Graded recruitment and inactivation of single InsP₃ receptor Ca²⁺-release channels: implications for quartal Ca²⁺release

Abstract

Modulation of cytoplasmic free Ca²⁺ concentration ([Ca²⁺]_i) by receptor-mediated generation of inositol 1,4,5-trisphosphate (InsP₃) and activation of its receptor (InsP₃R), a Ca²⁺-release channel in the endoplasmic reticulum, is a ubiquitous signalling mechanism. A fundamental aspect of InsP₃-mediated signalling is the graded release of Ca²⁺ in response to incremental levels of stimuli. Ca²⁺ release has a transient fast phase, whose rate is proportional to [InsP₃], followed by a much slower one even in constant [InsP₃]. Many schemes have been proposed to account for quantal Ca²⁺ release, including the presence of heterogeneous channels and Ca²⁺ stores with various mechanisms of release termination. Here, we demonstrate that mechanisms intrinsic to the single InsP₃R channel can account for quantal Ca²⁺ release. Patch-clamp electrophysiology of isolated insect Sf9 cell nuclei revealed a consistent and high probability of detecting functional endogenous InsP₃R channels, enabling InsP₃-induced channel inactivation to be identified as an inevitable consequence of activation, and allowing the average number of activated channels in the membrane patch (N_A) to be accurately quantified. InsP₃-activated channels invariably inactivated, with average duration of channel activity reduced by high [Ca²⁺]_i and suboptimal [InsP₃]. Unexpectedly, N_A was found to be a graded function of both [Ca²⁺]_i and [InsP₃]. A qualitative model involving Ca²⁺-induced InsP₃R sequestration and inactivation can account for these observations. These results suggest that apparent heterogeneous ligand sensitivity can be generated in a homogeneous population of InsP₃R channels, providing a mechanism for graded Ca²⁺ release that is intrinsic to the InsP₃R Ca²⁺ release channel itself.

Modulation of cytoplasmic free Ca²⁺ concentration ([Ca²⁺]_i) is a ubiquitous signalling mechanism that regulates many physiological processes, ranging from gene expression to apoptosis. Receptor-mediated hydrolysis of phosphatidylinositol 4,5-bisphosphate generates inositol 1,4,5-trisphosphate (InsP₃), which binds to its receptor (InsP₃R), a ligand-gated Ca²⁺-release channel in the endoplasmic reticulum (ER). Analyses of InsP₃-mediated [Ca²⁺]_i signals in single cells have revealed them to be extremely complex temporally and spatially, providing different signals to discrete parts of the cell (Berridge, 1993).

A fundamental aspect of InsP₃R-mediated intracellular signalling is the phenomenon of ‘quantal release’, defined here as the ability of cells to have graded release of Ca²⁺ from intracellular stores in response to incremental levels of extracellular agonist or cytoplasmic InsP₃ concentrations ([InsP₃]) (Muallem et al. 1989; Meyer & Stryer, 1990) (reviewed in Bootman, 1994; Missiaen et al. 1994; Parys et al. 1996; Taylor, 1998). Ca²⁺ release in response to InsP₃ has a transient fast phase, whose rate is proportional to [InsP₃], followed by a much slower one even in constant [InsP₃]. Consequently, sustained exposure to submaximal levels of agonists, even over extensive periods, only mobilizes a fraction of total releasable Ca²⁺ in a cell. Quantal Ca²⁺ release has been observed in many cell types under a variety of experimental conditions, including cells with the plasma membrane permeabilized, or with ATP depleted, or with [Ca²⁺]_i kept constant, and in response to poorly metabolizable InsP₃ analogues (Bootman, 1994; Missiaen et al. 1994; Parys et al. 1996; Taylor, 1998). Quantal Ca²⁺ release is surprising because it might have been expected that all InsP₃R channels should become activated in response to any agonist concentration, releasing all of the InsP₃-sensitive Ca²⁺ stores, albeit at different rates depending on the agonist concentration. Despite considerable investigation, there is no consensus regarding the mechanisms that either tune the initial rate of release of Ca²⁺ to [InsP₃], or subsequently significantly slow or terminate release. Several mechanisms involving either InsP₃R or Ca²⁺ store heterogeneity have been invoked to account for graded transient Ca²⁺ release, including the presence of discrete Ca²⁺ stores with different densities of InsP₃R or sensitivities to [InsP₃], or the presence of heterogeneous InsP₃R channels in a continuous store (different channel isoforms with alternatively spliced variants and variable post-translational modifications have been proposed) with different proposed mechanisms of release termination, including regulation of InsP₃R activity by ER luminal [Ca²⁺] or by desensitization or inactivation processes (Bootman, 1994; Missiaen et al. 1994; Parys et al. 1996; Taylor, 1998). Nevertheless, the mechanisms involved in graded transient Ca²⁺ release have remained controversial because experimental evidence has been obtained that has disputed every proposed scheme (Bootman, 1994; Missiaen et al. 1994; Parys et al. 1996; Taylor, 1998).

