Chemistry Reference
In-Depth Information
5.5 nm could also be clearly observed. Figure 2.7d shows a model for the Brownian
search by the myosin-V head for the actin forward target.
2.4
Biased Brownian Step Model
Scanning probe nanometry showed that type-II myosin (muscle myosin) move along
actin subunits by Brownian motion. Brownian motion is random, so it should be
biased in one direction to generate unidirectional movement of myosin. Here we
consider how the Brownian motion of myosin is biased in one direction [25].
2.4.1
Asymmetric Potential
Applying the asymmetric potential model [37, 38] presented in Figure 2.8a, we
analyzed the myosin Brownian sub-steps. The activation energy of the forward and
backward directions can be described by (u
þ
þ
Fd
), respectively,
where u
þ
and u
-
are the heights of the potential barriermaximumat zero load, and d
þ
and d
-
are the characteristic distances. Assuming the Boltzmann energy distribution,
the rates in the forward and backward directions will be proportional to exp[
-
(u
þ
þ
Fd
þ
) and (u
Fd
)/k
B
T], respectively. Differences between the
potential barriers for the forward and backward steps at load F is given by
Fd
þ
)/k
B
T] and exp[
(u
D
u
Fd
5.5 nm. Figure 2.5b shows
the ratios of Nf
if
to N
b
at various loads for myosin-II. Using these ratios,
k
B
Tln (N
if
/N
b
), where
D
u
¼
u
þ
u
and d
¼
d
þ
þ
d
¼
uis
calculated to be 2
-
3k
B
T (Figure 2.8b). Thus, Brownian steps are biased by a potential
energy of 2
-
3k
B
Tat zero load, similar to the experimental results for myosin-V [35].
At N
if
D
N
b
, F is calculated to be 2.5 pN, which gives the maximum force at zero
velocity, consistent with that measured directly (Figure 2.6). However, thismaximum
force is smaller than that estimated from the isometric force of muscle [21, 29].
Conformational changes in the myosin head coupled to Pi release may cause
additional forces [39, 40] as discussed later.
How do the myosin steps de
ne the potential? So far, several models have been
proposed [41
-
43]. Here, we propose a simple model assuming more realistic
situations in which the potential slope is produced by steric compatibility between
the orientations of the binding sites of actin and the myosin head. The actin
filament
has a double helical structure while the proto
¼
lament contains sevenmonomers and
rotates 180
per half helical pitch. The tail (neck domain) of the myosin head should
not be perfectly rigid so that themyosin head attached to the probe canmove along the
actin helical pitch. However, the binding sites of actin monomers rotate along the
helix relative to the myosin head attached to the probe and hence the steric
compatibility between the orientations of the binding sites of the myosin head and
the actin should change depending on their relative positions. Thus, this steric
compatibility should result in a potential slope along the actin helical pitch. For
example, if the binding site of the head faces the right side of the actin
filament
xed
