Biomedical Engineering Reference
In-Depth Information
Figure 4.4.
Brownian ratchet models. Models for microtubule force generation
and dynamics. Adapted from [6]. Copyright (2005), with permission from Elsevier.
(a) The Brownian ratchet principle for polymerization-based force generation (see
Section 4.3). Thermal fluctuations of the target allow for the occasional insertion
(with rate
k
on
) of a new subunit (with size
δ
,evenwhenanexternalforce
F
ext
opposes the motion of the target. Subunits detach with a constant rate
k
of f
.(b)
Generalization of the Brownian ratchet model for multifilament polymers such as
the microtubule. Shown is a (arbitrarily chosen) polymer with four protofilaments
that, in this case, are assumed to grow independently. (c) Schematic representation
of more realistic microtubule end-structures emphasizing the differences between
growing and shrinking states. In the cell, growing and shrinking microtubule ends
are decorated with end-binding proteins that regulate microtubule dynamics and
force generation, and mediate the connection to cellular interaction sites.
other, this prefactor is approximately 20. This means that any measurement
technique that relies on a straight growing filament pushing against a force or
position sensor can only be applied to suciently short filaments. For micro-
tubules (
κ
25pN
μ
m
2
) the maximum filament length that remains straight
when compressive forces of a few piconewton are generated is a few microm-
eter, whereas actin filaments (
κ
0
.
06pN
μ
m
2
) need to remain shorter than
a few hundred nanometer. When filaments buckle or bend under an applied
force, the increase in length cannot be detected anymore by the response of a
position sensor leading to diculties in measuring the growth velocity of the
filament, and thus the force velocity relation. Alternatively, if the buckling
