I. INTRODUCTION

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The remarkable work of Hodgkin and Huxley (39) set the physical basis of the nerve impulse generation and propagation using the giant axon of the squid as a model. In their description, the initiation and conduction of the action potential is the result of a transient influx of Na ions that is followed and overlapped by an outflux of K ions across the axon membrane. Their voltage-clamp studies revealed that the ion flow through these two specialized pathways occurs with distinctive kinetics and that the conductance of these pathways is voltage dependent. The voltage dependence of the conductances is the basis of the generation of the impulse, and it was later found that other selective pathways, such as Ca conductances, can also generate similar transient voltage changes. In the discussion of the origin of the voltage dependence of the conductances, Hodgkin and Huxley (39) noticed that there was no detectable outward current flux preceding the inward Na current. This was the basis of their hypothesis whereby the large flow of ions through the conductive pathway is gated by the position of only a few charged particles whose distribution is modified by the membrane potential. This visionary hypothesis implied the existence of a large number of conducting units, each modulated by voltage through the operation of a voltage sensor. This is the unit that today we call the voltage-dependent ion channel, which is gated open and closed depending on the position of charged groups that move in response to changes in the membrane potential.

Ion channels are specialized proteins embedded in the membrane. The ion selectivity of the channel is a property associated with its permeation pathway, normally called the pore. The magnitude of the current across the membrane depends on the density of channels, the conductance of the open channel, and how often the channel spends in its open position or its open probability. The salient feature of channels involved in excitable membranes is that the open probability is regulated by the transmembrane voltage or membrane potential. After the work of Hodgkin and Huxley (39), the tools of electrophysiology, molecular biology, X-ray crystallography, and optics have advanced significantly our knowledge on the operation of the pore and the voltage sensor.

This review focuses on the properties, operation, and molecular aspects of the voltage sensor. The gating charge movement is a direct measurement of the voltage sensor operation, and our main interest is to determine how this charge movement is coupled to the opening of the pore. Therefore, in section II we first develop the theoretical basis of how the voltage sensor is energetically coupled to gate the pore open or closed. From this treatment we get the basis of methods to estimate the electric charge moved by the sensor in each channel, or charge per channel. This is a fundamental property of the sensor because it determines the voltage dependence of the channel and it constrains physical models of charge translocation in the channel protein. Section III develops the operation of the sensor as seen by detection of electrical signals such as macroscopic ionic and gating currents as well as single-channel recordings and fluctuation analysis of gating current noise. Section IV addresses how the experimental results on the molecular aspects of the channel structure can explain the operation of the sensor. Section V summarizes the main aspects of the operation and molecular structure of the voltage sensor and its coupling to the pore with a model that accomodates existing data.

In general, the macroscopic ionic current (I_i) is given by

(1)

where V is membrane potential; N is the total number of channels; (V) is the conductance of the open pore, which is a function of voltage; P_o(V) is the probability that the pore is open, also a function of voltage; and V_e is the reversal potential of the ionic current through the pore. The voltage dependence of the ionic current in ion channels is not a property of the conducting pore. This is because, in general, the conductance of one open channel, (V), is almost constant unless there are extremely asymmetrical ionic conditions or a voltage-dependent block. Thus the extremely nonlinear dependence of the macroscopic ionic conductance with voltage (Fig. 1A) is the result of the modulation of the open probability (P_o) of the channel by voltage. This has been verified by recording single-channel currents and finding that the measured fractional open times of the channel become negligible at hyperpolarized potentials while it approaches unity at depolarized potentials. This means that to understand voltage-dependent channels we must find the mechanism by which the voltage can modulate the probability that the channel is open.

View larger version (37K): [in this window] [in a new window]   Fig. 1. A: voltage (V) dependence of conductance (G) and gating charge movement (Q) for a voltage-dependent ion channel. B: a schematic view of the parts forming a voltage-dependent ion channel. The channel molecule (gray region) is inserted into the lipid bilayer (dark slab). The charged rectangular region inside the channel molecule can move under the influence of the membrane voltage (pictured schematically as charge stored in the membrane capacitor) and move the gate by way of a linker (shown as a string in the picture) to open the pore and allow conduction. Thermal motion may open the pore spontaneously, but the outwardly directed field would increase the open probability by increasing the dwell time of the sensor into the open position.

Functionally, we can distinguish three basic structures in voltage-dependent channels. First, there must be a device that detects the voltage across the membrane, then this device must communicate this information to the pore to change the frequency at which the gate of the channel opens or closes (Fig. 1B). The detecting device has been called the voltage sensor. How can the sensor detect the membrane potential? An electric field can be measured by an electric charge position or by an electric dipole orientation, and we might envision a similar mechanism in the channel molecule. Then, a possible mechanism is that a change in the membrane potential results in a reorientation of dipoles or an actual charge movement within the membrane field that would produce a conformational change in the channel molecule, which in turn would result in favoring the open or closed state of the pore. The experimental evidence provided by site-directed mutagenesis combined with electrophysiology has given a solid basis to this basic mechanism.

Voltage-dependent channels such as Na, K, and Ca channels have a common structure with 24 transmembrane segments and a specialized pore region (Fig. 2). Potassium channels are made of four subunits, each containing six transmembrane segments plus a pore loop between the fifth and sixth transmembrane segments (Fig. 2, top). In contrast, the main molecule of the Na and Ca channels is one large subunit that contains four homologous domains, each with six transmembrane segments and a pore loop (Fig. 2, middle). Within this common structure, the pore is formed by the pore loops plus a contribution of the sixth transmembrane segments of the four subunits (or domains). The view of the pore has been beautifully clarified by the crystal structure of KcSa bacterial K channel (32). This channel is a member of a family of two transmembrane segment subunit channels. However, MacKinnon et al. (56) have shown that segments S5, S6, and the pore loop of the voltage-dependent Shaker K channel has close homology to the KcSa channel. We can hypothesize that the pore of voltage-dependent channels is similar to the pore structure of KcSa channel and try to build around this structure the unknown contribution and position of segments S1 through S4 (see sect. V).

