INTRODUCTION

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Voltage-dependent cation channels respond to changes in the electric field across the cell membrane by undergoing conformational changes that open and close an ion-permeable pore. These conformational changes involve the rearrangement of charges within the channel protein, making the rates of the conformational changes voltage dependent. The movement of the charge within the channel protein can be measured as gating current (Schneider and Chandler, 1973; Armstrong and Bezanilla, 1974; Keynes and Rojas, 1974; Stühmer et al., 1991; Bezanilla et al., 1991, 1994; Schoppa et al., 1992; Stefani et al., 1994; Zagotta et al., 1994a, 1994b). The elucidation of the molecular mechanism of the voltage- dependent conformational change has been a major goal of ion channel biophysics. This effort has been facilitated by the combination of powerful electrophysiological techniques and the ability to determine and alter the primary structure of channel proteins by recombinant DNA technology. For voltage-gated potassium channels, the minimum requirement to make a functional channel is the association of four alpha subunits, each with a core region containing six putative transmembrane segments and a pore loop (MacKinnon, 1991; Heginbotham and MacKinnon, 1992; Kavanaugh et al., 1992; Liman et al., 1992). A distinctive feature of voltage-dependent cation channels is the fourth transmembrane segment (S4). The S4 is ~21 amino acids long with positively charged basic amino acids, either arginine or lysine, at every third position, separated by hydrophobic and neutral residues (Noda et al., 1984, 1986; Salkoff et al., 1987; Tanabe et al., 1987, 1988; Papazian et al., 1987; Tempel et al., 1988; Baumann et al., 1988; Ellis et al., 1988; Kayano et al., 1988). Because of the high nominal charge density in this membrane spanning segment and the fact that the motif is highly conserved among voltage-gated cation channels, the S4 was initially proposed to be part of the voltage sensor (Noda et al., 1986; Catterall, 1988; Durrell and Guy, 1992).

If the S4 is part of the voltage sensor, the S4 and its charges should move through the electric field in response to membrane depolarization. Evidence from both skeletal muscle sodium channels and Shaker potassium channels indicates that a conformational change in the S4 or in adjacent channel regions occurs in the channel protein upon activation (Yang and Horn, 1995; Yang et al., 1996; Larsson et al., 1996; Mannuzzu et al., 1996; Aggarwal and MacKinnon, 1996; Seoh et al., 1996; Yusaf et al., 1996). Another prediction, that neutralization of S4 charges should decrease the amount of charge moved during channel activation, has also been confirmed in Shaker (Aggarwal and MacKinnon, 1996; Seoh et al., 1996). These experiments provide strong evidence for a role for the S4 in sensing voltage. However, the individual S4 charges do not seem to contribute equally to the gating charge, and properties of the charged residues other than the charge are also important determinants of gating behavior (see also Perozo et al., 1994). There is also evidence that a negatively charged residue in the S2 of Shaker potassium channels may serve as a counter ion for S4 charges and participate in the voltage-sensing process (Papazian et al., 1995; Seoh et al., 1996; Tiwari-Woodruff et al., 1997).

Mutation of nonbasic residues in the S4 through the S5 segments can also cause significant changes in voltage-dependent gating in Shaker potassium channels (Zagotta and Aldrich, 1990; Gautam and Tanouye, 1990; Lichtinghagen et al., 1990; McCormack et al., 1991, 1993; Lopez et al., 1991; Schoppa et al., 1992; Logothetis et al., 1993; Aggarwal and MacKinnon, 1996) and in sodium channels (Auld et al., 1988). In experiments by Aggarwal and MacKinnon (1996), simultaneous substitution of several nonbasic S4 residues, with no change in the charged residues, alters the voltage range over which gating charge moves but not the total amount of gating charge moved. Mutation of noncharged residues in this region could alter the coupling between voltage sensing and opening of the channel, or could alter movement of the charge through the membrane electric field.

Evidence for cooperative transitions leading to potassium channel activation has come from studies of activation kinetics in Shaker (Sigworth, 1993; Zagotta et al., 1994b; Bezanilla et al., 1994) and from studies of steady state channel kinetics in heteromultimeric mammalian potassium channels (Tytgat and Hess, 1992; Hurst et al., 1992). All of the several kinetic models that have been proposed to describe Shaker channel activation have in common multiple voltage-dependent transitions, with at least one transition involving the cooperative movement of subunits (Sigworth, 1993; Bezanilla et al., 1994; Zagotta et al., 1994a; McCormack et al., 1994). Because cooperativity can be a major determinant of the voltage dependence of channel opening, assessment of the contribution of cooperative interactions to the activation process is essential to a mechanistic understanding of potassium channel gating. Mutations that change cooperativity can lead to large changes in the slope of the conductance-voltage curve, giving the erroneous appearance of a change in the total gating charge (Schoppa et al., 1992; Sigworth, 1993; Sigg et al., 1994; Zagotta et al., 1994a).

In this study, we investigated further the role of the S4 in channel activation by generating several Shaker channel variants with chimeric S4 insertions. Much of the previous work targeted specific amino acids for replacement based on presumed functions of the residues or their conservation among related channels. Our goal was to reveal properties of the S4 not evident from this previous work. The strength of the chimeric approach is that it does not make assumptions a priori about the functional and structural importance of specific amino acids in the S4 sequence (see also Logothetis et al., 1993; Tang and Papazian, 1997; Koopmann et al., 1997).

While we generated several S4 chimeras, we focused our study on the Shaw S4 chimera because its gating behavior differs most significantly from that of the Shaker channel. Our analysis is based on a simplified model for Shaker gating, which we use to differentiate changes in the amount of charge moved during channel gating from changes in cooperativity in the activation pathway. We also examine activation in channels assembled from tandem heterodimer constructs with Shaker and Shaw S4 subunits to investigate further whether the mutations alter cooperative or independent transitions in the activation pathway. In the following paper, we determine which of the amino acid substitutions in the Shaw S4 chimera are responsible for differences in gating between Shaw S4 and Shaker and we present a more detailed model that can account for changes in both the kinetic and steady state properties of the mutant macroscopic ionic currents. The importance of these residues in determining the properties of voltage-dependent activation was not previously recognized. Preliminary results have been reported previously in abstract form (Smith-Maxwell et al., 1993, 1994; Ledwell et al., 1995).