High-resolution electrophysiological and imaging studies have provided more recent insights into the mechanisms of graded release. First, optical imaging of [Ca²⁺] indicator dyes has revealed the presence of highly localized Ca²⁺ release events whose numbers and frequency are graded with stimulus intensity (Parker & Ivorra, 1990b; Lechleiter et al. 1991; Bootman & Berridge, 1996; Horne & Meyer, 1997; Sun et al. 1998; Thomas et al. 1998). Second, recordings of single InsP₃R channels have suggested that feedback inhibition of channel gating by high [Ca²⁺]_i, tuned by [InsP₃], can grade channel activity with [InsP₃] (Mak et al. 1998, 2001). Together, these observations provide a mechanism to grade Ca²⁺ release that is based on ligand-dependent activity of independent release sites. Thus, in the presence of low [InsP₃] during weak agonist stimulation, sporadic random openings of InsP₃R channels (Mak et al. 1998, 2001, 2003a) generate small localized [Ca²⁺]_i elevations (termed ‘blips’) (Parker & Yao, 1996; Bootman et al. 1997). As [InsP₃] increases, sensitivity of the InsP₃R to Ca²⁺ inhibition is reduced (Mak et al. 1998, 2001), enabling Ca²⁺-induced Ca²⁺ release (CICR) (Iino, 1990) to coordinate openings of neighbouring InsP₃Rs in a local cluster (Yao et al. 1995; Horne & Meyer, 1997; Mak & Foskett, 1997; Thomas et al. 1998) to generate larger Ca²⁺‘puffs’ (Parker & Yao, 1995; Yao et al. 1995; Sun et al. 1998). Puffs remain localized when the level of released Ca²⁺ is insufficient to allow Ca²⁺ diffusing from puffs to activate InsP₃Rs beyond the local cluster (Parker & Yao, 1996), whereas even greater Ca²⁺ release at higher [InsP₃] can enable Ca²⁺ to diffuse far enough to activate channels in other clusters. This progressive recruitment of release sites by even higher [InsP₃] may then account for transitions from local to global Ca²⁺ signals (Bootman & Berridge, 1995; Berridge, 1997). Although this model can account for graded Ca²⁺ release, it is not known if InsP₃-tuning of high [Ca²⁺] inhibition is the primary mechanism used, or whether additional mechanisms also contribute to InsP₃R channel recruitment. Furthermore, this model does not account for observed apparent heterogeneity of InsP₃ sensitivity among release sites throughout different regions of the cytoplasm (Bootman & Berridge, 1996; Parker et al. 1996; Thorn et al. 1996), nor does it provide insights into the mechanisms that underlie time-dependent termination of Ca²⁺ release.

Here, we demonstrate that mechanisms intrinsic to the single InsP₃R channel itself can account for quantal Ca²⁺ release. Patch-clamp electrophysiology of nuclei isolated from insect Sf9 cells yielded a consistent and high probability of detecting apparently homogenous endogenous InsP₃R channels, which has enabled two novel observations. First, by accurate determinations of channel activity durations, we have established InsP₃-induced InsP₃R inactivation as an inevitable process that terminates single channel activity, with the rate of inactivation regulated by [InsP₃] and [Ca²⁺]_i. We established this ligand-dependent process as true inactivation by demonstrating its reversibility. Second, we have been able to accurately quantify the mean number of activated channels in a typical membrane patch under precisely controlled ligand conditions. Whereas it was anticipated that all channels in a homogeneous population would always become activated, even in suboptimal ligand conditions, albeit to lower levels of activity, we found instead that the number of channels activated is a graded function of both [Ca²⁺]_i and [InsP₃]. A qualitative model can account for graded channel recruitment by suggesting that apparent heterogeneous ligand sensitivities can be generated in a homogeneous population of InsP₃R channels. This model also accounts for the ligand concentration dependence of the rate of fateful InsP₃-induced channel inactivation. Thus, our results suggest that quantal Ca²⁺ release can be generated by mechanisms that are intrinsic to the InsP₃R Ca²⁺-release channel itself.