View larger version (59K): [in this window] [in a new window]   Fig. 2. Structure of voltage-gated channels. Top: basic subunit of ShakerB. Four of these subunits are assembled into a functional channel. Middle: human skeletal muscle Na channel (hSkM1) basic -subunit. -Subunits are not required in either channel for voltage-dependent operation. Bottom: amino acid sequences of the S4 segments for ShakerB and for the S4 segments in all 4 domains of the hSkM1 channel.

In voltage-dependent channels, the fourth transmembrane segment (S4) contains between four and eight basic residues (arginines or lysines), each separated from the next by two hydrophobic residues (see Fig. 2). Because these residues may be positively charged, the S4 segment was first recognized by Noda et al. (65) as a possible candidate for the voltage sensor. Several investigators tested the S4 voltage sensor hypothesis (52, 54, 70, 100), and indeed, the results suggested but did not prove that the S4 segment was the actual voltage sensor. The experiments examined the effects of neutralization of the basic residues of the S4 segment on the resultant ionic current. With the measurement of ionic currents, it is possible to infer the relative proportion of open channels as a function of the membrane potential, which is equivalent to the relative open probability (P_or). Two basic parameters can be measured from the voltage dependence of the P_or: the midpoint of the P_or and the steepness of the P_or with voltage. In a two-state channel, these parameters would be enough to fully characterize the channel, but if there are more states, some extra information is required, as we will see below. The displacement of the midpoint P_or in the voltage axis could be the result of stabilization of the open or closed states without involvement in the number of charges of the sensor. The steepness of a Boltzmann fit to the conductance versus voltage curve reflects the number of charges involved in voltage sensing, but it only can be interpreted unequivocally in two-state channels. As the Na and K channels have many more than two states, Boltzmann fits of the ionic conductance after neutralizing a suspected basic residue in the S4 segment were not enough to prove the involvement of that residue in voltage sensing. The limiting slope method, which is also computed from ionic currents, could be used to estimate the actual charges involved in gating, but its application is limited by theoretical and experimental constraints, as we will see in section IIC.

To determine the contribution of a particular charge to voltage sensing, it is necessary to count the charges moved per conducting channel. If the neutralization of a particular charge results in a decrease of the total number of charges per channel, it must be proven further that the charge movement was energetically coupled to channel opening, as is discussed in section IIB.

	II. THEORETICAL BACKGROUND

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Regardless of the type of electric sensor, a free charge moving in the field or a dipole reorientation as a consequence of changing the membrane potential is translated in the external circuit as a transient electric current. The current is transient because the charge or dipole reorientation will cease at long times when it reaches its new equilibrium position. Because this current is responsible for the change in P_o of the channel, it has been called gating current. Gating currents were predicted by Hodgkin and Huxley (39) and were first recorded in skeletal muscle by Schneider and Chandler (78) and squid axon by Armstrong and Bezanilla (6) and Keynes and Rojas (45). These small currents were visible using signal-averaging techniques after blocking the bulk of the ionic currents and using a subtraction procedure to eliminate the linear capacity current. With the advent of heterologous expression, a large density of Shaker K channels has been obtained on the plasma membrane of Xenopus oocytes. This large number of channels combined with the ability to make the channel nonconducting (73) has made possible the recording of gating currents in single trials without subtraction (99), where most of the membrane transient current recorded is gating current. The time integral of the gating current at a particular voltage V₁ is called the gating charge or Q(V₁). The full functional dependence of the charge with voltage Q(V) (or Q-V curve, Fig. 1A) shows a sigmoid shape with asymptotes at extreme potentials because at those voltages the charge has moved to its extreme position. It is important to note that the measured gating charge may correspond to a displacement of a charge within a certain fraction of the total field or the change of orientation of a dipole in that field because an electrical measurement of the gating current will not distinguish between dipoles and free charges. In fact, it is easy to see that it does not discriminate between positive and negative charges or distinguish how far the charge moves within the field, because the total displacement measured is the product of the absolute value of the charge times the fraction of the field it traverses. In a general case, assume that we have i elementary electronic charges e₀ of valence z_i moving a fraction of the field _i. Then the measured charge displacement q will be

(2)

Therefore, in our discussion of electrical measurements of gating charge, we refer to the charge q as the product of the charge moved times the fraction of the field. Notice that in this view the sensor could also operate by changing the field without moving the charge in question, and for this reason, the voltage sensor must be considered the ensemble of charges and/or dipoles together with the electric field where they are embedded.

Consider a general case of a channel that has a multitude of states, where some are closed states and others are states where the pore is open. We can represent the physical states of this channel in a diagram such as in Figure 3A, where each of the states will have associated an energy or potential of mean force F. Because our measured variable is the charge displaced q, we can associate each state with a particular value of q and thus use it as the reaction coordinate (axis of Fig. 3A). After a sudden change in membrane potential V, the occupancy of each of the states will be redistributed according to the new energy profile attained by the modification of V. The connection between states is totally general, such that some states may be connected to all of the others or to only a few. However, we distinguish the case of states that are connected from the ones that are disconnected from the ensemble of states that lead to the open state because the latter ones are not energetically coupled to channel operation. Then we define two types of charge: essential charge Q_e, which is energetically coupled to channel opening, and peripheral charge Q_p, which has no connection to pore function.

View larger version (44K): [in this window] [in a new window]   Fig. 3. A: general scheme depicting the states of the channel against the charge moved (q). Charge moving among the upper states (Qp) is peripheral because none of those states has a connection with the open state. Charge moving between the open state is labeled as QL. B: relation between open probability (Po), charge movement (Q-V), and activation charge (<qa>) for a channel that has no latent charge. In this case <qa> is the mirror image of QV plus the maximum charge Qmax.