	MATERIALS AND METHODS

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Chimera Construction

All S4 chimeras were generated in a mutant form of ShB (Papazian et al., 1987; Kamb et al., 1987; Pongs et al., 1988), designated ShB6-46, in which fast N-type inactivation was removed by deletion of amino acids 6-46 (Hoshi et al., 1990; Zagotta et al., 1990). This allowed us to study activation in isolation from the fast (N-type) inactivation process. This Shaker construct still undergoes a relatively slow inactivation process (C-type inactivation). The time constant for C-type inactivation of ~1.5 s is sufficiently slow that it does not interfere with measurement of activation parameters (Hoshi et al., 1991). ShB6-46 cDNA was further modified by introduction of a unique "silent" StuI restriction enzyme site 3' to the S4 coding region, at amino acid positions 380-382 (see Fig. 1). This modification, which does not alter the amino acid sequence, was made using the polymerase chain reaction method to generate a cassette that was inserted between two naturally occurring unique restriction enzyme sites within the Shaker cDNA, StyI and NsiI. To generate the S4 chimeras, sense and antisense oligonucleotides were made based on the S4 sequences of the cloned channels Shab, Shal, Shaw, and K_v3.2 (RKShIIIA) (Butler et al., 1989; McCormack et al., 1990). Sense and antisense oligonucleotides were annealed and inserted into the S4 of ShB6-46 between the unique StyI site 5' to the S4 coding region, at amino acids 357-359, and the silent StuI site 3' to the S4 (see Fig. 1). An S4 chimera with the S4 of Shaker inserted into Shaw was also constructed but did not express functional channels in oocytes. Verification of the inserted sequences was carried out in all instances using the dideoxy termination sequencing method (Sanger et al., 1977).

View larger version (16K): [in this window] [in a new window]   Fig. 1.   Amino acid sequences for the S4 chimeras and Shaker. S4 sequences from several Drosophila potassium channels including Shab, Shal, and Shaw, and one rat potassium channel, Kv3.2 (RKShIIIA), were substituted into the Shaker background channel as indicated. The standard single letter abbreviations are used to designate amino acids in the sequences. Dashes in the substituted segment indicate amino acids identical to Shaker. Numbers above the sequences designate the position of each of the seven basic residues in Shaker. Symbols at the positions where Shaker has basic residues are in bold. Numbers beneath the sequences indicate the number of each amino acid in the Shaker sequence, taken from Tempel et al. (1987). Unique restriction enzyme sites used for construction of the chimeras are indicated. The number of amino acids in each mutant sequence that differ from Shaker is given in the column designated aa diff. The net charge of the S4 assuming one positive charge for each arginine and lysine, one negative charge for each glutamate, and no charge for histidine is given in the column designated net chg.

Terminology

Chimeric channels are designated as the species of S4 substituted for the Shaker S4 sequence in ShB6-46. For instance, the Shal S4 chimera was made by substituting the S4 sequence of Shal into the Shaker channel in place of the Shaker S4 sequence. The specific amino acid replacements are shown in Fig. 1.

Dimer Construction

Tandem dimers were constructed by splicing together DNA coding for A and B protomers (Heginbotham and MacKinnon, 1992; Ogielska et al., 1995). The original protomers contain the sequence for Shaker potassium channels with the NH₂-terminal deletion to remove N-type inactivation, ShH46-46. The amino acid sequences of ShB and ShH4 are nearly identical, differing by only two amino acids, both near the COOH-terminal end of the protein (Schwarz et al., 1988; Kamb et al., 1988). The A protomer contains DNA coding for a hydrophilic linker (NNNNNNAMV) inserted in frame between the coding regions of each protomer. Protomers were spliced together at the NcoI and KpnI restriction enzyme sites. Shaw S4 was spliced into the A protomer or B protomer using RsrII and NsiI restriction enzyme sites. For the protomers A_k, B_k, A_w, and B_w, the A and B designate the NH₂- and COOH-terminal protomer, respectively, with each protomer containing either the Shaker (k) or Shaw S4 (w) construct. All combinations of dimers were constructed: A_kB_k, A_wB_k, A_kB_w, and A_wB_w.

Expression System

Channels were expressed in Xenopus oocytes by injection of G(5')ppp(5')G capped cRNA from the different channel constructs. cRNA was transcribed in vitro from linearized plasmid containing channel DNA constructs as described previously (Zagotta et al., 1989; Hoshi et al., 1990). For Shaker and the S4 chimeras, cRNA was made from KpnI-linearized DNA with T7 RNA polymerase. For Shaw and the S4 chimera in Shaw, cRNA was made from SacI- or SalI-linearized DNA with T3 RNA polymerase. For the tandem dimers, cRNA was made from EcoRI-linearized DNA with T7 RNA polymerase. Recordings were typically carried out 1-21 d after injection.

Electrophysiology and Data Analysis

Electrophysiological recordings of macroscopic ionic currents were carried out from excised membrane patches in the inside-out configuration (Hamill et al., 1981). Currents were recorded with either a List EPC-7 (Medical Systems Corp., Greenvale, NY) or an Axopatch 1B (Axon Instruments Inc., Foster City, CA) patch clamp amplifier and low pass filtered using an eight-pole Bessel filter (Frequency Devices, Inc., Haverhill, MA). Macroscopic currents from Shaw and Shal S4 were filtered at 9 kHz. All other data were filtered at 2 kHz unless otherwise noted. Two different systems were used to generate pulses and to digitize and store data for later analysis. The first was a Digital Equipment Corp. LSI 11/73-based minicomputer system (Indec Systems, Sunnyvale, CA). The second was a Macintosh-based system with hardware interface from Instrutech Corp. (Great Neck, NY) and software from HEKA (Lambrecht, Germany). Patch pipettes were constructed from VWR borosilicate glass and had initial resistances of 0.4-0.8 M. No series resistance compensation was used. The maximum error due to uncompensated series resistance for this series of experiments was ~4 mV; however, the error was typically <2 mV. Linear leak and capacitive currents were subtracted with either a P/4 protocol or appropriately scaled averaged responses to repeated 20-mV depolarizing steps, both typically from a holding potential of 110 mV. The temperature was held at 20 ± 0.2°C.

