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Address correspondence to: Catherine E. Morris, Neuroscience, Ottawa Health Research Institute, Ottawa Hospital, 725 Parkdale Ave., Ottawa, Ontario, Canada K1Y 4E9. Fax: (613) 761-5330; email: cmorris{at}ohri.ca
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIX AAPPENDIX BREFERENCES |
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Key Words: mechanosensitive • 5aa linker mutant • voltage-gated • stretch • S3–S4
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIX AAPPENDIX BREFERENCES |
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). In eukaryotes, mechanosensitive channels that transduce touch, sound, and gravity are thought to link to filamentous proteins that transmit mechanical gating energy. Curiously, these mechanotransducer specialists show no evidence of susceptibility to mild bilayer tension excursions (e.g., Goodman and Schwarz, 2003), whereas such susceptibility is reasonably common among eukaryotic channels not seen principally as mechanotransducers.
Among voltage-gated channels, mechanosusceptibility has diverse manifestations. An irreversible shift to fast gating occurs with stretch for Na channel 
subunits (Shcherbatko et al., 1999; Tabarean et al., 1999). Na channel mechanosensitivity in smooth muscle may have physiological and pathophysiological consequences (Ou et al., 2003). Stretch reversibly increases L-type (Langton, 1993) and N-type calcium currents without altering the speed of activation (Calabrese et al., 2002). Apparent mechanosensitivity has been noted for native voltage-gated K channels (Fig. 2 of Pahapill and Schlichter, 1992; Schoenmakers et al., 1995). Increased activity with stretch in Ca-activated maxi-K channels (Taniguchi and Guggino, 1989; Mienville et al., 1996) may be mediated by fatty acids (Ordway et al., 1995) and/or channel subdomains (Naruse et al., 2003). Of particular interest is the prototypical voltage-gated K channel, Shaker, where membrane stretch robustly affects the extent of voltage-dependent activation (Gu et al., 2001; Tabarean and Morris, 2002).
Insofar as bilayers are elastic springs coupled to embedded channels, increased membrane tension will increase the rate of transitions into larger-area channel conformations. Further, bilayers under tension become thin, so hydrophobic mismatch effects at lipid–protein interfaces may occur. Internal tension in a protein could influence conformational energies in many ways, so we require from Shaker a more detailed description of how elevated tension affects activation kinetics. In particular we seek to distinguish between two possibilities: (a) a separate activation pathway, a "mechanical gate" or mechanosensor motif, uses the energy of membrane tension to open the channel, and (b) Shaker is susceptible to stretch because voltage sensing is inherently sensitive to membrane tension.
Shaker Channel Activation
The activation of voltage-gated channels originates in movement of the voltage sensor—the part of the channel that senses and transduces changes in the transmembrane electric field. Shaker is a homotetramer whose subunits have six transmembrane segments, S1–S6, with S4 containing a periodic succession of positively charged amino acids that are major contributors to the gating charge movement (Aggarwal and MacKinnon, 1996; Seoh et al., 1996). During depolarization, some of these residues change their exposure from intracellular to extracellular (Larsson et al., 1996; Yusaf et al., 1996). S4 is thus seen as the crucial part of the voltage sensor.
During activation and deactivation, charged residues in S4 move, so the voltage sensor is a specialized dielectric in the membrane electric field. Energies of the resting and active subunit conformations, and thereby the probability of channel activation, change with voltage; depolarization favors activation. Models have S4 moving in an irregularly shaped aqueous "gating canal" formed by other parts of the protein. S4 rotation is envisaged (Cha et al., 1999; Glauner et al., 1999), with parts of S4 facing water-accessible vestibuli that penetrate the channel protein and define the region of steepest electrical potential gradient. In one hypothesis (Gonzalez et al., 2001; Bezanilla, 2002), a tilted S4 performs a rigid 
180° rotation that switches exposure of the positive charges from the intra- to the extracellular side. In another (Gandhi and Isacoff, 2002), this rotation is embedded in a helical screw motion that moves S4 relative to neighboring segments.
A recent crystal structure for the Shaker-related bacterial KvAP channel (Jiang et al., 2003a) challenges these views. It suggests S4 and part of S3 form a helix-turn-helix "voltage sensor paddle" at the perimeter of the channel, with depolarization making paddles move through lipid from more horizontal to more vertical positions (Jiang et al., 2003b). While radically different, this would make it no less likely that bilayer properties—tension, length, and flexibility of the lipid tails—would influence channel gating. We note, however, that marked slowing of activation by deletion of the S3–S4 linker (Gonzalez et al., 2000) makes good sense in models based on S4 movement relative to S3, but is counterintuitive for the paddle model, where S3 and S4 move together and should experience less resistance to movement after deletion of 25 residues at what would be the paddle's tip. In any event, new studies (Broomand et al., 2003; Gandhi et al., 2003) indicate that the paddle model does not apply for Shaker.
