Changes in the Inactivation of Rat Kv1.4 K 1 Channels Induced by Varying the Number of Inactivation Particles*

N-type inactivation of rat Kv1.4 channels with one, two, or four inactivation balls was investigated using homogeneous populations of channels expressed in Xenopus oocytes. Tandem dimeric and tetrameric constructs of Kv1.4 were made. Channels encoded by tandem cDNAs Kv1.4-Kv1.4 D 1–145 and Kv1.4-[Kv1.4 D 1–145] 3 have two or only one tethered inactivation ball, respec-tively, whereas Kv1.4 itself encodes channels having four inactivation balls. The time constants for inactivation of macroscopic currents were increased significantly as the number of inactivation balls was decreased, whereas the time constants for recovery from inactivation were not modified. The ratios of the rate constants of inactivation ( k inact ) of Kv1.4-Kv1.4 D 1–145 and Kv1.4-[Kv1.4 D 1–145] 3 channels to that of the Kv1.4 channel were 0.65 and 0.4, respectively, whereas the ratios of the rate constant of recovery ( k rec ) of these channels to that of Kv1.4 were almost unity. The rate constants k inact for channels having two and four inac- tivation balls are smaller than those that would be expected if inactivation balls on each channel are Tetrameric cDNA Construction— tandem tetrameric cDNA of Kv1.4 was constructed using Kv1.4-Kv1.4 D dimeric cDNAs linked by nucleotides recognized by Spl I. and ends partial tandem dimers were altered by for I site. using oligonucleotide EII site and antisense oligonucleotide into end

N-type inactivation of rat Kv1.4 channels with one, two, or four inactivation balls was investigated using homogeneous populations of channels expressed in Xenopus oocytes. Tandem dimeric and tetrameric constructs of Kv1.4 were made. Channels encoded by tandem cDNAs Kv1.4-Kv1.4⌬1-145 and Kv1.4-[Kv1.4⌬1-145] 3 have two or only one tethered inactivation ball, respectively, whereas Kv1.4 itself encodes channels having four inactivation balls. The time constants for inactivation of macroscopic currents were increased significantly as the number of inactivation balls was decreased, whereas the time constants for recovery from inactivation were not modified. The ratios of the rate constants of inactivation (k inact ) of Kv1.4-Kv1.4⌬1-145 and Kv1.4-[Kv1.4⌬1-145] 3 channels to that of the Kv1.4 channel were 0.65 and 0.4, respectively, whereas the ratios of the rate constant of recovery (k rec ) of these channels to that of Kv1.4 were almost unity. The rate constants k inact for channels having two and four inactivation balls are smaller than those that would be expected if inactivation balls on each channel are independent, suggesting some interaction occurs between inactivation balls. Furthermore, noninactivating current became apparent as the number of inactivation balls on a channel was decreased.
Isolation of the clone encoding the Shaker K ϩ channel from Drosophila has made it possible to examine the molecular mechanism of N-type inactivation of A-type K ϩ channels. The Shaker K ϩ channel provided the first example of "ball and chain"-type inactivation, which was originally proposed for voltage-dependent Na ϩ channels (1). The mechanisms of fast inactivation observed in mammalian homologues of Shaker K ϩ channels have been proved to be the same as that of Shaker K ϩ channels (2)(3)(4)(5). K ϩ channels are composed of four ␣-subunits (6 -12), each of which is encoded by a K ϩ channel gene. Functional K ϩ channels are also formed by the assembly of different ␣ subunits encoded by different genes within the same K ϩ channel subfamily (13)(14)(15)(16)(17)(18)(19).
In a previous study (20), we made dimeric cDNA by tandem linkage of the rapidly inactivating K ϩ channel clone Kv1.4 and the noninactivating K ϩ channel clone Kv1.2 isolated from rat heart. The dimeric cDNA encodes a hybrid channel that is composed of Kv1.4 and Kv1.2 subunits with 1:1 stoichiometry. In the hybrid channel there are two inactivation balls tethered to Kv1.4 subunits. This approach revealed that in the hybrid channel inactivation is determined not only by inactivation balls but also by the composition of the pore-forming ␣-subunits, of which intracellular loops form the receptor sites for inactivation balls. It is, however, inappropriate to use hybrid channels to examine the relationship between inactivation kinetics and the number of inactivation balls, because the heterogeneity of the receptors for inactivation balls has, in itself, a certain effect on inactivation kinetics.