For Shaker, Shab S4, and K_v3.2 S4, conductance-voltage curves were constructed by calculation of the chord conductance (G_chord) from maximum currents (I_max) during the test pulse at several voltages, assuming a reversal potential (V_rev) of 80 mV: G_chord = I_max/(V  V_rev). Conductance-voltage curves generated in this way are minimally affected by the nonlinearity of the single channel conductance if, as with these channel species, activation occurs over a more negative voltage range. For all other channel species, conductance-voltage curves were constructed from isochronal measurements of tail currents recorded at a fixed voltage following steps to voltages that activate the channels. Typically, isochronal measurements were made between 0.2 and 1 ms after the end of the test pulse. Conductance-voltage curves were normalized to the maximum value for comparison between patches and between channel species. Conductance- voltage curves were fit by a first or fourth power Boltzmann function of the form

with n equal to 1 or 4, to determine the voltage-dependent parameters of activation. G/G_max is the conductance normalized to the maximum value for each channel. For a first power Boltzmann function, V_1/2 is the voltage at which the channels are open half maximally. For a fourth power Boltzmann function, V_1/2 is the voltage at which each subunit is activated half of the time. V is the voltage of the test pulse, z is the equivalent charge, F is the Faraday constant, R is the gas constant, and T is the absolute temperature. The slope factor is equal to RT/zF.

Typically, a holding potential of 80 mV followed by a 1-s prepulse to 100 mV was used before the test pulses. For Shaw, 10-ms prepulses to 100 mV were often used. In some experiments with Shaw, a holding potential of 0 mV was used to minimize the capacitive transient during large positive voltage steps. This can be done because Shaw does not inactivate even during long depolarizations to 0 mV and its activation kinetics are not sensitive to holding potential (data not shown; see also Wei et al., 1990; Tsunoda and Salkoff, 1995).

The activation time course of the macroscopic ionic currents was fit using a single exponential function for times greater than the delay: I(t) = A{1  exp[(t + d)/]}. I(t) is the fit to the current at time t, A is the scale factor,  is the time constant, and d is the delay required to obtain an adequate fit of a single exponential function, which was required for some channel species. Tail currents were fit with a single exponential function.

Xenopus oocytes have endogenous potassium and chloride channels, which are known to activate at more positive membrane potentials (Dascal, 1987). The currents measured in this study from channel species requiring large positive voltage steps to activate, such as from Shaw or the Shaw S4 chimera, were clearly identified as currents through the exogenously expressed potassium channels for the following reasons. Our intracellular solutions typically contained 11 mM EGTA with little or no added Ca⁺⁺, which is expected to prevent activation of the calcium-activated chloride channels in Xenopus oocytes (Dascal, 1987). We never saw Shaw or Shaw S4-like currents in membrane patches from uninjected oocytes when using the standard recording solutions. Shaw S4 properties were similar whether expression levels gave currents of several nA or only 50-100 pA. This was true for Shaw as well. Also, Shaw S4 and Shaw currents clearly reverse near the calculated reversal potential for K⁺, between 80 and 100 mV, and not near the 0-mV reversal potential for Cl ions. Finally, expression levels for Shaw S4 and Shaw channels could give rise to several nanoamperes of current in a single patch, which is orders of magnitude larger than endogenous currents from similar membrane patches in uninjected oocytes.

Single channel currents for Shaker, Shaw, and Shaw S4 were recorded from inside-out membrane patches using the standard solutions (see below), unless otherwise stated. Currents were digitized at 20 kHz and filtered at 2 kHz, unless otherwise stated. Single channel conductance was calculated from single channel currents recorded during steps to voltages between 50 and +80 mV by fitting a linear function to the single channel current-voltage relation. Single channel current-voltage relations for all three channels are linear in this voltage range. Results from single channel analysis of ShB6-46 are taken from Hoshi et al. (1994).

Kinetic simulations were carried out as outlined in Zagotta et al. (1994b). Transitions between conformational states are assumed to obey time-homogeneous Markov processes. Voltage- dependent rate constants are assumed to be exponentially dependent on voltage.

Solutions

The standard extracellular (pipette) solution used for these experiments contained (mM): 140 NaCl, 2 KCl, 6 MgCl₂, 5 HEPES (NaOH), pH 7.1. The standard intracellular solution (bath) contained (mM): 140 KCl, 2 MgCl₂, 11 EGTA, 1 CaCl₂, 10 HEPES (N-methylglucamine), pH 7.2. For Shal S4, Shaw S4, and Shaw, the intracellular solution was modified by removing MgCl₂ and CaCl₂, unless otherwise noted. This was done because intracellular Mg⁺⁺ blocks these channels in a time- and voltage-dependent manner. Block of macroscopic currents becomes evident at voltages above +80 mV for these channels (data not shown), voltages at which the probability of opening for Shal S4, Shaw S4, and Shaw has not reached a maximum value. Even though intracellular Mg⁺⁺ blocks Shaker channels also, it was not necessary to record Shaker ionic currents in Mg⁺⁺-free solution since Shaker is fully activated at voltages well below those at which Mg⁺⁺ blocks the channel. Similar block by intracellular Mg⁺⁺ has been shown for the closely related K_v1.1 potassium channel (Ludewig et al., 1993). For Shaker and Shaw S4 channels, both the time course of activation and the position of the conductance-voltage curve along the voltage axis is unchanged by Mg⁺⁺ at voltages where there is little or no block (data not shown).

	RESULTS

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Alterations of Potassium Channel Gating by S4 Chimeric Substitutions

Chimeras were generated by substituting 21 amino acids from the S4 of several divergent potassium channels for the S4 of Shaker potassium channels (Fig. 1). The substituted potassium channel sequences were derived from Drosophila channel genes Shab, Shal, and Shaw, and from a rat Shaw homolog, K_v3.2 (RKShIIIA). Comparison of S4 amino acid sequences between these channels and Shaker reveals significant differences in amino acid composition. The sequence identity with Shaker S4 ranges from as little as 43% for Shab to as much as 62% for K_v3.2. The nominal net charge in the S4 regions ranges from +3 in Shaw to +7 in Shaker, assuming that arginine and lysine have a net charge of +1, glutamate has a charge of 1, and histidine is uncharged.

