Biology Reference
In-Depth Information
Fig. 18
Equilibrium forms of a microtubule. The
dot
marks the cell center. (
a
) The centrosome is
in the cell center. (
b
) The centrosome has been moved away from the center; the two alternative
forms are no longer equivalent. (
c
) A further displacement of the centrosome has led to disappear-
ance of the metastable form. (
d
) The centrosome has been moved back to the cell center from the
position shown in (
c
); only one of the two potentially existing forms is occupied (cf.
a
). Reproduced
from Maly and Maly (
2010
) with permission from Elsevier
microtubules will adopt the corresponding stable form. “Flipping” into the only
remaining equilibrium is an energy-dissipating process. Therefore it cannot be
reversed by returning the system to the domain of existence of the metastable solu-
tion. This phenomenon underlies our first example of emergent irreversibility in an
intrinsically elastic cell body, which is caused by its confinement within the cell
boundary.
Irreversibility accompanies the spontaneous evolution of the symmetric flat
microtubule aster in response to a perturbation of the centrosome position. The third-
power growth of the centrosome-displacing force that the microtubule system devel-
ops for small deviations of the centrosome from the center was considered in the
previous section (Fig.
4
). The system's evolution is reversible for such small defor-
mations of the fully symmetric structure. However, the new equilibrium is reached
only when the centrosome becomes removed from the center by a distance approxi-
mately equal to the difference of the microtubule length and cell radius (Figs.
2
,
19b
,
and
20
). Metastable forms of microtubules gradually become lost beginning with the
first inflection point on the forward branch of the force function (solid curve in
