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<h4 class="title"><a href="#" class="viewer-link">Analytical aspects of the Brownian motor effect in randomly flashing ratchets</a></h4>
<span class="authors"><a href="#">Dmitry Vorotnikov</a></span>
<br>
<span class="date">May 2012</span> in <span class="field"><a href="#">Math</a></span> » <span class="topics"><a href="#">Functional Analysis</a></span>
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<p>
The muscle contraction, operation of ATP synthase,
maintaining the shape of a cell are believed to be secured by motor proteins, which can be modelled using the Brownian ratchet
mechanism. We consider the randomly flashing ratchet model of
a Brownian motor, where the particles can be in two states, only
one of which is sensitive the applied spatially periodic potential
(the mathematical setting is a pair of weakly coupled reactiondiffusion and Fokker-Planck equations). We prove that this mechanism indeed generates unidirectional transport by showing that
the amount of mass in the wells of the potential decreases/increases
from left to right. The direction of transport is unambiguously determined by the location of each minimum of the potential with
respect to the so-called diffusive mean of its adjacent maxima. The
transport can be generated not only by an asymmetric potential,
but also by a symmetric potential and asymmetric transition rates,
and as a consequence of the general result we derive explicit conditions when the latter happens. When the transitions are localized
on narrow active sites in the protein conformation space, we find
a more explicit characterization of the bulk transport direction,
and infer that some common preconditions of the motor effect are
redundant.</p>
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<a href="#"><i class="icon-sort-up icon-large"></i></a> <a href="#">Michael Eisen</a> <span class="comment-date">6 days ago</span>
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<a href="#"><i class="icon-sort-up icon-large"></i></a> <a href="#">Michael Eisen</a> <span class="comment-date">6 days ago</span>
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<p>Lorem ipsum dolor sit amet, consectetur adipiscing elit. Quisque interdum ultrices ipsum sit amet hendrerit. Cras ligula lorem, ullamcorper eu pellentesque a, mattis ac orci. Proin tellus massa, tincidunt vel rhoncus luctus, gravida ut libero.</p>
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<a href="#"><i class="icon-sort-up icon-large"></i></a> <a href="#">Michael Eisen</a> <span class="comment-date">6 days ago</span>
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<p>Lorem ipsum dolor sit amet, consectetur adipiscing elit. Quisque interdum ultrices ipsum sit amet hendrerit. Cras ligula lorem, ullamcorper eu pellentesque a, mattis ac orci. Proin tellus massa, tincidunt vel rhoncus luctus, gravida ut libero.</p>
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<a href="#"><i class="icon-sort-up icon-large"></i></a> <a href="#">Michael Eisen</a> <span class="comment-date">6 days ago</span>
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<p>Lorem ipsum dolor sit amet, consectetur adipiscing elit. Quisque interdum ultrices ipsum sit amet hendrerit. Cras ligula lorem, ullamcorper eu pellentesque a, mattis ac orci. Proin tellus massa, tincidunt vel rhoncus luctus, gravida ut libero.</p>
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<a href="#"><i class="icon-sort-up icon-large"></i></a> <a href="#">Michael Eisen</a> <span class="comment-date">6 days ago</span>
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<p>Lorem ipsum dolor sit amet, consectetur adipiscing elit. Quisque interdum ultrices ipsum sit amet hendrerit. Cras ligula lorem, ullamcorper eu pellentesque a, mattis ac orci. Proin tellus massa, tincidunt vel rhoncus luctus, gravida ut libero.</p>
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<a href="#"><i class="icon-sort-up icon-large"></i></a> <a href="#">Michael Eisen</a> <span class="comment-date">6 days ago</span>
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<p>Lorem ipsum dolor sit amet, consectetur adipiscing elit. Quisque interdum ultrices ipsum sit amet hendrerit. Cras ligula lorem, ullamcorper eu pellentesque a, mattis ac orci. Proin tellus massa, tincidunt vel rhoncus luctus, gravida ut libero.</p>
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<a href="#"><i class="icon-sort-up icon-large"></i></a> <a href="#">Michael Eisen</a> <span class="comment-date">6 days ago</span>
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<p>Lorem ipsum dolor sit amet, consectetur adipiscing elit. Quisque interdum ultrices ipsum sit amet hendrerit. Cras ligula lorem, ullamcorper eu pellentesque a, mattis ac orci. Proin tellus massa, tincidunt vel rhoncus luctus, gravida ut libero.</p>
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<a href="#"><i class="icon-sort-up icon-large"></i></a> <a href="#">Michael Eisen</a> <span class="comment-date">6 days ago</span>
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<p>Lorem ipsum dolor sit amet, consectetur adipiscing elit. Quisque interdum ultrices ipsum sit amet hendrerit. Cras ligula lorem, ullamcorper eu pellentesque a, mattis ac orci. Proin tellus massa, tincidunt vel rhoncus luctus, gravida ut libero.</p>
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