Methods

Spodoptera frugiperda (Sf9) cells (Invitrogen) were grown and maintained in SF-900II serum-free media (Gibco) in suspension culture according to the manufacturer's protocols. For maximum detection of functional InsP₃R channels in patch-clamp experiments, each freshly thawed batch of cells was passaged 3–4 times before being used for electrophysiology. Cells were propagated for up to 7–8 weeks in culture before a new batch was thawed and expanded. Cells were moved from suspension culture to a T-25 flask, allowed to attach to the bottom of the flask for 1 h, and then washed twice with Ca²⁺- and Mg²⁺-free PBS. An ice-cold nuclear isolation solution, containing (mm): 140 KCl, 250 sucrose, 1.5 β-mercaptoethanol, 10 Tris-HCl (pH adjusted to 7.4), with complete protease inhibitor cocktail (Roche Molecular Biochemicals, Indianapolis, IN, USA) and 0.05 mm phenylmethylsulphonylfluoride (PMSF), was added to the flask and the cells were detached by gentle scraping. Homogenization of 1–2 ml of the mixture was performed using 2–4 strokes of the pestle in an ice-cold Dounce homogenizer. A 20–30 μl volume of the homogenized mixture was added to 1 ml standard bath solution (mm: 140 KCl, 10 Hepes, 0.5 BAPTA, pH 7.3, and free [Ca²⁺] adjusted to ∼300 nm) in an experimental chamber on the stage of an inverted microscope. Isolated nuclei are ∼10 μm in diameter, and were distinguished from intact cells based on their unique morphology (Fig. 1B). Fresh homogenizations were performed every 2 h (Mak et al. 2005). The standard pipette solution contained (mm): 140 KCl, 0.5 Na₂ATP, 10 Hepes, pH 7.3, and various [Ca²⁺] and [InsP₃], as indicated. All solutions were carefully buffered to desired free [Ca²⁺] (Mak et al. 1998), confirmed by fluorometry.

Figure 1. Single-channel recording of Sf9-InsP₃R in isolated nuclei.

A, typical multiple Sf9-InsP₃R channel current trace. Five channels, as indicated by open channel current levels (arrows), were activated at beginning of record. Lowest arrow denotes zero-current level. For this particular record, channel activity was recorded for 210 s from the beginning of the record to the last channel closing event. Channels inactivated sequentially until all were inactivated at the end of the record. Data were recorded at +20 mV holding potential in 10 μm InsP₃ and 1 μm Ca²⁺_i. An InsP₃R channel was in a subconductance level in the shaded region. B, identification of nuclei for patch-clamp electrophysiology. In the cell homogenate transferred to the recording chamber, isolated nucleus (arrow) and intact (1) and partially damaged (2) cells were present and morphologically distinguishable. Scale bar, 10 μm. C, single InsP₃R channel current recording during voltage ramp (from −12.5 to +12.5 mV). Open circles and dashed line indicate linear fits of open and closed channel current–voltage (I–V) relations, respectively. The record was obtained in standard bath and pipette solutions, with 10 μm InsP₃ and 1 μm Ca²⁺_i in the pipette solution. D, analysis of number of channels observed in 75 membrane patches with 10 μm InsP₃ and 1 μm Ca²⁺_i. The open bars show observed distribution with average 2.05 channels per patch. The shaded histogram is the theoretical Poisson distribution with same number of membrane patches and mean number of channels per patch.

Data were acquired as described (Mak et al. 1998). Segments of current traces exhibiting one or two InsP₃R channels were used for open probability (P_o) determinations (Mak & Foskett, 1997), and single-channel traces were used for dwell-time analyses by QuB software (Qin et al. 2000). To determine relative ionic permeabilities, patches were excised into normal bath solution, and then exposed to a solution containing (mm): 110 N-methyl-d-glucamine (NMDG) chloride, 30 KCl, 0.192 CaCl₂, 0.5 BAPTA, 10 Hepes, pH 7.3 (for P_K:P_Cl determinations, where P is permeability); 140 KCl, 10 CaCl₂, 10 Hepes, pH 7.3 (for P_K:P_Ca determinations); 140 KCl, 10 MgCl₂, 0.192 CaCl₂, 10 Hepes, 0.5 BAPTA, pH 7.3 (for P_K:P_Mg determinations). Independent polynomial fits (Igor Pro WaveMetrics) of channel open and closed current levels during voltage ramps (10–20 sweeps at 100 mV s⁻¹, from −70 to +30 mV (P_K:P_Cl) or from −50 to +50 mV (P_K:P_divalent) were used to determine reversal potentials, which were corrected for liquid junction potentials. Permeability ratios were calculated using the Goldman-Hodgkin-Katz (GHK) equation for either two or three ion species.

