The quantum-mechanical approach to channel gating described in this book is based on single-electron tunneling across arginine and lysine residues of the S4 transmembrane protein segment. Models for controlling the gating of ion channels by electrons have most likely been considered by other researchers; however, there is a problem - an electron gating model requires a mechanism for amplification in order to match the experimental data for ion channel voltage sensitivity. Amplification based on the inversion of NH3, addresses this sensitivity problem.

In this paper, an electron-tunneling model, equations were first derived for a tunnel track having two identical tunneling sites and a single tunneling electron was developed. In deriving the equations, certain assumptions and simplifications were made. It was assumed that the only electric field crossing the tunneling sites was due to membrane voltage and that the electric flux was parallel to the axis of the a-helix. Square energy wells could be used instead of parabolas, because the energy change due to membrane voltage is very small (<2kT), thus allowing a square well model for the ground state.

This chapter presents the Single Electron Tunneling Capacitor (SETCAP) model to understand the electron-tunneling response to a membrane voltage change and to derive equations based on a circuit analogy. This analogy helps in developing an equation for displacement energy and an equation for capacitance factor for each electron-tunneling site. The SETCAP model is also used for developing the equation for the rate constant for N electron-tunneling site. The variable constants are also discussed in this chapter. Ie, time-constant, capacitance equation which represents steady-state values at any given voltage.

In this paper, electron tunneling across proteins has been shown experimentally to approximately follow a Gaussian curve when rate is plotted against the free energy. When a log scale is used for the vertical axis, the curve is an inverted parabola.

In this chapter, distortions of the α and β rate constants are examined. These distortions produce the increased time constants for potassium gates and for sodium inactivation gates. Sodium activation gates have negligible distortion (below V_1/2) and the rate constants α_m and β_e are considered equivalent to α_e and βe for electron tunneling. Most of the distortions are due to the voltage sensitivity of ion fluxes crossing energy barriers in the channel. The exception is the sodium inactivation gate, which apparently has an additional edge distortion due to the location of the tunnel track control site near the protein/cytoplasm interface.

In this paper, the electron-gating model to experimental data wherever possible and to account for any differences between the model and the experimental data. A primary experimental link is the Hodgkin-Huxley equations. A detailed study was made to understand the significance of the coefficients and sensitivity factors in terms of the electron-gating model. The amino acid sequence data for the squid giant axon for sodium and potassium ion channels and the sequence data for Shaker B. The experimental data for gating current and gating current time constants was described. Experimental data for electron tunneling across proteins and the α-helix in particular. Experimental determination of the NH3 inversion frequencies. The measured frequencies narrow the range of possible parameter values.

This chapter presents a discussion on activation and inactivation flux gating in sodium (Na⁺) and potassium (K⁺) ion channels along with the equations used for plotting the ion channel curves. The influx gating latch-up effect is also tackled.

Site maps were created to clarify how electron tunneling could account for gating and to illustrate the various tunneling distances associated with gating current and inactivation. These maps have a scale representation for the spacing between the sites, along the α-helix axis, and show approximate alignment with the cavities in the channel used for the modulated energy barriers. To simplify the site maps for illustration, the electron tunneling sites are shown along a straight line and the cavities for the energy barriers, which gate the ion current flow, are indicated by triangular displacements in the channel.

In this chapter, the electron-gating model for the outward-rectifying potassium channels, in particular Shaker and Loligo opalescens - the potassium channel characterized by the rate constants of Hodgkin and Huxley are described. The potassium channel geometry presented is considered to be the most likely configuration, given the constraints imposed by the electron-gating model, the amino acid sequence, and published experimental observations.

This chapter discusses a new type of spectroscopy instrument for recording protein spectra using thermally modulated fluorescence, which would have to be constructed and a microwave swept signal generator and amplifier would need to be obtained.

This appendix contains geometric calculations for an α-Helix and Time Constant calculations for a tunnelling distance r.