Abstract
Transitions between states of ion channels have previously been considered in terms of classical statistical mechanics. However, transitions in many systems, including some organic molecules, are known to occur by quantum mechanical tunnelling. In this report, we have calculated the time for sodium channel activation by tunnelling, starting from a mechanistic model based on the structural models of Catterall and Guy. In doing this, we have calculated the Coulomb interactions between the S4 α-helix and negative residues on nearest-neighbor helices and have included longer range interactions in terms of an effective background interaction. Periodic pairing of charges between the S4 and adjacent helices in the model causes the resting and depolarized states of the channel to correspond to local minima in the S4 potential energy curve. Harmonic potentials closely fit the energy curves around each of the two minima and the energy barrier between them is closely modelled by a parabola. These approximations allow a semiclassical calculation of the S4 helix's tunnelling rate to be made. At 37°C, for an interhelix axial spacing of 10 Å, tunnelling times in the range of 1 μs to a few ms were computed for a single S4 segment, depending of the equilibrium temperature of the cell membrane.
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Chancey, C.C., George, S.A. & Marshall, P.J. Calculations of quantum tunnelling between closed and open states of sodium channels. J Biol Phys 18, 307–321 (1992). https://doi.org/10.1007/BF00419427
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DOI: https://doi.org/10.1007/BF00419427