Although physiological terminology has S4 "resting" at hyperpolarized voltages and "active" at depolarized voltages, absence of an electrical field causes S4s to collapse to their "active" state. Since native channels prefer being open at 0 mV, it might also be expected that "open" is the default state for Shaker's pore and gate region (S5s and S6s), but an energetics analysis of gating for pore mutants (Yifrach and MacKinnon, 2002) shows that the pore is at its lowest energy when closed. Thus, during activation the voltage sensors must overcome the intrinsically favored closed pore conformation, presumably by applying a lateral force that bends the S6 gating hinges, forcing the crossed inner helix bundle of S5 and S6 (Yellen, 2002) to splay apart.
Shaker Channel Inactivation
Native Shaker channels have complex inactivation. There is fast N-type (Hoshi et al., 1990), and two kinds of slow inactivation. The latter, C-type (Olcese et al., 1997) and P-type (Loots and Isacoff, 2000) inactivation, yield low conductivity channels with dramatically reduced K+ selectivity (Starkus et al., 1997). In contrast to deactivated channels, inactivated channels are not directly susceptible to new activation. N-type inactivation involves structures absent in the truncated channels used here (the NH2-terminally truncated wild-type will henceforth be alluded to as WT). In WT, C-type inactivation (which persists in the truncated channels) is markedly slower than activation. By contrast, for certain S3–S4 linker deletants, including the one used here, current rise and decline happen on similar time scales (Tabarean and Morris, 2002) and so can be studied simultaneously.
S3–S4 Linker Mutants
One approach to investigating S4 motions in Shaker activation has been deletion of the extracellular S3–S4 linker, a maneuver designed to reduce the freedom of S4 to move with respect to the transmembrane electric field. Gonzalez et al. (2000) defined this linker as residues 330–360, and found substantially slower activation with the linker reduced to 10, 5, or 0 amino acids (mutants "10aa", "5aa", and "0aa"). Also, activation was shifted toward more depolarized voltages.
In spite of sluggish responses to voltage steps, the S3–S4 linker mutants are mechanosensitive and, importantly, require no more mechanical energy than WT for comparable PO changes (Tabarean and Morris, 2002). This suggests that voltage-dependent activation in Shaker is inherently sensitive to bilayer stretch. A useful aspect of activation kinetics in S3–S4 linker mutants has been noted (Gonzalez et al., 2000)—unlike WT, 5aa conductance versus voltage (g(V)) relations are well fitted by fourth-order Gaussians, hinting that the 5aa tetramer has one rate-limiting activation step per subunit. Such simplicity, plus the similar time scales of activation and inactivation make 5aa particularly desirable for a kinetic study of Shaker mechanosensitivity by providing more (and more easily interpreted) kinetic information. Using 5aa we were able to ask if increased membrane tension affects the voltage-sensing and -inactivation steps themselves or if it modulates the channel in previously unknown ways.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIX AAPPENDIX BREFERENCES |
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-(330–355) mutant (Gonzalez et al., 2000) that differs from the NH2-terminally truncated Shaker version ShakerH4 (6–46) that we refer to as WT (Gu et al., 2001) by deletion of 25 of the 30 S3/S4 linker residues. Injected oocytes were maintained at 18°C in OR2 solution supplemented with 50 units penicillin, 50 µg streptomycin, and 0.125 µg amphotericin B (antibiotic/antimycotic from GIBCO/BRL).
Electrophysiological Recordings
The vitelline layer was removed manually after shrinking the oocytes in hyperosmolar solution. Up to three cell-attached patch clamp recordings were made per oocyte. Pipettes (3–6 M
) were pulled from borosilicate (Garner; 1.15 mm inner diameter, OD 1.65) using a L/M-3P-A (List Medical). Currents, filtered at 2 kHz, were recorded using an Axopatch 200B (Axon Instruments, Inc.) amplifier and digitized using pClamp6 (Axon Instruments, Inc.) software and A/D converter Digidata 1200 (Axon Instruments, Inc.). Currents were corrected for linear capacitive currents with the amplifier's compensation circuits, residual capacitive and leakage currents were usually corrected by linear subtraction.
As 5aa has slow kinetics, performing the time-consuming P/N (see pClamp; Axon Instruments, Inc.) linear subtraction (LS) procedure for every trial would limit the number of trials per patch and, for stretch runs, subject patches to long destabilizing periods of suction. Instead, we mostly opted for a more economical LS method: for each patch six responses to a step from –90 to –60 mV were averaged at the start of recording and also whenever the amplifier gain was changed. During analysis, this averaged LS trace was upscaled appropriately and subtracted from currents from that patch. Nevertheless, leak sometimes changes over time and capacitive transients are sometimes not entirely linear in voltage. Changes in leak were directly obvious from inspection of the base line currents, and data with such shifts were rejected. What of the capacitive transients? In Fig. 1 A, traces with and without P/4 LS are overlayed. In each panel the faster currents are with stretch, the slower ones, without (–45 mm Hg used for stretch). Unlike the minimal leak currents, capacitive transients without LS are large, though quite well separated from the channel currents (a benefit of 5aa over WT). As illustrated, however, even for a step from –90 to 90 mV, uncompensated capacitive currents minimally obstruct the channel currents during activation. Since even forgoing LS was not problematic, we are confident that the small capacitive transients remaining after using our LS procedure did not affect the kinetic analysis.
