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Department of Physiology, University of Pennsylvania, Philadelphia, PA 19104

Address correspondence to J. Kevin Foskett, Department of Physiology, B39 Anatomy-Chemistry Bldg/6085, University of Pennsylvania, Philadelphia, PA 19104-6085. Fax: (215) 573-6808; email: foskett{at}mail.med.upenn.edu

	ABSTRACT

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX REFERENCES

 
The InsP₃R Ca²⁺ release channel has a biphasic dependence on cytoplasmic free Ca²⁺ concentration ([Ca²⁺]_i). InsP₃ activates gating primarily by reducing the sensitivity of the channel to inhibition by high [Ca²⁺]_i. To determine if relieving Ca²⁺ inhibition is sufficient for channel activation, we examined single-channel activities in low [Ca²⁺]_i in the absence of InsP₃, by patch clamping isolated Xenopus oocyte nuclei. For both endogenous Xenopus type 1 and recombinant rat type 3 InsP₃R channels, spontaneous InsP₃-independent channel activities with low open probability P_o (0.03) were observed in [Ca²⁺]_i < 5 nM with the same frequency as in the presence of InsP₃, whereas no activities were observed in 25 nM Ca²⁺. These results establish the half-maximal inhibitory [Ca²⁺]_i of the channel to be 1.2–4.0 nM in the absence of InsP₃, and demonstrate that the channel can be active when all of its ligand-binding sites (including InsP₃) are unoccupied. In the simplest allosteric model that fits all observations in nuclear patch-clamp studies of [Ca²⁺]_i and InsP₃ regulation of steady-state channel gating behavior of types 1 and 3 InsP₃R isoforms, including spontaneous InsP₃-independent channel activities, the tetrameric channel can adopt six different conformations, the equilibria among which are controlled by two inhibitory and one activating Ca²⁺-binding and one InsP₃-binding sites in a manner outlined in the Monod-Wyman-Changeux model. InsP₃ binding activates gating by affecting the Ca²⁺ affinities of the high-affinity inhibitory sites in different conformations, transforming it into an activating site. Ca²⁺ inhibition of InsP₃-liganded channels is mediated by an InsP₃-independent low-affinity inhibitory site. The model also suggests that besides the ligand-regulated gating mechanism, the channel has a ligand-independent gating mechanism responsible for maximum channel P_o being less than unity. The validity of this model was established by its successful quantitative prediction of channel behavior after it had been exposed to ultra-low bath [Ca²⁺].

Key Words: single-channel electrophysiology • patch clamp • calcium • Xenopus oocyte • nucleus

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX REFERENCES

 
In many cell types, the second messenger inositol 1,4,5-trisphosphate (InsP₃) is generated in the cytoplasm in response to the binding of extracellular ligands to plasma membrane receptors. InsP₃ binds to its receptor, the InsP₃R, in the ER and activates it as a Ca²⁺ channel to liberate stored Ca²⁺ from the ER lumen into the cytoplasm. This rapid release of Ca²⁺ modulates the cytoplasmic free Ca²⁺ concentration ([Ca²⁺]_i), which serves as a ubiquitous cellular signal that can be manifested temporally as repetitive spikes or oscillations, and spatially as propagating waves or highly localized events (Meyer and Stryer, 1991; Berridge, 1993; Toescu, 1995). The temporal and spatial complexity of this signaling system involves sophisticated regulation of the activity of the InsP₃R by various mechanisms, including cooperative activation by InsP₃ (Meyer et al., 1988; Mak et al., 1998) and biphasic feedback from the permeant Ca²⁺ ion (Iino, 1990; Bezprozvanny et al., 1991; Mak et al., 1998).

A family of three InsP₃ receptor isoforms has been identified—types 1, 2, and 3, with different primary sequences derived from different genes (Patel et al., 1999). Recent studies have demonstrated that channel P_o of both the types 1 and 3 InsP₃R isoforms is modulated with biphasic dependencies on cytoplasmic free Ca²⁺ concentration ([Ca²⁺]_i), suggesting that the channels have two distinct types of functional Ca²⁺-binding sites: activating and inhibitory (Mak et al., 1998, 2001b). InsP₃ activates the InsP₃R by tuning the sensitivity of the channel to Ca²⁺ inhibition, with increases in the cytoplasmic concentration of InsP₃ ([InsP₃]) causing a decrease in the apparent Ca²⁺ affinity of the inhibitory binding sites of the channel. Nevertheless, the fully InsP₃-liganded channel can still be inhibited by Ca²⁺, albeit at sufficiently high concentrations (Mak et al., 1998, 2001b). Importantly, InsP₃ has little apparent effect on activation parameters (half-maximal activation [Ca²⁺]_i, K_act; and activation Hill coefficient, H_act) of the biphasic Hill equation that describes the Ca²⁺ response of the channel, nor does it affect the robust maximum open probability exhibited by either InsP₃R isoform under optimal activating conditions.

Whereas previous studies provided estimates of the affinity of the inhibitory Ca²⁺-binding sites in subsaturating and saturating concentrations of InsP₃ (Mak et al., 1998, 2001b), the apparent affinity of the inhibitory Ca²⁺-binding sites of an InsP₃R channel in the absence of InsP₃ has not been determined. The effects of InsP₃ have been modeled empirically assuming infinitely high affinity of the Ca²⁺ inhibition sites in a channel not bound to InsP₃ (Mak et al., 1998, 2001b), but it is more reasonable to expect that the inhibitory Ca²⁺-binding sites adopt a finite maximal Ca²⁺ affinity in the absence of InsP₃.

Here, we examined activities of the types 1 and 3 InsP₃R channels in the absence of InsP₃ to characterize the apparent affinity of the inhibitory Ca²⁺-binding site of the InsP₃R not bound to InsP₃. We reasoned that since InsP₃ activates the channel by preventing Ca²⁺ from inhibiting it, it might be possible to activate the channel in the absence of InsP₃ by removing Ca²⁺ from the inhibitory site by simply reducing [Ca²⁺]_i to very low levels. We demonstrate that the InsP₃R channel opens spontaneously in the absence of InsP₃ when the channel is exposed to [Ca²⁺]_i < 5 nM, but not when [Ca²⁺]_i is elevated to 25 nM. These observations establish the apparent affinity of the Ca²⁺ inhibition sites of an InsP₃R channel not bound to InsP₃, and they support an allosteric model of InsP₃R activation by Ca²⁺.

