Na⁺ and K⁺ channels: history and structure

Abstract

In this perspective, we discuss the physiological roles of Na and K channels, emphasizing the importance of the K channel for cellular homeostasis in animal cells and of Na and K channels for cellular signaling. We consider the structural basis of Na and K channel gating in light of recent structural and electrophysiological findings.

In this perspective, we discuss the physiological roles of Na and K channels, emphasizing the importance of the K channel for cellular homeostasis in animal cells and of Na and K channels for cellular signaling. We consider the structural basis of Na and K channel gating in light of recent structural and electrophysiological findings.

Significance

Recent structural insights into voltage-gated ion channels advance the possibility of understanding normal channel function and disease phenotypes at an atomic resolution.

Main text

In 1952, Hodgkin and Huxley published their famous formulation for the movement of sodium and potassium ions through the axon membrane as an action potential moves rapidly along the axon (1). They experimented on the squid giant axon after inserting an axial silver wire that converted the axon membrane, in essence, into a single giant patch with uniform voltage (2,3). The influx of Na⁺ ions, which initiates and propagates the action potential, was kinetically described by the m³h postulate; each unit of the Na conductance, gNa, now recognized to be individual channels, was activated in response to depolarization by the movement of three charged “m” particles and inactivated by one charged “h” particle moving more slowly. The K channel, which restores the resting potential, was activated by four charged “n” particles that moved more slowly than the “m” particles. Precisely how the ions moved through the membrane and the hypothetical “gates” that controlled their movement were questions for the future: did the ions diffuse through the thin lipid membrane or, as more often hypothesized, pass through a channel of some sort? The recent structures of K channels from MacKinnon and colleagues (4, 5, 6, 7, 8, 9) have definitively answered these questions, as described below.

The K channel functions in volume control and signaling

Before describing the channel, we consider the questions: Why is there high K⁺ inside? Why is the membrane selectively permeable to K⁺ at rest? Why is there a resting potential? The short answer is that osmotic room for life chemicals is made by a negative internal V_m that drives Cl⁻ out of the cell (10, 11, 12). Life probably began in the ocean or an estuary. In seawater, salts delivered to the oceans by rivers result, at present, in an ocean salt content of roughly (in millimolar) 440 Na, 10 K, 10 Ca, 50 Mg, and 470 Cl. In this milieu, it was necessary to package the life chemicals (e.g., DNA, RNA, proteins, and amino acids) inside cells surrounded by a semipermeable membrane. Their presence, inside but not outside, dilutes the water concentration within the cell, yielding a tendency to suck in water to swell the cell and dilute the life chemicals that are sequestered inside. One way nature prevents swelling is to place a rigid shell of calcium carbonate or wood around a cell and its contents. Animal cells, however, lack shells and have devised a strategy to make a shell unnecessary by means of a Na/K pump that removes Na⁺ from the cell in exchange for K⁺ ions. With a K⁺ selective ion channel, the cells develop a membrane voltage, negative inside, that drives anions (mainly chloride) out of the cell interior, making “osmotic room” for the life chemicals. Inside and out, with equal osmotic content, are then separated by a fragile, flexible, bilipid membrane. This works perfectly well as long as there is an energy supply for the Na/K pump, but turning off the pump causes the cells to swell (11), as in cerebral edema.

Adaptation to signaling

K channels and the negative V_m they generate are thus essential for volume control. The negative V_m also plays an essential role in signaling; it is the resting potential upon which the Na-dependent action potential is superimposed. An analogy to the action potential propagating along an axon is the trans-Atlantic cable, which is equipped with booster stations. In an axon, the boosting function is served by Na channels that detect the incoming signal, an action potential, and boost it by increasing sodium permeability, allowing Na⁺ to flow in and depolarize the axon membrane. This reinforces the action potential, causing it to spread further along the axon. Voltage-dependent K channels complete the action potential; they open to bring V_m back to rest after the sodium channels inactivate.

Structure of an open, voltage-gated K channel

Figs. 1 and 2 A show the structure of an open, voltage-gated K channel, the Kv1.2/Kv 2.1 chimera (8). The channel is made of four identical subunits, each with six transmembrane helices, S1–S6 (Fig. 1, A and B). The S6 helices from each subunit (flanked by S5) form the pore, while the S4 helices, with positively charged arginine and lysine residues, in association with helices S1–S3 form the voltage sensors. A structure of the closed channel has not been determined, but at the resting potential, inward motion of the S4 helices is thought to force the S6 helices together to form a closed gate at the inner end of the pore.