Particular consideration was given to the accurate determination of the number of active channels in nuclear membrane patches (N_A) from the experimental current records. For simplicity, we consider a membrane patch containing n active, identical and independent channels exhibiting Markovian stochastic kinetics with open probability P_o and a single open channel kinetic state with mean open duration of t_o. With these assumptions, events when all n channels open simultaneously follow Markovian kinetics with a probability (P_o)ⁿ and mean duration of t_o/n. If T is the minimum duration of an open event that is detectable after filtering in the experimental system, then average interval σ_n between two successive detectable events when all n channels were open is . Therefore, the number of active channels in a membrane patch (N) can be assumed, with high level of confidence (P < 0.01), to be the maximum number of open channel current levels observed if the channel record lasted longer than 5(σ_N+1). In our patch-clamp set-up, T was empirically determined to be 0.2 ms using test pulses of variable duration (Mak et al. 2001). The t_o value of the Sf9 InsP₃R channels is ∼30 ms over the range of experimental conditions used. In experiments performed using conditions that generated the lowest channel P_o (0.09 at [InsP₃]= 33 nm and [Ca²⁺]_i= 7.5 μm), at most one active channel was involved, and the current records analysed all lasted longer than 5(σ₂). In experiments using conditions that produced higher channel P_o, multi-channel current records were more common, but the duration of each current record analysed exceeded 5(σ_N+1), where N is the number of maximum open channel current levels detected in that record. Thus, the uncertainty in the determination of the number of active channels in a membrane patch was insignificant in the studies described here.

We observe that gating activities of all InsP₃R channels inevitably terminate, i.e. InsP₃R channel activities observed in nuclear patch-clamp experiments have finite durations. To quantify the activity duration for an InsP₃R channel in an experiment, we assume that all channels observed in one experiment inactivated identically, independently, following simple Markovian kinetics with a single time constant (T_a). Then, for an experiment with N active channels and channel activity lasting T_N from the beginning of the experiment to the last channel closing observed in the channel current record, .

Besides the durations of observation of channel activities, another factor affecting the accurate determination of the number of active channels in nuclear membrane patches is the finite time t_s between the initial exposure of the InsP₃R channels to the ligand conditions in the pipette solution as the tip of the patch-clamp pipette made contact with the outer nuclear envelope, and the quality of seal between the isolated membrane patch and the patch pipette tip becoming good enough (seal resistance >200 MΩ) for single-channel current recording. Because of the inactivation of the InsP₃R channels in every experiment, a fraction of all InsP₃R channels stimulated by ligand conditions in the patch pipette were not observed because they underwent inactivation during t_s. For isolated Sf9 nuclei, mean t_s was 6.0 s (standard deviation 2.8 s). With the same assumptions used in T_a evaluation, the actual number of InsP₃R channels activated in an experiment N_A was estimated as N_obs exp(t_s/T_a), where N_obs is the number of InsP₃R channels observed in the current record. For most ligand conditions t_s≪T_a so that the values of N_A are not significantly different from those of N_obs, except in 10 μm InsP₃ and 89 μm Ca²⁺_i, when T_a is so short (9.1 s) that N_A cannot be confidently estimated from N_obs.

All data points shown in all graphs are means of at least four experiments performed at the same [InsP₃] and [Ca²⁺]_i. Error bars indicate s.e.m. The s.e.m. for N_A under one set of ligand conditions was calculated by taking into account the effects of N_obs, T_a and t_s.

Results

Single-channel recording of native InsP₃R in Sf9 cell nuclear membranes

Single InsP₃R channels have been recorded in native ER membranes by patch-clamping nuclei isolated from Xenopus oocytes (Mak & Foskett, 1997) and COS-7 cells (Boehning et al. 2001a). This technique is rationalized by the continuity of the ER with the outer membrane of the nuclear envelope and the role of the nuclear envelope as a Ca²⁺ store similar to ER. Shortcomings of the previously used Xenopus and COS-7 cell systems include lack of consistency in detecting active InsP₃R channels and relatively rapid (t_½ <30 s) apparent channel inactivation following InsP₃-induced activation (Mak & Foskett, 1997; Mak et al. 2000; Boehning et al. 2001a). To discover a better system for studying single InsP₃R channels, we examined insect Sf9 cells. Gigaohm seals were readily achieved (>80% success rate) on carefully selected isolated nuclei (Fig. 1B). With 10 μm InsP₃ and 1 μm Ca²⁺ in the pipette solution, conditions that maximize activity of rat and Xenopus InsP₃R channels in nuclear membrane patches (Mak et al. 1998, 2001; Boehning et al. 2001a), Sf9 InsP₃R channels were consistently detected in 60–80% of patches obtained from nuclei isolated from different batches of cells. Channel activity was evident upon gigaseal formation, but the number of active channels decreased during continuous recording (Fig. 1A) due to abrupt activity termination. The channels had linear current–voltage relationship with slope conductance of 477 ± 3 pS (n = 10) (Fig. 1C), larger than the 360 pS of vertebrate channels (Mak & Foskett, 1998). Channels varied somewhat in their conductance, which sometimes fluctuated during a continuous recording (Mak & Foskett, 1998) (s.d. 12 pS), with occasional openings to subconductance levels that accounted for <2% of all open durations (Fig. 1A). The permeability sequence, determined from reversal potential measurements of currents in asymmetrical solutions, P_Ca:P_Mg:P_K:P_Cl was 10:6.8:1:0.22. No channels were observed in the absence of InsP₃ (0/13 patches) or presence of 10 μm InsP₃ and the competitive inhibitor heparin (100 μg ml⁻¹) (0/14 patches), whereas with 10 μm InsP₃ they were detected in 5/6 patches obtained from the same batch of cells. Thus, the channels observed were confirmed to be endogenous Sf9 InsP₃R channels.

