Renal Ion Channels, Electrophysiology of Transport, and Channelopathies

The Tubule is a Barrier

The structure of the tubule provides a barrier function separating fluid compartments; pro-urine from interstitial fluid. The electrical properties of the tubule and transport across the tubule can be understood in terms of equivalent circuits, such that ions cross a resistive barrier driven by electrochemical forces through conductive pathways. Figure 8.3 shows a simplified equivalent circuit representing tubule epithelium. In this regard, ion channels and tight junctions serve as conductive pathways across epithelial cell membranes and the epithelial barrier, respectively, with voltage and concentration gradients existing across these membranes and the barrier. Because channels, which are gated, make a significant contribution to membrane resistance, epithelial cell membranes are best described as variable resistors. Accordingly, channels affect the resistance of the epithelial cell membrane and electrochemical driving forces across these membranes and the epithelium.

Routes of Transport across the Tubule

Two different routes of transit from one fluid compartment to the other exist across the renal epithelial barrier. Movement through the epithelial cell is termed transcellular, and between epithelial cells across tight junctions is termed paracellular. Transcellular movement, as depicted in the simple equivalent circuit shown in Figure 8.3 , includes crossing both the apical and basolateral membranes. Channels facilitate the crossing of these membranes by ions. Tight junctions serve a similar function for paracellular movement across the epithelium. Tight junctions, like channels, are selectively permeable. Nothing to date, though, suggests that tight junctions act in a gated manner; rather, they function as doorways of fixed resistance that are selective in what they let pass. Diffusion through tight junctions is passive, driven by electrochemical gradients.

Epithelial Cells are Polarized

Tubule epithelial cells, and thus the tubule epithelium, are polarized with distinct membranes facing the pro-urine, the apical membrane, and the interstitial fluid, the basolateral membrane. These distinct membranes have different protein profiles, including the expression of ion channels. The net result is that each cell membrane has different capability, selectivity, and capacity for moving ions and other molecules. This, combined with the barrier function of the epithelium, provides epithelial cells with the ability to transport in a directional manner. This process is often termed vectoral transport.

Types of Transport and Transporters

Epithelial transport and specific transport proteins are covered in more detail in Chapters 1 and 2. In brief, transport across an epithelial cell can be divided into those that do not require a protein, and those that are protein-mediated. The former is termed simple diffusion and is passive, being dependent on the concentration gradient and surface area. If a molecule is capable of permeating the cell membrane, it will cross according to its chemical gradient. Molecules that move using this form of transport are exclusively small and non-polar, and are capable of crossing a lipid bilayer. Simple diffusion cannot be saturated and is not regulated. The movement of NH ₃ in parts of the tubule is a good example of this form of transport. Mediated transport, in contrast, is capable of being saturated, and is dependent on the presence of specific proteins. Moreover, it often is regulated by cell signaling. Figure 8.4 shows models representative of the different classes of transport proteins common to renal epithelial cells. Forces driving protein-mediated transport are discussed in more detail below, but they can include the concentration difference of the molecule to be transported across the membrane or barrier, electrical potential differences, and the activity of transport proteins.

Facilitative diffusion, similar to simple diffusion, is passive, allowing molecules to move down concentration gradients. Facilitative transporters translocate molecules across membranes. An example of a facilitative transport protein in the kidney is the proximal tubule glucose transporter, GLUT2.

Ion channels allow restrictive diffusion, a unique form of passive transport. Channels form selective pores in the membrane, allowing ions to cross the membrane through permeation rather than being translocated across the membrane. Restrictive diffusion through ion channels is driven by electrochemical gradients.

The two remaining types of transport proteins allow active transport: the active movement of molecules against gradients. This type of transport is directly, in the case of primary active transport, and indirectly, in the case of secondary active transport, tied to the consumption of energy. Primary active transporters require ATP to transport molecules against their concentration gradients. As discussed below, this ultimately energizes all transport across the renal tubule. The Na ⁺ ,K ⁺ -ATPase is a notable primary active transporter in the tubule and collecting duct system. Secondary active transporters use gradients established by primary active transporters. They couple the movement of one molecule against its gradient to the movement of another molecule down its gradient. NKCC2 in the TAL and the thiazide-sensitive Na ⁺ ,Cl ⁻ -co-transporter (NCC) in the DCT are prominent secondary active transporters in the kidney. The latter couples the inward movement of Cl ⁻ into the cell against its gradient to the inward movement of Na ⁺ into the cell with its gradient. Thus, Na ⁺ entering the cell downhill on this transporter pulls Cl ⁻ uphill with it.