To solve the relation between charge movement and channel opening, we now are set to find how the voltage dependence of charge movement relates to the voltage dependence of the P_o in thermodynamic equilibrium. This question was recently solved by Sigg and Bezanilla (84) for the general case pictured in Figure 3A, including the case of a continuous density of states. The basic assumption in that derivation is that the potential of mean force F_i in each state i is a linear function of the applied membrane voltage V and is given by

(3)

where G_i is the potential of mean force of state i in the absence of membrane voltage and q_i represents the charge of that particular state. We must remember that q_i is the product of the charge times the fraction of the field and that we will only consider the essential charge (q = Q_e).

To proceed, we will define a measure of the electrical energy required to activate or open the channel, which is quantified by the P_o. This we call the activation potential W_a and is defined in a similar fashion as the chemical potential is defined

(4)

where k is the Boltzmann constant and T is absolute temperature. Because W_a is an electrical energy, it will be the product of the membrane voltage and the activation charge moved. We then define the mean activation charge <q_a>(V) as the negative gradient of the activation potential W_a

(5)

By combining Equations 3 and 5 and the expression of the mean open probability P_o obtained from the Boltzmann distribution of each of the states, we obtain the final result (84)

(6)

where Q_max is the total charge movement, Q(V) is the charge versus voltage curve (or Q-V curve), and <q_L> is the mean latent charge defined as

(7)

where f_i is the fractional value of the maximum conductance of conducting state i and q_i is the charge associated with that state. Notice that the value of <q_L> is a weighted average value computed over all the conducting states where the weighting factor is a charge that has the origin at the maximum value of q = Q_max. Then, if the open states occur all at q = Q_max, the value of <q_L> is zero.

Equation 6 is the general relation between the voltage dependence of the logarithm of the P_o and the voltage dependence of the charge movement independent of the kinetic model representing the channel. The interpretation of this relation is as follows. For a channel that activates with depolarization, when the membrane potential is made very negative, the limiting activation charge, <q_a>(V  ), is the total charge required to open the channel, excluding <q_L> which is related to the charge moving between open states (a change of sign makes the derivation applicable for a channel that activates upon hyperpolarization).

We may consider two general classes of voltage-dependent channels that are contained by the general derivation presented, including Equations 6 and 7. The first type has strict coupling between the charge and the opening of the pore, such that there is no pore opening unless the charge has moved, and vice versa. In Figure 1B, this type of channel would be represented when the link joining the voltage sensor and the gate is rigid. In this type of channel, the first open state must occur at q > 0 in the diagram of Figure 3A. The second type of channel has loose coupling between the voltage sensor and the opening of the pore, such that it is possible to open the gate even when no charge has moved. This type of channel would be represented in Figure 1B with a loose link between the sensor and the gate, and in the diagram of Figure 3A, the first open state would be located at q = 0 and not depicted in the figure.

If we consider the special case when there is no charge movement between open states (<q_L> = 0), then

(8)

This is the basis of the limiting slope method used to determine the total charge involved in channel activation. An illustration of the relation between <q_a>, Q(V) (or Q-V), and P_o is shown in Figure 3B for a case without mean latent charge (<q_L> = 0); it can be seen that <q_a> is Q_max plus the inverted value of Q(V). A linear sequential model ending in one open state is a special case of this result and was derived originally by Almers (5).

Note that the charge per channel obtained with the limiting slope procedure will reflect the correct total activation charge only if there is no mean latent charge. It is still possible to obtain the correct value in a channel with multiple open states provided there is no charge movement between those states. However, one of the most serious difficulties of the limiting slope method is to determine <q_a>(V) at very negative potentials because P_o becomes too small to measure it accurately. One possibility is to estimate <q_a>(V) with single-channel measurements at those potentials where P_o is very small (38). Another method is to use the Q(V) relation (Q-V curve) that can be determined accurately to potentials at which P_o is negligible. In this method, it is possible to determine Q_max, the total charge per channel using Equation 6, a method we may call modified limiting slope. In that case, when the negative value of Q-V curve is shifted by Q_max, the result will superimpose on <q_a> after appropriate scaling (83). The scaling is valid because dln(cP_o)/dV = dlnP_o/dV, where c is an arbitrary constant. If the channel moves charge between the open states, we must use Equation 6, but it becomes difficult to determine the value of Q_max.

The derivation summarized above gives us a procedure to determine Q_max, the total charge per channel directly involved in channel activation. Knowing how much charge is necessary for channel gating is the first step in determining the physical basis of this charge in the general structure or in specific residues of the channel molecule.

The method outlined in section IIB for the case of no charge movement between open states (Q_L = 0) will determine the essential charge per channel Q_e, which will be equal to Q_max. This determination will be difficult when Q_L does not equal zero; therefore, a simple alternative procedure may be used. With the measurement of the total gating charge Q_tot in a cell membrane and the knowledge of how many channels N are present, it is possible to determine the charge per channel as Q_tot/N. This method, however, will include peripheral charge (Q_p) that is not energetically coupled to channel gating because Q_tot = Q_e + Q_p. The total charge can be easily measured by taking the difference between the two asymptotic values of the Q-V curve, which is obtained by integration of gating currents. Alternatively, integrating all the capacity transient at each potential, one can obtain the total charge that includes the charge of the membrane capacity (linear with voltage) and the gating charge. In this case, linear charge is subtracted by fitting the linear increase from the charge versus potential curve (1). Then, in the same area of membrane, N can be determined by counting the channels using a toxin that specifically binds with a one to one ratio to the channel (1, 50). If the area is small, then the number of channels may also be estimated using noise analysis of the ionic currents (88), and after blocking the ionic currents, the total charge is determined by measuring gating currents (79, 83).

