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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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<h3 class="name">Slavoj Zizek</h3>
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Strongly support <i class="icon-sign-blank plus-plus"></i>
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<h3 class="name">Carl Sagan</h3>
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Oppose with reservations <i class="icon-sign-blank minus"></i>
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<h3 class="name">Albert Einstein</h3>
<span class="title">PhD candidate in Physics, ETH Zurich</span>
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Strongly oppose <i class="icon-sign-blank minus-minus"></i>
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