Forces Driving Transport across the Tubule: The Importance of Disequilibrium

Filtration at the glomerulus, as discussed in Chapter 21, is governed by Starling forces. The difference in hydrostatic pressure between plasma in the glomerular capillary and ultrafiltrate in Bowman’s space, the beginning of the tubule, drives filtration. The difference in oncotic pressure between these fluids impedes filtration. The net result of filtration is that ultrafiltrate entering the renal tubule is similar in content to plasma minus blood cells and proteins. Electrolytes or other small molecules, therefore, have little gradient initially to cross the epithelial barrier, leaving pro-urine for interstitial fluid or vice versa . The activity of the Na ⁺ ,K ⁺ -ATPase pump localized to the basolateral membrane of all tubule epithelial cells changes this by providing the motivation, ultimately, for all transport. This protein consumes ATP to generate disequilibrium for Na ⁺ and K ⁺ across cell membranes. Because epithelial cell membranes are effective at separating fluid compartments, this disequilibrium can be maintained and converted into voltage differences and differences in ion concentrations by the activities of ion channels, other transport proteins, and the capacitive nature of cell membranes. Similarly, because epithelial cells, coupled together by tight junctions, effectively separate fluid compartments, disequilibrium across the tubule epithelium is maintained. Urine flowing in only one direction down the tubule also helps maintain disequilibrium, by moving processed fluid too quickly for equilibrium to be reached. Ion channels and other transport proteins tap these electrochemical gradients to transport molecules across the epithelium. Thus, disequilibrium enables modification of urine by tubule epithelial cells. Renal transport ultimately, then, is the movement of molecules through channels and other transporters, tending towards an equilibrium that is kept beyond reach by the continuous activity of the Na ⁺ ,K ⁺ -ATPase.

The Tubule Epithelium has Emergent Properties

The importance of the structure of the epithelial barrier and state of disequilibrium maintained across this barrier to transport is apparent when considering the similar Ca ²⁺ - and Mg ²⁺ -wasting phenotypes arising from inactivation in the TAL of NKCC2, ROMK, claudin-16, and claudin-19. Dysfunction of claudin-16 and -19 cause familial hypomagnesemia, with hypercalciuria and nephrocalcinosis (FHHNC ). These claudins are critical components of the tight junction in the TAL, where they provide cation-selectivity, allowing Na ⁺ back-flux into tubular fluid more rapidly than Cl ⁻ , contributing to a lumen-positive diffusion potential. The lumen-positive potential that results from the combination of this Na ⁺ back-flux with apical K ⁺ recycling mediated by the coordinated activities of luminal ROMK channels and NKCC2 drives paracellular Mg ²⁺ and Ca ²⁺ transport. Claudin dysfunction, like dysfunction of ROMK or NKCC2, then compromises the electrochemical gradient responsible for divalent cation reabsorption in the TAL. This illustrates that a break in function of any of several components of the whole leads to the same disease. This is an important concept: epithelial cells and epithelial barriers have emergent properties that are dependent on the proper functioning of each component part, including ion channels.

Urine Flows down the Tubule

An additional point important to recognize about renal transport is that urine flows in the tubule in one direction; what happens upstream affects transport downstream. This is so because the modification of urine in upstream segments determines the constituents of urine in downstream segments. For instance, inhibition of NKCC2 in the TAL by loop diuretics, in addition to compromising urine-concentrating ability by destroying the axial corticomedullary hyperosmotic gradient, also leads to an increase in K ⁺ secretion at the collecting duct (CD), and ultimately to K ⁺ excretion by the kidney. This is due to increased urine flow and Na ⁺ delivery to the CD. Increased urine delivery to the CD promotes flow-induced K ⁺ secretion by BK _Ca channels, which are activated by mechanical stimuli. Increased Na ⁺ delivery drives increased Na ⁺ reabsorption via the epithelial Na ⁺ channel (ENaC) across principal cells of the CD, due to a change in the electrochemical gradient for Na ⁺ across the apical membrane. This increase in Na ⁺ reabsorption in turn affects the electrochemical gradient across the apical membrane, driving additional K ⁺ secretion through ROMK channels. For the same reasons, any inactivating mutation in a TAL transport protein involved in NaCl reabsorption, including NKCC2, ClC-Kb, and ROMK channels, causes the renal K ⁺ wasting associated with Bartter syndrome. Moreover, disease resulting from inactivation of NCC and the ClC chloride channel beta subunit barttin, and diuretics such as thiazide inhibitors of the NCC co-transporter that decrease NaCl reabsorption in the DCT, also cause renal K ⁺ wasting by this common mechanism.

