INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

L-type calcium channels inactivate most rapidly through a mechanism driven by an elevation of intracellular Ca²⁺ within a few hundred angstroms of the channel pore. Such "Ca²⁺-dependent inactivation" (Brehm and Eckert, 1978) provides vital Ca²⁺ negative feedback in numerous settings, including the normal regulation of the cardiac action potential (Linz and Meyer, 1998), along with its abnormal prolongation in heart disease (O'Rourke et al., 1999; Winslow et al., 1999). As such, Ca²⁺ inactivation of these channels has been an intense focus of research spanning more than two decades.

Over the past four years there has been rapid progress toward understanding the molecular basis for such inactivation. We showed that critical determinants of Ca²⁺ inactivation were localized to the proximal third of the carboxyl terminus of the main _1C subunit of L-type channels (de Leon et al., 1995), referred to as the Ca²⁺ inactivation, or "CI" region (Peterson et al., 1999). The main supporting evidence was that deletion of the distal two-thirds of the _1C carboxyl tail spared Ca²⁺ inactivation; replacement of the _1C CI region by the homologous region of a non-inactivating _1E calcium channel (Soong et al., 1993) abolished Ca²⁺ inactivation; and donation of the _1C CI region to the _1E backbone conferred Ca²⁺ inactivation to the non-inactivating background (de Leon et al., 1995). In addition, substituting just 53 amino acids near the beginning of the _1C CI region with the homologous sequence from _1E eliminated Ca²⁺ inactivation. This short stretch of _1C contained a consensus Ca²⁺-binding motif (EF hand) (Babitch, 1990), leading us to suggest that this domain contained a Ca²⁺ sensor for Ca²⁺ inactivation.

Subsequent work has confirmed and extended the evidence that the _1C CI region figures critically in L-type channel inactivation by Ca²⁺. By using similar chimeric channel analysis between _1C and _1E, Zhou et al. (1997) confirmed the importance of the _1C CI region, as substitution of the entire _1C CI region into _1E conferred Ca²⁺ inactivation, while replacing proximal portions from the _1C CI region failed to confer the inactivating phenotype. More recently, Soldatov et al. (1998) found that Ca²⁺ inactivation was eliminated by simultaneous mutation of two stretches within the _1C CI region (IKTEG and LLDQV), residing just downstream of the consensus EF hand by 51 and 79 residues. Finally, Zuhlke and Reuter (1998) used systematic deletions within the _1C carboxyl tail to identify two additional sites within the CI region that are essential for Ca²⁺ inactivation. Of these two groups of amino acids, NE and IQEYFRKF (61 and 103 residues downstream of the consensus EF hand, respectively), the latter was notable, because it approximates the consensus pattern for an IQ calmodulin-binding motif (IQxxxRG) (Rhoads and Friedberg, 1997). This finding raised the possibility that calmodulin might play a role in Ca²⁺ inactivation.

In the past year, we (Peterson et al., 1999) and others (Qin et al., 1999; Zuhlke et al., 1999) have demonstrated that calmodulin (CaM) is indeed the dominant Ca²⁺ sensor for Ca²⁺ inactivation of L-type channels. CaM appears to be constitutively tethered to the channel like an integral subunit, and further Ca²⁺-dependent binding of tethered CaM to the IQ-like motif is an essential step for channel inactivation (Peterson et al., 1999; Zuhlke et al., 1999; Qin et al., 1999). Given the primacy of CaM as Ca²⁺ sensor, and of the IQ-like domain as CaM binding site, what role do the other critical sites on _1C play in the inactivation process?

This question is particularly relevant to the consensus EF hand, because the importance of this motif for Ca²⁺ inactivation has become controversial. Although we and others found that either exchanging the EF-hand segment from _1C with a homologous sequence from _1E (de Leon et al., 1995), or deleting the EF-hand segment from _1C altogether (Zuhlke et al., 1999) abolished Ca²⁺ inactivation, Zhou et al. (1997) could not confirm these findings. The latter group also found that substitution of only the distal two-thirds of the _1C CI region (not including the EF-hand motif) into _1E was sufficient to impart Ca²⁺ inactivation. Furthermore, mutation of residues presumed to coordinate Ca²⁺ within an EF hand failed to reduce (Zhou et al., 1997), or only partially blunted, Ca²⁺ inactivation (Bernatchez et al., 1998). These results call into question the importance of the consensus EF hand.

In this study we have therefore undertaken systematic mutagenesis of _1C channels, where small segments of the _1C EF-hand motif have been changed to their _1E correlates in two to four residue clusters. Not only do we confirm that the consensus EF-hand motif is essential for Ca²⁺ inactivation, we also identify a four-amino acid cluster (VVTL) within the F helix of the consensus EF hand that is itself essential for inactivation. Changing these residues to their _1E analogs (MYEM) almost completely eliminates Ca²⁺ inactivation, and point mutation of only the second residue in the cluster (V1548Y) mimics much of this effect. However, mutations of presumed Ca²⁺-coordinating residues in the EF-hand motif reduce Ca²⁺ inactivation by only ~2 fold, fitting poorly with the EF hand serving as a contributory inactivation Ca²⁺ sensor, in which Ca²⁺ binds according to a classic mechanism. We therefore suggest that, rather than serve as Ca²⁺ sensor for inactivation, the consensus EF hand may be essential to the transduction of CaM binding into inactivation. A novel inactivation model, incorporating multivalent Ca²⁺ binding of CaM, is used to evaluate the feasibility of the proposed transduction role for the EF-hand domain.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Site-directed mutagenesis

The segment of _1C cDNA (Wei et al., 1991) encoding the consensus EF-hand motif is flanked by recognition sequences for the restriction enzymes EcoRV at position 4566 and SfuI at position 5191. The SfuI recognition sequence was engineered by silent mutagenesis; 626-basepair DNA fragments containing mutations within the consensus EF-hand motif were generated by polymerase chain reaction (PCR) using mutagenic primers and the overlap extension strategy (Ho et al., 1989), and were subcloned into the shuttle vector, PCRSCRIPT (Strategene, La Jolla, CA). Pfu polymerase was used throughout. These plasmids were digested and the resulting EcoRV-SfuI fragments were gel-purified (GeneClean, Bio 101, Vista, CA) and subcloned into EcoRV-SfuI-digested _1C/pcDNA3. The integrity of all of the wild-type and mutant constructs used in this study was confirmed by qualitative restriction digests and sequence analysis. In particular, the _1CE-3 channel constructed previously (de Leon et al., 1995) was re-sequenced across the entire C-tail region subject to PCR.