Macroscopic ionic currents and normalized conductance-voltage curves from the S4 chimeras and the Shaker parent channel are shown in Figs. 2 and 3 (see also Table I). All S4 chimeras activate at more positive voltages and with a shallower conductance-voltage relation than Shaker. However, Shaw S4 requires much larger positive steps to activate than the other chimeras. This shift in the voltage range of activation indicates that the S4 substitutions tend to bias gating toward the closed states more than the wild-type S4 sequence of Shaker. Activation kinetics of Shab S4, Shal S4, and K_v3.2 S4 are relatively fast, similar to Shaker. In contrast, activation kinetics of the Shaw S4 chimera are much slower.

View larger version (33K): [in this window] [in a new window]   Fig. 2.   Macroscopic ionic currents from S4 chimeras and Shaker. Currents were measured in response to 50-ms positive voltage steps, after 1-s prepulses to 100 mV from a holding potential of 80 mV. Currents were recorded in the voltage ranges indicated in 10-mV increments. The last 6 ms of the prepulse preceding the test pulse is shown for each trace. The beginning of each test pulse is indicated by the left edge of the calibration bars.

View larger version (18K): [in this window] [in a new window]   Fig. 3.   Normalized conductance-voltage curves for S4 chimeras. Means and SEM are shown for Shab S4 (), Shal S4 (), Shaw S4 (), Kv3.2 S4 (), and Shaker (). For Shaker, Shab S4, and Kv3.2 S4, G/Gmax was constructed from the chord conductance as outlined in MATERIALS AND METHODS. For Shaw S4, the normalized conductance was constructed from isochronal currents measured at 0 mV at a fixed time after reaching the maximal current, ranging between 0.4 and 1.0 ms after the positive voltage step to activate the channel. Similar measurements of isochronal tail currents were carried out for Shal S4 at 50 mV. Smooth curves through the data represent fits to the mean values for each channel species with a fourth power Boltzmann function, as outlined in MATERIALS AND METHODS. The values from these fits are given below, with n representing the number of patches included to calculate each mean. Shaker, V1/2 = 57.4 mV, slope factor = 10.0 mV, n = 8. Shab S4, V1/2 = 58.1 mV, slope factor = 14.9 mV, n = 3. Shal S4, V1/2 = 1.1 mV, slope factor = 19.8 mV, n = 5. Shaw S4, V1/2 = 31.2 mV, slope factor = 28.4 mV, n = 7. Kv3.2 S4, V1/2 = 49.3 mV, slope factor = 25.0 mV, n = 5.

Contribution of S4 Charges to Voltage Dependence of Activation

One of the questions addressed in this study is whether or not a correlation exists between the charges in the S4 of the chimeras and the slope of the conductance- voltage relation. S4-charged residues have been shown to contribute to the gating charge associated with channel activation (Aggarwal and MacKinnon, 1996; Seoh et al., 1996). Although total gating charge per channel determines the slope of the conductance-voltage relation at very low open probabilities (Almers, 1978; Schoppa et al., 1992; Zagotta et al., 1994a, 1994b; Sigg and Bezanilla, 1997), the shape and slope of the relationship at higher open probabilities is additionally influenced by interactions between subunits (Zagotta et al., 1994a; Sigworth, 1993). Therefore, we were interested in studying the role of the S4 charges in determining the slope of the conductance-voltage relation in the voltage range of moderate probability of channel opening (Wei et al., 1990; Schoppa et al., 1992; Logothetis et al., 1993; Zagotta et al., 1994a).

For all S4 chimeras, the conductance-voltage relation is significantly more shallow than for Shaker, as might be predicted by the smaller number of basic residues present in the mutants (Fig. 3, Table I). The most shallow slope of the conductance-voltage relation appears in Shaw S4, consistent with the S4 of Shaw having the least amount of charge (+3) of the chimeras as well as the fewest of those charges thought to contribute most to channel activation (Aggarwal and MacKinnon, 1996; Seoh et al., 1996; Larsson et al., 1996). However, an almost equivalent slope occurs with K_v3.2 S4, which has the highest nominal charge density (+6) in the S4 of all the chimeras. K_v3.2 S4 includes the same five basic residues present in Shab S4 and Shal S4, which have fewer charges. K_v3.2 S4 contains all five of the S4 basic residues thought to contribute most to the gating charge. The only charge substitution in K_v3.2 S4 is a neutralization at the seventh charged residue in Shaker, a position that seems to contribute little to the overall charge movement associated with gating (Aggarwal and MacKinnon, 1996; Larsson et al., 1996). Clearly, the similar steepness of the conductance-voltage curves for Shaw S4 and K_v3.2 S4, despite the large difference in charge content of the S4 segments, indicates that properties of the S4 other than the amount of charge are important determinants of the voltage dependence of channel opening. Furthermore, these results suggest that molecular mechanisms other than charge movement, such as subunit cooperativity, greatly influence the shape of the conductance-voltage curve.

Distinguishing between Changes in Independent and Cooperative Transitions

To investigate further the role of S4 residues and cooperative interactions between subunits in gating, we wanted to use a prototypical model for channel gating that would incorporate several key features of voltage-dependent Shaker channel activation and thus would yield insights that are readily generalizable to models with more complexity. All of the several kinetic models that have been proposed to describe Shaker channel activation have in common multiple voltage-dependent transitions with at least one transition involving the cooperative movement of subunits (Bezanilla et al., 1994; Zagotta et al., 1994a; McCormack et al., 1994; Sigworth, 1993). The six-state model in Fig. 4 is the simplest kinetic model for a homotetrameric channel with both independent and concerted conformational changes. It incorporates a single independent conformational change in each of four identical subunits followed by a single concerted conformational change, and it can reproduce many of the key features of Shaker activation. Parameters for the six-state model were found that predict ionic currents similar to Shaker (control) and to those predicted by a more complete model for Shaker activation that quantitatively fits data from macroscopic ionic currents, single channel recordings, and gating currents (Zagotta et al., 1994a). The six-state model fits the steady state and kinetic properties of the macroscopic ionic currents of Shaker reasonably well using very few free parameters and predicts a considerable amount of delay in the activation time course. While the cooperative transition in this six-state model in Fig. 4 is voltage independent, the steady state and kinetic properties of Shaker activation can just as easily be fit by a cooperative transition that is voltage dependent (see Fig. 8; see also Zagotta et al., 1994a; Smith-Maxwell et al., 1998). The six-state model does not fit as well as the more complete model because it does not have enough transitions to fully account for the large delay in Shaker activation or enough gating charge. More complex models for Shaker increase the amount of charge moved during channel activation and the amount of delay in the activation time course by adding more independent transitions in each of the four channel subunits and by adding one or more concerted transitions. General conclusions from this six-state model are directly and easily transferable to other models in the literature that have been proposed for Shaker, despite differences in the details of the kinetic schemes (see Smith-Maxwell et al., 1998).