Figure 1.

Structure of a voltage-gated K channel. Shown are the structures of the chimeric Kv1.2/2.1 channel (8). (A) An extracellular view with the four subunits shown as wireframe and the S1–S6 transmembrane helices of one subunit shown as ribbons. The pore is formed by the S5 (black) and S6 (cyan) helices; pore lining residues from the S6 helices are in spacefill (gray). The voltage sensors, formed by helices S1–S4, are found next to the pore forming helices of an adjacent subunit. The S4–5 helix (dark blue) transmits downward movement of the S4 helix (blue) to the S6. (B) Shown is a side view after a 90° rotation of (A). (C) An enlarged side view of the pore is shown with the pore lining residues from two subunits in spacefill (gray). Three K ions (gold) are shown, two in the selectivity filter (black strands), that are coordinated by the backbone carbonyl oxygens of the selectivity filter residues (not shown). The third K ion is in the vestibule, or cavity, surrounded by eight waters of hydration (gray/pink). This hydrated K⁺ ion is at the position of the hydrated K⁺ ion in the KcsA structure (5). (D) Hydrophobic residues on the S4, S4–5, and S6 helices and on the S5 helix (S5_a) of the subunit adjacent to the voltage sensor are shown in spacefill (gray). Polar residues at the intracellular end of S6 are also in spacefill (color CPK). To see this figure in color, go online.

Figure 2.

Detailed view of the voltage-sensing mechanism. Helices from Fig. 1 are shown with selected residues in spacefill. (A) The open state structure from (8) is shown. The S4 helices are in an activated position, and the intracellular gate is open. Selected residues are shown in spacefill with CPK coloring. Residue numbering is for the chimeric structure, and add 72 to obtain corresponding residues in the Shaker sequence. Negatively charged residues QTC_O and QTC_i are E226 and E236 on the S2 helix. Not shown are F233 on S2 and D259 on S3, which also contribute to the QTC (9). R2–R6 are positively charged residues on S4. K7 is at the start of the S4–5 helix from which three leucine residues (gray, L310, L313, and L317) point into the membrane. Amino acid S320, at the end of the S4–5 helix, is hydrogen bonded to N408 on the S6 helix (inset). The two proline residues (P401 and P403, pink) are likely hinge points on the S6 helix. Two hydrophilic residues R415 and E416 at the intracellular end of the S6 are shown. K7 and E416 likely interact in the open and closed states. (B) A hypothetical closed state of the chimeric structure of Long et al. (8) is shown. The S4 moves downward and the S4–5 and distal S6 rotate so that the distal S6 helix approximates the position of the pore-lining M2 helix of KcsA (4,5). The S4–5 is rotated around S320 and the distal S6 around P401. To see this figure in color, go online.

Fig. 1 C shows an enlarged view of the pore with residues lining the “vestibule” or “cavity” from two opposite subunits in spacefill (gray). A hydrated K⁺ ion is inside the vestibule, while the selectivity filter (black ribbons), at the outer end of the vestibule, contains two dehydrated K⁺ ions (5,8). Y373 has an important role in stabilizing the outer hydration-dehydration site of the selectivity filter (cf. Y78 in KcsA (4)).

In Fig. 2 A, a side view of selected parts of one subunit are displayed in spacefill and ribbon formats; residue numbering is for the chimera. On the left are two electronegative charged residues in S2, labeled QTC_o and QTC_i. They are part of a “charge transfer center” (QTC) (9) that facilitates the sequential movement through the membrane of the positive gating charge residues on S4 (R2 to R6 shown). The S4 helix is in a channel-open position, with QTC_o occupied by R4⁺ and QTC_i by K5⁺. In this open state, R6⁺ remains as a hydrophilic anchor in the internal solution below QTC_i, serving to keep the inner end of S4 in the internal solution as S4 moves outward to trigger channel opening. K7⁺, which begins the S4–S5 segment, anchors the beginning of the S4–S5 helix in the internal solution. K7⁺ also bonds to E416 near the end of the S6 helix to stabilize the open state (Figs. 1 D and 2 A). In the hypothetical closed state presented in Fig. 2 B, this bond also serves to hold the beginning of S4–5 near the terminal end of S6.