Rationale for point mutations in the consensus EF-hand

In EF hands, Ca²⁺ is typically coordinated by six amino acids in the binding loop, with stereotypic coordinates as diagrammed at the top of Fig. 1 (x, y, z, y, x, and z). To test whether the consensus EF hand in _1C binds Ca²⁺ according to a mechanism demonstrated by classic EF hands, we made individual point mutations at amino acids at the presumably crucial coordinating locations (x, y, z, and z), as such point mutations reduce the Ca²⁺ affinity of classic EF hands by 10-1000-fold (Linse and Forsen, 1995). Hence, our expectation was that, if Ca²⁺ binding to the consensus EF hand triggers channel inactivation, then point mutations at these coordinates should severely attenuate Ca²⁺ inactivation. The rationale for the choice of mutations was as follows. In the mutant channel D1535A, we substituted an alanine for the aspartate residue at position 1535 (x), which is conserved in all EF-hand proteins and high-threshold calcium channels. In the mutants E1537A and K1539C, we altered residues that correspond to coordinates y and z of the consensus EF hand from their identities in _1C to those in _1E. The most impressive effects were expected of mutant D1546A, in which alanine was substituted for aspartate 1546, corresponding to the z coordinate, which contributes two Ca²⁺-interaction ligands in classic EF hands. The alanine substitutions in mutants D1535A and D1546A would be most likely to attenuate Ca²⁺ binding without disrupting the overall secondary structure of this segment. The residues corresponding to y and x coordinates were not altered, because carbonyl oxygen on the peptide backbone interacts with Ca²⁺ at the y coordinate, and the side chain corresponding to x coordinate complexes with Ca²⁺ indirectly via a water molecule (Falke et al., 1994). Consequently, the amino acid residues at these positions are highly variable in EF-hand proteins. Furthermore, arginine 1541 (y) is conserved between _1C and _1E, and could not have contributed to the reduction of Ca²⁺ inactivation seen with the chimera _1CE-3. The results of the mutations described above are summarized in Fig. 2. The effect of lysine 1543 (x) was assessed within the context of the cluster mutation KHL  HYT in Fig. 3.

View larger version (39K): [in this window] [in a new window]   FIGURE 1   An EF-hand-containing segment in the carboxyl terminus of 1C contains determinants that are critical for Ca2+-dependent inactivation. Top: putative transmembrane folding model for the main subunit (1C) of the L-type calcium channel. When a 53-amino acid segment in the carboxyl terminus (hatched box, amino acids 1510-1562 in 1C) is replaced by the analogous segment from 1E, the resulting chimera (1CE-3) lacks Ca2+-dependent inactivation. The primary sequences of 1C and 1E that correspond to this segment are aligned in the expanded view, below. A consensus EF-hand is identified using the Tufty-Kretsinger scoring method as indicated above the alignment where "n" denotes a hydrophobic amino acid, and amino acids that coordinate the Ca2+ ion are designated x, y, z, y, x, and z. The E and F helices of the EF-hand are identified using shaded boxes. An IQ-like domain (IQ), situated downstream of the consensus EF hand is also a crucial element in Ca2+ inactivation. Ca2+-dependent calmodulin binding to this element is an essential step in channel inactivation. (A-D) Inactivation properties of whole-cell current from cells overexpressing wild-type 1C (A, B) or chimeric 1CE-3 (C, D) subunits, which illustrate the robustness of Ca2+-dependent inactivation in wild-type channels and the loss of such inactivation in the chimeric channels. Only the 2a subunit was coexpressed with 1 in panels A and C. Both 2a and 2 were coexpressed in panels B and D. The format of all panels is as follows. Left: exemplar Ba2+ (black) and Ca2+ (gray, dashed) currents elicited by depolarizing steps to the indicated potentials. Here and throughout the figures, Ca2+ has been scaled upward ~3× to facilitate comparison of kinetics, and tail currents have been clipped for display clarity. Right: fraction of current remaining at the end of 300-ms depolarizations (r300) is plotted as a function of depolarizing potentials, with Ba2+ (closed circles) or Ca2+ (open circles) as the charge carrier. f is the difference between Ba2+ and Ca2+ r300 values at 10 mV, diagrammed in A. This parameter, which functions as a concise measure of the strength of Ca2+-dependent inactivation, is reported at the bottom of r300 graphs in B and D. Here, and in all the figures, r300 and f data are displayed as mean ± SEM and averaged from the number of cells indicated in parentheses. Statistically significant reductions in Ca2+ inactivationcompared to wild-type channels (panel B), as characterized by reduced values of f, are denoted by the symbols ** (p < 0.001) and * (p < 0.01). For example, the reduction in Ca2+ inactivation between panels B and D is statistically distinguished by the decreased in the mean f parameter, with significance at p < 0.001. The f value in panel A was 0.38 ± 0.04 (n = 11), and the f value in panel C was 0.03 ± 0.02 (n = 15, which is reduced significantly compared with panel A, p < 0.001). Population means in A and B include new data, supplemented with 6 and 5 cells, respectively, that were originally used in de Leon et al. (1995).

View larger version (25K): [in this window] [in a new window]   FIGURE 2   Alteration of residues thought to bind Ca2+ have modest effects on Ca2+-dependent inactivation. Residues corresponding to the x, y, z, and z positions of the consensus EF-hand were individually altered giving rise to the mutant channels D1535A, E1537A, K1539C, and D1546A, respectively. Left: exemplar Ba2+ (black) and Ca2+ (gray, dashed) currents elicited by depolarizing steps to 0 mV. Right: r300 plots following the same format as in Fig. 1.

View larger version (33K): [in this window] [in a new window]   FIGURE 3   Localization of residues within the consensus EF-hand that are critical for Ca2+-dependent inactivation. Top: the primary sequence of 1C (amino acids 1510-1562) is shown with the E and F helices marked by shaded boxes. For each of the six mutant channels presented in this figure, from 2 to 4 amino acid residues were changed to their 1E counterparts, as indicated beneath the primary sequence. Bottom: for each of the mutant channels, r300 plots appear below exemplar Ba2+ (black) and Ca2+ (gray, dashed) currents that were elicited by depolarizations to 0 mV. The format of exemplar currents and r300 summaries is identical to those in Fig. 1.