Many models have been developed to account for InsP₃R-mediated [Ca²⁺]_i signals, but all previously proposed models of InsP₃R single-channel gating (De Young and Keizer, 1992; Swillens et al., 1994; Kaftan et al., 1997; Marchant and Taylor, 1997; Swillens et al., 1998; Adkins and Taylor, 1999; Moraru et al., 1999) assumed that only the InsP₃-bound state(s) of the receptor is active. Thus, they fail to account for the spontaneous, InsP₃-independent activities of the InsP₃R observed in our study. To provide insights into the mechanisms underlying ligand regulation of InsP₃R channel activity, we have developed an allosteric molecular model that can quantitatively account for not only the spontaneous, InsP₃-independent channel activities in low [Ca²⁺]_i, but all other characteristics of InsP₃ and [Ca²⁺]_i regulation of both types 1 and 3 InsP₃R isoforms observed in nuclear patch clamp experiments (Mak et al., 1998, 2001b, 2003).

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX REFERENCES

 
Selection and Microinjection of Xenopus Oocytes
Maintenance of Xenopus laevis and surgical extraction of ovaries were performed as previously described (Jiang et al., 1998). The level of endogenous InsP₃R channel activity was determined for each new batch of oocytes by patch clamping at least 3 isolated nuclei, obtaining 4–6 patches from each (Mak et al., 2000, 2001b). Rat type 3 InsP₃R (r-InsP₃R-3) channels were expressed by cRNA injection into oocytes ascertained to have extremely low level of endogenous InsP₃R activities. In these studies, one endogenous Xenopus oocyte type 1 InsP₃R (X-InsP₃R-1) channel was observed in 100 patches from 5 batches of oocytes used for r-InsP₃R-3 cRNA injection. In contrast, 544 channels were detected in 330 membrane patches, with 108 patches containing multiple InsP₃R channels, from nuclei of r-InsP₃R-3-expressing oocytes 4–5 d after cRNA injection. Assuming that the types 1 and 3 InsP₃R associate randomly to form tetrameric channels, 97.6% of InsP₃R channels detected in these experiments were contributed by type 3 homotetramers (Mak et al., 2000).

The endogenous X-InsP₃R-1 was studied using batches of oocytes with high level of endogenous InsP₃R activities, up to four days after ovary extraction (Mak and Foskett, 1994, 1997, 1998).

Patch Clamp Data Acquisition and Analysis
Patch clamp electrophysiology of isolated nuclei was performed as described (Mak and Foskett, 1994, 1997, 1998; Mak et al., 2000) in "on-nucleus" configuration at room temperature with the pipette electrode at +20 mV (unless stated otherwise) relative to the reference bath electrode. Transmembrane currents were amplified, filtered at 1 kHz, digitized at 5 kHz and recorded directly onto hard disk.

Channel opening and closing events were identified with a 50% threshold, and channel open probabilities and mean open and closed durations, were evaluated using MacTac software (Bruxton). The number of channels in the membrane patch was assumed to be the maximum number of open channel current levels observed throughout the current record (Mak et al., 2001b). When low channel open probability (P_o < 0.1) was observed, generally only current records lasting >30 s and exhibiting only one open channel current level were used in our analyses to avoid under-estimating the total number of active InsP₃R channels present in the membrane patch, which would lead to over-estimation of channel P_o.

The data points shown for each set of experimental conditions are the means of results from at least four separate patch-clamp experiments performed under the same conditions. Error bars indicate the SEM.

Iterative fitting of the experimentally obtained channel P_o in various [InsP₃] and [Ca²⁺]_i by the different molecular models were performed using Igor Pro software (WaveMetrics) with a nonlinear least-square fit (Levenberg-Marquardt) algorithm.

Solutions for Patch Clamp Experiments
All pipette solutions used in patch clamp experiments contained 140 mM KCl and 10 mM HEPES, except the low KCl solutions, which contained 14 mM KCl and 1 mM HEPES. The pipette solutions were pH adjusted to 7.3 with KOH.

By using K1 as the current carrier and appropriate quantities of the high-affinity Ca²⁺ chelator, BAPTA (1,2-bis(O-aminophenoxy) ethane-N,N,N',N'-tetraacetic acid; Molecular Probes) (500–1,000 µM), Ca²⁺ concentrations in our experimental solutions were tightly controlled (Mak et al., 2003). For solutions with free [Ca²⁺] > 10 nM, free [Ca²⁺] was directly measured using Ca²⁺-selective minielectrodes (Baudet et al., 1994). For experimental solutions with [Ca²⁺] < 10 nM, the total [Ca²⁺] was determined by induction-coupled plasma mass spectrometry (Mayo Medical Laboratory) to be 6–10 µM. In the presence of 1 mM BAPTA in 140 mM KCl, 10 mM HEPES and 0.5 mM ATP at pH 7.3, the [Ca²⁺]_i was calculated to be 0.9–1.5 nM using the Maxchelator software (C. Patton, Stanford University, Stanford, CA). Direct measurement by Ca²⁺-selective electrode confirmed the free [Ca²⁺] to be <5 nM, but the accuracy of this measurement was limited by the nonlinearity of the calibration curve of the electrode in such low free [Ca²⁺].

Pipette solutions contained various concentrations of Na₂ATP, either 0 or 10 µM of InsP₃ (Molecular Probes) and either 0 or 100 µg/ml heparin (Sigma-Aldrich) as stated.

The bath solutions used in all experiment had 140 mM KCl, 10 mM HEPES, 300 µM CaCl₂, 500 µM BAPTA (measured [Ca²⁺] 400–500 nM), and pH 7.3.

Online Supplemental Material
The online supplemental material provides details, descriptions, and derivations of the allosteric models (both Monod-Wyman-Changeux [MWC] based and non-MWC–based models) that were considered to describe the ligand regulation of the InsP₃R channel gating. The mathematical derivations from first principles of the equations used to calculate the theoretical InsP₃R channel P_o according to each of those models are presented, and comparisons between the calculated channel P_o and experimental data under selected conditions are discussed. Online supplemental material is available at http://www.jgp.org/cgi/content/full/jgp.200308809/DC1.

