Biology Reference
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priority. Although the quantitative nature of the collective bending that breaks
symmetry is complex, the hypothesis that the source of asymmetry resides in the
basic cytoskeleton structure itself is simple, compared with hypotheses that involve
asymmetric regulation or asymmetric external forces applied to the structure.
The spontaneous development of asymmetry through unequal bending does not
by itself have a preferred direction: Each asymmetric equilibrium in the model has
a counterpart, which is mirror-symmetric about the cell center. External forces and
regulation mechanisms may be responsible for biasing the spontaneous symmetry-
breaking, even if they are not responsible for the generation of asymmetry.
Similarly, the action of the external forces, even transient, may be responsible
for selecting between the symmetric and asymmetric equilibria in the cases of
multistability.
Summarizing, the explicit numerical treatment of bending in systems of linked
and confined microtubules that was developed by Maly and Maly indicates exis-
tence of new types of collective mechanical behavior in confined microtubule cyto-
skeletons, which include symmetry-breaking and multistability. New types of
questions can be asked in experimental work in the light of the theory, which also
establishes a quantitative framework that can guide experiment design. Interpretation
of new experimental results, and, possibly, re-interpretation of those previously
obtained, will require generalization of the numerical model and its rigorous adap-
tation to the structural features of each cell type.
Boundary Dynamics
In the models presented so far the cell boundary was considered as a constraint on
the dynamics of the cell body. The simplification of unchanging boundary revealed
the complexity of the system-level mechanical behavior of the constrained microtu-
bule cytoskeleton and uncovered the autonomous capacity of the mechanics of the
confined cell body for generation of asymmetric cell conformations. Especially in
single, isolated animal cells, however, the boundary is far from rigid. The question
that can be asked in the light of the body mechanics models presented in the previ-
ous sections is as follows: Does a dynamic boundary participate in the symmetry
breaking, or does it counteract this tendency of the confined cell body? This ques-
tion can be addressed by examining the combination of the developed physical
models for the cell body and boundary.
In an ingenious experiment, microtubule asters assembled on artificial centro-
somes were placed inside lipid bilayer vesicles (Pinot et al.
2009
). The numerical
models developed in conjunction with these experiments, however, included only
rigid boundaries, like in the other models of confined microtubule cytoskeletons
that were reviewed in the previous sections. Numerical treatment of nonconstant
boundaries constraining microtubules requires a special approach. When construct-
ing such a model for the cell rather than the simplified experimental model, one has
