The Role of Proton Transport in Gating Current in a Voltage Gated Ion Channel, as Shown by Quantum Calculations

Alisher M Kariev; Michael E Green

The added energy in going from 0 K to room temperature could differ for different proton positions and voltages if the spectrum of vibrations of the protein were significantly different. However, almost all the degrees of freedom are likely to be unchanged. While the total thermal energy will correspond to well over a thousand kT (there are 976 atoms, so that there should be, in total, 2922 vibrational degrees of freedom), the differences should only affect a small number of these. Almost the entire system is unchanged with a local proton transfer. The differences in the energy of the minima will surely be less than the activation energy, amounting to about 20 -25 k B T, for the step we have calculated in the most detail. However, even the very small number of affected degrees of freedom, say n, are not going to make a difference of as much as nk B T since these will be very similar in the two forms of the VSD (if the vibrations are fully excited, we should see a difference of 3k B T for each mode from the value with the mode fully unexcited). To see a difference, the modes would have to be partially excited to different degrees, which requires that they have vibration frequencies that would be in the range of k B T/h (h = Planck's constant), about 6 x 10 12 Hz at room temperature. This frequency range would apply to relatively long wave vibrations, covering much more than local modes; these are the modes which should not change with a proton shift. Higher frequency local modes differ, but these modes have energy sufficiently above k B T as to be not excited at room temperature. Therefore, it should be possible to trust the differences in energy-the errors must cancel in the differences, not only in the 0 K minima, but also in the room temperature results. The latter may add 1 -2 k B T to the relative error, but a ±4 k B T error is not enough to change conclusions that are based on energy changes that are appreciably larger, by at least a factor of 4. In other words, the protein is large enough with its 2922 vibrations that it should behave somewhat as a solid, or at least a glass; therefore, many of the modes are, as in a solid, long . CC-BY-NC-ND 4.0 International license is made available under a The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/371914 doi: bioRxiv preprint wave vibrations covering distances over much more than local modes. The long wave vibrations will be excited by the time the temperature is raised to room temperature, but they will be the same for all local minima. The changes between cases are local, which necessarily involve short wavelengths, and with it vibrational frequencies greater than the frequency corresponding to room temperature; the local modes are generally at least 3x this frequency, so that these vibrations would contribute very little, and any alterations in local modes should not contribute much to the thermodynamics at 300 K. If the protein is analogous to a solid or glass, the local modes would be analogous to Einstein modes, and in this case, mostly with frequencies corresponding to the infrared, sufficiently above thermal energy that these modes can be ignored.