Distribution of InsP₃R channels on Sf9 nuclei

A significant proportion (41/53) of active patches in optimal conditions (10 μm InsP₃, 1 μm Ca²⁺) contained multiple InsP₃R channels, as identified by two or more equally spaced current levels, each corresponding to the predominant ∼480 pS state (Fig. 1A). Comparing the number of channels observed in 75 patches with the theoretical Poisson distribution revealed a significant disparity between the two (Fig. 1D), suggesting that the channels are not evenly distributed in the outer nuclear membrane. Thus, Sf9-InsP₃R channels may be organized in clusters, a conclusion similar to that reached in an analogous analysis of Xenopus oocyte InsP₃R in outer nuclear membrane (Mak & Foskett, 1997) and in Ca²⁺-imaging studies of several cell types (Yao et al. 1995; Horne & Meyer, 1997; Thomas et al. 1998; Bootman et al. 2001).

[Ca²⁺] and [InsP₃] dependencies of Sf9-InsP₃R channel gating kinetics

InsP₃R channel gating is under complex allosteric regulation by both InsP₃ and [Ca²⁺]_i. Activity of Sf9-InsP₃R is biphasically regulated by [Ca²⁺]_i with maximum channel P_o exhibited over a broad range of [Ca²⁺]_i in the presence of saturating [InsP₃] (Fig. 2A–C). The [Ca²⁺]_i dependence of P_o in the presence of 10 μm InsP₃ can be fitted with a biphasic Hill equation (Fig. 2B) (Mak et al. 1998):

Figure 2. Ligand regulation of the Sf9-InsP₃R channel activities.

A, representative current traces at various [Ca²⁺]_i with channels stimulated by saturating (10 μm) and subsaturating (33 nm) [InsP₃], as indicated. B, dependence of InsP₃R channel P_o on [Ca²⁺]_i and [InsP₃], with curves representing empirical fits to the observed channel P_o using the biphasic Hill equation (eqn (1)) with parameters shown in Table 1. Inset, [InsP₃] dependence of K_inh derived from biphasic Hill equation fits to data, fitted with a simple activation Hill equation (Mak et al. 1998), with parameters: apparent half-maximal InsP₃ concentration (K_IP3) and Hill coefficient (H_IP3) as tabulated. C, dependence of InsP₃R channel P_o on [Ca²⁺]_i and [InsP₃], with curves representing the theoretical fits to the observed channel P_o using the Monod-Wyman-Changeux (MWC)-based allosteric model described in Mak et al. (2003a). D, dependence on [Ca²⁺]_i and [InsP₃] of mean open channel duration (t_o) and mean closed channel duration (t_c). Data points are obtained under saturating and subsaturating [InsP₃] as tabulated.

1

with the Hill equation parameters – maximum P_o (P_max), half-maximal activating [Ca²⁺]_i (K_act), activation Hill coefficient (H_act), half-maximal inhibitory [Ca²⁺]_i (K_inh), and inhibition Hill coefficient (H_inh) – tabulated in Table 1. As [InsP₃] was reduced, the observed maximum P_o was reduced and the channel activity was more sensitive to high-[Ca²⁺]_i inhibition (Fig. 2A and B). The P_oversus[Ca²⁺]_i dependencies in subsaturating [InsP₃] were well-fitted using the same biphasic Hill equations with K_inh dramatically sensitive to [InsP₃]: K_inh decreased by nearly three orders of magnitude from 26 μm at 10 μm InsP₃ to 82 nm at 10 nm InsP₃ (Fig. 2B and Table 1). In contrast, the Ca²⁺ activation properties of Sf9-InsP₃R were not significantly affected by changes in [InsP₃] (Table 1). Thus, the main effect of InsP₃ on Sf9-InsP₃R channel activity was to reduce the sensitivity of the channel to inhibition by [Ca²⁺]_i. The half-maximal activating concentration of InsP₃, determined from a monophasic Hill equation fit of the InsP₃ dependence of K_inh, was 390 nm with Hill coefficient of 1.7 (Fig. 2B). Kinetically, [Ca²⁺]_i and [InsP₃] regulate the Sf9 InsP₃R channel P_o mainly by affecting the mean closed channel duration t_c, with relatively minor effects on mean open channel duration t_o (Fig. 2D). Dependence of Sf9-InsP₃R channel gating kinetics (P_o, t_o and t_c) on [Ca²⁺]_i and [InsP₃] are remarkably similar to that observed in its vertebrate homologs (Mak et al. 1998, 2001; Boehning et al. 2001a). Notably, the complex ligand regulation of the Sf9 InsP₃R channel gating kinetics can be well described by an allosteric Monod-Wyman-Changeux (MWC)-based model that was previously developed to account for ligand regulation of the vertebrate InsP₃Rs (Fig. 2C) (Mak et al. 2003a).