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). Gadolinium has been reported to right-shift the Shaker g(V) relation by 10–20 mV (Gu et al., 2001; Tabarean and Morris, 2002). The experiments were performed at room temperature.
Tension
Membrane patches were stretched by suction (negative pressure) applied via the patch pipette sideport. Suction was created with a syringe (a manual valve was opened to reset to atmospheric pressure) and measured with a pneumatic transducer pressure tester (DPM-1B; Bio-Tek). Positive pressure is not as practical because of poor seal stability, but we convinced ourselves that it had entirely comparable effects on currents. Suction is an effective way to reversibly stretch membrane patches. However, tip diameter (and hence patch size and curvature) and mechanical properties of membranes differ among patches and without imaging the patch, one cannot quantify membrane tension.
We adopted two different experimental protocols: "families" and "before, during, after". For families, the voltage was stepped from the holding potential (–90 mV) to increasingly depolarized levels, either with or without stretch. For "before, during, after", one or two measurements without stretch were followed by (usually) one measurement with stretch and then another without, repeated for as many test voltages as possible. In all protocols, pauses (>1 min) at –90 mV between voltage steps allowed for recovery from inactivation. We found that the voltage dependence of fits to kinetic parameters was usually smoother for "families" data.
Repeated stretching sometimes increased nonstretched current amplitudes, and in some cases also altered their kinetics. Such datasets were discarded; there may have been residual tension in some patches, while in others patch area might have increased, or oocyte membrane properties altered (see Tabarean et al., 1999).
Kinetic Analysis—5aa Activation
The opening of Shaker involves one or more preopening steps per subunit, plus one or more final concerted transition(s) (Hoshi et al., 1994; Zagotta et al., 1994a,b; Schoppa and Sigworth 1998a,b,c; Smith-Maxwell et al., 1998). Cooperativity between the voltage sensors has not been excluded but is not generally included in activation models.
As a kinetic signature of 5aa with and without stretch, we used the voltage dependence of the maximum slope and delay of macroscopic currents. This approach is similar to one described by Schoppa and Sigworth (1998a) who fitted exponentials to the late rising phase of WT currents, yielding an activation time constant and a characteristic delay. With 5aa, however, inactivation may corrupt the later rising phase, diminishing the maximum amplitude of the 5aa currents. Thus, the tangent to the current at the point of maximum slope (reached relatively early in the rising phase) was better for capturing the properties of 5aa activation, especially as a formula for this tangent can be straightforwardly derived for many activation models, a bonus for analysis. Fig. 1 B illustrates a by-eye determination of the maximum slope. This approach was used because, given the noise in the signal, determining a maximum slope from the maximum of the current derivative was not practical. Filtering and parameterizing the current then calculating a derivative would be no more precise than our method.
The slope and time axis intersection of the maximum slope line define two parameters (maximum slope and delay of the current) that are practical and reproducible, albeit in the case of delay somewhat arbitrary. Given a suitable activation model, they provide information about underlying (microscopic) properties of channel activation. The delay is a particularly valuable indicator of channel kinetics since (unlike slope) it withstands scaling of the current, and is thus independent of changes in driving force (reversal potential) or channel number that might arise in the course of prolonged experiments. Delays can be compared between patches, and kinetic information derived makes no assumptions about driving force.
Kinetic Analysis—5aa Inactivation
In 5aa, unlike WT, characteristic current rise and decline times are comparable, with currents declining to a plateau of small, but generally nonzero amplitude. The falling phase of the recorded currents was easily and consistently fit by the sum of one constant (the plateau current I1) and one exponentially declining component,
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Data analysis was performed with Origin 6.0 (Microcal Software Inc.) and Maple 8 (Waterloo Maple Inc.) was used for simulations and calculations.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIX AAPPENDIX BREFERENCES |
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). For a cell-attached patch tested over an 80-mV range with 20 µM Gd3+ in the pipette, Fig. 2 A illustrates how stretch (–45 mmHg suction) affected 5aa currents. At –40 mV, which is well below the foot of the 5aa g(V) relation (see Gonzalez et al., 2000), and recall that Gd3+ right-shifts the g(V), there was no detectable channel current before or after stretch. With stretch this patch showed current noise, presumably due to rare 5aa channel activation plus imperfect blockade of endogenous mechanosensitive cation channels (the latter evidenced by stretch-induced noise in the holding current). At –20 mV without stretch, 5aa current was negligible, but with stretch the voltage step elicited a substantial outward current. At 0 and 40 mV, stretch accelerated current time courses and increased their amplitude. Effects of stretch on current amplitude were progressively less dramatic as PO saturated at large depolarizations, but accelerated rising and falling phase kinetics remained evident. Fig. 2 B shows another patch below the foot of g(V); –40 mV elicited no current with or without stretch but stepping to –20 mV with stretch elicited time-dependent 5aa current (note the longer time base than in Fig. 2 A). Traces like Fig. 2 B make it qualitatively clear that stretch augmented 5aa activation, but larger depolarizations were used subsequently so 5aa kinetics with/without stretch could be compared quantitatively.