Transport does not Happen in a “Vacuum”

Another concept emerging from the above discussion is that the transport of one type of ion through renal ion channels influences the movement of different ions through other distinct channels. This coupling is a manifestation of ion channel activity influencing electrochemical driving forces. An example of this, as discussed above, is the electrogenic Na ⁺ reabsorption via ENaC influencing ROMK-mediated K ⁺ secretion in the CD. This will be touched upon again in more detail below. Similarly, as mentioned earlier, Mg ²⁺ and Ca ²⁺ reabsorption in the TAL are positively coupled to NaCl reabsorption with K ⁺ recycling across the luminal membrane via ROMK channels and paracellular Na ⁺ -back flux via claudin proteins, setting the electrochemical driving forces moving these divalent cations.

Ion Channels Provide a Unique Form of Passive Diffusion

As emphasized in the simplified forms of transport shown in Figure 8.5 , ion channels differ from other transport proteins, in that they form a physical hole through the membrane. No other type of transport protein does this. Rather, the molecule to be translocated by transport proteins other than ion channels interacts with a binding site on one face of the protein, but does not actually move across the membrane until a change in conformation takes place where the initial entry site closes as the exit site opens to allow the bound molecule to be released and egress out across the opposite face of the protein from which it entered. Ion channels also contain binding sites for permeant ions. Ions transiently bind to these sites during permeation, with the electrochemical gradient driving the direction of transport. In conjunction with properties of the pore and charge repulsion between permeant ions, this gradient determines the magnitude of ion flow. Because channels are pores that allow ions to permeate through the membrane, they facilitate crossing of the membrane with relatively little change in overall conformation. Transporters, in comparison, typically require greater relative changes in conformation to translocate molecules across the membrane. The result is that single-channel proteins move a far greater number of molecules per unit of time (10 ⁷ to 10 ⁸ ions/second) compared to any other single-transport protein.

Recording Ion Channel Activity with Patch-Clamp Electrophysiology

When open, a channel conducts the movement of ions across the cell membrane. This manifests as a decrease in resistance the membrane has to the permeant ion. Current through an ion channel is dependent on the electrochemical driving force, whether the channel is open or closed and the selectivity of the channel, and how well a certain ion moves through, or rather permeates through, the conduction pathway. The activity and biophysical properties of ion channels can be assayed in experiments with electrophysiological tools, including sharp electrodes and two-electrode voltage clamping. The most sophisticated tool used to probe the biophysical properties of channels is patch-clamp electrophysiology. Erwin Neher and Bert Sakmann were awarded the Nobel Prize in Physiology or Medicine in 1991, in part for this development. Patch-clamp electrophysiology enables the study of both macroscopic and single-channel currents. It has a high degree of precision and fidelity, allowing the resolution of the activity of a single protein in real-time. Figure 8.6 shows the different patch configurations available for the study of ion channels, and sample data from experiments investigating the single-channel properties of wild-type ENaC (left) and macroscopic currents from a mutant form of ENaC (right) that activates upon hyperpolarization due to the voltage-dependent block of the pore by intracellular Na ⁺ .

Adaptation of Ohm’s Law to Biological Systems: Explaining Current Carried by Ion Channels

Current flow in an electrical circuit obeys Ohm’s Law which, when reordered, states I= g E, where current (I) equals the product of the conductance ( g ) and voltage difference (E) across the conductor, which in biological systems is an ion channel protein. This simple formula was adapted to I _x =g _x (E–E _x ) by Hodgkin and Huxley, in their seminal electrophysiological studies (as explained by Hille and Cole in their books ) to fit biological reality better where current through an ion channel crosses a capacitive membrane that separates fluid compartments of different ionic activities. The gradient across the membrane acts like a battery represented by an equivalent circuit with an electromotive force, E _x , in series with a channel resistor, g _x . This conductive branch is in parallel with the capacitor representing the membrane. In this modified equation, E remains voltage across the membrane, and the net driving force on ion X is now E−E _x . Thus, current in biological systems is driven by an electrochemical gradient rather than by voltage alone.

