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Fig. 10
Transition between
q
max
= 0 and
q
max
= π in the
case of long astral
microtubules.
L
= 1.1
R
.
(
a
) Pole force function.
(
b
) Spindle force function.
S
= 0.3
R
. The line styles
correspond to values of
q
max
as in (
a
). Reproduced from
Maly (
2012
) under the
Creative Commons
Attribution License
occupies a position that lies toward the cell center from the pole force function
extremum, and the other occupies a position toward the cell margin from that pole's
extremum. With a further growth of
q
max
, the aster increases resistance at more
eccentric pole positions (Fig. 9a, dashed curve). This eventually erases the non-
monotonicity of the pole force function. Figure 9a shows that for sufficiently large
q
max
the function becomes monotonic as in the case of
q
max
= π (cf. Fig.
7
). The
spindle now possesses only one equilibrium, which is symmetric and stable. Thus
with short astral microtubules, there is an abrupt transition at some intermediate
q
max
to the behavior that is qualitatively like the one observed with
q
max
= π.
With long microtubules, the increase of
q
max
at first leads to the same changes
as with the short microtubules, namely the smoothing of the pole force function
extremum (Fig.
10a
, solid curve; cf. Fig.
6
). In addition, the function in this case
develops a discontinuity. It is caused by the conformational transition between
the lowest-energy conformations that differ on the two sides of
x
p
= 0, as dis-
cussed in the previous section in connection with the interphase model. The tran-
sition was non-observable in the case of
q
max
=0 because the alternative
conformations in that degenerate case were equivalent. A more consequential
difference from the case of the short microtubules is that the long microtubules