Electrophysiology

Whole-cell patch clamp recordings were acquired as described previously (Peterson et al., 1999). Briefly, complementary DNAs encoding wild-type or mutant _1C calcium channel subunits were cotransfected with _2a (Perez-Reyes et al., 1992) and ₂ (Tomlinson et al., 1993) in HEK 293 cells by calcium phosphate precipitation, and whole-cell currents were recorded at room temperature 2-3 days after transfection. Bath solution contained (in mM): 130 NMG-aspartate; 1 MgCl₂; 10 glucose; 10 4-aminopyridine; 10 HEPES (pH 7.4); and 10 CaCl₂ or 10 BaCl₂. Internal solution contained (in mM): 140 NMG-MeSO₃; 5 EGTA; 1 MgCl₂; 4 MgATP; and 10 HEPES (pH 7.3). Currents were low-pass filtered at 2 kHz, and digitally sampled at 10 kHz. Series resistance was typically <6 M and was compensated by 70%. Repetition intervals were 30 s, holding potential (V_H) was 90 mV, and leak and capacitive transients were subtracted by a P/8 protocol.

Mathematical modeling

Simulations in Fig. 6 were performed with MATLAB (MathWorks, Natick, MA), using the matrix exponential function (expm) to produce waveforms. Using least-squared error criteria, the simplex algorithm (fmins) was used to optimize fits to the I_norm-V relation between 50 and +40 mV, as well as to the I_norm current waveforms at 30, 0, and +30 mV. All parameters were allowed to vary in the fit to the wild-type channel data in Fig. 6 B. The fit for V1548Y (Fig. 6 C) was subsequently obtained by holding fixed all rate constants, except those at the final opening step (C₂  O₃) and transduction step (B₄  I₅). Rate constants for the latter two transitions were then optimized with the simplex algorithm. The change in the C2  O3 rate constants was primarily necessitated by a leftward shift in the voltage required for half-activation of the V1548Y channel. Details of the model parameters are given in Table 1.

The experimental data that were fitted represent average channel behavior, processed so as to "isolate" the effects of Ca²⁺-dependent inactivation from those of voltage-dependent inactivation. In each cell, Ca²⁺-current waveforms elicited by 300-ms depolarizations were normalized to peak current elicited by voltage steps to +10 mV. These normalized currents were averaged across cells. To eliminate the small contribution of contaminating voltage-dependent inactivation upon these averages, an analogous averaging procedure was performed on Ba²⁺ currents. For each step potential, the average of normalized Ba²⁺ current was then used as a template to generate a smooth fit (exponential and offset) through the slowly decaying portion of the waveform. The smooth fit was then scaled in amplitude to have a value of unity at the time when the corresponding average of normalized Ca²⁺ currents reached a peak. To obtain an I_norm waveform that reflects "pure" Ca²⁺-dependent inactivation, the average of normalized Ca²⁺ currents was then divided through by the scaled fit, which reflects the influence of voltage-dependent inactivation. Such I_norm waveforms, as illustrated by the gray traces on the left of panels B and C in Fig. 6, were used to compute average r₃₀₀-V and peak I_norm-V relations shown on the right.

The kinetic formulation in Fig. 6 A is not intended as a full-scale channel model. The scheme is only designed to predict coarse features of activation and Ca²⁺ inactivation during depolarizing steps, but is inadequate to explain recovery from inactivation at hyperpolarized potentials. Because the present set of experiments is limited to data obtained during depolarizing steps, we have, for simplicity, omitted additional B and I states (Fig. 6 A) that would connect more directly with the closed C₁ and C₂ conformations, such as would be required to adequately represent recovery from inactivation. Moreover, to explain detailed kinetic properties of the channel, the number of steps representing the inactivation process and the number of closed states representing the activation pathway are likely to far exceed two. Finally, voltage-dependent inactivation is absent in the simple model. Though these additional features can be introduced into the core structure, the simple formulation here is optimal for the initial task of first-order testing against the basic set of data obtained in this study.

Statistical analysis

The fraction of peak current remaining at the end of a 300-ms depolarization (r₃₀₀) as a function of voltage was used to quantitate the level of inactivation. The strength of Ca²⁺-dependent inactivation was quantified by the parameter , defined as the difference between r₃₀₀ values in Ba²⁺ versus Ca²⁺, taken at 10 mV. All data are presented as the mean ± SEM. Unpaired t-tests were used to compare f values between wild-type Ca²⁺ channels (_{1C 2a 2}, in Fig. 1 B) and other constructs. The ** symbol denotes significance at p < 0.001, and * denotes significance at p < 0.01. Higher values of p were not considered to be statistically significant.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Confirmation that the _1C consensus EF hand is essential for Ca²⁺ inactivation

Fig. 1 (A and B) summarizes the Ca²⁺ inactivation properties of wild-type L-type calcium channels, transiently expressed from cDNA clones in HEK 293 cells. In the original study of recombinant L-type channels from our lab (de Leon et al., 1995), Ca²⁺ inactivation was characterized for channels composed of _1C and _2a subunits, as illustrated in Fig. 1 A. Because L-type channels manifest distinct voltage- and Ca²⁺-dependent inactivation mechanisms (Lee et al., 1985; Kass and Sanguinetti, 1984), the _2a subunit (Perez-Reyes et al., 1992) was chosen for coexpression with the main _1C subunit, as the _2a subunit imparts the least voltage-dependent inactivation (Patil et al., 1998; Jones et al., 1998) in comparison to the other  subunits (Perez-Reyes and Schneider, 1994). Accordingly, the slow decay of Ba²⁺ currents in Fig. 1 A (black traces) primarily reflects the sluggish time course of voltage-dependent inactivation, because the Ca²⁺-inactivation mechanism is highly selective for Ca²⁺ over Ba²⁺ (Brehm and Eckert, 1978). By contrast, exemplar Ca²⁺ currents at +0 mV decay by about half at the end of the depolarizing pulse (Fig. 1 A, middle gray-dashed trace), as expected from the robust induction of the Ca²⁺-dependent inactivation process. Here and throughout, the Ca²⁺ traces have been scaled upward to facilitate comparison of kinetics, and the fraction of peak current remaining at the end of 300-ms depolarizations (r₃₀₀) is plotted as a function of voltage (Fig. 1 A, right). Consistent with slow voltage-dependent inactivation, the r₃₀₀ relation with Ba²⁺ declines only slightly and monotonically with increasing depolarization. In accord with hallmark behavior of Ca²⁺ inactivation, the corresponding r₃₀₀ relation with Ca²⁺ exhibits a characteristic U-shape, as expected of inactivation driven by Ca²⁺ entry rather than voltage. A direct measure of the extent of Ca²⁺ inactivation is therefore provided by the difference between the r₃₀₀ plots in Ba²⁺ and Ca²⁺, with the difference at 10 mV given by the parameter f.