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX REFERENCES

 
Regulation of Types 1 and 3 InsP₃R Channel P_o by Cytoplasmic Ca²⁺, InsP₃ and ATP
Single X-InsP₃R-1 and r-InsP₃R-3 channels observed in the same nuclear membrane system exhibit biphasic regulation by [Ca²⁺]_i, with open probabilities (P_o) well described by the empirical biphasic Hill equation (Mak et al., 1998, 2001b):

(1)

where P_max is the maximum channel open probability that can be achieved by the InsP₃R channel under optimal [Ca²⁺]_i and saturating [InsP₃], K_act is the half-maximal activating [Ca²⁺]_i, H_act is the activation Hill coefficient, K_inh is the half-maximal inhibitory [Ca²⁺]_i, and H_inh is the inhibition Hill coefficient.

In nuclear patch clamp experiments, both InsP₃R isoforms achieve a robust P_max of 0.8 under optimal conditions. X-InsP₃R-1 and r-InsP₃R-3 channels both exhibit similar inhibition by Ca²⁺: K_inh in the presence of saturating [InsP₃] is 40–50 µM, and H_inh is 3–4, indicating that the Ca²⁺ inhibition process is highly cooperative. InsP₃ activates both channel isoforms by increasing K_inh, i.e., decreasing the sensitivity of the channel to Ca²⁺ inhibition, with no effect on the other Hill equation parameters (P_max, H_inh, K_act or H_act) (Mak et al., 1998, 2001b). In the presence of 0.5 mM free ATP, the InsP₃-concentration dependence of K_inh of each InsP₃R isoform can be described empirically by a simple Hill equation (Mak et al., 1998, 2001b):

(2)

with similar parameters: the half-maximal activating [InsP₃] (K_IP3) 50 nM, the Hill coefficient (H_IP3) 4, and the maximum half-maximal inhibitory [Ca²⁺]_i at saturating [InsP₃] (K_inh) 45 µM.

Since the affinity of the inhibitory Ca²⁺-binding site must be finite even in the absence of InsP₃, we hypothesized that the InsP₃ requirement for channel activities could be waived if Ca²⁺ could be dissociated from the inhibitory Ca²⁺-binding site by an InsP₃-independent method. Although one straight-forward method to accomplish this would be by lowering [Ca²⁺]_i, channel opening requires Ca²⁺ binding to Ca²⁺ activation sites. We speculated that InsP₃-independent channel activities should occur in low [Ca²⁺]_i conditions in which Ca²⁺ would dissociate only from the inhibitory sites but not from the activating sites. Thus, we attempted to determine if simply dissociating Ca²⁺ from the inhibitory sites would be sufficient to activate channel opening, by using experimental conditions in which the affinity of the activating Ca²⁺-binding site was as high as possible. It was previously demonstrated that cytoplasmic free ATP acid (ATP^3- and ATP^4-) markedly enhances the Ca²⁺ affinity of the activation sites in both isoforms (Mak et al., 1998, 2001b). In saturating (10 µM) InsP₃, the r-InsP₃R-3 in 0.5 mM ATP and the X-InsP₃R-1 in 9.5 mM ATP both exhibit a moderate P_o of 0.2–0.4 in the presence of very low (25 nM) [Ca²⁺]_i (Mak et al., 1999, 2001a). Thus, the requirement for Ca²⁺ binding to the Ca²⁺ activation site is satisfied at this Ca²⁺ concentration under these conditions. We reasoned that if the minimum value of K_inh of the channel is not too low (for example, >20 nM), then InsP₃R channel activity should be observable at 25 nM Ca²⁺ in appropriate [ATP] even in the absence of InsP₃.

Lack of Channel Activity at 25 nM Ca²⁺ for InsP₃R Not Bound to InsP₃
A series of experiments was performed with membrane patches obtained from the same areas (±2 µm) of isolated nuclei from uninjected oocytes, where clustering of endogenous X-InsP₃R-1 channels gave an exceptionally high probability of observing channel activity in membrane patches (Mak and Foskett, 1997). The pipette solutions alternately contained either 25 nM Ca²⁺, no InsP₃, and 9.5 mM free ATP; or 1,150 nM Ca²⁺, 10 µM InsP₃, and 0.5 mM ATP. The latter solution is one that maximizes the P_o of the channel (Mak et al., 1998), and was therefore used to ensure that lack of channel activities in the former solution was not due to absence of InsP₃R in the patched membranes. Whereas X-InsP₃R-1 channel activities were detected in all eight patches with pipette solutions containing 10 µM InsP₃, no channel activity was observed in any of the 26 patches with pipette solutions lacking InsP₃. Thus, the type 1 channel cannot open in the absence of InsP₃ in 25 nM Ca²⁺. In a parallel series of experiments using nuclei from r-InsP₃R-3–expressing oocytes, in which the expressed recombinant channels exhibit similar clustering (Mak et al., 2000), no r-InsP₃R-3 channel activity was detected in any of the eight patches with pipette solutions lacking InsP₃, even though r-InsP₃R-3 channel activities were observed in all seven patches with pipette solutions that contained 10 µM InsP₃. These results therefore suggested that the apparent K_inh in the absence of InsP₃ (K_inh⁰) for both the X-InsP₃R-1 and r-InsP₃R-3 channel isoforms is lower than 25 nM.