The first accurate determination of total charge per channel was done by Schoppa et al. (79) using a combination of noise analysis and gating currents in patches expressing fast inactivation-removed Shaker K channel (we call this channel Shaker-IR). The value was between 12 and 13 e₀, a value larger than suspected from previous estimates done by fitting models to the macroscopic ionic currents (116) and larger than the value of 9.5 e₀ obtained with limiting slope determinations by the same authors (79). However, those limiting slope measurements were not done at sufficiently negative membrane potentials and may have missed some of the charge. This was confirmed by Noceti et al. (64) and Seoh et al. (83). Seoh et al. (83) measured the same value of charge using the Q/N method and the modified limiting slope method in the wild-type Shaker-IR. This result demonstrated that all the gating charge measured in Shaker K channel is essential, that is, energetically coupled to channel opening, and that there is no charge movement in parallel. In the case of the skeletal muscle Na channel, Hirschberg et al. (38) used single-channel measurements to estimate the limiting slope at very low probability and found a similar value of 12 e₀. Noceti et al. (64) studied the charge per channel of neuronal and cardiac Ca channels in presence and absence of -subunits. Their limiting slope result indicates a value of 8.6 e₀ regardless of the presence or absence of -subunits. In contrast, the Q/N method gave normally higher values and varied depending on the presence of the -subunit. However, _1E2a, which had the maximum P_o, gave a charge per channel similar to the limiting slope method using the Q/N method. They concluded that the correct value was the limiting slope result and that the higher charge per channel obtained with the Q/N method was the result of null events (low P_o) that produced an artificially low channel count.

	III. OPERATION OF THE SENSOR

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At the normal resting potential of the cell (ca. 70 mV, negative inside), most of the voltage-dependent Na, K, and Ca channels are normally closed. A sudden change of the membrane potential to more positive values (depolarization) increases or activates the conductance, and this activation becomes faster as the depolarization is made larger. Some channels (Na, Ca, and some K channels) will show a subsequent decrease of the conductance while the membrane is maintained depolarized, a phenomenon called inactivation. Upon sudden repolarization, channels will deactivate, reverting to their resting closed state.

A salient feature of the activation of conductance is its sigmoidal time course, which indicates that the channel evolves through many closed states before reaching the conducting state. One of the earliest demonstrations of multiple closed states was provided by Cole and Moore (27) using negative conditioning prepulses. They found that as the conditioning potential was made more negative, a larger delay was observed in the turn-on of the K current, consistent with the idea that negative potentials favor the closed states further away from the open state. In contrast to activation, the deactivation of the conductance is a simple process that normally does not show a delay, indicating that conduction stops when the channels leave the open state.

Until the early 1970s, the details of activation, inactivation, and deactivation were inferred only from macroscopic ionic currents, and several kinetic models of channel operation were advanced. Except for the initial delay in activation and the Cole-Moore shift, ionic currents are not expected to give a detailed account of the events preceding the opening of the channel because they only show the open state of the channel. The recording of single-channel events (63) opened the possibility of studying the operation of one channel in isolation and thus infer its statistical properties with higher accuracy than macroscopic ionic currents. However, single channels only report the open state and therefore are quite insensitive to the kinetic details of the channel operation in states far removed from the open state. The recording of gating currents opened the possibility of studying more directly some of the transitions between closed states, in addition to the transitions leading to the open states of the channel. This is because gating currents are proportional to the rate of charge movement of all the transitions that carry charge in the activation pathway (see sect. IIIB), including those that are far removed from the open states and that are practically invisible in macroscopic ionic currents and single-channel recordings. Thus, because each one of the electrophysiological types of recording has different sensitivities to the transitions of the activation pathway, ideally a detailed model of channel operation must be built on the basis of gating currents as well as single-channel and macroscopic current recordings (81, 108, 119).

Gating currents are transient currents because they represent the movement of charge trapped in the membrane electric field. They are normally a small fraction of the ionic currents because the equivalent of only ~10 electronic charges are needed to open a channel that can carry 10⁷ ions/s. The amplitude of the gating currents will be smaller as the kinetics of charge movement become slower. For example, at 0 mV, peak gating current is ~1/50 of the ionic current in squid Na channel and ~1/200 of the ionic current in Shaker K channel. These considerations set the stage for the requirements in recording gating currents. In preparations such as the squid axon, ionic currents were eliminated by substituting all ions by impermeant species, leaving only a time-independent leak and the capacity transient current needed to charge the membrane capacitance. The gating current can be extracted from this remaining current by subtraction of the linear capacity transient using voltage pulses in the region of voltage where the gating charge is not moving (6). The slower K channel gating current could be measured by increasing the temperature to speed up the gating kinetics (16). The separation of gating currents from different channels relies on pulse protocols, temperature changes, and pharmacology. Quantitative studies of gating currents are limited to channels that have predominant gating currents over the other channels in the same preparation.

With the advent of molecular cloning, many of the difficulties in recording gating currents were eliminated. Heterologous expression allows the recording of channel activity in virtual isolation, allowing a detailed description of gating currents properties (e.g., Refs. 12, 28). Some channels can be expressed at very high densities. For example, ~10¹⁰ Shaker K channels can be expressed in one oocyte which gives 3,000 channels/µm², which is 10 times larger than the K channel density in the squid axon. (The density per actual membrane area is 9 times less, as estimated by membrane capacitance.) This high density allows the visualization of gating currents even before subtraction of the capacity transient because the capacitance due to gating can be 10 times larger than the oocyte capacitance (99). Perhaps one of the most interesting capabilities of heterologous expression of channels is the possibility of introducing mutations to test the function of a particular residue or a region in the channel molecule or to introduce a marker that can be traced chemically or optically. For example, a mutation in the pore region of the Shaker K channel (W434F) eliminates ion conduction but keeps the gating process essentially unaffected (73, but see sect. IIIG), allowing the recording of gating currents in the presence of permeant ions (99).

