Biology Reference
In-Depth Information
The model considered in the last section was extended (Maly
2012
) to calculate
the force exerted on the spindle by astral microtubules that are bent by virtue of their
confinement within the cell boundary. It was found that depending on parameters, the
symmetric position of the spindle can be stable or unstable. Asymmetric stable equi-
libria also exist, and two or more stable positions can exist with the same parameters.
The theory poses new types of questions for experimental research. Regarding the
cases of symmetric spindle positioning, it is necessary to ask whether the microtu-
bule parameters are controlled by the cell so that the bending mechanics favors sym-
metry. If they are not, then it is necessary to ask what forces external to the microtubule
cytoskeleton counteract the bending effects sufficiently to actively establish symme-
try. Conversely, regarding the cases with asymmetry, it is necessary to investigate
whether the cell controls the microtubule parameters so that the bending favors
asymmetry apart from any forces that are external to the microtubule cytoskeleton.
Cells often divide symmetrically to produce two daughter cells that are of equal
or approximately equal size. Cell lines on which experiments are conducted in cell
culture tend to reproduce in this fashion. Asymmetric divisions that produce daugh-
ter cells of unequal size abound during development and differentiation in multicel-
lular organisms. Experimentally well-characterized examples include single-cell
embryos of the mussel
Unio
(Lillie
1901
), roundworm
Caenorhabditis
(Hyman and
White
1987
) and leech
Helobdella
(Symes and Weisblat
1992
),
Drosophila
neuro-
blasts (McCarthy and Goldstein
2006
), and mammalian oocytes (Schuh and
Ellenberg
2008
). In the roundworm, for example, the first unequal division creates a
larger cell that is the first somatic cell and a smaller cell that continues the germ line.
In addition to the significance of size as such, for example between the large stem
cell and its small progeny (Watt and Hogan
2000
), the division into daughter cells of
unequal size may lead to an unequal distribution of specific components of the
mother cell cytoplasm between the progeny. Such components may include cell fate
determinants (Whittaker
1980
). In this connection, the general notion of asymmetric
cell division includes cases where the daughter cells are of equal size, yet differ in
the complement of components that they inherit. For a broader review of such cases,
in addition to the cited work by McCarthy and Goldstein, one may be referred to
Knoblich (
2008
) or Siller and Doe (
2009
). Here the term “asymmetric division” is
used exclusively in reference to the division that generates daughter cells of unequal
size. This case presents an obvious challenge for biomechanical explanation.
Generally, cells divide through the middle of the mitotic spindle (Bray
2001
). The
spindle proper consists of microtubule bundles that connect the two spindle poles.
Precise terminology was developed (Maly
2012
) in order to formulate the theoretical
question posed by the symmetric and asymmetric cell division through the position-
ing of the bipolar dividing cell body within the still-common cell boundary. The line
segment connecting the two spindle poles was termed the physical spindle axis. In
the geometrical sense, this axis can be extended to define a coordinate axis that
passes through the cell. The instance of the (extended) spindle axis passing through
the cell center can be considered first. The paradigmatic cases, e.g., the HeLa cul-
tured cells (Théry et al.
2005
) or the first division in
Caenorhabditis
(Grill et al.
2001
), seem to exhibit this geometry. The cell center can be defined as the geometri-
cal center of the space delimited by the cell boundary. The fundamental question
