Electron-controlled sodium channels

28-May-2022. Wilson P. Ralston, BioKinetix Research Corp

Introduction
Voltage-dependent ion channels (Na, K, Ca, Cl) are nature's transistors for electrical and calcium signaling. These channels control our muscles, brain activity, heart rhythm, theta rhythm, memory and sleep. Defects in these channels are associated with many diseases. The sodium ion channel is a high-energy driver; it has amplification and energy gain. Understanding the structure and function of this channel is made possible by controlling the gates with tunneling electrons. The Hodgkin-Huxley equations for the Squid Giant Axon were used for analysis. The published sequence plus a 3-D Outside View for the Na channel (Fig. 10S-B.) provides a new framework that reveals two key modulation mechanisms that I call SIM and SAM. They are based on a new 3-D Sodium channel structure; (Fig. 10S and Fig. 10S-B).

Fig. 10M. Sub-Inactivation Modulator (SIM) Domain 4
SIM is q8 on D4. It has a positive charge that creates a force, hindering electron tunneling from q7 to q6. It causes the slow inactivation that reduces Na ion channel current above −30mV. A key finding is that the q8 side chain is not rigid. As the force on q8 increases, the side chain bends. This reduces q6 sensitivity of H = 5.5 by s = 0.55 giving H = 20. The q7 sensitivity increases from H = 5.5 to H′ = 5.42. The new Na channel structure with increased sensitivity (H′ = 5.42) led to a simpler equation (Eq. 5) for γeh(Vm).
Fig. 10M. SIM Modulator Domain 4 </a
Fig. 6-1 A.B,C curves represent the result of Domain 4 electron tunneling in S4 and the R8 SIM modulator.

Fig. 10S. Squid Sodium channel structure </a


Fig. 10M-SAM & Fig. 10G, Domain 3 </a


  Fig. 10. Sodium channel

Fig. 10.  In the Hodgkin and Huxley model (1952) for the squid giant axon, the sodium ion current was given by the following equation:  INa=gNam3h(Vm−ENa). For electron gating: INa=gNa(1−P1)4(1−P7)(1−PF5)(1−PF9)(Vm−ENa).  Here P1 is the probability for the gating electron to be at the S4 control site q1. P7 is the probability for the electron to be at S4 inactivation control site q7, etc. With −80 mV membrane potential the four gating electrons would all be at the q1 control sites and channel strongly closed. With depolarization to +30 mV, the domain IV electron tunnels to the fast inactivation site q7 in about 1 ms. Upon repeated depolarizations the domain III electron tunnels to qF5 and then with more depolarizations the domain I electron tunnels to qF9. This is a mechanism of adaptation. Inactivation energy barriers are smaller than activation energy barriers and a small leakage curremt can flow through inactivated channels. A study of noninactivating sodium channels has shown that the open probability fits an exponential down to 10−7, with a limiting slope of 2.2.mV per e-fold (Hirschberg et al., 1995). This implies that the sodium channel open probability is proportional to m4 not m3 as in the Hodgkin and Huxley model. This is in agreement with Fig. 10. Open probability curves for the sodium channel with voltage-sensitive amplification and exponents for m of 1 to 4 are plotted in Fig. 6-5 of Electron-gated ion channels (2005).
Fig. 10B,C,D Sodium channels S4-S6 open probability</a

Fig. 10B.  Sodium channel open probability curves for mn. These curves are plotted using the Hodgkin and Huxley rate constants (αm and βm) converted to membrane voltage; Vm= −(V+60). The exponent for mn gives the number of cascaded gating cavities. Saturation occurs with membrane voltage more negative than −100 mV. This is when the S4 gating electron has near 100% probability at the q1 site, thus exerting maximum force on a sodium ion in a gating cavity. At saturation the open probability (and ion current) is reduced by 178 for 1 gating cavity and by 109 for 4 cavities. For open probability less than 0.1 the electron seldom tunnels to q3 or above and it only occasionally tunnels to q2. Thus, mn can be represented by a 2-site model given by: mn=exp[(Vm+Vo)/9]n. For n=4 the denominator becomes the limiting slope of 9/4=2.25 mV per e-fold. For electron tunneling across S4 the αm rate constant equation for 4 tunneling sites is given in Table 6-1 of the book Electron-gated ion channels (2005).
Fig. 10C shows the 4 modulated energy barriers; one in each domain. The energy barriers for the above saturation attenuation (1/178) are ΔG =250 meV or 10.4kT. The rate constants are determined by the S4 tunneling site spacing. Each qn site has a component of force acting to close its activation gate cavity.

Fig. 10D shows a plot for the Hodgkin-Huxley βh rate constant for sodium channel inactivation. The curve shows saturation at a displacement voltage (V) more negative than −70 mV (or Vm more positive than −10 mV). With ΔGO =180 meV at saturation the open probability is reduced by about 42. The saturation factor is calculated as Ps = exp[−ΔG/(2kT)] = 0.0235. Sodium channel inactivation has a peak time constant 17 times that for sodium activation. This is due to the S4 control site q7 being located near the membrane interior surface and interacting with charged residue q8 in the cytoplasm. This local interaction gives the Hodgkin and Huxley alpha and beta rate constants a coefficient of bh=0.060 (Table 6-1. in the book Electron-gated ion channels). Fig. 6-1 in the book illustrates calculated time constant curves using Hodgkin and Huxley rate constants. The peak time constant for sodium activation is 0.5 ms and sodium inactivation is 8.5 ms or 17 times greater.