In Fig. 1 B, the ₂ subunit was coexpressed with _1C and _2a to approximate more closely the heteromultimeric structure of native channels (De Waard et al., 1996; Walker and De Waard, 1998). Interestingly, inclusion of the ₂ subunit resulted in more robust Ca²⁺ inactivation, as illustrated by the more rapid decay of specimen Ca²⁺ current at +0 mV in comparison to that observed in cells expressing _1C and _2a alone (compare Fig. 1, A and B). There is also a slight enhancement of voltage-dependent inactivation as observed by others (Ferreira et al., 1997), but this is still small by comparison to Ca²⁺ inactivation. Hence, in this study coexpression with the ₂ subunit was used to increase the sensitivity of our subsequent screen for mutants that affect Ca²⁺ inactivation.

The effect of the ₂ subunit to enhance Ca²⁺ inactivation may help to explain some, but not all, of the controversy regarding the importance of the consensus EF hand. Previously, we identified a 53-amino acid segment near the beginning of the _1C CI region that was critical for Ca²⁺ inactivation (Fig. 1, top) (de Leon et al., 1995). The extent of the consensus EF hand is defined by the lateral margins of the highlighted E and F helices. When this segment of _1C was replaced by the analogous segment from the _1E isoform (which lacks Ca²⁺ inactivation), the resulting chimera (_1CE-3) exhibited no appreciable Ca²⁺-dependent inactivation when coexpressed with _2a alone (de Leon et al., 1995), a result that we confirmed extensively in Fig. 1 C. However, when _1CE-3 was coexpressed with _2a and ₂ subunits, a small but statistically resolved amount of Ca²⁺ inactivation (f = 0.04) was observed in averaged data. Nonetheless, there was still an enormous reduction of Ca²⁺ inactivation relative to wild-type channels (compare Fig. 1, B and D), which emphasizes the essential nature of the consensus EF hand to Ca²⁺ inactivation. We therefore proceeded to map the structural basis for the virtual knockout of Ca²⁺ inactivation.

The _1C consensus EF hand may not bind Ca²⁺ according to a classic EF-hand mechanism

In an earlier report from our lab (de Leon et al., 1995), the simplest hypothesis was suggested to explain the functional reduction of Ca²⁺ inactivation by swapping EF-hand regions (Fig. 1, B and D): the _1C consensus EF hand is capable of binding Ca²⁺ and serving as the Ca²⁺ sensor for Ca²⁺ inactivation, while the homologous region in _1E binds Ca²⁺ far less well. Many EF hand-containing proteins such as calmodulin, troponin C, and recoverin have been studied at the atomic level by x-ray crystallography and nuclear magnetic resonance (Falke et al., 1994). These studies indicate that EF hands form a helix-loop-helix structure, where the Ca²⁺ ion is typically coordinated by six amino acids (designated x, y, z, y, x, and z) that lie mostly within the loop bracketed by E and F helices of this motif (Fig. 1, top). If Ca²⁺ binding to the consensus EF hand in _1C initiates the conformational changes that lead to inactivation, it should be possible to disrupt Ca²⁺ inactivation by altering the amino acid residues thought to bind Ca²⁺.

To test this hypothesis, we used site-directed mutagenesis to individually alter the amino acids located at the x, y, z, and z coordinates of the consensus EF hand in the _1C channels (see Fig. 1, top, and Methods). Fig. 2 summarizes the Ca²⁺-inactivation properties of these mutant _1C channels. For each mutant, exemplar Ba²⁺ and Ca²⁺ currents at +0 mV are shown at left, and averaged r₃₀₀ data at right. Mutations at two of the positions, E1537A (y) and K1539C (z), failed to alter Ca²⁺ inactivation significantly compared with control (Fig. 1 B). Alterations at the other two positions, D1535A (x) and D1546A (z), did reduce Ca²⁺ inactivation by about half, as demonstrated by statistically resolved changes in the parameter f. However, none of these alterations came close to eliminating Ca²⁺ inactivation, fitting poorly with the general trend that such mutations reduce the Ca²⁺ affinity of classic EF hands by 10-1000 fold (Linse and Forsen, 1995). Our data here agree with the results of similar experiments performed by other groups (Zhou et al., 1997; Bernatchez et al., 1998), and point to one of two conclusions. First, if the _1C consensus EF hand does bind Ca²⁺ as in classic EF-hand proteins, then such Ca²⁺ binding is not strongly linked to channel inactivation. Alternatively, if the EF hand serves as an important Ca²⁺ sensor for inactivation, then it must bind Ca²⁺ in an unorthodox and previously unreported fashion, unlike that of classic EF-hand proteins. Thus, it seemed unlikely that the consensus EF hand functions as the Ca²⁺ sensor for inactivation.

Ca²⁺ inactivation depends critically on residues in the F helix of the consensus EF hand

Regardless of its ability to bind Ca²⁺, the consensus EF hand of the _1C channel is still a crucial domain for Ca²⁺ inactivation (Fig. 1, B and D). We therefore screened all remaining differences between _1C and _1E in the 53-amino acid segment that was exchanged in the chimera _1CE-3 (Fig. 1). Starting with wild-type _1C, amino acid residues that differ between _1C and _1E have been changed in clusters, such that each mutant channel contains substitutions of 2-4 amino acids (Fig. 3, top). The Ca²⁺ inactivation properties for each of these mutants is summarized in Fig. 3, with exemplar Ba²⁺ and Ca²⁺ traces shown at the top, and averaged r₃₀₀ data at the bottom. Some of the mutants exhibited Ca²⁺ inactivation that was statistically indistinguishable from wild type (KI  VV and RRI  TLM). Interestingly, the KHL  HYT mutations include a change in the lysine residue at the x position of the consensus EF hand, and these mutations decreased Ca²⁺ inactivation by over a third. The reduction of inactivation was stronger in DW  ES and QF  SL channels, where Ca²⁺ inactivation was approximately halved. Most strikingly, Ca²⁺ inactivation was almost completely lost in VVTL  MYEM channels, with no statistically resolved difference from the _1CE-3 chimera (mean f values of 0.07 and 0.04, respectively). Hence, changes in just four amino acids in the F helix (VVTL  MYEM) account for most, if not all, of the functional effect in the chimeric channel _1CE-3.

To identify the single amino acid that is most critical to Ca²⁺ inactivation in this four-residue segment (VVTL), each amino acid was exchanged individually, giving rise to the mutants V1547M, V1548Y, T1549E, and L1550M (Fig. 4). Two of the mutant channels (T1549E, L1550M) showed Ca²⁺ inactivation that was statistically indistinguishable from wild type. By contrast, Ca²⁺ inactivation was almost halved in V1547M channels, and the single exchange of tyrosine for valine in V1548Y channels accounts for much of the virtual ablation of Ca²⁺ inactivation seen in VVTL  MYEM channels.