InsP₃-independent Activity of X-InsP₃R-1 at Ultra-low [Ca²⁺]_i
When [Ca²⁺]_i was further decreased to <5 nM (calculated to be 0.9–1.5 nM, see MATERIALS AND METHODS), with no InsP₃ and 0.5 mM ATP in the pipette solution, channel activities with low open probability of 0.03, and with conduction and gating properties very similar to those of the InsP₃R were observed in nuclei from uninjected oocytes (Fig. 1 A). Even though these channel activities were observed in the absence of InsP₃, several characteristics identified them as being contributed by the endogenous X-InsP₃R-1. First, the most frequently observed (>90%) channel conductance was 330 ± 15 pS (Fig. 2 A), indistinguishable from that of the InsP₃-activated X-InsP₃R-1 channels observed in the same system (Mak and Foskett, 1998). Importantly, no channel activities with conductances between 100 and 450 pS have been observed previously in the absence of InsP₃ in thousands of nuclear patch clamp recordings on isolated oocyte nuclei (Mak and Foskett, 1998; Mak et al., 1998). Second, although the P_o of the X-InsP₃R-1 channel has a strong [Ca²⁺]_i-dependence, the mean channel open duration <_o> lies within a narrow range (3–12 ms) in all the various experimental conditions previously investigated (Mak et al., 1998, 1999). <_o> of the channel activities observed in < 5 nM [Ca²⁺]_i was 3.4 ± 0.4 ms (Fig. 1 A), which is within the normal narrow range of <_o> exhibited by X-InsPR₃-1 channels (Fig. 1 F). Third, the probability of observing this channel activity in a membrane patch (P_d) in these experimental conditions was similar to that in the same nucleus with pipettes containing an optimal activating solution (1,150 nM Ca²⁺, 10 µM InsP₃, and 0.5 mM ATP; Fig. 3 A). Fourth, both the slope conductance (365 ± 20 pS) and reversal potential (56 ± 2 mV) of the channel observed in <5 nM [Ca²⁺]_i and 0 InsP₃ (Fig. 2 B) in the presence of asymmetric KCl conditions (14 mM KCl in the pipette and 140 mM KCl in bath) were very similar to those values (312 ± 20 pS and 54 ± 2 mV, respectively) observed for InsP₃R channel under similar ionic conditions in the presence of 1 µM [Ca²⁺]_i and 10 µM [InsP₃] (Fig. 2 C). This indicates that the channel responsible for the activities observed in the absence of InsP₃ has the same channel conductance and cation selectivity as the InsP₃R channel under the same ionic conditions. Together, these observations render it highly unlikely that the channel activities observed in <5 nM [Ca²⁺]_i were due to channels other than the X-InsP₃R-1.

View larger version (53K): [in this window] [in a new window]   FIGURE 1. Typical single-channel current traces of X-InsP3R-1 channels in various [Ca2+]i, [ATP] and [InsP3], as labeled. Arrows indicate closed channel current levels. 100 µg/ml heparin was used in +heparin experiments.

View larger version (16K): [in this window] [in a new window]   FIGURE 2. (A) Channel current versus applied transmembrane potential curve for InsP3R channels (n = 4) observed in symmetric 140 mM KCl in the presence of [Ca2+]i < 5 nM, 0.5 mM ATP and no InsP3. (B and C) Current traces with InsP3R channel observed under an applied potential ramp in 140 mM KCl bath and 14 mM KCl pipette solutions. For B, pipette solution contained [Ca2+]i < 5 nM, 0.5 mM ATP and no InsP3, whereas for C, pipette solution contained 1 µM [Ca2+]i, 0.5 mM ATP and 10 µM InsP3. The slope conductances of the channels were evaluated as the difference between the slopes of the open (dashed line) and closed (solid line) channel current levels. The positive reversal potentials (as tabulated in the graphs) indicate that the InsP3R channels observed are cation selective.

View larger version (25K): [in this window] [in a new window]   FIGURE 3. (A) Pd and (B) Po histograms of the X-InsP3R-1 channel in various experimental conditions. In the Pd graph, numbers above each bar represent the fraction of nuclear membrane patches obtained that exhibited X-InsP3R-1 channel activities. In the Po graph, the number above each bar is the number of single-channel current records used to evaluate Po. Given the variance of the channel Po in experiments performed under the same experimental conditions, the channel Po observed under the various set of experimental conditions are not statistically different (P > 0.05 from t test) from Po observed under control conditions (0 InsP3, 0.5 mM ATP, [Ca2+]i < 5 nM).

Of note, because K_act = 190 nM in 0.5 mM ATP (Mak et al., 1998), the activating Ca²⁺-binding site of the X-InsP₃R-1 channel was also effectively unoccupied when [Ca²⁺]_i < 5 nM. This result suggests that the spontaneous channel activity can occur when both the activating as well as the inhibitory Ca²⁺ sites are un-liganded. Because ATP stimulates channel activities by enhancing the functional affinity of the activating Ca²⁺-binding sites (Mak et al., 1999), the fact that the activating Ca²⁺-binding sites remain effectively unoccupied in <5 nM Ca²⁺ predicts that the InsP₃-independent channel activities should be unaffected by ATP. In agreement, channel activities with similar conductances were observed regardless of [ATP] (0–9.5 mM; Fig. 1, A, D, and E). Neither P_d nor P_o of the X-InsP₃R-1 channel in the absence of InsP₃ were significantly affected by [ATP] (Fig. 3, P > 0.05). Together, these results demonstrate that the X-InsP₃R-1 channel has an intrinsic, low P_o even when its InsP₃-binding sites and activating Ca²⁺-binding sites are not occupied, as long as its inhibitory Ca²⁺-binding sites are unoccupied.

InsP₃-independent Activity of r-InsP₃R-3 at Ultra-low [Ca²⁺]_i
Similar results were obtained for the recombinant r-InsP₃R-3 channels. In <5 nM [Ca²⁺]_i, channel activities with conductances very similar to those of the X-InsP₃R-1 were also observed in nuclei from r-InsP₃R-3 cRNA-injected oocytes, independent of [InsP₃] (0 or 10 µM), [ATP] (0 or 0.5 mM), or the presence of heparin (100 µg/ml) (Fig. 4 , A–D). Also similar to the X-InsP₃R-1, the P_o of the r-InsP₃R-3 channel at <5 nM [Ca²⁺]_i exhibited no systematic or statistically significant dependence (P > 0.05) on [InsP₃] or [ATP] (Fig. 5 B). <_o> of the observed type 3 channels were 3.5–9 ms, very similar to the <_o> of 3–20 ms exhibited by the channel in the presence of InsP₃ (comparing Fig. 4, A–D, with Fig. 4 E). P_d of the channel activities at [Ca²⁺]_i < 5 nM under various [InsP₃] and [ATP] were similar to that for experiments using the same cRNA-injected oocyte nuclei with a pipette solution containing 1,150 nM Ca²⁺, 10 µM InsP₃, and 0.5 mM ATP (Fig. 5 A). These results indicate that, similar to the X-InsP₃R-1, the inhibitory Ca²⁺-binding sites of r-InsP₃R-3 are mostly unoccupied in [Ca²⁺]_i < 5 nM, and the r-InsP₃R-3 channel has a low but nonzero P_o even when its InsP₃-binding sites and activating Ca²⁺-binding sites are not occupied, as long as its inhibitory Ca²⁺-binding sites are also unoccupied.