Figure 8.7 shows a graphical representation of an idealized current–voltage relation for an equivalent circuit describing an open ion channel obeying this modified Ohm’s Law. When voltage, E, is equal to E _x, no net current flows through the channel. When E<E _x , current flows into the cell. If this represents a cation channel, for instance ENaC, and extracellular [Na ⁺ ] is greater than intracellular [Na ⁺ ], as is the normal case in physiological systems, this inward current flow would be carried by Na ⁺ entering the cell through ENaC. This represents the normal conditions under which ENaC functions in CD principal cells, allowing Na ⁺ to enter the cell across the apical membrane during electrogenic Na ⁺ reabsorption. The typical concentration of ions in urine and intracellular fluid combined with the activities of K ⁺ channels in the apical and basolateral membranes set the potential (E) across the apical membrane lower than E _Na . This facilitates Na ⁺ influx through ENaC. In contrast, when E>E _x current flows outwards, Na ⁺ exits the cell. This explains the consequences of the electrochemical gradient driving Na ⁺ through ENaC. Sodium movement through ENaC across the membrane, in turn, influences electrochemical gradients. If no other parameter changed, Na ⁺ moving through ENaC would dissipate the E−E _Na difference, eventually arriving at equilibrium where E and E _Na are equalized. Restated, net flux through a channel occurs only as long as the system is out of electrochemical equilibrium. This is where the Na ⁺ ,K ⁺ -ATPase and separation of fluid compartments with different ionic activities by cell membranes come into play. They enable epithelial cells to remain out of equilibrium.

The Nernst Equation

In the above description, E _x is the equilibrium potential (or reversal potential) for ion X, a state where the tendency for further change vanishes, and all existing forces on X are in balance. This would be where voltage across the membrane containing the channel permeable to ion X equals the diffusion potential developed by the ionic gradient for ion X across this membrane. Mathematically, as noted above, this is where E=E _x . Equilibrium potentials are easily measured in the laboratory with electrophysiology. Moreover, they can be calculated empirically using a formula developed by Nernst in 1888. This led to the equilibrium potential sometimes being referred to as the Nernst potential. The Nernst equation states E _x =(RT/ z F)ln([X] _o /[X] _i ), where R and F are physical constants having the usual meanings of Universal Gas constant and Faraday’s constant, T is temperature in kelvin, z accounts for the charge and valence of ion X, ln indicates natural logarithm, and [X] _o and [X] _i are the concentrations of ion X outside and inside the cell, respectively. Accordingly, the equilibrium potential falls to zero in the absence of a gradient, reverses signs as the direction of the gradient is reversed (e.g., that for Na ⁺ compared to K ⁺ ) and as the charge of the ion is reversed, for example Na ⁺ versus Cl ⁻ . Equilibrium potentials across cell membranes for ions common to physiological solutions are ~130, −98 and 67 mV, respectively, for Ca ²⁺ , K ⁺ , and Na ^{+ 2} . The equilibrium potential for Cl ⁻ is more variable, because [Cl ⁻ ] _i varies more widely with cell type, but it usually is close to the resting membrane potential of the cell, often being slightly above or below that level. Calculating equilibrium potential across tubular epithelial cell membranes is complicated by the luminal and serosal membranes facing different solutions. The apical membrane may have a different equilibrium potential for Na ⁺ as compared to that across the basolateral membrane, because the concentration of this ion in urine may be greater or less than that of plasma, depending on Na ⁺ and water transport along the length of the nephron.