View larger version (21K): [in this window] [in a new window]   FIGURE 4   The amino acids that comprise the VVTL motif in 1C were changed individually to their 1E counterparts. Left: exemplar Ba2+ (black) and Ca2+ (gray, dashed) currents elicited from step depolarizations to 0 mV. Right: corresponding r300 plots. The format of exemplar currents and r300 summaries is identical to those in Fig. 1. Most of the knockout of Ca2+ inactivation produced by the VVTL  MYEM cluster mutation is reproduced by the V1548Y point mutation.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Although CaM is the dominant Ca²⁺ sensor for Ca²⁺ inactivation of L-type channels (Peterson et al., 1999; Zuhlke et al., 1999; Qin et al., 1999), this study unequivocally underscores the critical nature of the _1C consensus EF hand to the inactivation process. In agreement with previous work from our lab (de Leon et al., 1995), we here confirmed the essential knockout of Ca²⁺ inactivation in the chimeric channel _1CE-3, in which a 53-residue segment of _1C that contains the EF hand was replaced by the analogous segment from a non-inactivating _1E channel. Systematic mutagenesis of this 53-residue stretch in _1C further revealed that a four-amino acid cluster (VVTL) within the F helix of the EF-hand motif is itself critical for Ca²⁺ inactivation, and much of the essential chemistry resides in the second valine. Mutations of presumed Ca²⁺-coordinating residues in the consensus EF hand produced only ~2-fold reduction of Ca²⁺ inactivation, making it appear unlikely that the EF hand serves as a significant Ca²⁺ sensor for channel inactivation. Our findings have implications for previously reported results, the physiological potential for Ca²⁺ binding to the consensus EF hand, and the possible mechanistic interrelation between CaM and the EF-hand motif, as discussed below.

Relation to previous studies

The effect of the ₂ subunit to enhance Ca²⁺ inactivation (Fig. 1) helps to explain some, but not all, of the differing results concerning the importance of the consensus EF hand for Ca²⁺ inactivation. Although our chimera _1CE-3 exhibited no appreciable Ca²⁺ inactivation when coexpressed with _2a alone (Fig. 1 C) (as in de Leon et al. (1995)), addition of the ₂ subunits revealed a small but statistically resolved amount of Ca²⁺ inactivation (Fig. 1 D). Even so, there was still a virtual knockout of Ca²⁺ inactivation relative to wild-type channels (compare Fig. 1, B and D), which stands in contrast to the results of Zhou et al. (1997). Using the Xenopus oocyte expression system, they reported substantial Ca²⁺ inactivation in a chimeric channel (EC61) that is similar to our _1CE-3 chimera, in which a 53-amino-acid stretch containing the consensus EF hand of _1C has been replaced with homologous _1E sequence (Fig. 1). Although only the _2a subunit was specifically coexpressed with EC61 (Zhou et al., 1997), Xenopus oocytes do contain high levels of endogenous ₂ subunits (Singer-Lahat et al., 1992), so the slight enhancement of Ca²⁺ inactivation observed here by cotransfection of ₂ subunits in HEK 293 cells helps to explain some of the difference between results reported for expression in HEK 293 cells (de Leon et al., 1995) and oocytes (Zhou et al., 1997). However, close inspection of the exemplar traces in Zhou et al. (1997) reveals that Ca²⁺ inactivation, though substantially reduced compared to wild-type _1C, is clearly more prominent than in our results, even with coexpression of the ₂ subunit in HEK 293 cells.

To explore the possibility that a subtle difference in cDNA constructs could account for the contrasting results, we have also characterized the Ca²⁺ inactivation properties of a construct that is strictly comparable to EC61 at the amino acid level, in that only the 29-amino acid, EF-hand region of _1E has been substituted into _1C. Fig. 5 summarizes the inactivation properties of this construct (_1CE-3/QF/DW) when coexpressed in HEK 293 cells with _2a and ₂ subunits. Though not quite statistically resolved, the mean behavior of _1CE-3/QF/DW channels (Fig. 5) hints that Ca²⁺ inactivation is somewhat stronger than for _1CE-3 channels (Fig. 1 D), with f values of 0.08 ± 0.03 (n = 6) versus 0.04 ± 0.03 (n = 6), respectively. Nonetheless, the strength of Ca²⁺ inactivation for _1CE-3/QF/DW channels was still very weak, and there remains a substantial difference between the results reported by Zhou et al. (1997) and those we have presented here and before (de Leon et al., 1995).

View larger version (30K): [in this window] [in a new window]   FIGURE 5   Marked attenuation of Ca2+-dependent inactivation in a chimeric Ca2+ channel 1CE-3/QF/DW, corresponding to an 1C channel in which only the 29 amino acids comprising the canonical EF-hand motif have been replaced by their 1E counterparts. Top: alignment of 1C and 1E regions that are swapped in chimeric channel 1CE-3/QF/DW. Amino acids 1526-1554 of 1C are shown, corresponding to the strict extent of the 29-amino-acid, canonical EF hand. Bottom, left: exemplar Ba2+ (black) and Ca2+ (gray, dashed) currents elicited by step depolarizations to +0 mV. Bottom, right: corresponding r300 plots, averaged from 6 cells, with the Ba2+ data plotted as solid circles. The format of exemplar currents and r300 summaries are identical to those in Fig. 1.

Zuhlke and Reuter (1998) provide a different perspective on the importance of the consensus EF hand. They find that simple deletion of the EF-hand motif from _1C abolishes Ca²⁺ inactivation, in agreement with the implications of our mutagenesis and chimeric channel analyses. Zhou et al. (1997) made a similar deletion construct, but were unable to express functional channels.

With regard to voltage-dependent inactivation, our results echo the growing consensus that structural determinants for both Ca²⁺- and voltage-dependent inactivation appear to be interlaced along the _1C carboxyl tail (Zhang et al., 1994; Klockner et al., 1995; Soldatov et al., 1997). Some of our EF-hand mutations affect the decay of Ba²⁺ current, which presumably reflects properties of voltage-dependent inactivation (but see Ferreira et al., 1997). A particularly obvious example comes with mutation at the x coordinate of the consensus EF hand (D1535A, Fig. 2), which induces marked acceleration in the decay of Ba²⁺ currents.