View larger version (46K): [in this window] [in a new window]   FIGURE 4. Typical single-channel current traces of r-InsP3R-3 channels in various [Ca2+]i, [ATP] and [InsP3], as labeled. Arrows indicate closed channel current levels. 100 µg/ml heparin was used in +heparin experiments.

View larger version (23K): [in this window] [in a new window]   FIGURE 5. (A) Pd and (B) Po histograms of the r-InsP3R-3 channel in various experimental conditions. Numbers tabulated in the graphs have the same meanings as in Fig. 3. Given the variance of the channel Po in experiments performed under the same experimental conditions, the channel Po observed under the various set of experimental conditions are not statistically different (P > 0.05 from t test) from Po observed under control conditions (0 InsP3, 0.5 mM ATP, [Ca2+]i < 5 nM).

	DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX REFERENCES

To provide a better empirical description of the tuning by [InsP₃] of the channel sensitivity to Ca²⁺ inhibition that incorporates our present observations, the simple Hill equation describing the effects of InsP₃ (Eq. 2) has to be modified to:

(3)

where K_inh⁰ is the nonzero minimum K_inh in the absence of InsP₃. The empirical biphasic Hill equation describing the Ca²⁺ dependence of the P_o of the InsP₃R (Eq. 1) also has to be modified to:

(4)

with P_max⁰ and P_max being the maximum P_o when the activating Ca²⁺ sites are unoccupied or fully occupied, respectively. Because the values of P_max, H_act, H_inh, and K_act in the presence of various [ATP] have already been obtained in our previous studies for X-InsP₃R-1 (Mak et al., 1998, 1999) and r-InsP₃R-3 (Mak et al., 2001a,b), the channel P_o for various [Ca²⁺]_i, [InsP₃] and [ATP] can be evaluated using Eqs. 3 and 4. Therefore, even though the values of K_inh⁰ and P_max⁰ are not precisely defined by our observations of spontaneous ligand-independent InsP₃R channel activities, they can nevertheless be estimated using the constraints derived from our observations. First, even in the presence of optimal ATP concentrations, there were no detectable InsP₃R channel activities in 25 nM [Ca²⁺]_i in the absence of InsP₃. Because of the technical limitations of the experimental system, channel activity with P_o < 0.001 is not detectable in our experiments. Thus, the P_o must be lower than 0.001 (marked by the horizontal dashed lines in Fig. 6) in 25 nM [Ca²⁺]_i (marked by the vertical dashed lines in Fig. 6) in the absence of InsP₃. Second, both InsP₃R isoforms exhibited channel activities in 0.9–1.5 nM [Ca²⁺]_i in various InsP₃ and ATP concentrations with P_o as shown in Figs. 3 B and 5 B. The observed X-InsP₃R-1 channel P_o are consistent with those calculated from Eqs. 3 and 4 using P_max⁰ = 0.02–0.07, and K_inh⁰ = 1.2–5.5 nM (Fig. 6 A). Similarly, experimental r-InsP₃R-3 channel P_o agree with those calculated from Eqs. 3 and 4 using P_max⁰ = 0.005–0.018, and K_inh⁰ = 1.2–3.8 nM (Fig. 6 B).

View larger version (22K): [in this window] [in a new window]   FIGURE 6. Estimating Kinh0 and Pmax0 from channel activities at low [Ca2+]i for (A) X-InsP3R-1 and (B) r-InsP3R-3. Different colors correspond to different InsP3 and ATP concentrations as tabulated in the graphs. InsP3R channel Po observed in calculated [Ca2+]i of 0.9–1.5 nM are plotted as data points at [Ca2+]i = 1.5 nM (c.f. Figs. 3 B and 5 B). InsP3R channel Po at various [Ca2+]i can be calculated with Eq. 4 using the values of Pmax, Kact, Hact, and Hinh obtained in our previous studies for X-InsP3R-1 (Mak et al., 1998, 1999) and r-InsP3R-3 (Mak et al., 2001a,b). The values of parameters Kinh0 and Pmax0 in Eq. 4, which were not determined in previous experiments, must be constrained so that: (a) the calculated channel Po at various InsP3 and ATP concentrations agree with experimental observations (i.e., lie within the error limits of the data points at 1.5 nM [Ca2+]i), and (b) the calculated channel Po in the absence of InsP3 is <0.001 at 25 nM [Ca2+]i, so that no channel activity was detected at 25 nM [Ca2+]i. The continuous and dashed curves represent channel Po calculated using two extreme sets of values for Kinh0 and Pmax0 that satisfy those requirements. For X-InsP3R-1, the continuous curves are calculated with Pmax0 = 0.07 and Kinh0 = 1.2 nM; and the dashed curves are calculated with Pmax0 = 0.02 and Kinh0 = 5.5 nM. For r-InsP3R-3, the continuous curves are calculated with Pmax0 = 0.018 and Kinh0 = 1.2 nM; and the dashed curves are calculated with Pmax0 = 0.005 and Kinh0 = 3.8 nM. The observed channel Po data points in both graphs and the continuous curves in A are slightly offset along the [Ca2+]i axis for easier visualization.

Toward an Allosteric Model for the Regulation of InsP₃R Channel Activities by [Ca²⁺]_i and InsP₃
Although Eqs. 3 and 4 can describe the regulation of InsP₃R channel P_o by its ligands Ca²⁺ and InsP₃, enabling the channel P_o at any [Ca²⁺]_i and [InsP₃] to be evaluated in terms of a set of parameters (P_max⁰, P_max, K_act, H_act, H_inh, K_inh⁰, K_inh, K_IP3, and H_IP3) that are deduced from experimental data, the equations are empirical and they do not provide insights into the specific molecular mechanisms underlying ligand regulation of InsP₃R activity. Therefore, it is desirable to develop a molecular model for ligand regulation of InsP₃R activity that can, in terms of simple molecular mechanisms, account for all the features of the regulation of InsP₃R channels (both types 1 and 3 isoforms) by [Ca²⁺]_i and [InsP₃] observed in extensive nuclear patch-clamp studies (Mak et al., 1998, 2001b, 2003; Boehning et al., 2001; and this study), as well as satisfy constraints imposed by the known structure of the InsP₃R molecule and channel.