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0 mV under our recording conditions, so the stretch effects e.g., at –20 mV, where endogenous and Shaker currents have different polarity, and at 0 mV, where endogenous currents vanish, can only be due to the heterologous K channels. Two general ways whereby stretch might accelerate activation are: (a) stretch-induced deformation in some region of the channel might increase the probability of pore opening, independent of S4 movement. In this scenario, channels should open with stretch even at deeply hyperpolarized voltages. (b) Stretch could affect the rates of (some of) the conformational changes that occur during normal voltage-gating. However, as Fig. 2 illustrates, a particular suction stimulus could generate dramatic current response at –20 mV, but none at –40 mV, and since this alone argues strongly against hypothesis (a), we approach this study with a certain bias in favor of hypothesis (b).
To start, we asked a simple question motivated by the fact that moderate stretch has essentially the same effect on WT current amplitude and time course as applying several millivolts of additional depolarization (Tabarean and Morris, 2002). Are gating energies from stretch and depolarization completely interchangeable in Shaker channels? To test this exhaustively, a mutant like 5aa with a balanced, bipartite kinetic signature (i.e., activation and inactivation at similar rates) was desirable. We applied membrane stretch, stepped to test voltage X, and recorded the current. If stretch is strictly a surrogate for voltage, we reasoned, it should be possible to reproduce, without stretch, the same PO time course at a voltage some millivolts more depolarized (X + V).
Fig. 3 A illustrates a representative experiment: A recording at 50 mV with stretch was directly followed by 5aa recordings at stepwise increased depolarizations without stretch. To compare PO time courses, currents were scaled to compensate for the increased driving force at higher depolarizations. Rising phases at 50 mV with stretch and 85 mV without stretch were completely scaleable, indicating the same time course of PO rise (Fig. 3 B), but the current decline at 50 mV with stretch was much faster than that at 85 mV without stretch. (As Fig. 8 A illustrates, under all conditions late current relaxed to the same vanishingly small level, validating this kinetic interpretation.) The inescapable conclusion is that as sources of gating energy, voltage and stretch are not completely interchangeable for all steps, so we now examine stretch effects on current rise and decline separately.
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What about deactivation reactions? For the reversible four-step model, steady-state 
, with voltage-dependent activation and deactivation rates and ß. Half maximal steady-state activation is reached for 
. The midpoint voltage of the 5aa g(V) relation (Gonzalez et al., 2000) is 0 mV. Thus, for voltages positive to 0 mV, activation is >5x faster than deactivation, which may be ignored in a first approximation. Note that Gd3+ (used in stretch experiments) right-shifts Shaker g(V) curves (Gu et al., 2001). In APPENDIX A(2) we discuss how deactivation affects delay and maximum slope versus voltage relations.
The open probability time course for the irreversible 4-step model,
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has superscript P (for probability) to distinguish it from the maximum slope SMax of the current, which is Eq. 3 multiplied by the driving force. The voltage dependence of and td is determined by the exponential voltage dependence of the activation rate (V),
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We approximated F/RT by 0.039 mV–1 (Faraday constant, F = 96500C/mol; gas constant. R = 8.134 J/mol K; temperature, T = 298K).
Conformational changes during S4 movement and channel opening are discontinuous motions, a succession of fast transitions over energetically (sterically and electrostatically) unfavorable states, plus relatively long sojourns in more stable states (Bezanilla, 2000). If the total gating charge moved during a subunit conformation change with forward rate is z, then z (in Eq. 5) is the part of z moved during transformation into the transition state from the stable conformation further from the open state. Only z influences the forward rate, since the rest of the transition is energetically downhill and thus fast. zß = z – z then determines the voltage dependence of the back transformation rate.
Shaker WT activation models (more activation steps per subunit, additional concerted pore opening steps) do not generally produce monoexponential td(V) and (V) relations (unpublished result). Later we discuss effects of some model additions on td(V) and (V). The diminished S3–S4 linker of 5aa might simplify its activation by making one transition per subunit rate-limiting for opening. Interpreted in the context of the four-step model, delay and maximum slope monitor this rate-limiting step; the Eq. 3 fit of td(V) in Fig. 4 B yields estimates for 0 and z, of 12 s–1 and 0.68, respectively. Obviously, four times this z is only a fraction of the total 12–13 electronic charges moved during Shaker gating (e.g., Schoppa et al., 1992). For WT, Zagotta et al. (1994a) also obtained relatively small gating charges for single activation and deactivation steps and so concluded that charge movement was spread among many activation transitions. With our method, we observe only transitions that shape activation kinetics. Transitions faster than the rate-limiting ones influence neither opening kinetics nor the voltage dependence of td(V) and SMax(V), thus the gating charge they contribute goes unnoticed. Interestingly, too, the fit of the 5aa g(V) relation with a fourth order Boltzmann yields a gating charge of only four times 1.65 electronic charges, which would be z + zß of the rate-limiting activation step (Gonzalez et al., 2000).