View larger version (29K): [in this window] [in a new window]   Fig. 4.   Model predictions for voltage-dependent channel opening. (top left) The six-state model used for these simulations is a simplified model for Shaker channel activation gating with properties similar to the larger 15-state model previously developed for Shaker channel gating (Zagotta et al., 1994a). Despite the decrease in complexity, the six-state model fits the conductance-voltage relation of Shaker and has kinetic properties similar to Shaker. In the model, a single independent transition in each identical channel subunit is followed by a final concerted transition leading to channel opening. Values for the rate constants  and  are taken from the first set of identical and independent transitions in each subunit of the 15-state model, since they are largely responsible for the voltage-dependent properties of opening in Shaker. Expressions for the voltage-dependent rate constants assume an exponential dependence on voltage where  = 0ez FV/RT and  = 0ez FV/RT, 0 and 0 are values for the rate constants at 0 mV, and z and z are the equivalent charge moved between each state and the transition state. The rate constants for the final concerted transition,  and , are voltage independent. Model parameters for the control simulations with Shaker-like properties are: 0 = 1,120 s1, 0 = 373 s1, z = 0.25, z = 1.0,  = 8,000 s1, and  = 100 s1. (left) Normalized conductance-voltage curves for the control simulations and for the indicated modifications. Conductance-voltage curves predicted for three types of changes in the model are shown. Charge associated with the forward (z) and backward (z) transitions is decreased (top); the 0-mV rate constant (0) for all forward independent transitions is decreased (middle); and the forward rate constant for the final concerted transition () is decreased (bottom). Normalized conductance-voltage curves were constructed from simulated currents by normalizing isochronal tail currents as outlined in MATERIALS AND METHODS. *Values used for the control simulations. (middle) Simulated ionic currents for the control parameters and for the indicated modifications to the control parameters. The simulation with z = 0.25 decreases the total charge moved for the channel from 5.0 electronic charges to 2.0 by decreasing z from 1.00 to 0.25 electronic charges in each of four subunits. The simulation with 0 = 10 s1 decreases all 0-mV forward rate constants by two orders of magnitude. The simulation with  = 10 s1 decreases the forward rate constant for the concerted final transition by almost three orders of magnitude. (right) Simulated currents from the middle panel scaled for analysis of sigmoidicity. Simulated currents at all voltages were normalized to the same maximum value. Then the slopes at the half maximum current level were made equal by changing scaling along the time axis. This manipulation of the current traces facilitates comparison of the relative delay in the currents at different voltages and from different channel species. For scaled currents that follow a single exponential time course, the time it takes to reach the half maximum current is defined as 1.0. Values >1.0 are indicative of a delay in the activation time course. Arrowheads point to scaled current traces with the smallest and largest relative delays and indicate the voltage range over which currents were scaled.

View larger version (43K): [in this window] [in a new window]   Fig. 8.   Voltage-dependent opening of Shaw S4 and Shaker dimer constructs. (left) Macroscopic ionic current traces recorded from dimer constructs. 1-s prepulses to 100 mV, from a holding potential of 80 mV, preceded each test pulse to the voltages indicated. (right) G/Gmax was determined as outlined in MATERIALS AND METHODS from dimer constructs AkBk (, n = 5), AkBw (, n = 8), AwBk (, n = 6), AwBw (, n = 1), and the Shaker (, n = 8) and Shaw S4 (, n = 6) monomers. Mean values are plotted as a function of voltage with error bars indicating SEM. Note that data from AwBw superimpose on data from the Shaw S4 monomer and data from AkBk superimpose on data from the Shaker monomer. (top right) Predictions for steady state activation from an independent model. The independent model, based on the model of Hodgkin and Huxley (1952), assumes four identical and independent transitions lead to channel opening. The normalized conductance- voltage curves from AkBk and Shaw S4 were each fit with a fourth power Boltzmann function, as described in RESULTS, to determine the voltage-dependent properties of activating a single subunit in the tetrameric channel protein. The following values were obtained from fits to data from the homotetramers: for AkBk, Vk = 52.83 mV and zk = 2.62; for Shaw S4, Vw = 32.29 mV and zw = 0.88. The independent model predicts that the voltage dependence of the conductance-voltage curve will be equal to the product of first power Boltzmann functions for each of the individual subunits making up the channel tetramer. The solid line between the fits is the prediction of the independent model for a channel with two Shaker subunits and two Shaw S4 subunits. (bottom right) Predictions for steady state activation from two cooperative models. Model 1: the first model assumes that Shaker and Shaw S4 channels open from a single closed state to a single open state, and that the forward and backward transitions between the two states involve the concerted movement of all four subunits. Data for AkBk and Shaw S4 were each fit with a single Boltzmann function, as described in RESULTS (fits not shown). Values from fits of the homotetramers are: for AkBk, V1/2 = 35.55 mV and z = 3.53; for Shaw S4, V1/2 = +80 mV and z = 1.24. The predicted conductance-voltage curve for channels with two Shaw S4 and two Shaker subunits is represented by the dotted line in the bottom right panel. Model 2: the second model, which includes several independent transitions as well as a cooperative transition, is identical to the six-state kinetic scheme outlined in Fig. 4. Values for transitions in Shaker and Shaw S4 channels were obtained from fits to data from the AkBk dimer and the Shaw S4 monomer constructs, respectively. The probability of opening and the normalized conductance were calculated as outlined in Fig. 4. For Shaker, two variations of the model were used with the same values for the independent transitions, but differing by whether or not the final concerted transition is voltage dependent. The 0-mV rate constants and associated charge used for the independent transitions for both variations are: 0 = 1,120 s1, z = 0.25, 0 = 373 s1, z = 1.0. For the voltage-independent concerted transition,  = 8,000 s1 and  = 100 s1. These values are identical to those used for the control simulations in Fig. 4 and predict the conductance-voltage relation described by the dashed line through the data for AkBk. For the Shaker variation with a voltage- dependent concerted transition, the rate constants  and , like  and , were assumed to be exponentially related to voltage with  = 0e z F  V/RT,  = 0ez F  V/RT, 0 = 10,000 s1, 0 = 100 s1, and z = z = 0.1. These parameters predict a conductance-voltage relation described by the solid line through the data for AkBk. The Shaw S4 conductance-voltage relation was simulated by slowing the final concerted transition in the activation pathway of the Shaker models and increasing the voltage dependence of the transition. For the Shaw S4 kinetic scheme, the independent transitions have the same values as in the Shaker models and the concerted transition has the following values: 0 = 1 s1, z = 0.8, 0 = 50 s1 and z = 0.4. The conductance-voltage curve calculated for the Shaw S4 model is shown by the solid line through the data for Shaw S4. Since the models simulating Shaker and Shaw S4 differ only in the final transition, energy additive predictions for heterodimer opening were calculated, as described in RESULTS, by summing the energy contributions of each subunit to this final transition, assuming all other transitions have the same properties as Shaker. The solid line near the heterodimer data shows the prediction for steady state activation of a channel with two Shaw S4 and two Shaker subunits when the concerted transition in Shaker has a small voltage dependence, while the dashed line shows the prediction when the concerted transition in Shaker is voltage independent.

