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Driven diffusion against electrostatic or effective energy barrier across Alpha-Hemolysin

We analyze the translocation of a charged particle across an Alpha-Hemolysin (aHL) pore in the framework of a driven diffusion over an extended energy barrier generated by the electrical charges of the aHL. A one-dimensional electrostatic potential is extracted from the full 3D solution of the Poisson's equation. We characterize the particle transport under the action of a constant forcing by studying the statistics of the translocation time. We derive an analytical expression of translocation time average that compares well with the results from Brownian dynamic simulations of driven particles over the electrostatic potential. Moreover, we show that the translocation time distributions can be perfectly described by a simple theory which replaces the true barrier by an equivalent structureless square barrier. Remarkably our approach maintains its accuracy also for low-applied voltage regimes where the usual inverse-Gaussian approximation fails. Finally we discuss how the comparison between the simulated time distributions and their theoretical prediction results to be greatly simplified when using the notion of the empirical Laplace transform technique.