Three hydrophobic leucine residues (gray) line the upper surface of S4–5 (Figs. 1 D and 2 A), holding it in the membrane lipid. The hydrophilic inner surface of the amphipathic S4–5 helix faces the internal solution. The S4–5 helix extends almost horizontally (Fig. 2 A) to a serine residue, S320, at the base of the S5 helix (black ribbon). S320 forms a tight hydrogen bond to N408 (Fig. 2 A, inset), near the inner end of the S6 helix (cyan). As described in (13) and below, an equivalent S-N bond in the sodium channel is probably important in stabilizing the Na channel’s open state.

Passage of a K⁺ ion from inside to outside through the open K channel

Let us follow a K⁺ ion moving from inside to outside through an open K channel. Inside the cell, the [K⁺] is high thanks to the Na/K pump. Outside, in seawater or extracellular solution, [K⁺] is low, and [Na⁺] is high. Beginning inside the cell, the terminal residues of the S6 are hydrophilic (HRET, Figs. 1 D and 2 A) and serve to keep the widely spaced (∼40 Å diagonally across) inner ends of the four S6 segments in aqueous solution. Following the outward path of a K⁺ ion, the channel narrows steadily to the “gate” region, near P401 and P403. At P403, the channel opening is 12.2 Å, large enough for easy passage of a hydrated K⁺ ion into the aqueous vestibule above, which is slightly wider. On leaving the outer end of the vestibule, an outgoing K⁺ ion sheds its water coat as it enters the selectivity filter (Fig. 1 C), which is lined by oxygens from TVGY residues (4,5). These provide a close and energetically favorable fit for a dehydrated K⁺ ion. Perturbation of the network of residues connecting to Y373 (Fig. 1 C) at the outer mouth of the filter can lead to pore dilation and C-type inactivation; when dilated, the outer site is no longer a good fit for a dehydrated K⁺ ion (14). The vestibule is the blocking site for the experimentally important TEA⁺ ion, which is the size of a hydrated K⁺ ion. TEA⁺ blocks flow because it cannot shed its covalently attached ethyl arms to enter the selectivity filter. Finally, the K⁺ ion rehydrates as it leaves the selectivity filter for the extracellular solution.

Closed configuration of the K channel

Although a structure of the closed K channel is not yet available, closing is thought to involve a large (15–20 Å) inward movement of the S4 helices (8,9), resulting in the movement of the S6 helices to a position resembling the inner helices in the KcsA structure, which crystalized in a closed state (4,5). The construction in Fig. 2 B shows our guess regarding the closed configuration. In each of the four subunits, negative V_m draws the positively charged S4 residues R4, R3, R2, and R1 sequentially inward through the QTC. This downward motion of S4, from activated with K5 at QTC_i to the fully closed state, is 21 Å in the direction of the helix and 18 Å perpendicular to the membrane (9). In each domain, this pushes the S4–5 linker downward and inward toward the pore axis, pinching the S6s together below P401 and P403; these proline residues likely form a “hinge” in each of the four S6s. The gate itself, which controls the path from cytoplasm to vestibule, is probably formed by the side chains of P403 and V406, which are oriented toward the interior of the pore (15, 16, 17). In the fully closed state, R1 of the Shaker S4 (Q1 of the chimera) is at QTC_i. Ca²⁺ ions stabilize the deactivated position of the voltage sensors by binding to the negatively charged extracellular residues (18).

