Remarkable advances in nanotechnology and computational approaches enable researchers to investigate physical and biological phenomena in an atomic or molecular scale. Smaller-scale approaches are important to study the transport of ions and/or molecules through ion channels in living organisms as well as exquisitely fabricated nanofluidic channels. Both subjects have similar physical properties and hence they have common mathematical interests and challenges in modeling and simulating the transport phenomena. In this work, we first propose and validate a molecular level prototype for mechanoelectrical transducer (MET) channel in mammalian hair cells.Next, we design three ionic diffusive nanofluidic channels with different types of atomic surface charge distribution, and explore the current properties of each channel. We construct the molecular level prototype which consists of a charged blocker, a realistic ion channel and its surrounding membrane. The Gramicidin A channel is employed to demonstrate the realistic channel structure, and the blocker is a positively charged atom of radius $1.5$\AA\, which is placed at the mouth region of the channel. Relocating this blocker along one direction just outside the channel mouth imitates the opening and closing behavior of the MET channel. In our atomic scale design for an ionic diffusive nanofluidic channel, the atomic surface charge distribution is easy to modify by varying quantities and signs of atomic charges which are equally placed slightly above the channel surface. Our proposed nanofluidic systems constitutes a geometrically well-defined cylindrical channel and two reservoirs of KCl solution. For both the mammalian MET channel and the ion diffusive nanofluidic channel, we employ a well-established ion channel continuum theory, Poisson-Nernst-Planck theory, for three dimensional numerical simulations. In particular, for the nano-scaled channel descriptions, the generalized PNP equations are derived by using a variational formulation and by incorporating non-electrostatic interactions. We utilize several useful mathematical algorithms, such as Dirichlet to Neumann mapping and the matched interface and boundary method, in order to validate the proposed models with charge singularities and complex geometry. Moreover, the second-order accuracy of the proposed numerical methods are confirmed with our nanofluidic system affected by a single atomic charge and eight atomic charges, and further study the channels with a unipolar charge distribution of negative ions and a bipolar charge distribution. Finally, we analyze electrostatic potential and ion conductance through each channel model under the influence of diverse physical conditions, including external applied voltage, bulk ion concentration and atomic charge. Our MET channel prototype shows an outstanding agreement with experimental observation of rat cochlear outer hair cells in terms of open probability. This result also suggests that the tip link, a connector between adjacent stereocilia, gates the MET channel. Similarly, numerical findings, such as ion selectivity, ion depletion and accumulation, and potential wells, of our proposed ion diffusive realistic nanochannels are in remarkable accordance with those from experimental measurements and numerical simulations in the literature. In addition, simulation results support the controllability of the current within a nanofluidic channel.
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