Finally, although this study has focused on the _1C CI region in general and the consensus EF hand in particular, it should be mentioned that other regions have been suggested as additional structural mediators of Ca²⁺-dependent modulation of channel gating. Portions of the _1C carboxyl tail that are distal to the CI region, as well as I-II and II-III interdomain linkers, have been proposed to be important for Ca²⁺ inactivation (Adams and Tanabe, 1997). The potential contribution of the distal _1C carboxyl tail seems all the more plausible, given the recent discovery of Ca²⁺-dependent facilitation and inactivation of P/Q-type calcium channels that involves CaM binding to a "CBD" domain located distally on the _1A carboxyl tail (Lee et al., 1999). However, with regard to the distal _1C carboxyl tail, the impact on Ca²⁺ inactivation seems limited to a modulatory rather than essential role, as we have previously observed that Ca²⁺ inactivation appears largely unchanged upon truncation of such distal regions (de Leon et al., 1995). Furthermore, whatever role the interdomain linkers play in Ca²⁺ inactivation, it must be conserved across different channel types, as donation of the _1C carboxyl tail confers Ca²⁺ inactivation to backbones for _1E (de Leon et al., 1995; Peterson et al., 1999) and _1A (D. T. Yue and J. G. Mulle, unpublished results).

Does the consensus EF hand engage in physiological Ca²⁺ binding?

The results of mutations on presumed Ca²⁺-coordinating residues in the consensus EF hand square poorly with a scenario in which the EF hand represents a significant Ca²⁺ sensor for inactivation while binding Ca²⁺ according to a classic EF-hand mechanism (Fig. 2) (Zhou et al., 1997; Bernatchez et al., 1998). However, these results in themselves do not exclude Ca²⁺ binding to the consensus EF hand under physiological conditions. First, it is possible that Ca²⁺ does bind to the EF hand in a classic manner, but that such binding is not tightly linked to channel inactivation. Alternatively, the EF hand could still provide an important Ca²⁺-sensing function for inactivation, given the presumed proximity of the consensus EF hand to the inner mouth of the channel pore. In this region, Ca²⁺ diffusion modeling (Simon and Llinas, 1985) would predict that the Ca²⁺ concentrations presented to the EF-hand domain could extend toward the millimolar range, far higher than presented to conventional EF-hand proteins. To accommodate such unusual performance criteria, the consensus EF hand may be designed to coordinate Ca²⁺ in a fashion that differs considerably from that in conventional EF-hand proteins. Otherwise, the consensus EF hand might be immediately "blinded" by the enormous Ca²⁺ signal emanating from the very first opening of the channel. In fact, preliminary biophysical studies of peptides encoding the consensus EF hand indicate Ca²⁺ binding in the 10-50 µM range (Villain et al., 1999). However, any such Ca²⁺ binding would be unlikely to serve as the primary Ca²⁺-sensing event for inactivation, as we showed essentially complete ablation of Ca²⁺ inactivation upon overexpression of mutant CaMs lacking appreciable Ca²⁺ binding (Peterson et al., 1999). Nonetheless, low-affinity Ca²⁺ binding to the consensus EF hand could still serve to modulate the efficacy of the primary Ca²⁺-sensing mechanism carried by CaM.

The high Ca²⁺ concentration environment near the inner mouth of the channel also raises a paradox in connection with the role of CaM as Ca²⁺ sensor for inactivation, as follows. Because CaM interacts with the IQ-like motif, we also presume that CaM is situated near the inner channel mouth. Given that the C-terminal domain of CaM appears to be the relevant Ca²⁺-sensing domain for channel inactivation (Peterson et al., 1999), and that Ca²⁺ may have submicromolar affinity for this domain (Falke et al., 1994), it remains challenging to understand how CaM can mediate smoothly graded changes in the extent of Ca²⁺ inactivation that vary with the rate of Ca²⁺ entry.

Proposed mechanistic interrelationship between CaM and the consensus EF hand

How do CaM, the IQ-like motif, and the consensus EF hand interrelate within the context of an overall molecular mechanism of Ca²⁺ inactivation? Although it is premature to draw firm conclusions, the identification of major pieces in the puzzle make it possible to raise a working hypothesis.

An intriguing aspect of our results is that the primary molecular determinant within the consensus EF hand turns out to be a hydrophobic patch in the F helix (VVTL). In structural models of the conformational changes induced by Ca²⁺ binding to EF-hand proteins, such hydrophobic patches figure prominently in transducing Ca²⁺ binding into functional sequelae. According to the classic HMJ model (Herzberg et al., 1986) and its subsequent refinements (Chazin, 1995), hydrophobic residues in E and F helices tend to interact with each other in apo EF hands, but become exposed to the outside world subsequent to large changes in interhelical angles induced by Ca²⁺ binding. The exposed hydrophobic patches then interact with target surfaces, and thereby modulate effector molecules. Perhaps, hydrophobic patches in the helices of the _1C consensus EF hand (e.g., VVTL) serve such a transduction function, somehow linking Ca²⁺ binding to channel inactivation.

The problem with such a proposal is that Ca²⁺ binding to CaM, rather than the consensus EF hand, serves as the primary initiatory event for inactivation. A possible solution comes from extensive studies of recoverin (Flaherty et al., 1993; Zozulya and Stryer, 1992; Ames et al., 1997; Tanaka et al., 1995), a Ca²⁺ sensor involved in vision that contains four EF-hand motifs (EF-1 and EF-2 in one pair, EF-3 and EF-4 in a second). Of particular relevance is the fact that although EF-1 does not bind Ca²⁺, Ca²⁺ binding to EF-2 ultimately induces a large conformational change in EF-1, which in turn ejects a buried myristoyl group. Exposure of the latter group results in translocation of recoverin from the cytosol to the membrane. The analogy for L-type channels could be that the consensus EF hand acts like EF-1, and CaM like EF-2. Ca²⁺ binding to CaM would then induce conformational changes in the consensus EF hand, leading to exposure of its helical hydrophobic patches, and interaction of these patches with target regions on the channel would bring about inactivation. The only variation required for the L-type channel is that the coupling between CaM and the consensus EF hand must occur in trans across molecules, but this seems plausible given that CaM may be constitutively tethered to the channel like an integral subunit (Peterson et al., 1999).

As a first step in testing such a working hypothesis, we asked whether the proposed transduction role for the consensus EF hand is compatible with the detailed Ca²⁺ inactivation properties of wild-type and mutant V1548Y channels. Although numerous kinetic models of Ca²⁺ inactivation have been developed (e.g., Standen and Stanfield, 1982; Sherman et al., 1990; Shirokov et al., 1993; Noceti et al., 1998), none have incorporated key elements of our working hypothesis, such as separate steps for Ca²⁺ binding and subsequent transduction into channel inactivation, and multivalent Ca²⁺ binding of CaM. To evaluate the quantitative feasibility of our working hypothesis, we therefore developed the simplest form of a kinetic mechanism incorporating these key features (Fig. 6 A).

