Electron-gated ion channel structures (2019)

Voltage-dependent ion channels (Na, K, Ca) are nature's transistors for electrical and calcium signaling. These channels control our muscles, brain activity, heart rhythm, theta rhythm, memory and sleep. They are associated with many diseases. A great leap forward in understanding these channels is made by controling the gates with tunneling electrons. The gating mechanism and structure for controlling ion channel conduction and timing is encoded in the amino acid sequence. The first published amino acid sequence was for the sodium channel of an electric eel. It was determined by a group at Kyoto University led by S. Numa (Noda et al., 1984). An arginine or lysine amino acid was found at every third residue in four S4 segments. They proposed that positively charged arginine and lysine on the S4, moving across the membrane electric field, could be associated with gating. For more than 30 years all sodium and potassium ion channel gating models and their structures published in peer reviewed journals have been based on this idea and there is still no satisfactory gating mechanism. The positively charged arginine and lysine approach is unworkable.

Only the negatively charged electron can solve the ion channel gating problem.
The potassium channel needs four independent gates to give the Hodgkin and Huxley open channel probability n4 and the inactivation gates and timing need to be modeled. A breakthrough in decoding the amino acid sequence is shown in Fig. 1. The much-studied Shaker B potassium channel is ideal for decoding the sequence because each subunit has an activation gate, a fast N-type inactivation gate, and a C-type inactivation gate. That is a total of 12 gates and it only needs one tunneling electron in each subunit to control all the gates and give the published experimental time constants. Ion channel researchers have published many experimental observations on potassium channels and this data was used to configure the structure. Inactivation times depend on the location of the N-terminus as shown in Fig. 1A and Fig. 1B.

Deletion of N-terminus residues 6-46 removes fast inactivation (ir Δ6-46)—How does this occur?
The electron-gating model provides an explanation for the inactivation gating mechanism. The N-terminus is located next to S6 and S4 keeping water from entering the crevice in each subunit (Fig. 1B). The long side chain of L7 is pointed towards A463 and closing the U3 gating cavity for N-type inactivation.

Two things occur with residues 6-46 deleted:
1. Residue L7 is no longer present to close the U3 gating cavity: N-type inactivation is disabled.
2. On subunit KA in Fig. 1B the S4 site q6 has an angle of 60° and now q6 is exposed to water in the crevice. Exposure to water stops the NH3 inversion and amplification. Without q6 the electron tunneling distance is q5 to q7 and tunneling time for inactivation at the U2 gating cavity increases to seconds. Now with a membrane voltage change of −80 to +60 mV the U1 activation gates would open with fast electron tunneling between q1 and q5. This gives a maximum charge displacement of 16e0 for 4 subunits. Activation charge displacements of 12-16e0 have been reported in published experiments with residues 6-46 deleted.

        

Fig. 1.  Structure required for 4 tunneling electrons to control activation and inactivation in Shaker K+ channels.
(A) Amino acid sequence shows α-helices S1 to S6 aligned for controlling activation and inactivation gates in one of four identical subunits. An electron tunnels across arginine (R) and lysine (K) NH3 sites on S4 increasing the energy barrier at adjacent gating cavity. The α-helix cross-section angles φ (in black) are for the residue backbone center with 180° furthest from the channel center. Arg/lys NH3 tunneling sites (q1, q2, etc.) have cross-section angles φ (in red) with 0° nearest the channel center. Angles in italic are for α-helices end termini. Gating cavities U1, U2, U3 need additional residues to close the cavity and maximize the gating energy barrier. Residues T442 and V474 close one side of cavities U1 and U2. Open ends for U1 and U2 are closed by a cuff formed by residues 431-435 and 478-482. The N-terminus residue L7 has a long side chain that closes the U3 gating cavity for fast N-type inactivation. ShIR has residues 6 to 46 deleted. This stops fast inactivation by placing alaine (A) with a short side chain next to the U3 gating cavity. (B) Outside view shows alignments for subunits KA to KD. The subunits are incremented by 1/4 α-helix pitch (1.35 Å) along channel z-axis to form four sequential cavities for U1, U2, U3. Only U1 cavities are shown. Efflux K+ Ions and water sequentially pass through activation-gate cavities (U1A to U1D) until an electron tunnels to a q1 control site blocking ion transit (Fig. 1.A). Negatively charged glutamate (E) side chains on S1, S2, S3 are adjacent the lipid membrane and likely provide an energy landscape to optimize tunneling. Intersubunit distances between cysteine termini (gray boxes) are within ±10% of reported Shaker intersubunit distances for eight sites. The structure is based on many published experimental observations, which are referenced in the book: Electron-Gated Ion Channels : With Amplification by NH3 Inversion Resonance (2005).


