Systems Biomechanics of the Cell - Systems Biomechanics of the Cell - page 28

Fig. 14 Spindle force
as a function of displacement
orthogonal to the spindle.
( a ) L = 0.7 R , S = 0.8 R , q max = π.
( b ) L = 1.1 R , S = 0.3 R , q max = π
displacement along the orthogonal coordinate axis y . The relevant coordinate of the
center of the spindle proper can be denoted y s , and the projection of the total force
acting on the spindle proper, F y .
Figure 14a demonstrates that long spindles with short astral microtubules exhibit
stability of the axial symmetry. Figure 14b demonstrates that short spindles with
long astral microtubules exhibit instability of the axial symmetry and stability of a
nonaxisymmetric equilibrium. Note that in the limit of short spindles, the model
becomes identical with the single interphase aster, and also identical with the axi-
symmetric spindle model taken to the same limit.
The results pertaining to nonaxisymmetric conformations lend support to the
general form of the conclusions that can be drawn about symmetry and stability of
static equilibria of spindles and bipolar cell bodies confined by the cell boundary.
Collectively the computational results call attention to the theoretical fact that
intrinsically symmetric assembly of the spindle microtubules in the absence of
external forces will not necessarily result in symmetric positioning of the spindle
within the cell boundary. This general conclusion does not apply exclusively to the
cases of symmetric vs. asymmetric positioning of the spindle midplane, with which
the above exposition has been mainly concerned due to its importance for the