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. Author manuscript; available in PMC: 2019 Jul 1.
Published in final edited form as: Phys Rev E. 2018 Jul;98(1-1):012404. doi: 10.1103/PhysRevE.98.012404

FIG. 4.

FIG. 4.

Universality of the golden aspect ratio with pore size. (a) The resistance versus L for cylindrical cells with α = 1.07, hp = 1 nm, γ = 71 MΩ·nm, and various pore radii. The golden aspect ratio is fairly constant over this range of a. The solid lines show the fits R=4γπL(αf)+R and the dashed lines show the extrapolations – which make good predictions of R at large L. The fit parameters are shown in bold. The errors of the fits for f’s and R’s are less than 0.5 % and 0.1 % respectively. As the pore radius increases, we examine fits for larger L, to roughly keep proportionality between L and a as there are (non-scaling) finite-size effects that will affect the simulations when the radius starts to become comparable to the cell cross-sectional length. The range of the fitting can influence the extracted f (we expect that ultra-precise calculations at really large L will reveal the exact golden aspect ratio, which will be close to 1.07). (b) ΔR from fits to R=γ(1/2a+heff/πa2)+ΔR for cylindrical cells of various α, with heff and ΔR as fitting parameters. We get ΔR ≈ 0 for the “golden aspect ratio” α= 1.07 (dashed lines), the fit of which is shown in the inset. The effective height, heff, is (5±1) % larger than the 1 nm membrane thickness, see Fig. 5. (c) ΔR in the fits R = γ/4aR for half cylinders of different aspect ratios with the pore mouth set at potential V = 0. We again get ΔR ≈ 0 for α = 1.07 (dashed lines), whose fit is shown in the inset. The interpolated lines in the insets are for visual clarity only.