Table 1.

Hill equation parameters for [Ca²⁺] dependence of insect Sf9 InsP₃R at different [InsP₃]

[InsP3]	Pmaxa	Kact (nm)b	Hactb	Kinh (μm)b	Hinhb
10 μm	0.75	200	1.4	30	1.1
100 nm	0.75	280	1.4	2.2	1.2
33 nm	0.75	300	1.4	0.38	1.0
10 nm	0.75	250	1.4	0.08	1.3

^aP_max (maximum open probability) was constant for all [InsP₃] because according to the Monod-Wyman-Changeux-based model for the InsP₃R, the value of P_max is determined by ligand-independent transitions between various channel configurations, and therefore exhibits no ligand dependence.

^bThe values of K_act (half-maximal activating [Ca²⁺]_i), K_inh (half-maximal inhibitory [Ca²⁺]_i) and H_inh (inhibition Hill coefficient) were determined by fitting the biphasic Hill equation to the experimental data obtained in the presence of various [InsP₃] with H_act (activation Hill coefficient) fixed.

Sf9-InsP₃R channel inactivation following InsP₃-mediated activation

In all ligand conditions, channel activity invariably terminated in the continuous presence of InsP₃ and absence of local change in [Ca²⁺]_i (Figs 1 and 3A). In optimal ligand conditions, the mean channel activity duration (T_a) was ∼120 s. Similar apparent inactivation has been observed for nuclear membrane-patched InsP₃R in Xenopus oocytes (Mak & Foskett, 1994, 1997) and COS-7 cells (Boehning et al. 2001a) but with significantly shorter T_a. In 10 μm InsP₃, T_a of the Sf9-InsP₃R was reduced in [Ca²⁺]_i >1 μm, with reduction by over 10-fold at 89 μm Ca²⁺ (P < 0.05) (Fig. 3A). In subsaturating (33 nm) InsP₃, T_a began to decrease in [Ca²⁺]_i∼300 nm, substantially lower than that observed in saturating InsP₃ (P < 0.05) (Fig. 3A). The [InsP₃] and [Ca²⁺]_i dependencies of T_a suggest that the observed inevitable termination of channel activity represents the InsP₃R channels entering a true inactivated state instead of an experimental artefact.

Figure 3. Dependencies on [Ca²⁺]_i and [InsP₃] of InsP₃R channel activity duration and recruitment.

A, channel activity duration. Points represent average of channel activity durations for multiple experiments (n > 10) in ligand conditions as shown. Asterisks (*P < 0.05, **P < 0.01) indicate data points that are statistically significantly different from the reference point (circled points). Red is for comparisons of data obtained in 10 μm InsP₃. Blue is for comparison of data obtained in 33 nm InsP₃. Green is for comparisons of data obtained in optimal 1 μm Ca²⁺_i. Smooth curves were drawn by hand for clarity. B–D, ligand-dependent recruitment of InsP₃R. B, channel detection probability (P_d) in ligand concentrations as shown. Total numbers of membrane patches obtained in each set of ligand conditions are displayed next to data points. C, mean number of active channels in membrane patches (N_A) in ligand concentrations as shown. Asterisks (*P < 0.05, **P < 0.01) indicate data points that are statistically significantly different from the reference points (circled points). Red is for comparisons of data obtained in 10 μm InsP₃. Blue is for comparisons of data obtained in 33 nm InsP₃. Green is for comparisons of data obtained in optimal 750 nm Ca²⁺_i. D, the product N_AP_o determined using data shown in Figs 2B and 3C, in ligand concentrations as shown. The smooth curves were hand drawn for clarity.