The kinetic simplicity of 5aa activation was probed further by testing how well the current rising phase was fitted by Eq. 2 (i.e., PO(t) for Scheme I)
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0 and z from the td(V) fit shown in Fig. 4 B. The four-step model fits the rising phases well at all voltages, indicating that Scheme I adequately describes 5aa activation kinetics. Because currents from some patches were less clear-cut, we later show how inactivation, deactivation, additional activation steps per subunit, and concerted steps would affect our ability to fit simulated td(V), (V) and PO(t) using the irreversible four-step model.
However, in eight of eight patches without stretch, td(V) was well-described with Eq. 4 and z = 0.64 ± 0.02 (mean ± SEM). In six of those eight, SMax(V) was well described by the same exponential function (multiplied by a constant and (V + 90 mV) for the driving force). In one case, SMax(V) could not be described by a single exponential, in another the fitted single exponential had a different exponent. The estimates of 0 from the td(V) fit (8.9 s–1 ± 1.4 s–1) varied with a negative correlation (r = –0.46) between 0 and z. Temperature variations might explain this since 0 will increase with temperature while z will seem smaller: a temperature-related exponent decrease in the fits of Eqs. 3 and 4 to experimental td(V) and SMax(V) will decrease the resulting z, which we calculate assuming 298°K (see Eq. 5). Oocyte batch–dependent membrane properties might also affect 0. In any case, it is reassuring that z, representing gating charge, was less variable.
For four of eight current families, Eq. 2 with z and 0 from the fit of their td(V) described well at all voltages both the current rising phases and current amplitudes at large depolarizations. In two other families the rising phases were well fitted at all voltages, but Eq. 2 did not reproduce amplitude saturation at large depolarizations (see Fig. 9 B, insets, in APPENDIX). In another case, at mild depolarizations, the amplitude of an Eq. 2 fit that matched the initial current rise was smaller than the current amplitude (see Fig. 11 B, insets).
Stretch Effects on Activation Kinetics
Fig. 5 A shows td(V) and SMax(V) for currents at 0–90 mV with and without stretch. At all voltages, stretch increased the maximum slope and decreased the delay. The exponential voltage dependence of td and SMax was preserved and, moreover, could be described with the same exponent for both functions, with and without stretch. This strongly indicates that both stretch and voltage act on the rate-limiting activation step, with stretch increasing 0, the subunit activation rate at 0 mV. This sensitivity of 0 points to a stretch-induced decrease in the conformational energy barrier between the two stable voltage sensor states of the rate-limiting gating transition. There may be stretch effects on transitions in the voltage-dependent activation path too fast to shape current kinetics. We can, however, exclude the possibility of another, solely stretch-activated opening pathway. In that case, stretch would affect the voltage dependence of SMax and td differently, change the voltage-dependent exponential or, very likely, render the voltage dependence nonexponential.
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0 and z from the td(V) fits there. Those fits capture the early rising phase, but at the lower voltages the current deviates from the scaled PO(t) earlier than in the example without stretch in Fig. 4, probably because 0 without stretch was 8 times slower in Fig. 5 B than in Fig. 4, so inactivation would have more strongly influenced the current rising.
In five such experiments, td(V) and SMax(V) with and without stretch were well-described by exponentials with the same exponent z (multiplied by a linear driving force term for SMax(V)). z was 0.71 ± 0.10 (mean ± SEM), similar to the value obtained for the eight patches not subjected to stretch (0.64 ± 0.02) (by t test, the two means have 60% probability of being from the same distribution). Again, 0 was more variable: 0 = 7.7 s–1 ± 4.4 s–1 without stretch and 19.5 s–1 ±13.5 s–1 with. Although stretch was always applied via –45 mm Hg suction, tensions would differ among patches. The SEM of 0 was made large by one experiment (0 = 25 s–1 without, 73 s–1 with stretch and z = 0.43—an example of the above-mentioned correlation between large 0 and small z). In four of five patches, current rising phases with and without stretch were satisfyingly fitted with Eq. 2, using z and 0 obtained from fits of td(V). As in Fig. 5 B, the fits reproduced the initial current rise. They overestimated the later amplitudes at small depolarizations, but approximated the full activation time course at large ones. In the fifth experiment, the fit underestimated current amplitude at moderate depolarizations and exceeded it at large ones.