The Goldman–Hodgkin–Katz Voltage Equation

Work performed by Hodgkin, Huxley, and Goldman and others led to the realization that cell membrane potential reflects the equilibrium potentials of all permeant ions at a given time, and that this can be mathematically represented. When calculating membrane potential (E _mem ), the magnitude of ion movement through any given class of channel, for example K ⁺ versus Na ⁺ channels, is accounted for by using weighted averages of each ion’s equilibrium potential. These weighted averages convey the relative permeability (P _x ) of each ion to total ion permeability (P _tot ). By using the simplified condition of only considering flux of monovalent cations through channels, which is not too distant from reality, the Goldman–Hodgkin–Katz (GHK) equation is E _mem =(P _K /P _tot )E _K +(P _Na /P _tot )E _Na . Figure 8.8 shows an equivalent circuit representing the cell membrane and individual ionic conductances contributing to this membrane potential. Because K ⁺ channel activity predominates at rest with P _K approaching P _tot , membrane potential is closest to E _K . An increase in the activity of Na ⁺ channels, which increases the relative permeability of this ion, causes the membrane to become more depolarized, as represented by the volt meter in Figure 8.8 moving E _mem towards E _Na as ENaC becomes active.

What do Ohm’s Law, the Nernst Equation, and the GHK Equation Tell us About Transport?

Reconsidering now Figure 8.7 and the scenario described earlier, inward Na ⁺ flow through ENaC depolarizes the apical membrane, moving E _mem towards E _Na . Because the ionic gradient for K ⁺ across the apical membrane is the reverse of that for Na ⁺ , depolarizing the apical membrane would move E _mem further away from E _K , driving more K ⁺ out of the cell through apical K ⁺ channels, for instance, through ROMK channels in the apical membrane of principal cells. Figure 8.9 shows an idealized current–voltage relation for an open K ⁺ channel, and notes the influence of membrane depolarization (moving from A to B) on K ⁺ current through this channel as the apical membrane is depolarized by Na ⁺ reabsorption through ENaC, activated perhaps by the addition of aldosterone. There is greater outward K ⁺ current and greater K ⁺ secretion. The idealized graphs of cumulative K ⁺ secretion, membrane voltage, and relative K ⁺ and Na ⁺ permeability shown in Figure 8.10 expand on this concept. Basolateral leak K ⁺ channels, which provide the majority of ion permeability at rest, sets E _mem of CD principal cells to near E _K . There is little electrochemical force, therefore, for K ⁺ to exit the cell through ROMK under these conditions. This resting condition is time A, with little K ⁺ secretion across the apical membrane. The introduction of aldosterone to the system activates ENaC, increasing the relative permeability of Na ⁺ and allowing this ion to enter the cell down its electrochemical gradient. This begins to depolarize the apical membrane, as E _mem moves towards E _Na . As E _mem moves towards E _Na , K ⁺ exits the cell at an increased rate across apical ROMK channels. This is time B.

Another consequence of ENaC opening is that the relative permeability of K ⁺ begins to fall as that of Na ⁺ rises; however, as K ⁺ exits the cell through ROMK, a new steady-state is reached where membrane potential has increased, and P _Na and P _K have stabilized with constant K ⁺ secretion. Neither the K ⁺ nor Na ⁺ concentration gradients change substantially across the apical membrane, due to the constant activity of the Na ⁺ ,K ⁺ -ATPase pump. These gradients are also protected by the constant flow of urine, bringing Na ⁺ to the cell and washing away K ⁺ that has been secreted through ROMK. This scenario is simplified compared to the real-life situation, but it shows how the equations described above can be used to understand the role played by renal ion channels better. This simplified description, moreover, reveals the mechanistic underpinnings of why K ⁺ secretion from CD principal cells is tied in a positive manner to Na ⁺ reabsorption by these cells, as initially raised in earlier sections. In addition, it explains why diuretics, such as amiloride and triemterene, which block ENaC, also have K ⁺ -sparing action. They retard the development of the normal electrochemical driving forces favoring K ⁺ secretion from the CD, because they block the entry of Na ⁺ across the apical membrane necessary to drive K ⁺ from the cell. Because the CD is the final site along the nephron where urinary [K ⁺ ] is fine-tuned, decreased secretion here leads to K ⁺ retention in plasma.