Nevertheless, without evidence of reversibility, the ligand dependence of the channel activity duration by itself is still insufficient to determine definitively whether the activity termination represents true channel inactivation. The orientation of the channel, with its ligand binding sites facing into the pipette solution, does not allow for wash out and re-addition of InsP₃ to test whether the observed termination process is reversible. We therefore used an alternative protocol in which the channels in isolated nuclei were first exposed to InsP₃ that had been added to the bath for variable amounts of time before the nuclei were patched. If channel activity termination observed in patched membranes is an intrinsic feature of the InsP₃R, then pre-exposure of nuclei to InsP₃ should reduce the number of active channels detected (N_A) during patch clamping. Furthermore, if the termination process is reversible, the number of channels detected should increase again after the InsP₃ is washed out of the bath. With the bath containing 300 nm free Ca²⁺ and 10 μm InsP₃, and the patch pipette solution containing 10 μm InsP₃ and 1 μm Ca²⁺, N_A decreased with time until no channels were detected (N_A= 0) by 900 s exposure to InsP₃ (Fig. 4, protocol A). Channels could not be detected during the remainder of the 30 min exposure to bath InsP₃, but N_A recovered quickly upon washout of the bath InsP₃. As control, N_A in patches obtained from nuclei not pre-exposed to InsP₃ remained constant over this period. This reversible disappearance of detectable channels indicates that the InsP₃R undergoes true InsP₃-dependent channel inactivation. We also examined the effects of pre-exposure to InsP₃ in the presence of high Ca²⁺, because we expect from the channel duration measurements that the inactivation rate should be considerably faster. Here, nuclei were first exposed to 10 μm InsP₃ in the presence of 300 nm Ca²⁺ for 2 min, to enable channel activation, and then the bath Ca²⁺ was raised to 49 μm in the continuous presence of InsP₃, to accelerate inactivation rate (Fig. 4, protocol B). N_A was rapidly reduced to zero within 2 min (approximately the temporal resolution of this approach), and then recovered when the bath was changed to one that lacked InsP₃ and contained 300 nm Ca²⁺. This reversible disappearance of detectable channels again indicates that the InsP₃R undergoes true InsP₃-dependent channel inactivation, and the much more rapid kinetics in high Ca²⁺ agree with the shorter activity duration measurements observed in high [Ca²⁺] (Fig. 3A). The kinetics of inactivation measured by the InsP₃-pre-exposure protocol were slower than those determined from the measurements of channel activity durations of patched nuclei in both 300 nm and 49 μm Ca²⁺, but the results of the two protocols are qualitatively similar, i.e. inactivation is several fold faster at 49 μmversus 300 nm Ca²⁺ in both protocols.

Figure 4. Reversible loss of detectable InsP₃R channels by pre-exposure to InsP₃.

Isolated nuclei were exposed to 10 μm InsP₃ during a 30–34 min period in normal bath (300 nm Ca²⁺; protocol A) or in the presence of 49 μm Ca²⁺ (protocol B), as indicated. Nuclear patch clamping was performed at various times during and after the exposure of the nuclei to bath InsP₃, with the pipette solution always containing 10 μm InsP₃ and 1 μm Ca²⁺. The number of active channels observed in each patch (N_A) is shown in the graph. The data are combined from three separate batches of isolated nuclei. Filled circles, N_A in patches from nuclei exposed to bath InsP₃ up to the time of patching; open circles, N_A in patches from nuclei that had been previously exposed to InsP₃, and subsequently washed free of bath InsP₃ by multiple bath replacements before patching; diamonds, N_A in patches from control nuclei exposed to bath solution containing 300 nm Ca²⁺ and no InsP₃. Pre-exposure to bath InsP₃ caused N_A to decrease to zero, slowly in 300 nm bath Ca²⁺ and rapidly in 49 μm bath Ca²⁺. N_A recovered to control levels in both protocols upon removal of InsP₃ and restoration of normal bath conditions.

Probability of detecting Sf9-InsP₃R channels in membrane patches

The conductance, activation and inactivation gating properties and their regulation by InsP₃ and [Ca²⁺]_i, and spatial distribution of the observed Sf9 InsP₃R channels are all highly reminiscent of other InsP₃R channels observed in nuclear patch clamp studies. In those previous studies, the probability of detecting an active InsP₃R channel in the patched membrane (P_d) was generally low, i.e. most patches contained no active channels; and there was significant variability in P_d (Mak & Foskett, 1997; Mak et al. 2000; and unpublished observations in COS-7 cells). In contrast, active Sf9-InsP₃R channels were detected in optimal ligand conditions in up to ∼80% of patches obtained from nuclei from different batches of cells. This consistency allowed us to examine the possible ligand dependence of P_d (Fig. 3B). In 10 μm InsP₃ in low [Ca²⁺]_i (50 nm), P_d was 0.47. That is, nearly half of all patches contained at least one active InsP₃R channel. P_d increased to 0.81 when [Ca²⁺]_i was raised to 500 nm. Between 0.5 and 7.5 μm, P_d remained high (∼0.6–0.8). When [Ca²⁺]_i was increased beyond 10 μm, P_d gradually decreased. Thus, P_d varied as a biphasic function of [Ca²⁺]_i. With 33 nm InsP₃, P_d increased from 0.5 at [Ca²⁺]_i= 100 nm to 0.67 at [Ca²⁺]_i= 500 nm, and then decreased to 0.21 at [Ca²⁺]_i= 10 μm (Fig. 3B). P_d was sensitive to [InsP₃] as well as [Ca²⁺]_i, with decreasing [InsP₃] within the subsaturating range enhancing high [Ca²⁺]_i reduction of P_d, reminiscent of the effect of suboptimal [InsP₃] on high [Ca²⁺]_i inhibition of channel gating (Fig. 2B).

