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Abstract An integral equation method is presented for the 1D steady-state Poisson-Nernst-Planck equations modeling ion transport through membrane channels. The differential equations are recast as integral equations using Green’s 3rd identity yielding a fixed-point problem for the electric potential gradient and ion concentrations. The integrals are discretized by a combination of midpoint and trapezoid rules, and the resulting algebraic equations are solved by Gummel iteration. Numerical tests for electroneutral and non-electroneutral systems demonstrate the method’s 2nd order accuracy and ability to resolve sharp boundary layers. The method is applied to a 1D model of the K$$^+$$ ion channel with a fixed charge density that ensures cation selectivity. In these tests, the proposed integral equation method yields potential and concentration profiles in good agreement with published results.
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null (Ed.)• To compute protein pKas, a continuum dielectric Poisson-Boltzmann model defined on a molecular domain and a solvent domain is used for computing the related electrostatic free energies (top left). • The PB model in its boundary integral form is accurately solved on the triangulated molecular surface (e.g. BPTI) accelerated by a fast Treecode algorithm (top right). • The method obtains the intrinsic pKa and then computes the protonation probability for a given pH including site-site interactions by going through an energy driven titrating procedure. Comparison with experimental results are provided (bottom left and right).more » « less