Channels are Selective

Ion channels need to be selective to perform their role of converting chemical disequilibrium into electrical signals. In epithelial cells, moreover, they need to be selective to facilitate vectoral transport. The chemistry of selectivity (often called the selectivity sequence), for a channel can also be empirically determined using the GHK Voltage Equation discussed above. The extended equation is E _rev =(RT/F) ln {(P _K [K] _o +P _Na [Na] _o +P _Cl [Cl] _i )/(P _K [K] _i +P _Na [Na] _i +P _Cl [Cl] _o )}. This equation allows one to calculate permeability ratios by measuring reversal potential, but it does not allow the determination of absolute permeabilities. Bi-ionic conditions, where only one permeant ion is presented to either side of the channel, are the simplest when testing selectivity. Under such conditions, the equation reduces to E _rev =(RT/ z F) ln {(P _x [X] _o )/(P _y [Y] _i )}. Figure 8.11 shows predicted results from a hypothetical excised inside-out patch-clamp experiment with bi-ionic conditions used to determine that the channel within the patched membrane is selective for Na ⁺ over K ⁺ . With Na ⁺ in the bath and recording pipette, there is no gradient across the membrane, and reversal potential is 0 mV (condition 1). Next, when the bath contains K ⁺ as the sole cation, condition 2, the reversal potential moves to E _Na , which is ~70 mV. Similarly, when the cations in the pipette and bath are reversed, the equilibrium potential again moves to E _Na , which is ~−70 mV with condition 3.

What provides a channel with selectivity? In the simplest sense, it is how capable binding sites within the pore are at coordinating an ion permeating through the pore. If we view a channel pore as a tunnel with consecutive constrictions followed by recesses, as shown in Figure 8.12a , then the selectivity-filter is the tightest constriction. A pore can also be understood by considering thermodynamics. As shown in Figure 8.12b , there would be energy wells followed by energy barriers along the length of the pore. The selectivity-filter then is the greatest barrier that a permeant ion must cross to move through the channel. Using equivalent circuits to describe ion channels, as shown in Figure 8.12c , a change in selectivity would be observed as a change in the electromotive force driving current across the channel upon ion substitution.

The physical basis of selectivity is set by the selectivity-filter defining an internal diameter within the pore, which prohibits molecules larger than this diameter from crossing. This represents the idea that ion channel pores are sieves, selecting on size. With such a description, a selectivity-filter that passes large ions, presumably, would also pass smaller ions, but clearly this is not the case. There are, obviously, other factors contributing to selectivity. Ions move through channel-selectivity filters only after they shed their layer of surrounding water. So, it is the dehydrated diameter of an ion, and its ability to shed surrounding water molecules, that are important when moving through a selectivity-filter. Moreover, selectivity-filters also select on the basis of charge: side chains of amino acids defining or near the selectivity-filter present as a charge barrier. The side chains and backbone carbons of residues within or near the selectivity-filter also form transient bonds with the permeant ion and, thus, there is a chemical component to selectivity. Selectivity, then, is a culmination of several factors, including size and charge, and the ability to shed solvating water molecules and interact with residues at or near the selectivity-filter. The precision of selectivity among ion channels varies widely from ENaC having a P _Na /P _K >100 being at the highly selective end of the spectrum, to some TRP channels with P _Na /P _K ≈1 being at the other end of the spectrum of non-selective channels.

It is easiest to view selectivity as fixed and immutable. However, this is not exactly the case. Channel selectivity can be influenced by experimental conditions, and even the presence or absence of permeant ions in the pore. Moreover, the selectivity-filter can be involved in channel gating, as it is in ROMK and ClC channels. Gating is discussed in more detail below.

Ions Permeate Through Channels

Selectivity and permeation are related, but they are not exactly the same thing. Selectivity, as emphasized in Figures 8.12a and 8.12b , is set by the physical properties of ion-binding sites within the pore, and how well they coordinate permeant ions when bound. Permeation refers to how fast or rather how many ions move through the pore per unit of time, and speaks of how well an ion surmounts energy barriers within the pore. Stated another way, selectivity can be viewed as a filter with certain physical properties, and permeation is how well molecules cross this filter. Experimentally, as shown in Figure 8.12d , permeation is measured as conductance, where a channel passing a more permeant ion has a higher conductance relative to when it passes a less permeant ion. Ions permeate through the narrowest portions of a channel pore in a single-file manner. One then might expect a channel that is less selective to have a higher conductance compared to a highly selective channel. In general, this rule is only loosely obeyed. The reasons for this are discussed below. One might also expect that the ion for which a channel is most selective would permeate through the channel best. This is most often the case, but it is not absolute.

