Biomedical Engineering Reference
In-Depth Information
shape itself can be measured with high precision, curve-fitting of the buckled
filament can provide a measure of both the applied force and the filament
length. We used this so-called “buckling” technique to measure force velocity
relations for relatively long microtubules [25]. More recently, we developed an
optical tweezers-based technique in which growing filaments shorter than 1
micrometer can be followed directly [26, 27].
The experimental set-up for the buckling experiment is shown schemati-
cally in Figure 4.5. A microtubule is nucleated by a short stabilized micro-
tubule (a seed) that is attached to the surface of a microscope coverslip. On
this coverslip glass barriers of 2 micron high with slight undercuts are built
using microfabrication techniques. A growing microtubule that reaches a bar-
rier is caught underneath the undercut and forced to grow against the glass
wall. Fluctuations of the microtubule end allow for the continued insertion of
tubulin dimers, and the microtubule buckles while its length increases. Fitting
of the shape of the growing microtubule to the theoretical shape of an elastic
rod under compressive force allows us to determine both the length of the mi-
crotubule and the elastic restoring force that is acting on the microtubule end
as a function of time (see Figure 4.6a). Using the component of the force that
is parallel to the microtubule growth direction, average force velocity relations
can be obtained for microtubules growing at different tubulin concentrations
(see Figure 4.6b). Although this buckling technique does not allow us to ob-
tain a convincing measurement of the stall force (the external force required
to reduce the growth velocity to zero), it is clear from these data that (fairly
slow-growing) microtubules
in vitro
can resist forces of at least 5 piconewton,
which is comparable to the stall force of molecular motors such as kinesin.
In Figure 4.6b, we compare the normalized force velocity data with predic-
tions of two idealized versions of the multi-filament Brownian ratchet model.
The force velocity relation (but not the stall force itself [20]) depends on
the assumed details of microtubule growth: optimal force generation (i.e., a
smallest decrease in velocity for a given external force) is accomplished when
growth occurs in a regular fashion, and each added subunit pushes the target
a small, equal distance forward. When growth is more irregular, and not all
subunit additions can perform work (see Figure 4.4b), the growth velocity
decreases faster with force. Comparing our force velocity data to these two
possibilities leads to the suggestion that microtubules, growing
in vitro
with-
out the assistance of cellular microtubule associated proteins, do not in fact
eciently convert all their assembly free energy into work.
These experiments can also be used to measure the effect of force on the
catastrophe rate [28]. When microtubules are growing under force, we observe
that catastrophes occur more frequently. When we plot the average time it
takes before microtubules experience a catastrophe as a function of their re-
duced velocity under force, we find a more or less linear relationship (see
Figure 4.6c). A similar relationship is found when we observe free-growing
microtubules and reduce the growth velocity by reducing the tubulin concen-
tration. The simplest explanation for this is that force reduces the growth