Considering Some Realistic Model Additions
We have illustrated successful attempts to explain 5aa activation over a voltage range with and without stretch with the four-step model in Scheme I. Usually td(V) and SMax(V) were well fitted with the exponentials in Eqs. 3 and 4, and current rise could be described by scaled versions of PO(t) from Eq. 2, using the parameters from the delay fit. Given the (relatively fast) "slow" inactivation of 5aa, one would not expect Eq. 2 to reproduce current rise and final amplitude at mild depolarizations, and it is satisfying that at large ones (saturated PO) the fit and current amplitudes were often identical. In APPENDIX A, however, we consider two issues. (1) Might activation kinetics really be substantially different and only accidentally described by the four-step model? (2) Even though Eqs. 3 and 4 usually described td(V) and SMax(V) with/without stretch satisfyingly, for some recordings Eq. 2, with the parameters from the delay fit, failed to reproduce at large depolarizations the combination of current rise and amplitude.
As an attempt to explain such failures while keeping an eye to issue 1, we consider the impact of some realistic additions to Scheme I: inactivation, deactivation reactions, cooperative last activation steps, and finally, more activation steps per subunit. Some of these extended models do not yield analytical expressions for td(V) and SMax(V). Others do, but with more unknown parameters than Eqs. 3 and 4, making their fits to the experimental delay and maximum slope relations less meaningful. Instead of trying to fit our data with the latter models, our strategy is to take their output—simulated td(V) and SMax(V) relations—and try to fit them with the expressions from the irreversible four-step model, looking for signature inadequacies in the fits that might resemble inadequacies observed when fitting our experimental data.
Thus, we eventually exclude some extended models and make a case for others. We never observed behavior characteristic for an activation pathway with more than one kinetically significant step per subunit. We also exclude five-step models with voltage-independent final concerted steps. To explain most of our data, and even most deviations encountered from the behavior of the basic four-step model, a simple irreversible four-step model with inactivation from the open state (see Scheme II)
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), though its effect on current activation properties is practically indistinguishable from that of inactivation (which is, in any case, required to explain the fast current decline). We also cannot fully exclude a contribution from deactivation reactions; they may explain rarely encountered deviations of our data from expectations of Scheme I (see Figs. 10 and 11 B, insets).
Slow Inactivation in 5aa
5aa currents are transient, with characteristic decline times comparable to those of WT. Having acknowledged that inactivation can affect current rise, we ask how activation might affect the falling phase, using a simple model of 5aa inactivation (Scheme II), in which "inactive" can only be reached via "open". Inactivation from states with closed activation gates may occur for Shaker WT (Klemic et al., 2001), but 5aa currents did not show the characteristic minimum in decline rate indicative of this "U-type inactivation".
In the most extreme case (rate-limitation of genuinely fast channel inactivation by slow activation) the inactivation rate i has no influence on current kinetics. If activation and inactivation rates are similar, both shape current rise and decline in a multiexponential fashion (Hille, 2001). Finally, if inactivation is slower than activation, the inactivation rate will be the main determinant of falling phase kinetics and what little influence the activation rate still has dies away with increasing depolarization. Which of the three regimes describes the falling phase of 5aa currents? A brief model analysis shows how to answer this question. We extend Scheme I by one inactivation step:
The resulting time course of O(t) (and the related PO(t)) is a sum of exponentials. See APPENDIX B for a discussion of activation's influence on the current falling phase in the three regimes i >> , i 
and i << . In a nutshell, for i << , O(t) kinetics are solely determined by multiples of the rate . Normalizing the currents and rescaling the time then completely maps O(t) time courses for different voltages (see Eq. A6), a property that distinguishes this inactivation regime from the others.
Fig. 6 A shows a typical current family at –10 to 80 mV. In Fig. 6 B, currents are normalized, with times rescaled to match the rising phases. If inactivation were rate limited by activation, the currents would overlap completely. Instead, there was a progressive slowing of the scaled falling phase with increasing voltage. Evidently, a less voltage-dependent process than activation largely governed the current decline. The current falling phases are well described by the exponential decline in Eq. 1, as illustrated in Fig. 6 C for unscaled currents at several voltages. The late current plateau likely originated in rare returns from the inactive to the open state (neglected in Scheme II). Fig. 6 D shows the decline time constant (
in Eq. 1) as a function of voltage. The current decline rate increased only 1.5-fold between 0 and 80 mV, while the activation rate increased eightfold.
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, decline not rate limited by activation—were typical, with eight of nine families (no stretch) showing all these features. The pattern illustrated in Fig. 6, B–D, strongly argues against rate limitation of the current decline by activation (i >> ), as does the finding (Gonzalez et al., 2000) that 5aa PO saturation starts around 50 mV (i >> and PO saturation are mutually exclusive, see APPENDIX B). Experiments with stretch (see below) had Gd3+ (which right-shifts Shaker g(V) relations (Gu et al., 2001)), but we still expect PO saturation near the range of voltages studied. For large depolarizations, inactivation must be in the i 
or i << mode. If i << , (V) must reflect genuine voltage dependence in i. For i 
, voltage dependence of i is not required to explain that of . If keeps decreasing for voltages beyond PO saturation, i must be voltage dependent. Unfortunately, it is uncertain if PO saturated in experiments like that in Fig. 6, i.e., for voltages less depolarized than 80 mV. Arguing against an influence of activation on the falling phase above 0 mV, and in favor of (weakly) voltage-sensitive inactivation, is the monoexponential decline of the current falling phases (see Fig. 8 C).
