An Oscillating Gate Hypothesis for the Potassium Channel: Quantum Calculations on the Vestibule

Abstract

Quantum calculations (DFT) on the vestibule, or cavity, region of the potassium channel, with 12, 14, 16, and 18 water molecules, plus a K+ ion, give the free energy profile for the ion at five positions: the center of the cavity, and 2, 4, 5 and 6 A above this position. This is sufficient to show that 16 or 18 water molecules are approximately the correct number, and that the ion must move up a free energy gradient to reach the selectivity filter. The conductivity of the channel depends on the intracellular K+ concentration (LeMasurier et al, JGP,118, 303, 2001); their data, replotted, shows a linear dependence of log σ on log(K+ activity); log(K+ activity) is proportional to the ion free energy, implying a free energy barrier to K+ conductivity, as calculated in this work. We show that this is most easily understood with an oscillating gate that alternates complexing K+ and releasing it (see Abstract, Kariev and Green:The Switch at the Potassium Channel Gate: Quantum Calculations Comparing Open and Closed States.) The amount of water in the cavity largely controls the energy barrier, which is approximately 20 kcal. The calculations show substantial charge transfer to the K+, which at the center has a charge of only 0.8 - 0.85 e. However, this would suffice to repel an ion entering the gate, leading to a reverse “knock-on” effect, hence no conductivity.However, a complexed ion at the gate could push the central K+ up to the selectivity filter, leaving space for the ion at the gate to follow to the cavity center, repeating the cycle. This is also a part of the oscillating gate hypothesis.