The observations, for both types 1 and 3 isoforms, that must be accounted for in such a molecular model are as follows:

(i) The InsP₃R channel can be active when none of its ligand-binding sites are occupied ([InsP₃]= 0 and [Ca²⁺]_i = 1.5–2 nM << K_act and K_inh). Spontaneous activities of the InsP₃R channel in the absence of all ligands observed in the present study are reminiscent of the spontaneous activities observed in the acetylcholine receptor channel (Jackson, 1984) and cyclic nucleotide–gated channels (Picones and Korenbrot, 1995). In those channels, ligand-independent gating suggested that allosteric models, in which the channel has a nonzero probability of being open even when its ligand-binding sites are unoccupied, were more appropriate than schemes that assume ligand binding to be necessary for channel opening. The ligand-independent opening of the InsP₃R channels observed here cannot be accounted for by previously proposed models of InsP₃R single-channel gating (De Young and Keizer, 1992; Swillens et al., 1994; Kaftan et al., 1997; Marchant and Taylor, 1997; Swillens et al., 1998; Adkins and Taylor, 1999; Moraru et al., 1999), in which only the InsP₃-bound state(s) of the receptor is assumed to be active. Instead, our new observations suggest that an allosteric model in which the InsP₃R channel has a finite probability of being open even when its activating Ca²⁺ and InsP₃ binding sites are unoccupied (Monod et al., 1965) probably offers a better molecular picture for the ligand activation of the InsP₃R. Furthermore, the model must also account for the absence of any spontaneous InsP₃-independent channel activities in [Ca²⁺]_i = 25 nM.

(ii) When the channel is studied in regular bath [Ca²⁺] (400–500 nM), InsP₃ has no effect on Ca²⁺ activation parameters (specifically K_act and H_act) in the empirical Hill equation (Eq. 2 or 4) of the channel (both isoforms). At a low [Ca²⁺]_i (for example, 100 nM), the channel P_o remains unchanged at either sub-saturating (33 nM) or saturating (10 µM) concentrations of InsP₃. InsP₃ activates the InsP₃R by reducing the sensitivity of the channel to high [Ca²⁺]_i inhibition (i.e., increasing K_inh in Eq. 2 or 4) (Mak et al., 1998, 2001b). This lack of effect of InsP₃ on K_act and H_act cannot be accounted for by any previously proposed model for the InsP₃R channel (De Young and Keizer, 1992; Swillens et al., 1994; Kaftan et al., 1997; Marchant and Taylor, 1997; Swillens et al., 1998; Adkins and Taylor, 1999; Moraru et al., 1999), in which InsP₃ binding to the channel affects Ca²⁺ binding to the activating site, and vice versa.

(iii) When studied in the presence of regular bath [Ca²⁺] (400–500 nM), InsP₃R channel P_o exhibits biphasic regulation by [Ca²⁺]_i in the presence of both saturating (10 µM) as well as subsaturating (100 nM) [InsP₃] (Mak et al., 1998, 2001b).

(iv) Ca²⁺ inhibition of InsP₃R channel activity is extremely sensitive to small changes in [InsP₃] when 10 nM < [InsP₃] < 100 nM. When the [InsP₃] is raised from 10 to 100 nM, the K_inh value for InsP₃R-1 increases by over two orders of magnitude (Mak et al., 1998). Fitting the experimentally derived K_inh for types 1 and 3 isoforms by Eq. 3 indicates that the empirical Hill coefficient for the InsP₃ dependence of K_inh is 4.

(v) The response of InsP₃R channel activity to InsP₃ saturates very abruptly. InsP₃R-1 channel activity is already maximal when InsP₃ = 100 nM, so that the sensitivity of the channel to Ca²⁺ inhibition exhibits no discernible change when [InsP₃] is further increased by over three orders of magnitude from 100 nM to 180 µM. Despite the effect of InsP₃ on the apparent affinity of the inhibitory Ca²⁺ sites of the InsP₃R, once the InsP₃R is fully activated by InsP₃ (i.e., [InsP₃] > 100 nM), the presence of a higher [InsP₃] does not necessitate a higher [Ca²⁺]_i to inhibit the channel. Indeed, the P_o of InsP₃R-1 is equally low at 60 µM [Ca²⁺]_i in the presence of 180 µM or 10 µM InsP₃ (Mak et al., 1998).

(vi) The maximum channel P_o (P_max) attained when the InsP₃R is optimally activated is 0.8, less than 1 (Mak et al., 1998, 2001b).

(vii) The regulation of the InsP₃R channel P_o by Ca²⁺ and InsP₃ mainly affects the mean closed channel duration <_c>, which correlates inversely with the channel P_o, decreasing when the channel is activated and increasing when the channel is inhibited (Mak et al., 1998, 2001b,c). On the other hand, <_o> remains within a narrow range (5–15 ms) over all [Ca²⁺]_i and [InsP₃] until the channel P_o drops to <0.1 (Mak et al., 1998, 2001b,c).

(viii) In addition to the observed properties of the ligand regulation of single-channel InsP₃R activity, a molecular model of the regulation of the InsP₃R channel must also take into consideration the molecular structure of the channel. It is well established that a functional InsP₃R channel is a tetrameric unit (Mikoshiba et al., 1993). Although different isoforms of InsP₃R can assemble to form heterotetramers (Joseph et al., 1995), the InsP₃R channels (both types 1 and 3 isoforms) studied in our nuclear patch clamp experiments were overwhelmingly homotetrameric (Mak and Foskett, 1994; Mak et al., 2000), made up of four identical InsP₃R molecules. Thus, the molecular model for InsP₃R channel should exhibit either a fourfold symmetry or a twofold symmetry (dimer of dimers: Liu et al., 1998; Richards and Gordon, 2000).

(ix) Biochemically, multiple (>3) Ca²⁺-binding regions in the InsP₃R sequences have been identified experimentally (Sienaert et al., 1996, 1997). These sequences, which are located mostly on the cytoplasmic side of the InsP₃R molecule with one exposed to the lumen of the ER, may regulate InsP₃R channel activities. In contrast, only one InsP₃-binding region has been identified in the InsP₃R sequence (Yoshikawa et al., 1996).