Permeation is a result of how easily an ion surmounts every energy barrier within the pore, as well as interactions between permeant ions with each other when occupying the pore. Ions occupying the pore can exert a pushing effect on each other, impeding and propelling progression depending on the relative order of these ions within the pore and opposing energy barriers each ion is facing. Repulsion between ions within a pore is indicated in Figures 8.12a and 8.12b with two-headed arrows and decreases in the size of energy barriers, respectively. Such repulsion contributes to highly selective channels passing large numbers of ions per second. For instance, charge repulsion between the Cl ⁻ ions occupying the pore of ClC channels makes a significant contribution to the conductance of these channels. In addition, most channels have large aqueous vestibules lined by polar residues at the extracellular and intracellular mouths of their pores. The vestibules act as reservoirs concentrating the permeant ion, increasing conductance.

The pores of ClC and ENaC channels contain three binding sites for permeant ions. In ENaC, sites immediately adjacent likely are not occupied simultaneously, due to charge repulsion between permeant ions within the pore. This is also the case for K ⁺ channels, such as Kv and Kir, which use a single-file mode of multiple ion permeation with four pause/binding sites within the pore. As illustrated in Figure 8.13 , only two sites are occupied at any one time, with the occupied pairs always separated by an empty site filled with water.

Channels Gate

Channels transition between closed and open states as they gate. By definition, no current flows through a closed channel. Upon opening, current flows through the channel obeying i=g _x (E–E _x ). The open current level of a single channel then is a determinant of its conductance, which is measured by taking the slope of i–V curves for single-channel currents captured with a voltage-clamp recording (see Figure 8.12d ). Current flow through a channel, as shown in Figure 8.14 , is an all-or-nothing event: with no change in driving force, the channel transitions from closed to open and back again, always the same as defined by a normally distributed Gaussian curve unitary step in single-channel current.

Channels gate in a stochastic manner: a new and random pattern of openings is observed for each trial period. The stochastic nature of gating makes it possible to describe gating in terms of probabilities, where the sum of the probability of a channel being in either the open (P _o ) or closed (P _c ) state is equal to 1. Channel open probability is calculated from single-channel activity (NP _o ) defined as NP _o =∑( t ₁ +2 t ₂ +… nt _n ), where N and P _o are the number of channels in a patch and the mean P _o of these channels, and t _n is the fractional open time spent at each of the observed current levels. P _o is calculated by dividing NP _o by the number of active channels (N) within a patch, as defined by all-point amplitude histograms. Another common way of representing this is:

where T is the total recording time, N _A is the observable number of current levels corresponding to channel number as established with all-point histograms, i is the number of channels open, and t _i is the time during which i channels are open. P _o can be calculated as above, by dividing NP _o by the channel number.

Macroscopic channel current is related to unitary current by I= i NP _o , where i is unitary single-channel current at a given voltage. Similarly, macroscopic conductance is G= g NP _o . This provides another means for estimating NP _o from experimental data where NP _o can be estimated as I/ i . This latter estimation is often used in experiments where N cannot be fixed with certainty, but i can be or when N and I (and i ) are measured independently of each other.

All channels have inherent gating activity: with time, they transition between open and closed states in a random manner driven by thermal energy. So, all channels have at least one gate. The physical nature of a channel gate, though, may be different among different kinds of channels. Moreover, channels often have more than one distinct gate. This seems to be the rule rather than the exception. For example, ClC channels are double-barreled channels containing two proto-pores, each having an independent gate . Both proto-pores, moreover, are also covered by a common gate. For the channel to be open, both the gate of the proto-pore and the common gate must be open. Similarly, Kir channels, such as ROMK, have fast and slow gating, showing the effects of at least two different gates.

Types of Gates

We typically think of a channel gate as a domain or residue that occludes or covers the pore in a dynamic manner. This may be the case for gates in many types of channels typified by the regulated gate in Kv channels, the slow-gate in Kir, and the common gate in ClC channels. The crystal structures of many ion channels have recently advanced the understanding of gates. As depicted in Figure 8.15 , at least two types of gates are now known to exist. Several channels contain both types of gates, as typified by the fast and slow gates in Kir channels. These two types of gates share some properties, such as they both prevent further permeation of the conductance pathway, but also have important differences albeit sometimes subtle. In addition to a physical gating particle that may obstruct the pore, collapse of the pore around a permeant ion prohibiting further permeation has also been identified as a means of gating. During pore-gating, the channel is open when the pore is open, and closed when the pore is collapsed. So, there is no true gate with a pore-gating mechanism, rather the physical diameter of the pore is the gate.

