmetric conformations, when constrained within the cell. In this respect,
the model is conceptually derivative from the treatment of the interphase microtu-
bule cytoskeleton that was developed in the last section and from the pioneering
work of Holy (
1997
) on the interphase microtubule asters. The mitotic model reveals
the differences of the mechanics of two coupled asters of microtubules that are found
at the two poles of the mitotic spindle. The individual confined asters in the inter-
phase models always break the symmetry with respect to the cell center. The mitotic
model, at least under certain conditions, exhibits stable equilibria that are centrally
symmetric, as well as bistability between the symmetric and asymmetric equilibria.
The model does not distinguish between equilibrium structures that are identical
but for rotation with respect to the cell center, because microtubules in such struc-
tures are bent equally against the spherical cell outline. When the cell shape deviates
from the sphere, the model should apply qualitatively insofar as the position of the
spindle along the common axis of the spindle and the cell outline is concerned. An
example is the ellipsoidal egg of
Caenorhabditis
. The model is more quantitatively
applicable to the other mentioned cases of the first divisions in eggs that are approx-
imately spherical.
The theoretical possibility of the spontaneous development of asymmetry
through bending of astral microtubules, and the existence of special requirements
for the stability of symmetric conformations, pose new types of questions that can
be asked when designing and interpreting experiments. Symmetric spindle position-
ing cannot be considered a “default” state of the system. Just as importantly, the
source of the asymmetry should not be sought necessarily outside an intrinsically
symmetric structure consisting of the mitotic microtubule cytoskeleton and the con-
fining cell boundary.
When studying a case of symmetric positioning, it is worth investigating what
makes it symmetric. Do the parameters such as the length of the astral microtubules
(
L
) and of the spindle proper (
S
) have values that support the stable symmetry? If
they do not, what forces external to the microtubule cytoskeleton act against the
collective bending forces and actively establish the symmetry?
When studying a case of asymmetric spindle positioning, it is worth investigating
the possible contribution of the collective bending effects of the astral microtubules
to the generation of asymmetry. In fact, in the light of the theory this question acquires