A gating current I_ij will occur every time a charge moves between two conformational states of the channel S_i and S_j according to

(9)

where _ij and _ji represent the elementary forward and backward transition rate constants between the states, respectively, and z_ije₀ is charge times the fraction of the field moving between the states. With the assumption that the charge may take many conformational states, the gating current I_g is the sum of the contributions of all possible transitions between states

(10)

The rate constants will depend on the height of the energy barrier F_ij separating the states so they have the general form

(11)

where _ij^* is a constant. Assuming that the electric energy of the charge is linearly dependent on the voltage as was done for the equilibrium (see Eq. 3), we separate the total energy into electric energy and all others as F_ij = G_ij^c  z_ije₀V and F_ji = G_ji^c  z_jie₀V with _ij + _ji = 1. We can write the voltage dependence of the rates as

(12)

and

(13)

with _ij0 and _ji0 as the rates in the absence of electric field. This simple formulation predicts that forward rates will increase with depolarization and backard rates will increase with hyperpolarization. The actual time course of the gating current will be given by the solution of the state equations, which will give a sum of exponentials with rate constant (eigenvalues) containing a combination of the elementary rates _ijji for all i and j values. The kinetic features of gating currents can be quite complicated (see Fig. 4) and rarely seem like simple processes.

View larger version (22K): [in this window] [in a new window]   Fig. 4. Family of gating currents recorded from Shaker(IR) W434F mutant K channel for a series of pulses from 100 to +20 mV in steps of 5 mV from a holding potential of 90 mV. These are single-sweep unsubtracted records.

The basic question is how the current kinetics originate at the molecular or single-channel level. There are two extreme possibilities. The first possibility is that the time course of the gating current results from a continuous movement of charge in each channel with a similar time course of the ensemble gating current. The second possibility is that in each channel the charge moves through discrete, jumplike process that in an ensemble adds up into a continuous decaying current. The second view has been the predominant trend in the literature, and early predictions of a jumplike process (see Fig. 1 in Bezanilla, Ref. 10) were experimentally confirmed in Na channels (28) and K channels (86).

The nature of the charge movement at the single-channel level could be resolved if the elementary charge movement were recorded, but it has not been experimentally possible. Instead, the analysis of the fluctuations of the ensemble gating currents (30, 85) has yielded information on the elementary event. Conti and Stuhmer (28) were the first to record gating current fluctuations from a population of Na channels expressed in Xenopus oocytes and found that the elementary event is ~2.3 e₀. The time course of the event itself was limited by the filter used, indicating that it was much faster than 5 kHz. The analysis of the autocorrelation showed that these events were consistent with a process that carries discrete packages of charge in the channel (a shotlike process). Sigg et al. (86) studied the fluctuations of gating currents in the Shaker K channel, which has slower kinetics, allowing a larger effective bandwidth. The elementary charge per event was estimated to be 2.4 e₀ for large depolarizations. The analysis of fluctuations at moderate depolarizations showed larger fluctuations, as expected from the noise introduced by the discrete charge packages (shot events) that return charge to its resting position. However, at these potentials, the time course of the fluctuations lagged significantly with respect to the ensemble gating current, showing that at small depolarizations most of the gating current produced no detectable fluctuations. This result indicates that the early movement of the charge is not the result of large shots, as is the case for transitions near the open state. Recently, Stefani et al. (98) have extended these measurements to 20-kHz bandwidth, and the elementary event for large depolarizations was confirmed to be 2.4 e₀. In this study, the off elementary event was 2.7 e₀, consistent with the idea that the large shot event occurs near the open state. In the off gating current, the recorded fluctuations have less contamination from the smaller events that occur in the deeper closed states, and the estimated elementary event should be closer to the true shot size.

The question of whether the large shot of charge is the contribution of each subunit or of several subunits moving in concert is not resolved yet for the Shaker channel. However, the results from the Na channel (28) indicate that the large shot is the contribution of one or at the most two of the four voltage sensors. This is because in that study they found that the size of the shot (2.3 e₀) was the same during activation and during the return after a long pulse when the channels were inactivated. Because we know now that two of the subunits do not go back until inactivation is recovered (see sect. IVD and Cha et al., Ref. 21), we must conclude that the 2.3 e₀ they determined in the off is not the result of the concerted return of the four domains but at the most two, giving a value of 1.15 to 2.3 e₀ per subunit.

Gating currents from the Shaker K channel recorded with 5-kHz bandwidth show a rising phase followed by a decaying phase (see Fig. 4). The rising phase becomes more pronounced for large depolarizations. The decaying phase show single exponential behavior for small depolarizations, double exponential for intermediate depolarizations, and single exponential for large depolarizations. The first component is faster than the second, but as the potential increases, the second becomes progressively faster to the point that the first is no longer detectable and is replaced by the rising phase. A rising phase in the gating current indicates a sequential set of steps in which the initial steps carry less charge or move more slowly than the following steps (15). A simple interpretation of these results is that the initial transitions are faster and carry less charge than the subsequent transitions so that at small depolarizations the gating current is predominantly given by these transitions. At higher depolarizations, the slower transitions that carry more charge become visible as a second component and at even higher depolarizations become very fast because their charge is larger (see Eq. 12) and predominant while the first transitions produce the rising phase. The charge versus potential (Q-V) curve of this channel (obtained by integration of the gating current traces) also shows two main components called Q₁ and Q₂ (see Fig. 5 and Bezanilla et al., Ref. 13) when fitted by the sum of two Boltzmann distributions or by a sequential three-state model. In both cases, the fit indicates that the first component is centered toward hyperpolarized potentials with a smaller elementary charge than the second component, which is centered at more depolarized potentials (Fig. 5). A confirmation of two sequential charge movements comes from the differential effects of temperature on the early and late components of the gating currents (76). The Q₁₀ of the early transitions (Q₁) is less than 2 whereas in later transitions (Q₂) is ~3. In addition, the Cole-Moore shift has a very low temperature dependence (76), and this shift has been traced to charge movement between early closed states of the channel (99, 102).