Stretch Effects on Slow Inactivation
As Fig. 3 illustrated, stretch dramatically accelerated the current falling phase. As summarized there, a certain voltage increment that reproduced the stretch-induced acceleration of current activation did not reproduce that of the falling phase: slow inactivation must be directly stretch sensitive and, compared with activation, proportionately more stretch than voltage sensitive. Fig. 7 plots falling phase (V) and despite scatter ( was extremely variable, sometimes even within a patch), a clear separation of values with and without stretch emerges.
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(Fig. 8 B), producing a similar speeding of the current falling phase at all voltages. This further indicates that stretch effects on current decline cannot be entirely mediated via accelerated activation, which must wane as PO saturates with depolarization. Fig. 8, C and D, show normalized currents from A without (Fig. 8 C) and with (Fig. 8 D) stretch, with times scaled so the rising phases of all currents match the rise at 10 mV. With or without stretch, current decline above 10 mV was not rate limited by activation. The progressive slowing of the decline with depolarization indicates that a less voltage-dependent rate—the slow inactivation rate i—progressively dominated the current decline.
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and its multiples (i >> , see APPENDIX B, Eq. A6), and that the stretch sensitivity of the current time course was purely mediated by that of : Rescaling the time takes care of all stretch-induced kinetic changes, because they are caused by the same change in . But Fig. 8, C and D, showed that the inactivation rate did have an influence on current decline above 10 mV. Current kinetics are described by Eq. A7—there is a new exponential component with rate i. If stretch increased , but not, or differently, i, then a rescaling of the time could not match the exponential components in the stretch and no-stretch curves, and the currents would not overlay completely. Since they do, we must conclude that stretch affected the inactivation rate in exactly the same way as —e.g., if is doubled by stretch, i doubles too. We tested 10 patches for the occurrence of this surprising pattern. The match was nearly perfect across all voltages in four patches, showed only minor deviations of the scaled time courses in four others, and there was no match in two. Eq. A7 does not yield a change in PO for proportional changes in and i but we did observe reversible amplitude increases by stretch, perhaps because stretch increases channel conductivity, but more likely, because it also alters the equilibrium of additional nonrate limiting activation steps. We could dismiss the proportional stretch acceleration of activation and inactivation as coincidental, and simply retain the conclusion that inactivation, too, must be stretch sensitive. Alternatively, we can speculate about shared properties of activation and inactivation. A simple explanation for their identical response to stretch would be that the rate-limiting steps in activation and slow inactivation both involve expansion of the channel protein in the plane of the bilayer, which is likely to be facilitated by lipid decompression caused by membrane stretch.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIX AAPPENDIX BREFERENCES |
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10 linker residues is the norm for six transmembrane voltage-gated channels (e.g., prokaryotic Na; Ren et al., 2001b) and K (Jiang et al., 2003a) channels, and eukaryotic cation (Ren et al., 2001a) and hyperpolarization-activated cyclic nucleotide–gated (Gauss et al., 1998) channels). 5aa was chosen for kinetic scrutiny because both the rise and fall of its currents are reversibly sensitive to membrane stretch and because the two processes occur on comparable timescales and so could be monitored during the same stretch stimulus in any given patch. Moreover, the slow activation of 5aa relative to passive charging times facilitated resolution of early currents. The goal was to determine, from a kinetics standpoint, whether the voltage-dependent transitions of this class of channel are inherently susceptible to the level of membrane tension. Macroscopic cell-attached patch currents were examined without and with stretch, with membrane tension increased reversibly by patch suction. The fact that membrane tension in a given patch was not quantified was not a major shortcoming because analyses were designed around tests at several voltages for each patch before, during and after a fixed level of pipette suction. As was hoped, simultaneous application of within-patch comparisons to both of two putatively stretch-sensitive kinetic processes, activation and slow inactivation, proved to be particularly worthwhile. Our intent was not to quantify the mechanical contribution of stretch to gating (this has been done in a rudimentary fashion, Tabarean and Morris, 2002) but to identify tension sensitive transitions. Gonzalez et al. (2000) showed that 5aa is kinetically simpler than the parent molecule, making it attractive for extracting microscopic kinetic information from macroscopic currents. Because of the relative simplicity of 5aa gating compared with WT we could seek a parsimonious description of the rate-limiting steps and the kinetic "site" of stretch sensitivity in the two processes of interest, activation and inactivation. In this context, the question of whether gating currents are stretch sensitive is extremely interesting, but achieving channel densities that would permit gating currents to be recorded from patches with and without stretch would be difficult. For activation, the voltage dependence of current delay (td) and maximum slope (SMax) was the same with and without stretch. We interpret the single exponential form of this voltage dependence as reflecting a simple four-step activation pathway with one rate-limiting activation step per subunit. The conservation of general form and voltage dependence of SMax and td with and without stretch signifies that stretch and voltage act on the same rate-limiting activation steps. Stretch might additionally influence activation steps (e.g., pore opening) that are not rate limiting in 5aa, but our kinetic approach does not monitor them. We discussed the input of several model extensions, the most important of which is slow inactivation, whose influence on activation characteristics explains most of the encountered deviations from the behavior of the simple four-step model.
