Biomedical Engineering Reference
In-Depth Information
•
Elastic stress-limited regime.
For larger
E
actin polymerization at the
surface might be limited by the accumulated elastic stress. In this case, the
gel thickness saturates at a value close to the stress-limited, steady-state
thickness of the gel, leading to a velocity [48]
Δμ
l
2
a
3
/
2
1
ξE
1
/
2
,
v
∼
(1.47)
where
Δμ
is the energy of the polymerization reaction, and
l
and
ξ
denote
(as above) the mesh-size of the actin network and the friction coecient,
respectively.
•
Diffusion-limited regime.
Here, one must take into account that mo-
nomers have to diffuse to the bead surface. An analysis similar to the one
given in Section 1.4.2 yields [48]
c
∞
D
k
b
+
R/l
2
+
D
.
c
i
(1.48)
Thus, the polymerization velocity
v
p
=
v
and
v
p
=
k
b
+
c
i
a
, implying
c
∞
Dl
2
a
R
v
.
(1.49)
The state of the system is determined by two dimensionless variables [48]
a dimensionless modulus
e
=
Eξv
p
(
l
2
a/Δμ
)
2
and a dimensionless diffusion
coecient
d
=(
Dc
∞
l
3
a
3
/
2
/R
)(
ξ/v
p
Δμ
)
1
/
2
. The corresponding state diagram
is shown in Figure 1.12.
Experimentally, the different morphologies of the comet tails in the dy-
namic regimes can be characterized by photobleaching of lines perpendicular
to the comet axis. In the diffusion-limited regime, bleached vertical lines de-
form and newly grown actin layers open up and reduce their curvature. In the
elasticity-dominated regime newly grown gel layers are first stretched. Fur-
ther away from the bead surface, the layer reduces its area by reducing its
curvature.
Finally, the surface concentration of Wiskott-Aldrich Syndrome protein
(WASP) also has a direct influence on the motion of polystyrene beads. Similar
to
Listeria
, actin-driven beads can also exhibit different kinds of motion. The
different regimes are characterized by, e.g., velocity of motion and frequencies
of periodic motion. In [31] a dynamic state diagram has been experimentally
derived and it has been shown that bead motion generally depends on both
bead diameter and protein surface density.
1.5.3 Actin-Based Propulsion of Disks
Recently, Schwartz et al. have experimentally confirmed the theoretical pre-
diction (see Reference [19] and Section 1.3.2) that actin-polymerization can
