Biomedical Engineering Reference
In-Depth Information
+
u
2
+
__
2
l
u
s
2
1
ξ
s
1
__
2
l
Figure 7.1.
The geometry of overlap between two interacting filaments of length
l
cross-linked by an active cluster. The cross-link is a distance
s
1
,
(
s
2
)fromthecenter
of mass of filament 1(2). The distance between centers is
ξ
=
r
2
−
r
1
=
s
1
n
1
−s
2
n
2
.
with
γ
P
and
γ
NP
motor-induced rotation rates due to polar and nonpolar cross-
linkers, respectively (see Figure 7.2). The motor-induced translational velocity has
the form
v
a
(1; 2) =
1
2
v
r
+
V
m
, with [36]
(a)
(b)
Figure 7.2.
Polar and nonpolar clusters interacting with polar filaments. Assuming
that clusters always bind to the smallest angle, polar clusters bind only to filaments
in configuration (a) while nonpolar clusters bind to both configurations equally.
β
2
(
u
2
−
u
1
)+
α
2
l
ξ
,
V
m
=
A
(
u
2
+
u
1
)+
B
(
u
2
−
u
1
)
,
v
r
=
u
2
)and
β
=
β
(1 +
u
1
where
α
=
α
(1 +
u
1
u
2
). The expressions for
A
and
B
have been obtained in [36] using momentum conservation. For long thin rods with
ζ
⊥
=2
ζ
≡
·
·
2
ζ
, to leading order in
u
1
·
u
2
, we find
A
=
−
[
β
−
α
(
s
1
+
s
2
)
/
2]
/
12 and
B
=
α
(
s
1
−
s
2
)
/
24.