In this study we investigated how inactivation kinetics are regulated by inactivation balls in rat Kv1.4 channels. For this purpose we made tandem dimeric and tetrameric cDNAs from a Kv1.4 clone, and homogeneous populations of K ϩ channels with one, two, or four inactivation balls were expressed in Xenopus oocytes. The ratio of the inactivation rate constant of the channel with one or two inactivation balls to the Kv1.4 channel with four balls was larger than expected. This suggests that in rat Kv1.4 channels some interaction may exist between inactivation balls although previous studies in Shaker K ϩ channels have suggested that inactivation balls are independent (21,22).
Tetrameric cDNA Construction-The tandem tetrameric cDNA of Kv1.4 was constructed using Kv1.4-Kv1.4⌬1-145. Two dimeric cDNAs were linked by six nucleotides recognized by SplI. 5Ј and 3Ј ends of partial tandem dimers were altered by PCR for introduction of the SplI site. PCR was performed using a sense oligonucleotide containing the BstEII site and an antisense oligonucleotide containing SplI and EcoRI sites and the last 21 nucleotides. The PCR product was ligated into a partial dimeric cDNA in pBluescript digested with BstEII and EcoRI (3Ј end modified partial dimeric cDNA). A fragment was amplified by PCR with a sense primer containing HindIII and SplI sites, and 21 nucleotides from 436G and an antisense primer containing the MluI site in Kv1.4. The amplified fragment was ligated into the corresponding site in a partial dimeric cDNA following digestion with HindIII and MluI (5Ј end modified partial dimeric cDNA). Both 3Ј and 5Ј end modified partial dimeric cDNAs were digested by SplI and NotI and ligated into the complete tandem tetrameric constructs.
Expression of Dimeric and Tetrameric Constructs and Current Recording-The pBluescript vectors containing the dimeric or tetrameric constructs were linearized with EcoRI, and cRNAs were prepared from these templates with T7 RNA polymerase using MEGAscript RNA synthesis kit (Ambion, Austin, TX). Procedures for preparation of Xenopus oocytes and injection of the synthesized cRNAs were the same as those described previously (20). The K ϩ currents were recorded by conventional two-microelectrode voltage clamp with 3 M KCl filled electrodes. The bath recording solution consisted of ND 96 (mM): NaCl, 96; KCl, 2; CaCl 2 , 1.8; MgCl 2 , 1; Hepes, 5; pH 7.5 adjusted with NaOH. All electrophysiological measurements were carried out at room temperature (21 Ϯ 1°C).
Data Analysis-Statistical analysis of the data was performed with analysis of variance and significance isolated by Dunnett's test. Values in the text, figures, and tables are given as means Ϯ S.E.

RESULTS
The schematic diagrams of the polypeptides encoded by tandem dimeric and tetrameric Kv1.4 cDNAs are shown in Fig. 1A. Polypeptide (Kv1.4-Kv1.4) encoded by the full tandem dimeric cDNA has amino acid sequence corresponding to ball and chain region in the second (3Ј site) subunit as well as in the first subunit. On the other hand, polypeptide (Kv1.4-Kv1.4⌬1-145) from the partial tandem dimeric cDNA lacks amino acid sequence corresponding to ball and chain region in the second subunit. Channels formed by the partial tandem polypeptide of Kv1.4 have two tethered inactivation balls, whereas the full tandem dimeric cDNA encodes channels with two tethered inactivation balls and two positioned in the loops connecting the subunits (Fig. 1B, b and c). Because the polypeptide encoded by the tandem tetrameric cDNA lacks amino acid sequences preceding the assembly domain in each subunit except the first one, there is only one inactivation ball per channel (Fig. 1B, d).
The currents observed when cRNAs of the tandem dimeric and tetrameric constructs were injected into the oocytes showed similar characteristics to Kv1.4 (Fig. 2, B-E 3 were about 3, 6, 9, and 18% of the peak currents, respectively.
