Biology Reference
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FIGURE 8.2 The elastic Brownian ratchet at the leading edge. Random bending motions of peripheral actin
fibres, driven by Brownian motion, fleetingly expose their ends; this allows them to be extended so that they are
longer by the time they spring back and push against the membrane again. This diagram is a simplified repre-
sentation; all components are in continuous random motion and the average of the activities of all of the Brownian
ratchets results in cell advance.
the membrane must advance forwards when a filament meeting it at an angle 4 extends is
proportional to sin( 4 )( Figure 8.3 ), and would therefore be greatest when the filament meets
the membrane at 90 degrees. In such an orientation, though, there would be little opportunity
for new monomers to find space to attach. All else being equal, the probability of the end
being free and amenable to a new monomer entering would be expected to be proportional
to cos( 4 ), although some steric effects very close to the membrane may modify this slightly.
For that one filament, the rate of advance would therefore be proportional to sin( 4 ) $ cos( 4 ),
and would peak at 4 ¼
45 degrees. ) This back-of-the-envelope calculation may provide
a teleological explanation for the range of angles actually observed. The flexibility of actin
filaments, so necessary for the working of the Brownian ratchet, also acts as a limitation
for the length of actin filament that can push on the membrane because very long filaments
will simply bend over and start to extend uselessly along from the membrane or just buckle.
) Because sin( 4 )cos( 4 )
0.5sin(2 4 ) then the first derivative f 0 (2 4 )
¼
0.5sin(2 4 ) d 'the sine rule'; if f (2 4 )
¼
¼
0.5cos(2 4 ). At the peak of the function, f 0 (2 4 )
¼
0, so cos(2 4 )
¼
0, so 2
90 degrees making 4 ¼
45 degrees.
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