Steady state and kinetic behavior for the Shaker (control) model and for several variations are presented in Fig. 4. Control simulations have steady state activation properties and gating kinetics similar to Shaker (see Fig. 2 and Fig. 8, bottom right). The opening kinetics are sigmoid and have a voltage-dependent pattern of delay similar to the pattern observed for Shaker currents and for the complete model for Shaker activation described by Zagotta et al. (1994a, 1994b). Shaker channel opening is delayed because it undergoes multiple voltage-dependent transitions between closed states before it opens. The relative delay compared with the overall rate of activation can be determined by scaling the currents at all voltages to the maximum current level and then changing the scaling of the currents along the time axis so that the slope at the half maximal current is the same for all traces. This manipulation of the current traces facilitates comparison of the relative delay, or sigmoidicity, at all voltages and between different channel species, despite differences in current magnitude and absolute rates of activation (Zagotta et al., 1994a, 1994b). For the control simulations, as with Shaker, there is little delay in channel opening during small depolarizing voltage steps due to the relatively slow rate of return from the open state. With larger depolarizations, the relative delay increases because the relative contribution of the slow first closing rate to the overall rate of activation decreases. With even larger positive voltage steps, the relative delay tends to saturate because the dominant transitions in channel activation have similar rates over this voltage range (Zagotta et al., 1994a, 1994b). In contrast, with an independent model such as the Hodgkin-Huxley model (Hodgkin and Huxley, 1952), the sigmoidicity of the activation time course is a constant function of voltage.

Since the channels under study are homotetramers, identical substitutions within each subunit could alter four independent transitions in the kinetic scheme. Alternatively, if the mutations change a cooperative transition, a single transition in the kinetic scheme can be affected. To illustrate the predicted effects of such mutations, three distinct types of modifications to the control parameters are considered. In the first, the total charge associated with channel gating is decreased by decreasing the gating charge associated with either the forward (z) or the backward (z) rate constants in each of the four subunits. In the second, the forward rate constant of the independent transitions in all four subunits (₀) is decreased without changing its voltage dependence. In the third, cooperativity is altered by decreasing the forward rate constant only in the concerted transition leading to channel opening () (see Zagotta et al., 1994a).

These different types of modifications of the gating transitions predict distinct changes in channel activation. Decreasing the amount of charge associated with each of the four voltage sensors decreases the slope of the conductance-voltage curve and predicts a shift to more negative voltages, regardless of whether charge associated with the forward or backward rate constants is decreased. This result was not observed with any of the chimeras, despite the fact that all chimeras decreased the number of basic residues in the S4 region. The predicted channel kinetics and sigmoidicity are similar to the properties of the control channel, though the voltage range is negatively shifted.

Decreasing the rate at which each individual subunit changes conformation, ₀, without changing its voltage dependence, causes a positive shift in the conductance-voltage curve along the voltage axis but does not change the slope of the curve. The slowing of the independent transitions slows activation kinetics but has little effect on the sigmoidicity of the kinetics when compared with the control. This voltage-dependent pattern of sigmoidicity occurs, as with the control, because of the cooperativity of the final transition (see also Zagotta et al., 1994a).

Altering subunit cooperativity by decreasing the forward rate constant for the final opening transition, , causes the time course of activation to become less sigmoid. As  is decreased more and more, activation is slowed and the cooperative transition becomes rate limiting. When the transition is slowed sufficiently, the activation time course becomes single exponential, as shown in Fig. 4. Decreasing  also gives rise to a positive shift in the conductance-voltage curve and a decrease in the apparent voltage dependence. While the cooperative transition in our six-state model is voltage independent, making the transition voltage dependent does not change the predictions (see Smith-Maxwell et al., 1998). Thus, we can decrease the slope of the conductance-voltage relation either by changing the cooperative interactions in a channel or by decreasing the amount of charge moved per channel (see also Zagotta et al., 1994a). The amount of charge per channel can be determined independently from gating current measurements in combination with fluctuation analysis or toxin binding to determine the number of channels present (Schoppa et al., 1992; Aggarwal and MacKinnon, 1996). However, in terms of the model, we can distinguish between changes in cooperativity and changes in the amount of charge moved independently in each subunit, without charge per channel measurements, because they differ in their predictions for the position of the conductance-voltage curve along the voltage axis and in the effect on sigmoidal delay.

Interpretation of mutant data is not completely straightforward, however, since there is no reason to expect that a mutation, even a single amino acid substitution, will change only a single parameter of activation or a single transition. Even if a mutation were to change the energy of a single state, more than one transition will likely be affected, depending on how the states are connected together. The positive shift in the voltage range of activation for the S4 chimeras and the decrease in slope suggest that the substituted S4 segments may alter cooperativity in the Shaker channel in addition to any changes due to charge content of the S4. We tested this idea further in the Shaw S4 chimeric channel.

