title: Analytical aspects of the Brownian motor effect in randomly flashing ratchets.
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.
authors.affiliation: CMUC, Department of Mathematics, University of Coimbra, 3001-454 , Coimbra, Portugal, mitvorot@mat.uc.pt.
authors.forename: Dmitry
authors.initials: D
authors.lastname: Vorotnikov
mesh_terms: D004058:Diffusion; D055641:Mathematical Concepts; D008954:Models, Biological; D020409:Molecular Motor Proteins / Q000737:chemistry* / Q000502:physiology*; D009119:Muscle Contraction; D011487:Protein Conformation
chemical_list: D020409:Molecular Motor Proteins