View larger version (14K): [in this window] [in a new window]   Fig. 5. Relation of the normalized charge versus potential (Q-V) and conductance versus potential (G-V) for ShakerB K channel. Continuous line through Q-V points is a fit to the data using a 3-state sequential model where the 2 components are plotted as Q1 and Q2. Notice that Q1 is left shifted with respect to Q2 and is less voltage dependent.

With all these results, it is tempting to propose that the charge in the channel moves in two sequential steps, the first carrying less charge than the second step. However, two steps are not enough to account for the delay in the ionic current turn on (119) and the pronounced Cole-Moore shift of the gating and ionic currents (99). For this reason, models proposed include many more steps in two major classes: a sequential model with an initial set of states with small charge movement between states followed by a large charge movement preceding channel opening (13); or a model with four subunits, each with two transitions (3 states), the first with a large charge movement followed by the second transition with a smaller charge movement. In this second type of model, when all four subunits have reached the third state, the channel undergoes a final transition to the open state strongly biased in the forward direction, introducing cooperativity and explaining the very steep voltage dependence of the Q-V curve at high depolarizations (119). After these two sequential steps, there is at least one more step preceding the channel opening. This extra step(s) has been studied in detail in mutants that change their equilibrium by Schoppa and Sigworth (80) and by Ledwell and Aldrich (48).

The off gating currents recorded from the nonconducting W434F ShakerB (IR) mutant show a drastic change in kinetics as the magnitude of depolarization is changed. Thus, at small depolarizations, the charge returns quickly as one exponential component while at larger depolarizations the charge returns slowly after a pronounced rising phase in the off gating current (see Fig. 4). The potential at which this change occurs is close to the voltage at which ionic conduction is first observed, indicating that the return of charge is slowed down when the channel reaches the open state. Chen et al. (25) carried out a systematic study of the off gating currents as a function of the permeant ions in Kv1.5 K channel. Their results show that the off gating current at potentials at which the channel opens is slowed down when there are no permeant ions present, but they are much faster when there is K or Cs inside the cell. In addition, they showed that the nonconducting mutant W472F also exhibits slow off gating after pulses that populate the open state. These results indicate that the anomalously slow kinetics of the off gating recorded in the nonconducting mutant are not the kinetics of off gating in the normal channel. Chen et al. (25) proposed that the empty open channel progresses faster to an inactivated state than the filled channel. This explanation would account for the slow down of the off gating currents in the absence of permeant ions because the channel would have to exit from this inactivated state before closing, and that step would be rate limiting. In the case of the nonconducting mutant, the channel would be devoid of permeant ions, and it would also show this slow recovery from this inactivated state. It is interesting to note that when temperature is lowered, the rising phase of the off gating current disappears (76), indicating that the closing rate becomes comparable to the exit rate from the hypothetical inactivated state.

The results of Chen et al. (25) imply that in attempting a fit to a global model that considers ionic and gating currents simultaneously in the K channel, corrections must be applied when using ionic current data from the conducting channel and gating current data from the nonconducting channel.

When gating currents of Shaker K channels are recorded with bandwidths reaching 200 kHz, Stefani and Bezanilla (96, 97) found that the main gating current is preceded by a fast event that can be two to three times larger than the peak of the main gating current and decays with a time constant of ~10 µs. Extremely extended bandwidth is required to observe this fast transient, which means that the combination of the preparation and recording apparatus must have high-frequency responses. This can be achieved with large or giant patches where the access resistance times the membrane capacitance can charge the membrane patch with time constants shorter than 3 µs (53 kHz) provided the patch is homogeneous (98). This patch, when combined with an integrating headstage followed by a high-speed differentiator, can give the required frequency response to record the early gating event. The subtraction of the capacity transient must be done at positive potentials, which is a region with minimal nonlinear charge movement. The fast early event is observed in the on and off gating current preceding the rising phases of both currents as if it were a parallel movement of charge that only amounts to ~1% of the total gating charge. Forster and Greeff (35) recorded a similar event preceding the Na gating current in the squid axon where a very fast clamp can also be achieved with series resistance compensation that is not required in the giant patch.

The early fast event is proportional to the main gating current and has not been observed in nonexpressing oocytes (96, 97). In addition, fluctuation analysis of the gating currents does not show noise associated with this fast event (98). These considerations indicate that the movement of charge that generates the early event current is not a separate peripheral charge, but it may be part of the main charge moving a very small elementary event that does not produce detectable shot noise. A simple interpretation of the early fast event may be found when the transfer of charge between conformations of the channel is modeled as a Brownian motion instead of a purely discrete process (see sect. IIIF and Sigg et al., Ref. 85).

Consider again that the independent variable is the charge displacement q (see Fig. 3A). The progress of the channel activation in the q axis occurs as a diffusion of a charged particle in a unidimensional landscape of energy. This energy landscape can be tilted up or down depending on the voltage applied to the membrane according to Equation 3. It is easy then to see that the kinetics of the outward charge movement will increase with depolarization and, correspondingly, the inward current will increase with hyperpolarization (see Fig. 6). If the landscape is flat and the friction coefficient is constant, then the predicted currents will differ significantly from the recorded gating currents because they will show a pronounced shoulder before the decaying phase (14, 51). In addition, there will be no large shots of charge as the gating charge progresses from one end to the other of the energy landscape.

View larger version (10K): [in this window] [in a new window]   Fig. 6. A: energy barrier and position of the charged gating particle for 2 different voltages before making the jump across the barrier. By changing the voltage from V1 to V2, the shape of the energy well changes enough such that the new equilibrium position of the charge is displaced an amount Q. B: gating current predicted by the Brownian motion approach. Large spike corresponds to relocation of the charge in the energy well, whereas the decaying component corresponds to the movement of the charge across the energy barrier. [Adapted from Sigg et al. (85).]