Comparison of the Shaw S4 Chimera to Shaw and Shaker

The most dramatic changes in channel function were introduced into Shaker by substitution with the S4 of Shaw. Before proceeding with the determination of the types of conformational changes that are altered, we compared Shaw S4 to both of its parent channels, Shaker and Shaw, to determine which gating properties resemble those of the parent channels. Current traces and conductance-voltage relations are shown in Fig. 5 and analysis of the gating kinetics is shown in Fig. 6.

View larger version (31K): [in this window] [in a new window]   Fig. 5.   Macroscopic ionic currents and conductance-voltage curves for Shaker, Shaw S4, and Shaw. (left) Macroscopic ionic currents measured during positive steps to the voltages indicated. For Shaw S4 and Shaker, test pulses to activate the channels followed prepulses to 100 mV from a holding potential of 80 mV. For Shaw, a holding potential of 0 mV was used. (right) Normalized conductance plotted as a function of voltage. Normalized conductance-voltage curves were constructed for Shaker and Shaw S4 as outlined in Fig. 3. For Shaw, isochronal measurements of tail currents were made at 40 mV, between 0.2 and 0.3 ms after the end of the test pulse. Since the maximum probability of opening for Shaw currents was not reached in the voltage range studied, Shaw isochronal currents were normalized to the maximum current obtained at +180 mV. Data shown represent six patches for Shaw, six patches for Shaw S4, and eight patches for Shaker.

View larger version (21K): [in this window] [in a new window]   Fig. 6.   Gating kinetics for Shaker, Shaw S4, and Shaw. (left) Single exponential fits to activation time course. Macroscopic ionic currents typical of each channel type are shown in response to positive voltage steps to the voltages indicated to the right of each trace (millivolts). For Shaker and Shaw S4, the voltage steps followed prepulses to 100 mV from a holding potential of 80 mV. For Shaw, a holding potential of 0 mV was used and positive test pulses were preceded by 10-ms prepulses to 100 mV. Superimposed on the current traces during activation are fits with a single exponential function, as outlined in MATERIALS AND METHODS. For Shaw and Shaw S4, each trace was fit over most of the time course of activation, from between 1 and 5% of the maximum current to the maximum current obtained during the test pulse. For Shaker, traces were fit starting at 10-20% of the maximum current and up to the maximum current obtained during the test pulse because of large delays in Shaker opening that are not well fit by a single exponential function. (middle) Relative delay of the activation time course. Current traces measured at the voltages indicated were scaled to compare the relative delay between voltages and channel species as outlined for Fig. 4. The scale bar indicates the time it takes for a channel to activate half maximally when it activates with a single exponential time course and no delay. Arrowheads point to scaled current traces from Shaker with the smallest and largest relative delays and indicate the voltage range over which currents were scaled. (right) Time constants plotted as a function of voltage. Time constants were obtained from fits of single exponential functions to currents during channel opening and closing, as outlined in MATERIALS AND METHODS. The time course of channel closing was reasonably well fit by a single exponential function for all three channel types. The time constants for Shaker and Shaw S4 were derived from 7 patches each, while the time constants for Shaw came from 13.

The steady state voltage dependence of Shaw S4 activation is much more shallow than that of Shaker and is shifted to more positive voltages, in the direction of the conductance-voltage curve of the S4 donor Shaw, but not to such extreme voltages. Fits of a first power Boltzmann function to conductance-voltage curves from Shaw S4 and Shaker channels show that activation of Shaw S4 is shifted ~+120 mV, and the slope is decreased 2.7-fold. The S4 donor channel, Shaw, requires even more positive voltages to fully activate than Shaw S4 and has an even shallower voltage dependence (see also Wei et al., 1990; Tsunoda and Salkoff, 1995). We cannot quantify the voltage dependence of Shaw activation by fitting with a Boltzmann function because the probability of opening does not saturate within the limits of our measurements (<+200 mV). The conductance- voltage relation for Shaw is normalized to the value of the conductance at +180 mV in Fig. 5 to facilitate comparison with Shaw S4 and Shaker. The probability of opening for Shaw increases with a very shallow voltage dependence over a wide voltage range. Shaw begins to open at voltages more negative than Shaw S4, around 60 mV, and does not reach a maximum open probability until voltages well above the voltage where Shaw S4 open probability saturates. In contrast, the probability of opening for the Shaw S4 chimera, which begins to increase at voltages greater than 0 mV and saturates around +180 mV, has a steeper voltage dependence than Shaw.

In Fig. 6 (left), currents recorded in response to positive voltage steps are shown for each channel species. Superimposed on the current traces are fits by a single exponential function as outlined in MATERIALS AND METHODS. Note the different time scales, which were selected to enable comparison of the relative amounts of delay at the beginning of the activation time course for each of the three channel species. It is clear from these fits that Shaw S4 and Shaw currents follow a single exponential time course to activate with little or no delay. This can be seen more clearly for a wide range of voltages by scaling the currents to compare the delay in activation relative to the overall time course of activation (Fig. 6, middle). The lack of delay in the activation time course of Shaw and Shaw S4 suggests that the activation kinetics are dominated by a single rate-limiting transition over a wide range of voltages. In contrast, Shaker requires the addition of 1-4-ms delays for adequate fit to the activation time course. Previous work on Shaker has indicated that this large sigmoidal delay is the result of multiple voltage-dependent transitions, each moving relatively small amounts of charge of similar magnitude (Sigworth, 1993; Hoshi et al., 1994; Zagotta et al., 1994a; Bezanilla et al., 1994). A kinetic model for Shaw has not yet been developed.

Time constants obtained from fits to the activation time course similar to those shown in the Fig. 6 (left), from several patches with the Shaw S4 chimera and its parent channels, are plotted in Fig. 6 (right). Also plotted are time constants from single exponential fits to tail currents at negative membrane potentials. Tail currents measured during closing of all three channels are reasonably well fit by a single exponential function. Shaw S4 opens and closes much more slowly than either Shaw or Shaker. The kinetics of Shaw S4 are strongly voltage dependent, as are those of Shaker. The voltage range over which the kinetics of Shaw S4 change most dramatically is shifted to more positive voltages compared with Shaker and is shifted to the same extent as the probability of channel opening. In contrast to both Shaker and Shaw S4, the opening and closing kinetics of Shaw exhibit a very shallow voltage dependence over a wide range of voltages, encompassing 360 mV. Thus, while the activation time course for both Shaw and Shaw S4 is dominated by a single, rate-limiting transition, for Shaw S4 this transition is strongly voltage dependent while for Shaw it is nearly voltage independent. This difference in voltage dependence suggests that the rate-limiting conformational changes in the activation of Shaw and Shaw S4 may be different.