Two other interactions that hypothetically stabilize the closed state are shown in Figs. 1 and 2. The first, as described above, is an electrostatic interaction between K7 at the end of the S4–5 linker and E416 on the intracellular end of S6. The second involves interactions between hydrophobic residues on the S4, S4–5, and S6 helices (Fig. 1 D, gray). Also involved may be residues on the S5 helix of the subunit adjacent to the S4 voltage sensor. Mutations of the hydrophobic residues in or near to the S4 are known to have strong effects on channel gating (19, 20, 21, 22, 23, 24). In the ILT triple mutant of the Shaker K channel (23,25,26), mutation of two of the hydrophobic residues in S4, V369I and I372L, coupled with a third mutation, S376T, right shifts the G-V curve by ∼90 mV and isolates a late cooperative transition in the activation pathway. A right shift in a late opening transition of the Shaker channel is also revealed by the V2 mutant (21,27,28) in which the first leucine in the S4–5 linker (L310 in the chimera, Figs. 1 D and 2 A) is mutated to valine. The structural details underlying these physiological effects are, as yet, unknown. Long et al. (8) described lipid-filled, “concave hemi-circles” between the voltage sensors of the chimera structure (Fig. 1 A). Many of the hydrophobic residues from the S4, the S4–5 linker, and the S5 of the adjacent subunit are directed toward this lipid environment. Given the large downward motion of the S4 between open and closed states, there is the clear possibility for hydrophobic interactions to stabilize open and closed states and to influence the transitions between states. For example, if L310 is in lipid in the open state but removed from the lipid in the closed state, then hydrophobic interactions with nearby residues (Fig. 1 D) may play an important role in stabilizing the closed state.

Energetics of channel gating

Full motion of the S4s transfers four electronic charges per helix or 16e per channel across the membrane. At a membrane potential of −60 mV, this corresponds to an energy of 960 meV or ∼92 kJ/mol. Because in the absence of membrane potential (V_m = 0), most voltage-gated channels are open, the S4s must spontaneously adopt their activated configuration. On changing to −60 mV, work is done to force the S4s inward to close the channel. K channel block by 4-aminopyridine (4-AP) shows that most of this energy must be released spontaneously upon channel opening. 4-AP enters the cavity of an open K channel, where it binds and stabilizes a closed state (29, 30, 31). In this closed state, 90–95% of the gating charge is still able to move, with only small effects on voltage dependence (31,32). Thus, the S4s can readily move outward even though the S6s are held in a closed conformation, suggesting that there is not a rigid link connecting S4 and S6 motions (33,34). When the S4s are in their active (outward) position, the S4–5 linkers are no longer locked down, and the intracellular gate can open. Bombardment of the S6 helices by intracellular K⁺ ions in both K and Na channels is likely to be a strong contributor to this opening; squid giant axons perfused with low internal [K⁺] are depolarized to about −10 mV, but even with this abnormally low resting potential, the axons still generate 100 mV action potentials (35), indicating that activation of the Na conductance has been shifted to more positive potentials by the lowered internal [K⁺] (and probably, more generally, by the lowered internal salt concentration (35)).

Intracellular TEA⁺, similar to 4-AP, also enters the vestibule of an open K channel and blocks current flow. Unlike 4-AP, the TEA⁺-blocked channel cannot close (except at large negative V_m). With the channel held in an open position by TEA⁺ in the vestibule, charge movement is immobilized (36), indicating that the S4s are constrained in their activated position and can no longer move downward on repolarization. Mutation of cavity residue I470 (Shaker) to cysteine, I470C, makes it possible for the channel to close and trap TEA⁺ in its inner mouth (37).

During depolarization from the resting state, only ∼5% of the total charge movement is blocked by 4-AP. This 5% must represent the charge moved in one of the final steps leading to channel opening; these final steps are thought to involve the concerted movement of all four subunits (21,26, 27, 28,38). Once the channel has fully opened, the relative stability of the open state compared to that of earlier closed states delays the return of the S4s on repolarization, thereby generating a “hook” (rise followed by a fall) in the charge movement signal as the channels close (32).

Na channel gating

Unlike the homotetrameric K channel, in which the four subunits are identical in sequence, the α-subunit of eukaryotic Na channels has four distinguishable domains, each with S1–S6 transmembrane helices reminiscent of a K channel subunit (39, 40, 41, 42). Recent structural studies have revealed that the domains of eukaryotic Na channels (43, 44, 45, 46) and individual subunits of bacterial Na channels (47) all have QTCs similar to that of the chimeric K channel. The four domains of eukaryotic Na channels are not identical, in particular, in most eukaryotic Na channels; the total numbers of gating charges (arginines or lysines) found in the S4 helices and the S4-5 junction of domains D1–D4 are 4, 5, 6, and 8, respectively. In Fig. 3, we speculate about the positions of the S4 helices relative to the QTC in multiple states of the human skeletal muscle Na channel: closed, open, inactivated, and refractory. Our speculations are guided by the idea that, as in the K channel structure, the innermost two charged residues are hydrophilic anchors that, in the open state, keep the inner end of the S4 helix and the start of the S4–5 linker in the internal solution. Neutralization of the fourth S4 charge in D1 and D2, (K4), shifts the G-V curve to more positive V_m, consistent with the removal of a screening internal positive charge (48) that, in normal function, does not enter or cross the membrane during channel activation.