          
      Fig. 2. Schematic for electron gating and timing of Shaker potassium channels.
      Summary of time intervals for Shaker B and Shaker A channels

      TL        Activation lag time
      TN        N-type inactivation time
      TC        C-type inactivation time
      TD        Deactivation time
      TO        Open-gate time for Shaker B (all switches closed)
      TO+T7   Open-gate time for Shaker A (all switches closed)
      TOD      Open-gate time during deactivation (subunit only)
      T7        7-residue tunneling time for q7 to qF7
      T7D      7-residue tunneling time for qF7 to q7
      T3        3-residue tunneling time for qF7 to qF10
      T3D      3-residue tunneling time for qF10 to qF7

Fig. 2.  A brief description of timing: Arginine and Lysine NH3 groups function as electron tunneling sites on the S4 voltage sensor of the four potassium channel subunits (KA, KB, KC, KD). When a gating electron tunnels to a control site (q1, q7, qF7, or qF10) the electric field across the adjacent cavity (U1, U2 or U3) creates an energy barrier that traps an ion in the cavity. The electron-activated energy barrier, for each gating cavity, is represented by a switch. Subunit KA is used to illustrate the timing. When a gating electron tunnels to a control site, the associated switch opens, thus blocking current flow. At −80 mV resting potential, the gating electron is at q1, causing switch S1A to be open. When the membrane is depolarised to +30 mV at time t0 there is a brief lag time TL and then the electron tunnels across 6 Arg/Lys sites to the Shaker B control site q7. The electron's field causes switch S3A to open, resulting in N-type inactivation. The N-type inactivation time is reported to be about 2-4 ms and the gate open time is TO = TN − TL. For Shaker A, there is no N-type inactivation, thus q7 is not a control site and switch S3A remains closed. After an interval T7, the electron tunnels across the 7-residue distance to the inactivation control site qF7 and opens switch S2A. It then tunnels on to qF10, keeping S2A open. The inactivation time TC for C-type inactivation, reported to be 10-30 ms, is determined by the tunneling distance between q7 and qF7. When membrane voltage returns to −80 mV at time t1 the membrane field causes the gating electron to return to q7 after an interval T3D + T7D. Then the electron tunnels back to q1. During time interval TOD the gate is open (all switches closed) for the subunit, but since the tunneling time has a random component, an electron in one subunit can return to q1 while in another subunit it is still at inactivation site qF7 blocking current flow. The deactivation time TD can be much greater than inactivation time TC, because of a local field from positively charged arginine (R394, R309) and other charges near the far sites qF7 and qF10.

Table 1.  Alignments for functional gating in Shaker K+ channels
Experimentally determined amino acid sequences for gating        Requirements for optimized gating
1. Shaker family channels have 7 Arg/Lys on S4 with 3-residue spacing. This gives an 18-residue spacing between q1 and q7. This 18-residue spacing gives q1 = 0° and q7 = 0°, maximizing gating barriers for both activation and N-type inactivation.
2. There is an 18-residue spacing between Shaker selectivity filter center residue Y445 and key residue A463 for N-type inactivation. This aligns cavity U1 and U3 with tunneling sites q1 and q7 maximizing gating barrier for both activation and N-type inactivation (Fig. 1.A).
3. There is a 5-residue distance between Shaker L7 and charged E12, D13. This critical distance aligns L7 in crevice with U3 cavity. Charged residues E12 and D13 remain at cytoplasm/membrane interface.
4. Shaker N-terminus residue L7 is hydrophobic with moderately long side chain. This allows side chain penetration near U3 cavity, increasing gating energy barrier for N-type inactivation.
5. Shaker family channels have a key residue I470 spaced 25 residues from Y445. (Published experiments place I470 at the center of a cavity for inactivation). This spacing places I470 at the center of gating cavity U2 and in alignment with R387 and K390 for C-type inactivation.
6.Shaker R387 is 7 residues from K380. This spacing sets tunneling distance for a fast C-type inactivation time (10−30 ms).
7. In Kv1 channels, with Q387 instead of R387, Arg R390 is 10 residues from K380.(Kv1.1, Kv1.2, Kv1.4, sqKv1A) This spacing sets tunneling distance for a slow C-type inactivation time (0.2−5 s).


