Biology Reference
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force density, except that it is much higher for all values above 150 pN/μm than it is
below 140 pN/μm (Fig.
27d
). In the intervening range, the
z
-oscillations are not
sustained (Fig.
27b
).
The range of the distance (
z
) of the centrosome from the synapse exhibits a simi-
lar step-like dependence on the pulling force density, collapsing fully in the narrow
transition zone (Fig.
27e
). It can be observed that the farther away from the synapse
the centrosome is at any given time, the smaller the amplitude of the movement
parallel to the synapse will be. Figure
27f
shows that this relation is essentially
independent of the force density and is quasi-linear. The exception to its linearity is,
apparently, the natural limit of zero amplitude. When this limit is reached (this can
happen only at high force densities), the amplitude-distance relationship displays a
breakpoint at the axis intercept (Fig.
27f
). The zero amplitude of motion parallel to
the synapse is observed during the intervals between the pulses, as shown in
Fig.
27c
. Notably, the breakpoint of the
x
-amplitude versus
z
-position curve
(Fig.
27f
) is near the centrosome-synapse distance of 1 μm, the same distance that
characterizes the breakpoints of the dependencies of the
z
-position and
z
-period on
the force density (Fig.
27d, e
).
Close examination shows that this transition corresponds in individual trajecto-
ries to complete but temporary loss of contact between the microtubule system as
a whole and the synapse. This phenomenon appeared to arise from the viscous-
drag-induced “liftoff” of the microtubules (Fig.
25a
). During particularly vigorous
movement that can occur at the higher force densities, not just one side but the
entire microtubule system may lose contact with the synapse. In the absence of the
active driving force, it will take the motile system a considerable time to relax elas-
tically against the cytoplasmic drag and contact the synapse again. These periods
of time correspond to the long, high arcs of the
z
-trajectory and no
x
-movement, as
seen in Fig.
27c
.
Overall, intuition does not keep up with the complexity of the movement arising
in this relatively simply constructed mechanical system. At the same time, the com-
plexity revealed by the sufficiently accurate numerical analysis closely resembles
the multi-periodic and variable-amplitude movement seen in the experiments (Kuhn
and Poenie
2002
). It should be noted that the mechanistic explanation of this move-
ment that is offered by the model will be difficult to test using the existing live-cell
imaging techniques. Testing it would depend on resolving optically the small dis-
tances around the predicted breakpoints (~1 μm, Fig.
27d-f
).
Following a simultaneous development of two synaptic areas, the model centro-
some moves to one of them. After pausing at the first synapse (the pause can last for
a significant period of time), the model centrosome spontaneously moves to the other
synapse (Fig.
28a
). The cycle of movement, pause, and movement to the other syn-
apse appears to continue indefinitely with a well-defined periodicity. The character-
istic delay before the reverse movement is as seen in the experiments (Kuhn and
Poenie
2002
). The model predicts that for the delay to take place, the angle between
the two synaptic planes must be narrower than 150° (Fig.
28b
). The angle was indeed
sharp in the experiment (Kuhn and Poenie
2002
). By adjusting the pulling force
density and effective cytoplasm viscosity, both the duration of the pause and the