Differences between Shaw S4 and the parent channels can also be seen at the single channel level (Fig. 7). The first latencies of Shaw S4 are substantially longer than the first latencies of Shaker and Shaw, consistent with altering transitions in the activation pathway (data not shown). However, once the channel opens, the Shaw S4 single channel events much more closely resemble the behavior of Shaker than Shaw in their kinetics and single channel conductance (Fig. 7). The single channel conductance for Shaw S4 of 9.5 pS (n = 18) is the same as the 9-10 pS conductance of Shaker (Hoshi et al., 1994), and much smaller than the 23.3 pS (n = 3) single channel conductance of Shaw (see also Tsunoda and Salkoff, 1995).

View larger version (32K): [in this window] [in a new window]   Fig. 7.   Single channel openings recorded from Shaker, Shaw, and Shaw S4 during voltage steps to the indicated voltages. Shaw and Shaw S4 records were filtered at 2 kHz. Shaker recordings were taken from Hoshi et al. (1994; see Fig. 1) with filtering ranging from 0.5 kHz at 50 mV to 1.2 kHz at 0 mV. Shaker and Shaw S4 currents were recorded from excised inside-out patches while Shaw currents were recorded from a cell-attached patch. The oocyte used for the cell-attached patch was bathed in the standard intracellular solution with a high concentration of potassium, depolarizing the resting potential to near 0 mV. A holding potential of 80 mV was used in all cases. The patch with Shaw contained at least two channels, the patch with Shaker contained one channel, and the patch with Shaw S4 contained two channels. The intracellular solutions for Shaker and Shaw S4 contained 2 mM MgCl2.

The rate of inactivation of Shaw S4 ionic currents (1.57 ± 0.28 s [SEM] at +50 mV, n = 5) closely resembles the 1.5-s C-type inactivation rate of Shaker (Hoshi et al., 1991). In contrast, there is no detectable inactivation in the macroscopic ionic currents of Shaw during positive voltage steps lasting 20-30 s (data not shown; see also Wei et al., 1990; Tsunoda and Salkoff, 1995). These results are consistent with the Shaw S4 substitution primarily altering conformational changes in the activation pathway and not introducing global changes that perturb other channel functions.

Alteration of Cooperative Gating by Shaw S4 Substitution

The slower gating kinetics and decreased sigmoidicity suggest that the Shaw S4 mutations alter activation gating fairly specifically, slowing a highly cooperative transition in the activation pathway sufficiently to make it rate limiting. Since introducing the S4 of Shaw into all four subunits of Shaker changes the activation time course from sigmoid to single exponential, the rate-limiting transition in Shaw S4 cannot be due to the slowing of independent transitions in each subunit. This suggests that the single rate-limiting transition in Shaw S4 is a highly cooperative transition in the activation pathway. The simplified model for Shaker gating is illustrative (Fig. 4). While slowing the independent transitions slows channel gating, the time course of channel opening maintains considerable sigmoidicity, a characteristic clearly different from the single exponential time course of Shaw S4 activation. However, we can simulate currents with properties similar to Shaw S4 simply by slowing the forward rate of the final cooperative transition in the activation pathway (Fig. 4, bottom). Decreasing only the rate constant, , with no other changes, leads to slowing of activation kinetics, a positive shift in the voltage range of activation, a decrease in the slope of the conductance-voltage curve, and activation kinetics with a single exponential time course over the entire voltage range of activation. These are all characteristic of Shaw S4 macroscopic currents.

Although we used the six-state model for our predictions, as discussed previously, it does not fully account for the large delay in the activation time course of Shaker or the large amount of charge associated with activation gating. We used the six-state model to interpret the results of the S4 substitutions because it is the simplest model possible that will describe several key features of activation gating in Shaker. Therefore, conclusions from this model are fairly general and are not obscured by complexities introduced by models with many more transitions. However, more complex models are necessary to fit quantitatively the wild-type and mutant kinetics. For example, simply decreasing the forward rate constant of the cooperative transition in the six-state model predicts many of the functional changes observed with Shaw S4, but it does not predict the maximum probability of opening observed in the single channel records. However, as seen in the next paper (Smith-Maxwell et al., 1998), modifications to the final closing step in the more complete model for Shaker (Zagotta et al., 1994a) can quantitatively account for Shaw S4 kinetics. Therefore, our conclusion that a late cooperative step is altered in Shaw S4 is valid both for a simple model that incorporates the key features of Shaker gating and a more complex model that quantitatively fits Shaker activation.

Shaw S4 and Shaker Tandem Dimers

The change to slow, single exponential kinetics upon substituting the S4 of Shaw for the S4 of Shaker indicates that a single transition in the activation pathway has become rate limiting. Since we can assume from studies with the Shaker channel (MacKinnon, 1991; Heginbotham and MacKinnon, 1992; Kavanaugh et al., 1992; Liman et al., 1992) that the Shaw S4 chimera assembles into a tetramer with four identical subunits, the rate-limiting transition in Shaw S4 activation most likely arises from highly cooperative interactions between subunits. To test further the hypothesis that the Shaw S4 mutation slows a cooperative transition, we constructed tandem heterodimers containing the slowly activating Shaw S4 subunit and the rapidly activating Shaker subunit in either position of the dimer (A_kB_w and A_wB_k) along with homodimers containing either two Shaker subunits (A_kB_k) or two Shaw S4 subunits (A_wB_w) (see Tytgat and Hess, 1992; McCormack et al., 1992; Heginbotham and MacKinnon, 1992; Ogielska et al., 1995). Macroscopic currents and normalized conductance-voltage curves from the dimer constructs are shown in Fig. 8, along with predictions for the independent or cooperative movement of subunits. Values from fits of Boltzmann functions to data from the dimer constructs are given in Table II. Macroscopic currents recorded from channels assembled from the homodimer constructs, A_wB_w and A_kB_k, activate with properties that are indistinguishab