Figure 3.

Position of S4 helices and functional states of the Na channel. Upper: possible positions of the S4 helices of the four domains of the Na channel in different functional states are shown relative to the QTC. Lower: highly simplified cartoons show the intracellular gate and inactivation particle in the different states. The black circle represents a Na ion and the gray circle waters of hydration.

Closed state of the Na channel

In the closed state, the S4s of all domains are drawn by negative internal voltage to or near to their innermost position, such that R1 of D1, D2, D4, and K1 of D3 are interacting electrostatically with the negatively charged inner QTC_i of their respective domains. A reasonable guess is that in the closed state, an external Ca²⁺ ion is attracted to the unoccupied QTC_o of each domain, stabilizing this state and providing the well-known sensitivity of g_Na to external [Ca²⁺]. The negative charge of QTC_o is also the probable binding site for extracellular Zn²⁺ ions, which slow g_Na activation and charge movement (49). The remaining positive charges of all S4s are in the cytoplasm, as shown in Fig. 3(closed).

Open state of the Na channel

The transition from the closed to the open state (at 0 mV in Fig. 3) requires, we think, outward S4 motion in all domains: one step for D1, two steps for D2 and D3, and three steps for D4. In each domain, the first step displaces Ca²⁺ from that domain’s QTC_o. In the open state, D1 and D2 are in full outward position with D1R1 and D2R2 at QTC_o. D1R3 and D2K4 are in the cytoplasm, just internal to QTC_i, whereas D1K4 and D2K5 serve to keep the beginning of the S4–5 linker (not shown) in the internal solution. The illustrated outward motions of D3 and D4 are sufficient for activation.

As with K channel subunits (see Fig. 2 A), all domains of the Na channel have a serine residue near the end of the S4–5 linker and an asparagine residue ∼10 residues from the end of S6. We hypothesize that, similar to the K channel, the open state of the Na channel is stabilized by hydrogen bonds between the S6 asparagines and the S4–5 serines. Cardiac Na channels, with the asparagine in D4 mutated to cysteine or alanine, exhibit large gating currents, but the channels conduct very little Na current (13). This is consistent with the ideas that D4 of the Na channel is involved in activation rather than just with inactivation (50,51) and that the D4 asparagine is involved with stabilizing an open state. Similar mutations of the equivalent D3 asparagine also preserve charge movement but reduce the Na current (13).

Inactivated state 1 of the Na channel: Nact 1

After roughly a millisecond in the open state, the Na channel begins to inactivate. The transition from open to Nact 1 in Fig. 3 requires a further outward step of the S4s of D3 and D4 that permit the movement of an inactivating particle.

In the model of Hodgkin and Huxley (1), inactivation is a voltage-dependent process independent from activation. Subsequent work (52,53), however, has shown that Na channel activation and inactivation are coupled and that the properties of inactivation are consistent with block of the open channel by a tethered, intracellular channel component. This idea received strong support by the demonstration that rapid inactivation of Shaker K channels was a consequence of open channel block by an N-terminal peptide (54,55). The inactivating particle of the Na channel has been found to be the intracellular linker between D3 and D4 (56, 57, 58), in which a cluster of three hydrophobic residues, IFM, plays an essential role (59). Where the IFM residues bind is less clear because inactivation is inhibited by mutation of residues in both the pore-lining S6 segments of D4 (60,61) and the S4–5 linker of D4 (62,63). In recent cryo-electron microscopy structures of eukaryotic NaV channels, the inactivating particle is found outside the pore in a binding site involving residues in the S4–5 linker that, when mutated, perturb inactivation. However, the channels in these studies are either closed (43,46) or the pore is blocked by a detergent molecule (44,45), conditions under which it is unlikely that the IFM residues could have reached a pore binding site. In the cartoons of Fig. 3, we illustrate inactivation by a direct block of the open pore.