  

Fig. 3.  New Blue Fluorescent Protein microwave thermal fluorescent spectrum confirms that Arg/Lys NH3 group is Inverting. The rotational J,K states show alignment with scaled frequencies fG1 in Table 2. More than 20 inversion lines are within 1% of the scaled down NH3 gas phase inversion lines. The NH3 inversion is required for amplified electron tunneling. It should be present in all life forms. The labeled peaks are the Rotational States (J,K) shown in Table 2. The gas phase NH3 inversion frequency of 23.786 GHz is scaled down by *S1 = 0.695. This gives an inversion frequency of f0-G1 = 16.5 GHz for the NH3 Group 1 inversion at the end of the Arg/Lys side chain. This is near the 16.8 GHz Group 1 inversion frequency determined with an HP 83630B signal generator and HP 8348A amplifier rented for 3 months in 2002. This BFP spectrum is published in my book Electron-gated ion channels. BioKinetix Research now has a unique Microwave Oscillating Temperature Spectral Analyzer System called MOTS-SCAN ONE. The lowest frequency for a scan is 0.5 GHz. A scan of 0.5 GHz to 5 GHz, which includes the cell phone frequency range, did not show any resonant peaks. The microwave power was 100 mW and the antenna was increased in length to maximize coupling. MOTS-SCAN ONE is designed to also obtain microwave spectra on non-fluorescent biological specimens. This is an exciting new development that opens a window into what is happening at the cellular level related to arginine and lysine resonances and oxidation.

  

  

L-type Ca2+ channels are found in skeletal muscle, heart muscle and regions of the brain associated with learning and memory. These channels are natural oscillators, able to produce a wide range of frequencies when combined with potassium channels. Hundreds of peer-reviewed studies of L-type Ca2+ channels have been published in leading journals. But after more than two decades of research there is no simple mechanism for how oscillations of Ca2+ currents are generated. This is because ion channel researchers are stuck with a wrong and unworkable theory for channel activation based on positive charges on S4 moving across the membrane electric field. Electron gating of ion channels solves this problem. Electron-gating of the Ca2+ inactivation gates gives a simple mechanism for generating the observed oscillations of EEG waves and long time intervals of circadian rhythm and sleep. An S4 tunneling electron closes the channel when it tunnels to a U2 inactivation gate. The frequencies and time intervals are determined by the electron tunneling distance between S4 Arg/Lys far sites (Table 3). Various modulating factors can alter the frequency and time intervals. The long time interval for the circadian clock and sleep are determined by the tunneling distance q5–qF17 on S4 domains I and II. An important function of L-type Ca2+ channels is providing a trigger pulse for heart muscle contraction. The gating electron in S4 domain III tunneling between q8–qF11 can oscillate (with associated modulating factors) giving a trigger pulse 60–100 times a minute for heart muscle contraction.

Medical Conditions: The inactivation gate arrangement for L-type Ca2+ channels may help in connecting site mutations with medical symptoms. The mutation R926S (Fig. 5) in domain III for (Q13698) would disable the domain III inactivation function. It would probably cause a muscle disorder. Many site mutations and symptoms are reported for the Human L-type channel Q13936. The electron gating region is shown in Fig. 6. Further details for the L-type Ca2+ channel oscillator (Figs. 4 and 5) are in Sect. 8-7 of the book Electron gated ion channels.

   

Fig. 5. Timing:  The S4 segment for Na, K and Ca ion channels has an activation region with an arginine (R) or lysine (K) amino acid spaced every third residue. Why are the Arg/Lys spaced every third residue? This is because it gives the smallest electron tunneling distance with the smallest tunneling time (Book Table 8-1). A 5-residue spacing gives a large increase in tunneling time and is labeled a far site when it is toward the cytoplasm. The inactivation region in L-type Ca2+ channels has a different far site spacing in domains II, III and IV.

  

Fig. 6.  The L-type Calcium channel is a major oscillatory channel generating EEG oscillations in conjunction with potassium channels. It is a pacemaker for the heart, producing a trigger pulse 60–100 times per minute. It is widely expressed in skeletal muscle and in neurons of the brain associated with learning and memory. How does this channel oscillate? The answer to this is in the electron gating structure. The electron tunneling distances on the S4 are the primary determinant of the frequency. Other factors, such as intervening residues, temperature and calcium space charge influence the frequency. Antagonists and tranquilizers like benzodiazepine enter the outer vestibule. There they reduce Ca channel current and lower the Ca oscillation frequency by reducing the space charge. In Fig. 6 we show how the 4 domains are aligned to allow passage of calcium ions into the cell. Each domain is located 90° to the adjoining domain. From the outer vestibule calcium ions enter at domain IV, then transit the gating cavities U1D, U1C, U1B, U1A in sequence. It is like going down a spiral staircase with a side cavity every 90°. When the ions reach the inactivation gates they again transit a spiral staircase-like region with cavities 90° apart. They transit gating cavities U2D, U2C, U2B, U2A and then exit into the cytoplasm. How long an ion remains in the cavity depends on the electric field intensity crossing the cavity.