In the pore-gating model, the selectivity-filter or another portion of the pore is the working part. This is the case for the fast gating seen in the ROMK channel, where K ⁺ occupancy of the pore has a profound influence on the structure of the selectivity-filter. Fast gating is characterized by the rapid transition between the open and shortest-lived closed states. The role of pore-gating and the selectivity-filter in this fast-gating process was noticed because the rate of entering the shortest-lived closed state varies as a function of K ⁺ concentration, and is proportional to current amplitude. The crystal structures of bacterial Kir channels, sharing structure with ROMK as discussed below, provides additional support for this mechanism, showing how a pore may collapse around a permeant ion to gate the channel. A similar relation between extracellular Cl ⁻ and gating of ClC channels has also been noticed. This has led to speculation that the proto-pores of ClC channels may also use a pore-gating mechanism. This is supported by the crystal structure of ClC channels.

An alternative to mechanical collapse of the pore/selectivity-filter around the permeant ion to explain pore-gating is a variable energy-of-binding model. Simply put, in some instances, such as that during the shortest-lived closed state of ROMK channels, K ⁺ may be bound so tightly to the pore that it briefly plugs the permeation pathway. This latter mechanism shares similarities with a traditional gate, in that it is a manifestation of a particle physically clogging the pore to prevent further permeation, but here the gating particle is also the permeant ion rather than a distinct part of the channel. It is different from a pore-collapse mechanism, in that the pore remains in an open state in the variable energy-of-binding model, merely being clogged. Both the mechanical pore collapse and variable energy-of-binding modes of gating result from interactions between the ion permeating the pore and pore residues.

Regulation of Gating

The inherent activities of gates can be influenced by factors that change the kinetics and equilibrium between the closed and open states. This change can be reversible or irreversible. Only the former is involved in the dynamic regulation of channel activity. The latter permanently changes the gating state. Factors that influence gating assume many forms. They can be extracellular and intracellular ligands that bind the channel, for instance Ca ²⁺ binding to calcium bowls and RCK domains in the intracellular portions of BK _Ca channels. They can be enzymes, for instance kinases and proteases, which chemically modify channels or change channel structure. For instance, ROMK is activated and maintained in a high-P _o state by PKA phosphorylation, and inhibited by intracellular acidification. Voltage also can influence the gating of some channels. This represents a special case as discussed below in the section titled “Some Channels Rectify.” Channel oligomerization and association with accessory subunits can also influence gating. Barttin plays such a role for ClC-Ka and ClC-Kb channels. As shown in Figure 8.16 , the presence of barttin reverses the voltage-dependence of the rat ClC-Ka ortholog, ClC-K1, switching it from being activated by membrane depolarization to being activated by membrane hyperpolarization. Such regulation of gating allows ClC-Ka and ClC-Kb channels to be active under physiological conditions, facilitating NaCl reabsorption in both the TAL and DCT.

Many factors that influence gating to change P _o work through an allosteric mechanism, using a binding or effector site that is away from the pore. With such a mechanism, the effector molecule or influence of voltage affects an allosteric site where the free energy of interaction at this site is translated into a change in conformation that alters gating kinetics, equilibrium or both. As discussed further below, channel subunits in the Kv channel family have a core structure containing six transmembrane domains with an extracellular pore-forming loop between S5 and S6. In these channels, S4 is the voltage-sensor. This transmembrane domain contains conserved positive charged residues that sense voltage and move the S4 domain in response to a voltage-change across the membrane. In this sense, S4 is a molecular voltmeter. Movement of S4 is conveyed to the gate to change its position. BK _Ca channels contain intracellular Ca ²⁺ -binding sites that also act as allosteric regulators of gating. Occupancy of these sites by Ca ²⁺ increases P _o by making it more likely that the channel will be in an open state.

Pore-gates, like those in ClC channels, can also be influenced by modulators to change gating. For instance, ClC channels are also voltage-dependent (see Figure 8.16 ). Because of the nature of the gate in these channels, regulation of ClC gating by voltage, though, is not allosteric. Rather, voltage directly influences the interaction of Cl ⁻ with residues in the pore.