Time courses of recovery from inactivation for the channels are shown in Fig. 4. Recovery from inactivation was significantly faster in the hybrid channel than in Kv1.4 channels. There were no differences in the time constants for recovery between Kv1.4 channels with different numbers of inactivation balls. Time constants for recovery from inactivation rec of the channels tested are presented in Table I.
To gain a more precise insight into the inactivation process, we estimated the microscopic rate constants of inactivation (k inact ) and recovery from inactivation (k rec ) for individual channels as described previously (20). We calculated the values of k inact only from the oocytes in which both the time constants for inactivation and recovery from inactivation were measured (Table II). The ratio of k inact for Kv1.4-Kv1.4⌬1-145 to Kv1.4 is 0.65. This indicates that the microscopic inactivation rate constant of the channel with two inactivation balls is more than half that of Kv1.4 channel with four inactivation balls. Furthermore, the ratio of k inact for Kv1.4-[Kv1.4⌬1-145] 3 to Kv1.4 is 0.4, indicating that the microscopic inactivation rate constant of the channel with only one inactivation ball is larger than one-fourth that of Kv1.4 channel. The k inact value of the Kv1.4-Kv1.4 channel was smaller than that of the Kv1.4 channel, although both types of channels have the same number of inactivation balls. When the values of k inact were compared between Kv1.4-Kv1.4⌬1-145 and Kv1.4-Kv1.2 channels, it became evident that k inact for the Kv1.4-Kv1.4⌬1-145 channel is smaller than that of the hybrid channel. This could be attributed to the difference in the composition and the structure of the receptor sites for inactivation balls, because Kv1.4-Kv1.4⌬1-145 and the hybrid channels have the same number of inactivation balls.
To further characterize the properties of the channels encoded by the dimeric and tetrameric cDNAs, the steady-state voltage dependence of their activation and inactivation was studied. The average values of the parameters are summarized in Table III Table I.

TABLE I Time constants for inactivation and recovery from inactivation of macroscopic currents
Inactivation time constants ( inac ) were measured from exponential fits to the onset of inactivation of currents recorded from oocytes injected with the indicated cRNAs. All of the currents were best fitted by a single exponential. Time constants of recovery from inactivation ( rec ) were calculated by fitting curves of fractional recovery (means Ϯ S.E.). The numbers given in parentheses represent oocytes tested. Differences between channels were analyzed by variance, and the statistical significance was isolated using Dunnett's test. in the N terminus of the polypeptide as in the Shaker K ϩ channel (2,5). The ball binds to its receptor via electrostatic and hydrophobic interactions. As polypeptides of the principle subunit of voltage-gated K ϩ channels form tetramers (6 -9), it is evident that Kv1.4 has four inactivation balls on each channel when expressed alone. Relationship between inactivation balls and rate of inactivation has been examined using Shaker B channel. To investigate the relationship, MacKinnon et al. (21) studied channels carrying a specific mutation in a single subunit quantitatively by monitoring scorpion toxin sensitivity. On the other hand, Gomez-Lagunus and Armstrong (22) used the approach of gradually removing inactivation with intracellular papain. However, these analytical procedures were based on the assumption that co-assembly of wild-type and mutated subunits or the predicted fraction of channels with various numbers of inactivation balls after protease treatment obeys the rules of a binomial distribution. In this study we have investigated the role of inactivation balls in the rate of inactivation by use of a different strategy than these reports. This approach seems to have the advantage that interpretation of the results does not need any assumptions about subunit stoichiometry. To constrain the number of inactivation balls in the expressed channels, dimeric and tetrameric cDNAs were constructed from rat cDNA clone Kv1.4, which encode two or four Kv1.4 subunits on a single polypeptide chain (Fig. 1A). It has been demonstrated that two polypeptides encoded by the dimeric cDNA construct can assemble to form functional channels with tetrameric structure (7,11,18,24,25). For K ϩ channels, tetrameric cDNA constructs also encode functional channels resembling, in their electrophysiological properties, those expressed from monomers (7,11,24). Therefore, it is probable that the channels have two or only one inactivation ball when the partial tandem dimeric or tetrameric cDNAs of Kv1.4 are expressed in Xenopus oocytes.