Allosteric Models Considered for Describing the Ligand Regulation of the InsP₃R Channel
Because previously proposed models of InsP₃R gating, in which only the InsP₃-bound state(s) of the receptor can be active, fail to account for the spontaneous, InsP₃-independent channel activities of the InsP₃R, we systematically examined a series of allosteric models in increasing levels of complexity to find the simplest molecular model that can account for all the characteristics of the regulation by [InsP₃] and [Ca²⁺]_i of the InsP₃R channel tabulated in the previous section. We started with allosteric schemes based on the Monod-Wyman-Changeux (MWC) model. As outlined in (Monod et al., 1965), the four identical InsP₃R molecules in the homotetrameric channel occupy equivalent positions (condition viii) with an axis of rotational symmetry along the axis of the pore of the channel (as depicted in Mikoshiba et al., 1993), and the four monomers in the channel always adopt the same conformation, changing from one conformation to another concertedly. The InsP₃R channel can change from one conformation with any number of ligands bound to its ligand-binding sites to another conformation with the same number of ligands bound. The equivalent ligand-binding sites of all the identical monomers in an InsP₃R channel have the same affinity. Furthermore, whereas the affinities of the ligand-binding sites can differ in different conformations of the channel, they are not affected by the state of occupation of any other ligand-binding site (Monod et al., 1965; Changeux and Edelstein, 1998). The following MWC-based models were examined:

(a) MWC models in which the InsP₃R tetramer can assume two conformations (one open and one closed), and each InsP₃R monomer has two or more Ca²⁺-binding sties (at least one activating and one inhibitory);

(b) MWC-based models in which the InsP₃R tetramer has three conformations (one open and two closed conformations, or two open and one closed conformations), and each InsP₃R monomer has two Ca²⁺-binding sites;

(c) an MWC-based model in which the InsP₃R tetramer has four conformations (two open and two closed conformations), and each InsP₃R monomer has two Ca²⁺-binding sites;

(d) an MWC-based model in which the InsP₃R tetramer has four conformations (two open and two closed conformations), and each InsP₃R monomer has three Ca²⁺-binding sites;

(e) a variation of model (d) in which the InsP₃R tetramer has two extra closed conformations.

Besides MWC-based models, we also examined allosteric models in which the constraints assumed in the MWC-based models were relaxed to various extents to allow more degrees of freedom to describe the gating behaviors of the InsP₃R channel. In those non-MWC models we considered, the constraint that all the InsP₃R monomers in the tetrameric channel change conformation concertedly is retained. However, the constraints that the equivalent ligand-binding sites of all the monomers in an InsP₃R channel have the same affinity, and that the affinities of the ligand-binding sites are not affected by the state of occupation of any other ligand-binding site, are selectively relaxed. We examined the following non-MWC models:

(f) a "type I" non-MWC model—an allosteric model in which the affinity of the inhibitory Ca²⁺-binding site is affected by the binding status of the InsP₃-binding site on the same InsP₃R monomer—with the InsP₃R tetramer having two conformations, and each InsP₃R monomer having one activating Ca²⁺-binding site and one inhibitory Ca²⁺-binding site;

(g) a type I non-MWC model with the InsP₃R tetramer having two conformations, and each InsP₃R monomer having one activating and two inhibitory Ca²⁺-binding sites, with only one of the inhibitory Ca²⁺-binding sites affected by InsP₃ binding;

(h) a "type II" non-MWC model—an allosteric model in which InsP₃ binding to the InsP₃-binding sites in the tetramer affects the affinities of all the inhibitory Ca²⁺-binding sites and InsP₃-binding sites in the tetramer—with the InsP₃R tetramer having two conformations, and each InsP₃R monomer having one activating and one inhibitory Ca²⁺-binding sites;

(i) a type II non-MWC model with the InsP₃R tetramer having two conformations, and each InsP₃R monomer having one activating and two inhibitory Ca²⁺-binding sites;

(j) a variation of model (i) in which the InsP₃R tetramer has three conformations.

In all the models considered, each InsP₃R monomer has only one InsP₃-binding site because of condition (ix). Detailed descriptions of all the models considered, mathematical derivation of analytical formulas to calculate the InsP₃R channel P_o at various [InsP₃] and [Ca²⁺]_i, the rationales for selecting those models to be studied and not considering other possible allosteric models, and comparisons of experimental InsP₃R channel P_o with those calculated according to the various models, are provided in either the APPENDIX (model (e)), or the online supplemental material section (all other models) available at http://www.jgp.org/cgi/content/full/jgp.200308809/DC1.

Basic Features of the Simplest Allosteric Model That Can Describe the Ligand Regulation of InsP₃R Channel Activity
Among all the models considered, the simplest model, defined as the one involving the fewest number of free parameters (Jones, 1999), that can account for all our observations of the regulation by [Ca²⁺]_i and [InsP₃] of InsP₃R channel activity, and can satisfy the constraints imposed by the structure of the InsP₃R channel, is the MWC-based, four-plus-two-conformation model (model e above). This model postulates that the InsP₃R monomers, and therefore the InsP₃R tetrameric channel as a whole, can adopt six different conformations (Fig. 7) . The channel is open when it is in the A* and C* conformations. The B, D, A', and C' conformations are closed. The equilibria between A*, B, C*, and D conformations are dependent on InsP₃ and Ca²⁺ binding to the channel, which confers regulation of channel activity by [InsP₃] and [Ca²⁺]_i. In contrast, the equilibrium A*A' is not affected by [InsP₃] or [Ca²⁺]_i, i.e., the affinities of the InsP₃ and Ca²⁺ sites of the InsP₃R channel are the same in A* and A'. The ratio of the total durations an InsP₃R channel spends in the A* conformation and in the A' conformation is the same regardless of [InsP₃] and [Ca²⁺]_i. Thus, the A* and A' conformations can be grouped together as the "active" A conformation (a conformation in which the channel can open, denoted by a green box in Fig. 7) when we consider the effects of InsP₃ and Ca²⁺ on channel conformations. Similarly, C' and C* are grouped together as the active C conformation (denoted by a green box with dashed border in Fig. 7) because the equilibrium C*C' is likewise not affected by [InsP₃] or [Ca²⁺]_i. Thus, even in the presence of optimal [InsP₃] and [Ca²⁺]_i, when the InsP₃R channel hardly exists in the closed B and D conformations, the maximum observed channel P_o is <1 because the channel exists a fraction of the time in the closed A' and C' conformations. This accounts for the observation that the maximum InsP₃R channel P_o in saturating [InsP₃] (10 µM) and optimal [Ca²⁺]_i is only 0.8 (<1) (Mak et al., 1998). The model also postulates that each of the four InsP₃R monomers has one InsP₃-binding site (Q) and three different functional Ca²⁺-binding sites (F, G, and H) on the cytoplasmic side of the channel. Because of its tetrameric structure, an InsP₃R channel can bind a maximum of four InsP₃ molecules in its Q sites and four Ca²⁺ in each of the three types (F, G, and H) of Ca²⁺ sites. The affinities of these ligand-binding sites are different in the different channel conformations (A, B, C, and D). InsP₃ and Ca²⁺ regulate channel activity because binding of InsP₃ or Ca²⁺ to these sites will stabilize those conformations in which the sites have higher affinities, thereby affecting the equilibria among the A, B, C, and D conformations, as outlined in Monod et al. (1965).