A more realistic situation arises when the Brownian motion of the charge occurs in a rough energy landscape as discussed in detail by Sigg et al. (85). In this case, the energy landscape has valleys and peaks, i.e., it has energy barriers. Because the charge is subject to diffusion, it can be at any point of the landscape as opposed to the discrete case in which it only can dwell in the valleys or wells. The exact treatment of this problem using the Fokker-Planck equation and using a discretization technique allows the solution in terms of a large number of exponential components that can be traced to the drift process (fast) and the actual barrier crossing (slow). The fast process corresponds to the diffusion process and induces fluctuations of very high frequency that correspond to the thermal noise (Nyquist equivalent). The slow processes induce low-frequency fluctuations that correspond to the waiting times of the charge before they drift over the barriers. However, the actual transition times are extremely short because the drift of the charge is very fast, and they appear as shot events in the gating currents. In the limit when barrier heights are larger than 4-5 kT, the slow process is indistinguishable from the classical discrete treatment of the problem (85). In this view, an application of a depolarizing pulse will produce a sudden tilt of the energy landscape, and the equilibrium distribution of the diffusing particle in the wells will be changed according to the change in the well shape induced by the voltage change (see Fig. 6A). The redistribution of the charge in the new well shape will produce a current in the external circuit with a speed limited by the drift motion of the voltage sensor charge (see spike in Fig. 6B). This transient charge rearrangement corresponds to the early event in gating described in section IIIE. Only after a longer delay will the particle overcome the barrier in a fast event that originates the gating shot described above which will show as an exponential decay for the macroscopic gating current (see the decay phase of the gating current shown in Fig. 6B). The application of this theory to several examples with different number of energy wells and peaks is illustrated in Sigg et al. (85).

It is possible to qualitatively account for the results of macroscopic gating currents, the noise behavior, and the early event in gating by considering an energy landscape with small barriers, each spanning a small amount of charge favored at hyperpolarized potentials, followed by a few large barriers, each spanning a large amount of charge before leading into the open state of the channel (when q = Q_max). A sudden depolarization will first redistribute the charge within the first few wells creating the fast early event. Then the first few barriers will be traversed generating the Q₁ portion of the gating current. As these barriers span a small charge, the evolution of Q₁ will generate small fluctuations that may well be undetected. Only after the charge evolves across the large barriers, which span a large charge, will the bulk of the gating current be generated together with large fluctuations due to the shots produced by crossing those barriers.

A detailed study of macroscopic currents and single-channel recordings of the Shaker B (IR) channel was done by Hoshi et al. (43) and Zagotta et al. (118). The time course of activation could not be explained by a simple model with 4 independent subunits each with 2 states (39) but required more than 2 states per subunit, generating a multistate model that has a total of 15 distinct states in the case of a 3-state subunit. Their analysis of single-channel recordings indicated that after the channel is open it can evolve to a closed state that, as it is favored at positive potentials, does not belong to the activation pathway leading to the open state. In addition, because their results indicated that the opening step has a small voltage dependence, it constrained the large charge to a step preceding the opening step of the channel.

Oxford (67) introduced a pulse procedure that allows the investigation of the kinetics of the last step in opening. It consists of giving a large depolarization that opens most of the channels, followed by a brief hyperpolarization that closes the channels but not long enough to allow them to return to the resting state. After this brief hyperpolarization, another large depolarization is given, and the current kinetics are analyzed. If the hyperpolarization is brief enough and the opening step is not extremely fast, most of the activation during the second depolarization will be a reflection of this opening step. If the last step is rate limiting, the current during the second depolarization will be close to a single exponential. When this pulse procedure was applied to Shaker B (IR) channel, it was found that there were three exponential components, but clearly, the fastest one was predominant (75). In this same study, the rate of this very fast (100 µs) predominating component was found to be voltage and temperature independent. On the other hand, the closing rate from the open state, estimated by the time constants of the ionic current tails, had a large temperature dependence (Q₁₀ > 4) and had an estimated charge of 0.5 e₀. These results allow estimating that the open state is favored with respect to the last closed state by a decrease in enthalpy and entropy, which indicates that the channel becomes more ordered in the open state. A similar result was found in batrachotoxin-modified squid Na channels by Correa et al. (29) using single-channel analysis. The open state is enthalpically favored but entropically hampered, giving a very small net free energy change. The decrease in entropy in the open state as compared with the last closed state implies a decrease in the degrees of freedom of the channel molecule. For a class of models that requires all subunits contributing symmetrically to channel opening, this finding is expected because to maintain the channel in the open conformation requires all the subunits to be in their optimal position; any deviation from this optimal conformation would render the channel nonconducting.

Chapman et al. (24) have described subconductance levels in the Drk1 K channel. The levels seem to be associated with the degree of activation of the channel, indicating that some of the closed states may actually not be completely closed or completely open. In the tetrameric channel there are conformations that will have one, two, or three subunits in the open conformation while progressing through the activation pathway. The authors indicate that some of these conformations may be stable enough to show up as intermediate levels of conductance in single-channel records, suggesting that the pore formation, although incomplete, allows conduction at a lower rate. Zheng and Sigworth (120) have also recorded subconductance levels in Shaker mutants and have been able to determine differential selectivity between the levels, indicating a different conformation of the selectivity filter in those subconductance states. Although these subconductance levels have not been observed in the wild-type Shaker (IR) channel, these results are in agreement with the notion that the formation of the open pore is the contribution of the four subunits and that it may be possible to observe an incomplete pore as the channel progresses to the fully open state. In the wild-type channel, the states that give origin to the subconductance levels may be populated too briefly to be detected reliably.

One of the salient features of Na conductance is that in response to a depolarizing pulse, the magnitude of the current first increases and later decreases during the pulse. The current decrease was called inactivation by Hodgkin and Huxley (39), and it was characterized as another voltage-dependent process, albeit with slower kinetics than activation, which is the process that increases the current during a depolarization. As a voltage-dependent process, inactivation also had a voltage sensor in the Hodgkin and Huxley formulation and in fact was modeled as a completely independent process with intrinsic voltage dependence. Goldman and Schauff (36) proposed that inactivation might be a process coupled to activation, and they could account for the macroscopic current data. When gating currents of the Na channels were recorded, the component associated with inactivation was not found. Instead, it was found that the inactivation process modified the activation process, suggesting coupling.