In the highly conserved primary sequence of the D3-D4 linker, the IFM motif is flanked by strongly hydrophilic residues. For example, the rat brain sequence is (...KKKFGGQDIFMTEEQKKYY…). These residues, most of them either positively charged (K⁺), negatively charged (F⁻,D⁻,E⁻), or hydrophilic (T, Q, Y), keep the IFM motif and the linker on either side of it in the cytoplasm at rest and prevent the inactivating particle from going too far into the channel’s inner mouth in the inactivated state.

Inactivated state 2 of the Na channel: Nact2

If the depolarization is sufficiently prolonged, the Na channel transitions from Nact1 to the more stable Nact2 state, as D4S4 moves one step further outward. This step probably corresponds to the second, slower time constant of inactivation (64,65).

Refractory state of the Na channel: Closed and Nact2

During repolarization after an action potential, the bound inactivating particle acts like a “foot in the door” and prevents the closing movement of the S6 helices of D3 and D4, which are held in activation gate-open position. Inward motion of the S4 helices of D3 and D4 is prevented, and about two-thirds of the charge moved in a normal opening from rest to 0 mV or more is immobilized. Although full closure of the channel’s inner gate cannot occur until the inactivating particle unbinds, movement of the S6 helices of D1 and D2 is likely not impeded, and these helices return rapidly to their normal gate-closed position upon repolarization to −40 mV or more negative (66). The S4s of D1 and D2, which are not immobilized, generate a small, fast, inactivation-resistant spike of gating current. The ability of the Na channel to close upon repolarization while the inactivating particle remains bound is functionally very important because it prevents a potentially disastrous, depolarizing leak of Na⁺ as the particle finally unbinds. This leak, driven by the very strong driving force, V_m − E_Na, of ∼130 mV, could lead to unwanted, long-lasting repetitive firing. For the K channel, the scenario is quite different. The K channel does conduct for a brief period as the inactivating particle exits the mouth of the inner channel (67), but this reopening has only a small effect on function because the driving force on K⁺ is small at the resting potential. Some neurons, in particular high-frequency neurons, do make use of a small Na leak current on repolarization. This current, named resurgent current, arises from a second, rapid inactivation process that involves open channel block by auxiliary, channel-associated proteins (68, 69, 70).

Closed state inactivation of the Na channel, CSI

When channels in the closed state are subjected to a prolonged subthreshold depolarization from, e.g., V_m −70 mV to V_m −40 mV, they enter CSI after a fraction of a second (71). In CSI, the S4s of D3 and D4 have moved to a partially activated position, but D1 and D2 remain in their closed position, preventing ion movement through the channel. The end result is similar to the refractory state. Recovery from CSI requires repolarization to the resting potential for a suitable interval.

Recovery of the Na channel from inactivation

Full recovery from inactivation requires some milliseconds at rest, while the S4s of D3 and D4 move inward, forcing the inactivating particle out of its binding site and into the cytoplasm, thus restoring the fully closed position. Recovery from inactivation requires inward movement of R4 through the QTC and is dramatically slowed by the S4 mutations D4R4H (72) and D4R4Q (73), presumably because the neutral H and Q residues are not strongly attracted inward by the negative membrane potential. The potential Na⁺ current leak as the inactivating particle comes out of the channel mouth is prevented by D1 and D2, which, near resting V_m, are in channel-closed position. As the S4 charges of each domain move inward through the QTC at negative V_m, the S3–S4 linker must be pulled inward (cf. (74) for a study on the corresponding linker in the Shaker K channel). As estimated in (42), the lengths of the S3–S4 linkers of the four domains of the Na channel (1, 1, 7, and 13 residues for D1–D4, respectively) are in rough agreement with this idea: quite short for domains D1 and D2 and longer for domains D3 and D4.

Final comment

When Hodgkin and Huxley reported their voltage-clamp studies on squid giant axons, they had hoped to describe, in detail, a carrier model for the permeability changes. The data forced them to conclude that the permeability changes required a voltage-dependent “gate,” and they had to settle “for the more pedestrian aim of finding a simple set of mathematical equations which might plausibly represent the movement of electrically-charged gating particles.” (75). Hille (76) notes that they had in fact described, in detail, the properties of the first two ion channels to be recognized. The subsequent decades have witnessed a remarkable story of scientific discovery so that we are well on the way to an understanding of normal channel function and disease phenotypes at an atomic level. The structural insights from Rod MacKinnon’s laboratory regarding the K channel laid a strong foundation for this understanding to deepen rapidly.

Editor: Meyer Jackson.