View larger version (28K): [in this window] [in a new window]   FIGURE 7. The MWC-based four-plus-two-conformation model for InsP3R channel gating. Only conformation transitions are represented in the schemes. Reactions involving binding of InsP3 and Ca2+ to the InsP3R channel and the state of occupation of the various ligand-binding sites of the channel are omitted from the schemes for clarity. The green boxes represent the grouping of the open A* and closed A' conformations into the active A conformation, and the grouping of the C* and C' conformations into the active C conformation.

The mechanisms for Ca²⁺ and InsP₃ regulation are mostly segregated in this model (see the APPENDIX for more detailed reasoning behind this assertion), allowing further reduction in the number of free parameters involved. This means that in our model, InsP₃ binding to the Q sites only affects the equilibria AC, and BD (red double arrows in Fig. 7). In the absence of InsP₃, the equilibria overwhelmingly favor the A and B conformations. InsP₃ regulates the InsP₃R channel solely by stabilizing the C conformation relative to the A conformation; and stabilizing the D conformation relative to the B conformation (indicated by the pink arrows in Fig. 7). Thus, in saturating [InsP₃], the channel exists mostly in the C and D conformations. The equilibria AB and CD (brown double arrows in Fig. 7) are InsP₃-independent, i.e., the affinities of the Q sites in A and B conformations are the same, and so are those of the Q sites in C and D conformations.

The F sites are responsible for the InsP₃-independent Ca²⁺ activation of the channel. Ca²⁺ binding to the F sites only affects the InsP₃-independent AB and CD equilibria (brown double arrows in Fig. 7), stabilizing the active A and C conformations (indicated by the yellow arrows in Fig. 7). The affinities of the F sites are the same in A and C conformations, and so are the affinities of those in B and D conformations. Thus, Ca²⁺ binding to the F sites does not affect the InsP₃-dependent AC, or BD equilibria (red double arrows in Fig. 7).

The H sites are responsible for inhibition of the channel by high [Ca²⁺]_i. The affinities of the H sites are the same in the A and C conformations and are the same in the B and D conformations. Thus, InsP₃-induced shifts (pink arrows in Fig. 7) in the AC and BD equilibria (red double arrows in Fig. 7) do not affect Ca²⁺ binding to the H sites. Ca²⁺ binding to the H sites only affects the InsP₃-independent equilibria AB and CD (brown double arrows in Fig. 7), stabilizing the closed B and D conformations relative to the active A and C conformations (indicated by the yellow arrows).

Regulation of the InsP₃R by the G sites is more complex because the G sites have different affinities (Table I) in the four conformations (A, B, C, and D). The G sites in the closed B conformation have higher Ca²⁺ affinity than those in the active A conformation, so that the G sites are inhibitory Ca²⁺-binding sites (as indicated by the top yellow arrow in Fig. 7) in the AB equilibrium, which is the dominating equilibrium in the absence of InsP₃. Most interestingly, however, the G sites in the active C conformation have higher Ca²⁺ affinity than those in the closed D conformation, so in the CD equilibrium, which is the dominating equilibrium under saturating [InsP₃], the G sites are activating Ca²⁺-binding sites (as indicated by the yellow arrow in the lower half of Fig. 7). Between zero and saturating [InsP₃], InsP₃ binding to the channel shifts it from the A and B conformations toward the C and D channel. Thus, in subsaturating [InsP₃], the "effective" dissociation constant of the G sites in the closed channel lies between those in the B and D conformations, according to the equilibrium position of the channel among the conformations as dictated by [InsP₃]. Similarly, the "effective" dissociation constant of the G sites in the active conformations lies between those in the A and C conformations. As [InsP₃] increases, not only do the G sites change from being inhibitory to activating, the difference between the effective affinities of the G sites in the closed and active channel also changes. As discussed earlier, the InsP₃-induced change in the magnitude of the affinity difference of the G sites alters the full extent of the effect of the G sites on the channel, i.e., how much activation (or inhibition) the G sites produce between zero and saturating [Ca²⁺]_i. It should be noted that since the F and H sites are both InsP₃ independent, the G site is the only one modulated by InsP₃ binding to the channel. Thus, all InsP₃ regulation of the InsP₃R stems from the effect of InsP₃ binding on the properties of the G site.

Considering the InsP₃-independent equilibria AB and CD, the affinities of the Ca²⁺-binding sites are in the order G F > H. For the CD equilibrium, Ca²⁺ will tend to bind first to the G sites and the F sites, both stabilizing the open C conformation, and then to the H sites, stabilizing the closed D conformation. For the AB equilibrium, as [Ca²⁺]_i increases, Ca²⁺ will tend to first bind to the G sites, stabilizing the closed B conformation, and to the F sites, stabilizing the open A conformation. However, Ca²⁺ binding to the F sites cannot overcome the inhibitory effects of the G sites, so the channel remains mostly in the closed conformation. This is because the magnitude of the difference between the affinities of the G site in the closed B and active A conformations is greater than that of the F sites (Table I). Thus, the F site is less effective at activating the channel than the G site is at inhibiting it.

It should be noted that this molecular model does not take into consideration the kinetically abrupt termination of the InsP₃R channel activities that causes the channel activities observed in our