  

Fig. 7.  P/Q-type calcium channels are high-voltage activated channels found in the Purkinje cells of the cerebellum and in the hippocampus. Some neuroligical disorders, such as familial migraine, convulsive epilepsy and Alzheimers disease have been attributed to malfunctioning P/Q-type channels. These channels have 24 transmembrane proteins, 6 are in each of the 4 domains. The gating region includes S4, S5 and S6. The distance between U1 and U2 gating cavities for P/Q and L-type calcium channels is the same. The big difference is the location of the S4 Arg/Lys inactivation sites. Becaues of this, P/Q Calcium channels would be sensitive to different EEG oscillation frequencies than L-type Calcium channels. N-type calcium channels are similar to P/Q-type channels. They have the same S4 tunneling site locations and the same S6 gating cavity locations.

  

Fig. 8.  BK-type Ca1.1 potassium channels are large conductance channels that activate by both voltage and elevated levels of intercellular Ca2+. They are widely expressed in the CNS where they control neuronal excitability. The alignment of the gating region is illustrated above. The 15 residue distance from R278 (q3) to K293 (qF15) would have a tunneling time of hours, but on S3 there are two intervening amino acids that reduce the time. They are K239 and R232. With only 3 arginine residues for activation, potassium ions can move faster through the long region between R278 and K293 with no slowing by tunneling electrons. With a large depolarization (+60 mV) the gating electron would tunnel from R278 to K239 (S3) then to R233 (S3) and to S4 lysine qF15 and lysine qF21 (Ref: Kv2.1 structure). Like Kv2.1, the BK Ca 1.1 channel has arginine qB6 tunneling back sites. With hyperpolarization the electron probability at qB6 increases. The back sites qB6 have an 11.3À tunneling distance to q1 and an estimated time constant of 100 ms. The qB6 sites would slow activation. The model indicates they are protected from water by S3 like Kv2.1 (Fig 9A).

  

Fig. 9. The Kv2.1 is a major delayed-rectifier voltage-dependent potassium channel found in the CNS and Pancreatic ß cells. It has been linked to neuronal apoptosis. Kv2.1 has an unusually complex inactivation system with many different time constants that give it a U shaped voltage versus time curve. To understand the functioning of this unusual channel a 3-D structure is needed. Electron tunneling provides a mechanism to derive a structure and explain the gating and timing with four tunneling electrons per channel. A 3-D geometry was assembled based on published experimental data and the alignments needed for electron gating of the activation and inactivation gating cavities. Kv2.1 has no N-type inactivation, but it needs the N-terminus for enabling inactivation. The N-terminus prevents nearby arginine and lysine NH3 end groups from becoming charged. The N-terminus is located in the crevice with a stabilizing positively charged arginine R7 or lysine K7 at the protein-cytoplasm interface. It shields S4 tunneling site qF14 and S3 site K255 with q255 from water allowing these NH3 groups to be neutral and inverting with amplification. There is a 13 amino acid tunneling distance to the S4 inactivation site R321 with qF13. This would give a tunneling time of minutes, but the observed initial time is about 1 s. The tunneling time is reduced by water shielded lysine sites on S3. Lysine K255 with q255 at −20° on S3 is protected from water by the N-terminus. Lysine K252 with q252 on S3 is protected from water by S4. These sites are in near alignment with qF14 (Fig. 9A). These two intermediate lysine sites reduce the electron tunneling time between q5 and qF14 on S4. A third site K249 on S3 with its NH3 group at −20° is also protected from water and may contribute to reducing tunneling time. A stabilizing positively charged residue for S3 alignment is K250. Its lysine NH3+ at −80° is pointing into the cytoplasm just below the membrane. Pointing into the outer vestibule is a likely charged S4 site R289 with NH3+ at 20°. The S4 R290 back site qB6 is shielded from water at 120° by S3 and is an electron tunneling site. The unusual U shaped voltage versus time inactivation curve is due in part to R321 with qF13 at −20° near S5 making the tunneling distance longer to q252 than from qF14. With depolarization (+60 mV) the electron rapidly tunnels from q5 to q255 then to q252 and finally to qF14. After repeated depolarizing pulses or a single pulse over an extended period of time the electron tunnels against the electric field to qF13.

