Geometrical modelling of Ohmic conductance in ion channels

In an Ohmic model, channel conductivity can be described in terms of the geometry of a conducting cable. The essential features of such devices are the arc length of the curve describing the channel's longitudinal path, and the cross-sectional areas transversal to this curve. In a first approximation, conducting channels can be represented by an average molecular shape with estimated lengths and cross-sectional areas. Whereas the physical shortcomings of this approach are known, its accuracy limitations in practice have not been established. In this work, we discuss an improved model for the channel's shape, one that allows us to gauge how much of the Ohmic conductivity can be assigned purely to geometrical features. In the present algorithm, we investigate all regions inside the pore that are accessible to ions using various choices for the molecular surface of the inner channel. We discuss the agreement with experimental conductances in the case of 12 channels (cholera toxin B-subunit pentamer, Staphylococcus aureus alpha-hemolysin, Streptomyces lividans KcsA channel, seven porins, gramicidin A, and phospholamban). Our results can be regarded as a benchmark for the best performance that can be expected from a geometrical model of conductance. Consequently, significant deviations from experimental trends can safely be assigned to non-geometrical factors, namely the specific composition of the ion channel and the detailed electrostatic interactions between the channel and a particular ion.