The return of the charge after a depolarizing pulse was greatly affected by the duration of the pulse, such that for short depolarizations all the on charge returned in the off charge, but for long depolarizations, the off charge seemed to be only about one-third of the on charge. The time course of this charge decrease (or charge immobilization) corresponded to the time course of the ionic current inactivation. This inequality of charge seems like a direct violation of the basic conservation required in a displacement current. The explanation is that in fact all the charge returns in the off but in two separate components: a fast component that is easily detectable and a slow component that at 70 mV escapes detection. By making the voltage at the off more negative, the slow component becomes visible, and the total off charge matches the on charge. In addition, it was found that the slow component in the off had the time course of recovery from inactivation (Ref. 7, Fig. 7A).

View larger version (36K): [in this window] [in a new window]   Fig. 7. Effects of inactivation of the Na channel on gating currents. A: gating current resulting from a depolarizing pulse showing a total charge Q. Upon repolarization after a long pulse that has produced ionic current inactivation, return of the charge occurs in 2 components; the fast component carries one-third of the charge, whereas the slow component carries the rest of the charge. B: schematic representation of the ball and chain model showing the 3 basic states of the channel: closed, open, and inactivated. The inactivating particle plugs the internal mouth of the channel and, while is in position, prevents the return of some of the voltage sensors, producing the charge immobilization. Site-directed fluorescent labeling (see sect. IVD5) has shown that the sensors of domains I and II are not immobilized by the inactivating particle (explaining the fast tail of charge Q/3), whereas domains III and IV interact with the particle, and they cannot go back until the particle is released (the 2/3 of Q part of the tail).

From these experiments a clear picture emerges. During a depolarization, first the voltage sensor repositions the activation charge to open the channel. Then a separate conformational change in the channel prevents conduction and at the same time freezes up to two-thirds of the activation charge that moved to open the channel. Upon repolarization, the third of the charge that was not immobilized returns quickly, and the other two-thirds of the charge returns as the inactivation is recovered.

To explain these results, Armstrong and Bezanilla (7) proposed that inactivation of the ionic current is the result of an inactivating particle (ball and chain, see Fig. 7B) that blocks the channel from the inside and at the same time hampers the movement of the activation charge. The affinity of this particle for its site is increased as the channel progresses toward the open state. This inactivation particle could be cleaved off by internal perfusion of the axon with the protease pronase (8). As expected from this hypothesis, when the particle is cleaved off, the charge immobilization was no longer observed. This hypothesis could be cast in a kinetic model that explained most of the observations of ionic and gating currents, and this model did not require a voltage-dependent step for the inactivation itself. In this view, the voltage dependence of the inactivation process is borrowed from the steep voltage dependence of the activation process. It was later found that to account for the experimental data of single channels, macroscopic ionic currents, and gating currents, a small voltage dependence in the inactivation step is required. The voltage dependence is small and amounts to the equivalent of less than one charge (3, 4, 107, 108).

A first step in understanding the operation of the voltage sensor and its coupling to the conducting pore is to propose a kinetic model that is able to reproduce the experimental data. The first successful model of channel activation and inactivation was proposed by Hodgkin and Huxley (39). For the K channel, their model is based on the independent operation of four gating particles each undergoing a single transition from a resting state to an active state; the channel only conducts when all four are in the active state. Although this model has served as a basis of much of our understanding of voltage-dependent channels, it does not account for the details of activation when data of macroscopic ionic currents are complemented with single-channel and gating current recordings. It is clear that to account for the delay in activation and the Cole-Moore shift, a minimum of six sequential steps is required and the Hodgkin-Huxley model only has five. To account for the details of gating currents, about eight states are required, and the progression of the rate constants from the most closed states to the open state does not follow the predicted 4,3,2,1 ratios calculated from the progress of four identical independent subunits.

We can classify kinetic models in two general types: tetrameric (scheme I) and strictly sequential (scheme II)

(Scheme I)

(Scheme II)

The tetrameric structure of the Shaker K channel gives a solid basis to build a model around four subunits as Hodgkin and Huxley originally proposed. Because the original Hodgkin-Huxley model is not adequate, it was modified by adding one more state in each subunit, a model we may call three state, four subunit (119). The physical interpretation of the three-state four-subunit model is very simple because it assumes that each subunit acts independently of each other while it evolves toward the open state. This model generates a total of 15 states (after reducing the degenerate states) with an added blocked state after the open state. All the rates between states are predicted from the individual rates and the stoichiometry except for the return path from the open state where the first transition was made much slower than predicted to account for the details of the currents. The other approach was to add more states (to a total of 8) to the sequential equivalent of the Hodgkin-Huxley (8-state) model (13). The physical interpretation of the 8-state model is not as straightforward, but it could be thought of as a modified Hodgkin-Huxley model where there are interactions between subunits and extra concerted steps before channel opening. The three-state four-subunit model does a fair job in reproducing the major features of the ionic currents, but it does not do as well as the eight-state model in reproducing the features of gating currents.

The substitution of hydrophobic residues in S4 segment of Smith-Maxwell et al. (90) and Ledwell and Aldrich (48) indicates a high degree of cooperativity in the last step of channel opening, which was incorporated as one more concerted step in the three-state four-subunit model and built in for the eight-state model. In their study of the multiple mutant V369I, I372L, and S376T (called ILT mutant), they found that the last step becomes rate limiting and allows the measurement of as much as 1.8 e₀ during that transition. In contrast, Rodriguez and Bezanilla (75) measured 0.5 e₀ in the last step of wild-type Shaker(IR). In their modeling (4