Biomedical Engineering Reference
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here: the run length decreases strongly with increasing coupling strength. The run
length of the two-motor complex, however, is always larger than the run length of a
single motor (which is approached for large coupling strength), i.e., the interference
between the motors decreases the effect of motor cooperation, but does not reduce
it below the level of a single motor. The average velocity shows even less reduction
than the velocity
v
2
of 2-motor runs and increases again for strong coupling, because
with increasing coupling strength, 1-motor runs become more and more likely, and
thus the reduced velocity of 2-motor runs contributes less and less to the average.
Nonlinear couplings have also been considered within the stochastic stepper
approach [
8
]. For example, cable-like springs (that are linear springs with respect to
stretching but exhibit no resistance to compression) leads to a much weaker effect
because it takes longer to build up substantial strain forces between the two motors
[
8
]. In addition, several studies have considered springs with a force-dependent spring
constant, specifically, the case of a spring that is rather soft at low force and stiff at
large forces. Such a spring can be characterized by two spring constants and is sug-
gested by some experiments on the kinesin tail [
3
,
27
]. The latter spring also leads to
weaker coupling effects, indicating that the lower spring constant (for which building
up strain requires some time) is dominant during 2-motor runs [
8
].
3.4.1.3 Different Types of Elastic Coupling and Cargo Geometry
Finally, the impact of the type of spring was also studied in simulations of bead
movements with explicit representation of the cargo geometry. Two different types
of springs were studied, a linear spring and a cable-like (or semi-harmonic) spring
that behaves as a linear spring when stretched, but does not resist compression. In
addition, different rest lengths were used in both cases. For all cases, run length
distributions were determined from extensive simulations. The distributions were
approximately given by double-exponentials, and the average run length was found
to increase almost exponentially with the number of motors attached to the cargo.
For the same number of motors on the cargo, the average run length was found to be
longer for longer springs [
52
]. This result can be explained by the observation that, in
this case, more motors are bound to the filament simultaneously. This means that the
longer spring rest length provides more flexibility to accommodate a larger number of
motors on the filament. Moreover for all rest lengths, cable-like springs lead to longer
run lengths than linear springs. This has been interpreted as an effect of the average
distance between the cargo and the filament, which is expected to be smaller for
cable-like motors, where the springs do not induce upward forces on the cargo, than
for linear-spring motors [
52
]. However, our more recent discussion of interference
effects for nonlinear springs suggests another explanation (not mutually exclusive
with the first): For cable-like linkers, forces between the motors build up more slowly
than for linear springs [
8
], so interference effects are less pronounced. Specifically,
for linear springs, forces built up because of the nonsynchronous stochastic stepping
of the motors, enhance unbinding, thus effectively reducing the number of bound
motors.
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