The 3-D structure for Kv2.1 potassium channel reveals arginine back-site qB6 can retain gating charge and slow channel activation.
Arginine R290 has an NH3 group qB6 at 120° that is protected from water by S3 (Fig. 9A subunit KD). The calculated tunneling distance from qB6 to q1 is 11.3À and the estimated time electron tunneling constant is 100 ms. As membrane voltage becomes more negative the electron has increasing probability to be at tunneling site qB6. Thus, the qB6 sites would slow channel activation and likely reduce the open probability range for Kv2.1, shab and BK potassium channels.

  

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−P8)(1−PF5)(1−PF9)(Vm−ENa).  Here P1 is the probability for the gating electron to be at the S4 control site q1. P8 is the probability for the electron to be at S4 inactivation control site q8, 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 q8 (P8=1) 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. Other sodium channels like eel (Accession APH07649) and human cardiac muscle (Accession Q14524) have a lysine (K) at qF10 in domain II to which the electron can tunnel. Domain I for eel also has an arginine (R) tunneling site at qF13. 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.  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 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.
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 time constant 17 times that for sodium activation. This is due to the S4 control site q8 being located near the membrane interior surface and interacting with charged residues in the cytoplasm. This local interaction gives alpha and beta rate constants a coefficient of 0.06. (1/ 0.06 =17).

  

Fig. 11.  T-type calcium channels are low-voltage activated channels that open during cell membrane depolarization. These Transient opening calcium channels are different from the Long lasting (L-type) calcium channels (Fig. 6) because of their smaller inactivation time delays and smaller residue spacings. The electron-tunneling distance for T-type channel inactivation is only 5 or 6 residues. Also, there is a resonant electron tunneling back site at qB6 in domain III, which likely contributes to T-type channels being activated at more negative membrane potentials. T-type calcium channels are reported to be located within the brain, peripheral nervous system, heart, smooth muscle, bone, and endocrine system.

Medical Conditions:

The CACNA1G gene (Cav3.1) has reported mutations related to epilepsy (Long QT syndrome and Timothy syndrome).
A reported loss of function mutation is R1715H. This is the arginine tunneling site q3 on S4 domain IV (Fig. 11).
This would slow the opening of the activation gate in domain IV.

The CACNA1H gene (Cav3.2) with alignments in Fig. 11 has two reported loss of function mutations observed in a few indivudals with autism spectrum disorder (ASD). The mutation R212C (q5 domain I) would disable fast activation in domain I. The mutation R902W (qF6 domain II) would increase inactivation time in domain II. Figure 11 shows how these mutations increase the inactivation time and slow down channel activity.

References:

1. Weiss N, Zamponi GW. (REVIEW) Genetic T-type calcium channelopathies. J Med Genet 2019:0:1-10.doi:10.1136/ medgenet-2019-106163 on 19 June 2019.

2. Splawski I, Yoo DS, Stotz SC, Cherry A, Clapham DE, Keating MT. CACNAIH mutations in autism spectrum disorders. J Biol Chem 2006:281:22085-91.

3. Coutelier M, Blesneac I, Monteil A, Monin M-L, Ando K, Mundwiller E, Brusco A, Le Ber I, Anheim M, Castrioto A, Duyckaerts C, Brice A, Durr A, Lory P, Stevanin G. A recurrent mutation in CACNA1G alters CaV3.1 T-type calcium-channel conduction and causes autosomal-dominant cerebellar ataxia. Am J Hum Genet 2015:97:726-37.

Notes on the alignment of cascaded gating cavities:
1. The α-helices in cell biology are right handed.
Because of this the S6 gating cavities must advance inward with each 90° clockwise rotation.
2. Viewed from outside the cell membrane, sodium or calcium ions transit clockwise through a spiral staircase like region with side gating cavities every 90°. For potassium channels the ions are flowing outward and viewed from outside they are going counter-clockwise.
3. The S6 gating cavities advance by 1.5Å for each 90° rotation. The advance may be as little as 1.35Å (pitch height divided by 4) depending on the protein geometry.
4. The protein α-helix geometry was first described by Pauling et al., (1951). It has a rise per residue of 1.5Å and a pitch height of 5.4Å, corresponding to 3.6 residues per turn. The backbone radius is 2.3Å, which does not include the outward sloping side chains.
Reference: Table 8-1, Figs. 9-3 to 9.6. Electron-gated ion channels.

These pages were started May 2, 2019 and later figures were added. Fig. 11 was added July 1, The last update was Oct 25, 2019.

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