View larger version (37K): [in this window] [in a new window]   FIGURE 6   Proposed mechanism of Ca2+-dependent inactivation, in which calmodulin serves as Ca2+ sensor for inactivation, and the consensus EF hand serves in subsequent transduction steps that translate calmodulin binding into channel inactivation. (A) Five-state kinetic scheme used to model calcium-channel activation and Ca2+-dependent inactivation. Depolarization causes the voltage sensors (ellipses with "+" charges) to move outward as the channel traverses closed states (C1, C2) toward the channel open state (O3). Opening is viewed as rearrangement of a cytoplasmic gate, which is permitted by the outward disposition of voltage sensors. Ca2+ entering through the channel binds to the tethered calmodulin (CaM, dumbbell shape), which in turn binds to the IQ motif located downstream of the EF-hand (B4). State B4 still conducts Ca2+ current, as channel inactivation requires a subsequent conformational change of the consensus EF hand that stabilizes (thick dashed curve) the closed position of the cytoplasmic gate (I5). Before this conformational change, the EF hand is proposed to interact weakly (or differently) with the cytoplasmic gate (thin dashed line), in a manner that permits ready opening of the gate. Although CaM binds four Ca2+ ions in the transition between O3 and B4, our previous work (Peterson et al., 1999) suggests that Ca2+ binding to only the C-terminus of CaM (with 2 Ca2+ sites) is critical for Ca2+ inactivation. Hence, within the context of Ca2+ inactivation, the relevant stoichiometry of Ca2+ binding is two, as marked near the k34 step. In addition, to signify the apparently non-essential role of Ca2+ binding to the N-terminal domain of CaM in mediating channel inactivation, the N-terminal domain of CaM is "retracted" somewhat from the IQ domain in states B4 and I5. (B) Comparison of averaged wild-type channel (1C 2a 2) properties (gray traces and symbols, averaged from 6 cells) and model simulations (smooth curves, generated by the model in A with parameters given in Table 1). Left: Ca2+-current waveforms during depolarizations to the indicated potentials. Amplitudes have been normalized to peak current amplitude at +10 mV, and the scale is given by the y axis of the Inorm-V relation shown at right. Right: r300 and peak normalized Ca2+ current (Inorm), plotted as a function of voltage (V). The leftward shift observed in the minimum of the r300-V plot with respect to the peak Inorm-V relation is designated with by the parameter s. (C) Comparison of averaged mutant channel (1C(V1548Y) 2a 2) properties (gray traces and symbols, averaged from 7 cells) and model simulations (smooth curves, generated by the model in A with parameters given in Table 1). Format as in B. Consistent with a transduction role for the consensus EF-hand region, fits to the mutant data only required significant changes to the rate constants between B4 and I5, and between C2 and O3. Other parameters were essentially identical to those for the wild-type channel in B.

The core attributes of this kinetic formulation are as follows. The activation pathway describing outward movement of S4 voltage sensors (Yang and Horn, 1996; Larsson et al., 1996) and opening of a cytoplasmic gate (Liu et al., 1997; Perozo et al., 1999) is minimally represented by two closed (C₁, C₂) and one open (O₃) conformation(s) (Imredy and Yue, 1994), linked by voltage-dependent transitions.

As in more recent models of Ca²⁺ inactivation (Sherman et al., 1990; Shirokov et al., 1993; Noceti et al., 1998), we adopt a "local Ca²⁺ domain" approximation, in which 1) the Ca²⁺ responsible for inactivation is situated within ~100 Å of the inner channel pore, and 2) Ca²⁺ influx through an individual channel is solely responsible for driving its own inactivation. The first part of the local domain approximation is easily justified based on the apparent proximity of the IQ-like motif to the channel pore, and on the insensitivity of Ca²⁺ inactivation to intracellular dialysis with even fast chelators of Ca²⁺ (BAPTA) (Noceti et al., 1998; Deisseroth et al., 1996). The second part is not strictly true (Imredy and Yue, 1992); however, it seems a reasonable simplification in HEK 293 cells, because the strength of Ca²⁺ inactivation grows only slightly with large increases in channel expression (Fig. 2 C in Peterson et al. (1999)). Under the local domain approximation, the Ca²⁺ concentration that drives tethered CaM ([Ca²⁺]_domain) would be virtually synchronized in time with single-channel openings, and directly proportional to the unitary current i (Sherman et al., 1990), such that [Ca²⁺]_domain  i (when the channel is open) or 0 (when it is closed or inactivated).

In the local domain case, then, we need only consider Ca²⁺ binding to CaM when the channel is in the open state (O₃). For computational simplicity we combine Ca²⁺ binding to CaM and its subsequent interaction with the IQ-like domain into a single transition, yielding a CaM-bound form of the channel (B₄). This channel conformation still conducts current. Only after CaM is bound does the channel undergo a subsequent conformational change to reach a non-conducting, inactivated state (I₅). This transduction step could correspond to CaM-induced, full opening of the consensus EF hand, and ensuing strong interaction of target regions with exposed helical hydrophobic stretches. This strong interaction is schematized as a thick dashed curve in Fig. 6 A, symbolizing stabilization of a cytoplasmic activation gate (Liu et al., 1997; Perozo et al., 1999) in the closed position (Imredy and Yue, 1994). Before full opening of the consensus EF hand induced by CaM, the EF hand is presumed to adopt a relatively closed conformation, in which helical hydrophobic patches interact only weakly (or differently) with the cytoplasmic gate, in a manner that permits ready channel opening. This form of interaction is represented as a thin, dashed curve in Fig. 6 A.

