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Title: Analytical aspects of the Brownian motor effect in randomly flashing ratchets
Authors: Vorotnikov, Dmitry 
Keywords: Diffusion; Mathematical Concepts; Molecular Motor Proteins; Muscle Contraction; Protein Conformation; Models, Biological
Issue Date: 2013
Publisher: Springer
Project: PEst-C/MAT/UI0324/2011 
Serial title, monograph or event: Journal of Mathematical Biology
Volume: 68
Issue: 7
Abstract: 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 reaction-diffusion 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.
Other Identifiers: 10.1007/s00285-013-0684-4
DOI: 10.1007/s00285-013-0684-4
Rights: embargoedAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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