Biomedical Engineering Reference
In-Depth Information
information about the forces involved in actin-based propulsion, to analyze in
detail the properties of the comet tail, and to test the theoretical predictions
on the influence of bead curvature. Here, we give a short summary of these
new developments.
1.5.1 Direct Measurement of Actin-Generated Forces and
Velocities
The forces generated in the process of actin-based propulsion can be di-
rectly probed in novel micromanipulation experiments [41]. Here, motility
of polystyrene spheres attached to a “flexible handle” are probed with their
growing comets held with micropipettes. In this way, external pulling and
pushing forces of a few nanonewtons can be directly applied.
By using this setup, forces in the range from -1.7 to 4.3 nN have been
applied to beads (where pushing forces are positive). An example is shown
in Figure 1.9(a) and (b) where a force of 1.7 nN was imposed. Thus, the
comet lengthens with constant velocity. By combining such measurements at
different
f
ext
, the force velocity relation shown in Figure 1.9(c) is obtained.
As can be seen from the experimental data in Figure 1.9, the force velocity
relation is essentially linear for pulling forces, while for pushing forces the
decrease in
v
with increasing
f
ext
is somewhat slower. The stall force cannot
be reached experimentally due to comet buckling at large forces
f
ext
.The
gel thickness
e
increases with decreasing velocity, see Figure 1.9(d). For small
velocities,
e
tends to a saturated value.
Within the framework provided above, the force velocity relation and the
velocity dependence of the gel thickness can be understood quantitatively. By
using Equations (1.7) and (1.8) for spherical beads with radius
R
, the relation
between external force and velocity is given by
f
ext
+
E
e
3
R
Aξv,
(1.44)
where
A
=4
πR
2
is the contact area between bead and gel. The dependence of
the velocity
v
on the gel thickness
e
is well-described by the empirical formula
1
exp
.
v
p
R
ve
∗
e
(
v
)=
e
∗
−
−
(1.45)
The last equation simply interpolates between the steady state value
e
=
e
∗
for small velocities and the value of
e
for large velocities given by Equation
(1.9).
It is also possible to demonstrate actin-based propulsion with softer ob-
jects than polystyrene beads. For example, (VCA-covered) oil droplets [42]
or (ActA-covered) synthetic vesicles [43, 44] move once put into cell extract.
Their surfaces are deformed by the elastic stresses exerted by the actin tail
comet. Such squeezing effects have also been observed in endosomes [29].