The transitions among O₃, B₄, and I₅ states merit special attention. Because the molecular events underlying these transitions probably occur outside the membrane electric field, the corresponding rate constants are considered voltage independent. Finally, to incorporate multivalent Ca²⁺ binding of CaM, we considered our previous result that Ca²⁺ binding to only the C-terminal lobe of CaM (with two Ca²⁺ binding sites) appears to be important for inactivation (Peterson et al., 1999). Hence, the rate constant pertaining to O₃  B₄ is set proportional to [Ca²⁺]_domain², in accord with two possible scenarios of dual Ca²⁺ binding to CaM followed by CaM-Ca₂ binding to the IQ domain (O₃  O₃Ca₂  B₄). These scenarios lend themselves to the computationally simple outcome that the O₃  B₄ rate constant is proportional to [Ca²⁺]_domain². One case is that Ca²⁺ (un)binding to CaM (O₃  O₃Ca₂) is rate-limiting relative to (un)binding to the IQ domain (O₃Ca₂  B₄), and that two Ca²⁺ ions (un)bind simultaneously to CaM. This case coincides exactly with our simplified representation. The other case is that CaM (un)binding to the IQ domain (O₃Ca₂  B₄) is rate-limiting relative to Ca²⁺ (un)binding to CaM (O₃  O₃Ca₂), and that two Ca²⁺ ions (un)bind to CaM in a highly cooperative manner described in the steady state by a Hill equation. This case also reduces to a lumped, two-state representation (O₃  B₄), but here the O₃  B₄ rate constant is proportional to [Ca²⁺]_domain²/(K_half² + [Ca²⁺]_domain²), where K_half is the [Ca²⁺]_domain required to half-saturate the O₃  O₃Ca₂ reaction. The latter term reduces to [Ca²⁺]_domain² when [Ca²⁺]_domain K_half, a condition that is partially satisfied because the maximal steady-state Ca²⁺ inactivation that we model is ~50% (Fig. 6 B). Because CaM is probably tethered constitutively to the channel complex (Peterson et al., 1999), there is uncertainty about the detailed reaction kinetics of the relevant CaM, as such tethering could well alter kinetic properties via allosteric interactions. In the absence of reliable kinetic data for the relevant CaM, we have implemented the computationally simple O₃  B₄ representation, with the O₃  B₄ rate constant proportional [Ca²⁺]_domain². This approximation suffices to illustrate some of the behaviors that may arise from multivalent Ca²⁺ binding to CaM, but will likely be subject to revision with regard to quantitative details. Finally, in this version, no Ca²⁺ binding to the consensus EF hand is represented in the B₄  I₅ step. Details of the model formulation are described in Table 1 and the Methods.

Fig. 6 B compares quantitative fits of the kinetic model (black curves) to averaged data from wild-type channels (gray waveforms and symbols). The experimental Ca²⁺-current waveforms (gray traces) have been averaged from actual Ca²⁺-current traces in several cells after normalization by peak current amplitude elicited at +10 mV. As displayed, the decay of averaged Ca²⁺ waveforms almost exclusively reflects Ca²⁺ inactivation, because average Ca²⁺ currents have been divided through by smooth exponential fits to similarly averaged Ba²⁺ waveforms (see Methods). Experimental r₃₀₀ and I-V relations, shown at right, have been calculated directly from such corrected averages of normalized Ca²⁺ current. Using parameter values as summarized in Table 1, the agreement between kinetic simulation and experimental data is impressive, especially given the simplicity of the model as formulated (Fig. 6 A).

To evaluate the feasibility of the proposed transduction role for the consensus EF hand, we examined whether the altered Ca²⁺ inactivation properties induced by mutation in the EF hand could be predicted by adjustment of rate constants that were limited to the transduction step (B₄  I₅), and to gating transitions closely linked with the target action of the activated EF hand (C₂  O₃ reaction, by virtue of thin dashed-line interaction in Fig. 6 A). V1548Y was chosen for this particular test because the residual Ca²⁺ inactivation was sufficient to quantify with certainty, while the overall reduction in Ca²⁺ inactivation was large. A 5-fold reduction in k45 (B₄  I₅) largely accounts for the marked effects of the mutation (Fig. 6 C), as if the V1548 mutation renders less effective the stabilization of state I₅ via the strong interaction between the full-open EF hand and the cytoplasmic gate (Fig. 6 A, thick dashed line). An additional 2-5-fold slowing of transitions corresponding to the actual opening and closing of the channel (C₂  O₃) also contributed to the quantitative fits, as if the V1548Y mutation also affected the weak interaction of the consensus EF hand with the cytoplasmic gate (Fig. 6 A, thin dashed line), thereby influencing the final opening transition of the channel. Table 1 details the precise parameter values for the fits. Overall, the Ca²⁺ inactivation properties of V1548Y are consistent with a transduction role for the consensus EF hand, although such a transduction role is certainly not proven, given the early developmental stage of the model.

Prediction of a shift between the voltages evoking maximal inactivation versus maximal Ca²⁺ current

An intriguing, but unanticipated, capability of the kinetic model was the ability to predict the shift between the voltage at which Ca²⁺ inactivation is strongest (minimum of r₃₀₀ plot), and the voltage at which the largest peak currents are evoked (Fig. 6 B, s). This shift was considered to be an important mechanistic clue by Noceti et al. (1998), but what does it mean?

Sherman et al. (1990) deduced that local domain models of Ca²⁺ inactivation would almost invariably predict that inactivation would be strongest at the same voltage that elicited the largest peak currents. The theoretical basis for the deduction is surprisingly direct. If activation is fast relative to inactivation (true in our data), then peak current is proportional to P_o|A(V) × i(V), where i(V) is the amplitude of unitary currents at voltage V, and P_o|A(V) is the conditional probability that the channel will be in the open state (O₃) in the steady state at V, given that the channel resides in the "active" states (C1, C2, or O₃). P_o|A(V) × i(V) will then be proportional to P_o|A(V) × (VV_rev) = P_o|A(V) × V. Under the same assumption of fast activation and slow inactivation, the steady-state extent of Ca²⁺ inactivation increases monotonically with P_o|A(V) × rate constant leading toward inactivated states, which is proportional to P_o|A(V) × i(V) (also proportional to P_o|A(V) × V) in the formulation of Sherman et al. (1990). An analogous argument applies to the rate of Ca²⁺ inactivation. Given that the same voltage-dependent terms (P_o|A(V) and V) are present in the expressions for magnitude of peak current and the strength of Ca²⁺ inactivation, peak current and inactivation must be maximal at the same voltage V.

Contrary to the expectation of simple local Ca²⁺ domain models, Noceti et al. (1998) observed a clear-cut shift between the voltages where maximal inactivation and peak current were obtained. They could account for the shift, despite adoption of the local Ca²⁺ domain approximation, by postulating a complex kinetic scheme with 12 states and 3 modes of gating.

However, we also predict such a shift (Fig. 6, B and C), even though our local Ca²⁺ domain mechanism is simple (Fig. 6 A), and should be subject to the clear-cut deduction of Sherman et al. (1990). How is this possible? The answer comes with close re-examination of the term for the steady-state extent of Ca²⁺ inactivation, which will still increase monotonically with P_o|A(V) × rate constant for transition from states 3 to 4. However, because we postulate that CaM binds two Ca²⁺ ions to initiate inactivation, the relevant term now goes as P_o|A(V) × k34 × i(V)², where k34 is constant with respect to V so that the entire term is thus proportional to P_o|A(V) × V². The squaring of the V term accounts for the dissociation of the peak extent of Ca²⁺ inactivation and the peak current amplitude, because plots of P_o|A(V) × V² and P_o|A(V) × V reach their maxima at different voltages (Fig. 7).

View larger version (18K): [in this window] [in a new window]   FIGURE 7   Potential explanation for the shift in voltage required to evoke maximal Ca2+ and maximal Ca2+-dependent inactivation. Top:<