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The mechanism behind the high throughput rate in K$^{+}$ channels is still an open problem. Recent simulations have shown that the passage of potassium through the K$^{+}$ channel core, the so-called selectivity filter (SF), is water-free against models where the strength of Coulomb repulsion freezes ions conduction. It has been suggested that quantum coherent hopping might be relevant in mediating ion conduction. Within the quantum approach and the hypothesis of desolvated ions along the pathway, we start with a number of particles in a source to see how they go across the SF modeled by a linear chain of sites to be collected in a drain. As a main result we show that there is a threshold SF occupancy is three ions on average, which is in agreement with recent classical model simulations., Comment: 11 pages, 4 figures

Assuming that the selectivity filter of KcsA potassium ion channel may exhibit quantum coherence, we extend a previous model by Vaziri and Plenio (2010) to take into account Coulomb repulsion between potassium ions. We show that typical ion transit timescales are determined by this interaction, which imposes optimal input/output parameter ranges. Also, as observed in other examples of quantum tunneling in biological systems, addition of moderate noise helps coherent ion transport., Comment: 12 pages, 10 figures