Quantifying the voltage dependence of 5aa slow inactivation is challenging because the current falling phase may be contaminated by events in the activation pathway. Moreover, inactivation can be variable even within a patch. However, voltage dependence in the decline time constant persisted even at very depolarized voltages, where decline is likely not influenced by activation.
For Shaker WT excised patches with high Na and low K at the intracellular face, Starkus et al. (2000) suggested that at positive voltages the voltage dependence of the decline time constant arises from increased Na permeability. K in the pore inhibits inactivation (Lopez-Barneo et al., 1993), so displacing it with Na might speed inactivation. In our experiments, this might contribute to whatever part of the voltage dependence of inactivation was not activation mediated, but it is unclear if the Starkus et al. (2000) effect applies for the physiological ionic conditions used here. A U-shaped voltage dependence of inactivation, with maximal inactivation speed at 0 mV, has been reported by Klemic et al. (2001) for Shaker WT, who propose a model involving inactivation from closed states, but we detected no sign of U-type inactivation in 5aa.
Stretch Susceptibility of 5aa in Light of Sensor Motion Models
In the paddle model (Jiang et al., 2003a), the voltage sensor moves through lipid rather than inside the generally accepted (e.g., Horn, 2002) gating canal. Interestingly, deletion in 5aa of 26 residues between S3 and S4 render its primary sequence far closer to KvAP through this part of the protein than is WT Shaker. The paddle would be dragged through lipid from a closed position almost perpendicular to the pore to the open (then inactivated) position almost parallel to the pore. While this implies substantial lipid displacement during gating it is unclear if a net expansion in the plane of the bilayer is expected. "Gating canal" models of sensor motion are also silent on whether activation would involve net expansion of the channel protein (e.g., Bezanilla, 2002; Gandhi and Isacoff, 2002; Horn, 2002), but as we have emphasized (Tabarean and Morris, 2002), expansion by only a few percent would suffice to explain Shaker stretch sensitivity.
Voltage-gated K-channel gating kinetics slow with hyperbaric pressure (Conti et al., 1982; Meyer and Heinemann, 1997). This may be the reciprocal of the effect of membrane stretch (Tabarean and Morris, 2002). Hyperbaric pressure effects on channel gating are generally interpreted in terms of protein compression and hence of reduced activation volumes (e.g., Macdonald, 2002). Somewhat overlooked is the fact that, because of increased chain ordering, bilayer compression is anisotropic and so high pressures yield a thicker bilayer (Scarlata, 1991). Insofar as stretch thins the bilayer, the reciprocity of elevated pressure/elevated bilayer tension may relate to increased/decreased membrane thickness at the channel–bilayer interface. For either an expanding channel or a voltage-sensor paddle moving through the membrane, displacing lipids should be slower in a thicker more orderly bilayer. Mechanosensitivity and the slowing of both activation and inactivation in human T lymphocyte Kv1.3 channels by high membrane cholesterol (Hajdu et al., 2003]) could have common explanations.
Our findings (like those with cholesterol; Hajdu et al., 2003) are consistent with the possibility that inactivation involves voltage sensor movement, as suggested from the voltage clamp fluorometry of Loots and Isacoff (2000). Merely from the isolated rates, we need not demand that stretch act on activation and inactivation via the same mechanism. Strikingly, however, the kinetics with and without stretch matched after a simple rescaling of the time axis: stretch seems to affect activation and inactivation in a concerted fashion. Since inactivation was not rate limited by activation, this concerted action seems most explicable if both transitions involve, e.g., an expansion of the channel protein, or movement of the same structural groups. There is, of course, an apparent contradiction because the weak voltage dependence of inactivation (compared with activation) does not fit with the substantial voltage sensor movement perpendicular to the electric field needed to explain activation. A hypothesis that could unify the apparent contradictions and predict the stretch-and-voltage sensitivity pattern of 5aa would be this: inactivation and the rate limiting step of activation involve similar degrees of lateral voltage sensor motion, hence their common stretch sensitivity, but the activation motion entails substantially more perpendicular charge movement (e.g., from helix rotation) than does the inactivation motion.
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APPENDIX A |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONAPPENDIX AAPPENDIX BREFERENCES |
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