Biomedical Engineering Reference
In-Depth Information
Figure 1.4.
The grey gel layer, initially with inner radius
r
must stretch to a new
radius
r
+
δe
toallowanewgellayertoform.
Figure 1.5.
The elastic force gives rise to a propulsion force
F
1
along the bacterium
axis. The surface friction equilibrates
F
1
with
F
2
.
In the first, neither the developed stress nor the actin monomer depletion
are large enough to influence the polymerization process. Then, in steady state
e
=
v
p
v
L,
(1.9)
because the time
e/v
p
needed to generate a thickness
e
must equal the time
L/v
to advance one length
L
. Then
L
r
1
/
2
v
1
/
4
i
v
3
/
4
p
v
.
(1.10)
Note that in this regime, the bacterium velocity relative to the gel
v
can
be larger than the polymerization rate
v
p
, and that it is not proportional to
it. Note also that it depends only weakly on the comet gel properties
v
i
:a
two orders of magnitude change of the gel elastic modulus (everything else
being kept constant) results in a factor of three change of the velocity
v
only.
This explains why the experimentally observed velocity spread is by no means
comparable to the one found for the gel modulus.
