The spatial distribution of mass forms the structure studied so successfully by molecular and structural biologists. The spatial distribution of permanent charge forms (most of) the electrical structure of the channel protein. The spatial distribution of side chains in a specific channel defines the permanent charge of the channel. Within a large class of ion channels, amino acid side chains are distributed mainly over a “short” and “narrow” portion of the channel, with acidic side chains contributing permanent negative charges and basic side chains contributing permanent positive charges, analogous to the doping of semiconductor devices, e.g., bipolar PNP and NPN transistors. The shape of a typical ion channel is often approximated as a cylindrical-like domain with a non-uniform cross-sectional area. To unravel how ion channels operate, one needs to understand the physical structure of ion channels, which is defined by the channel shape and the spatial distribution of permanent and polarization charge.
Ion channels permit the selective passage of charged ions formed from dissolved salts, including sodium, potassium, calcium, and chloride ions that carry electrical current in and out of the cell. They have an aqueous pore that becomes accessible to ions after a change in the protein structure that makes ion channels open. Ion channels are proteins found in cell membranes that create openings in the membrane to allow cells to communicate with each other and with the outside to transform signals and to conduct tasks together. In the opinion of the authors, many results in the paper are not intuitive, and it is difficult, if not impossible, to reveal all cases without investigations of this type.
Moreover, the dependence of current and fluxes on voltages and permanent charges is investigated. The numerical investigations on profiles of the electrochemical potentials, ion concentrations, and electrical potential across ion channels are also presented for the zero-current case. We summarize and extend these results with numerical observations for biological relevant situations. For 1:1 ionic mixtures with arbitrary diffusion constants, Mofidi and Liu (arXiv:1909.01192) conducted a rigorous mathematical analysis and derived an equation for reversal potentials. Numerical observations are obtained from analytical results established using geometric singular perturbation analysis of classical Poisson–Nernst–Planck models. The study is conducted for the setup of a simple structure defined by the profile of permanent charges with two mobile ion species, one positively charged (cation) and one negatively charged (anion). In this work, the dependence of reversal potentials and zero-current fluxes on diffusion coefficients are examined for ionic flows through membrane channels.
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