The voltage dependence of activation and inactivation of the channels with different numbers of inactivation balls is similar, suggesting that alterations in inactivation should be attributed to the difference in the number of inactivation balls. We have demonstrated directly that the channels that have only one ball can inactivate, which is consistent with the results with Shaker K ϩ channels described by MacKinnon et al. (21). However, inactivation of the current from the channel with only one ball was incomplete in our experimental conditions, compared with the channel with four balls. Increases in the noninactivating currents may be due to less frequent occlusion of the pore by a smaller number of particles. Transitions between open and closed states before entering the inactivated state might be another possibility.
The ratios of the inactivation rate constants from the channel with one and two balls were larger than one-fourth and one-half that of the channel with four balls, respectively. MacKinnon et al. (21) described that in Shaker K ϩ channels the rate constant for the channel with a single gate was one-fourth that of channels with four gates and suggested independence of each inactivation gate. We considered the following possibilities that might account for the difference. First, there may be some interaction between inactivation balls: electrostatic repulsion between balls due to positive charges on their surfaces could decrease access of inactivation balls to their receptor sites when a channel has more than a single ball. Second, slow recovery of Kv1.4 may result in larger rate constants than expected for the channels with one and two inactivation balls. Recovery from inactivation of Kv1.4 is much slower than that of the Shaker K ϩ channel. Kv1.4 has more positive charges than the Shaker K ϩ channel in its ball structure, which could result in a higher affinity of the inactivation ball for its receptor. There is also another possibility that might arise from the experimental strategy. Structural changes induced by linkage of the subunits in a single polypeptide chain might alter accessibility of inactivation balls to their receptor sites.
The channels that have two tethered balls and two in the connecting loop showed an inactivation rate constant that was intermediate between channels with four tethered balls and those with two balls. This indicates that the ball structure positioned in the loop also functions as an inactivation gate, but FIG. 4. Time courses of recovery from inactivation. Recovery from inactivation was determined by recording currents using the twomicroelectrode voltage-clamp method. A control 400-ms depolarization from a holding potential of Ϫ80 mV to ϩ20 mV was given. Each control pulse was followed by a second identical depolarization after an interval of increasing duration from 0.3 to 30 s at Ϫ80 mV. The peak amplitude of the current evoked by the second depolarization was expressed as a fraction of the values obtained by the control depolarization. Fractional recovery was plotted as a function of the interpulse interval. Data points are means Ϯ S.E. and were fitted by a single exponential. Time constants of recovery from inactivation for each channel are presented in Table I

TABLE II
Rate constants of inactivation and recovery from inactivation of the expressed channels Rate constants of inactivation (k inact ) and recovery (k rec ) were calculated using equations inact ϭ (k inact ϩ k rec ) Ϫ1 and rec ϭ k rec Ϫ1 derived from the simple reaction rate model described previously (20). Values are means Ϯ S.E., with the number of oocytes tested given in the parentheses. Differences in the rate constants were analyzed as in Table I its access to the receptor was decreased due to restricted movement.
In this study we have isolated the current of Kv1.4 channel with a single or two inactivation balls for the first time by expressing homogeneous populations of channels in Xenopus oocytes. It was demonstrated that rat Kv1.4 channel could inactivate even with only a single inactivation ball, although inactivation was not complete. The calculated microscopic rate constants for inactivation of the channels with a single and two inactivation balls were larger than would be expected if inactivation balls were independent, suggesting the possibility of some interaction between inactivation balls. Single channel analysis will provide unequivocal estimation of differences in microscopic rate constants of inactivation and the mechanism underlying the noninactivating fraction of the currents.

TABLE III
Parameters of voltage-dependent activation and inactivation for the expressed channels Parameters of steady-state activation and inactivation were fitted by a Boltzmann distribution. V a and V h are half-activation and -inactivation voltages, respectively; a n and a h are slope factors for activation and inactivation, respectively; ␣ is the noninactivating component. The values given are mean Ϯ S.E. The number of oocytes tested is given in the parentheses. Differences of the values between channels were analyzed as in Table  I