To calculate P_d, a membrane patch containing multiple channels was given the same weight as one containing a single channel. However, it was noted that patches obtained under optimal ligand conditions usually contained several active channels, whereas those obtained under suboptimal conditions often contained only one. The relatively long channel lifetimes allowed the number of channels to be determined accurately under most conditions (see Methods). To more accurately characterize the number of channels activated, we defined N_A as the total number of channels observed in all patches divided by the total number of patches obtained under that set of experimental conditions. In [Ca²⁺]_i= 50 nm, in the presence of 10 μm InsP₃, N_A was 1.3 ± 0.3. That is, on average each patch contained 1.3 active InsP₃R channels. In higher [Ca²⁺]_i, more channels were detected in each patch, with maximum N_A of 3.0 ± 0.4 at [Ca²⁺]_i= 500 nm (P < 0.01). In 1 μm < [Ca²⁺]_i < 8 μm, N_A ranged between 2.2 and 2.8 (Fig. 3C). Further increases in [Ca²⁺]_i were associated with reduced N_A(P < 0.01). Compared with N_A observed in 10 μm InsP₃, consistently lower N_A was observed in 33 nm InsP₃ over all [Ca²⁺]_i (P < 0.01). In [Ca²⁺]_i= 110 nm, N_A was 0.7 ± 0.2. It increased to 1.6 ± 0.3 at [Ca²⁺]_i= 500 nm. Higher [Ca²⁺]_i then decreased N_A(P < 0.01), such that at [Ca²⁺]_i= 7.5 μm, only 0.26 ± 0.10 channels per patch were detected.

The observation that N_A was a function of stimulus strength was unexpected since it was anticipated that the entire channel population in a membrane patch would always become activated, albeit to different levels of activity (P_o) depending on the strength of ligand activation. These differences in N_A cannot be explained by under-estimation of the number of channels when P_o was low, since Sf9-InsP₃R channels were observed long enough for N_A to be accurately determined (see Methods). Furthermore, since the observation period following exposure of the membrane patch to ligands was many tens of seconds, the inability of suboptimal ligand concentrations to engage all channels cannot be accounted for by stochastic probabilities of ligand binding to the channels. These results indicate that suboptimal ligand concentrations are insufficient to activate all InsP₃R channels in a membrane patch that can be activated by optimal ligand concentrations. Therefore, ligand activation of InsP₃R is associated with recruitment of channels to an activated state, as well as with increasing the P_o of those channels that are recruited.

The total ion flux (J) associated with activation of the entire population of InsP₃R in the ER membrane is defined by:

2

where γ is the single-channel conductance, N is the number of activated channels, and P_o is the average single-channel open probability. The patch-clamp experiments were able to measure all three parameters independently, enabling the effects of ligand stimulation on the magnitude of InsP₃R-mediated Ca²⁺ release from the ER store to be estimated. With γ being ligand independent, N_AP_o is a measure of the ligand-induced InsP₃R-mediated Ca²⁺ release. As both parameters were sensitive to ligand concentrations, N_AP_o is a more accurate assessment of the consequences of ligand activation of the channel than either parameter alone. In saturating [InsP₃], the dependence of N_AP_o on [Ca²⁺]_i was biphasic: N_AP_o increased by over 10-fold as [Ca²⁺]_i was increased from 50 to 500 nm (Fig. 3D), and then gradually decreased as [Ca²⁺]_i was further increased. N_AP_o was also strongly dependent on [InsP₃]. With [InsP₃] reduced to 33 nm, the dependence of N_AP_o on [Ca²⁺]_i was again biphasic, with maximal N_AP_o observed in [Ca²⁺]_i≈ 0.5–1 μm, but peak N_AP_o was an order of magnitude lower than that observed in saturating [InsP₃] (Fig. 3D).

Discussion

We characterized the single-channel permeation and gating properties of the endogenous Sf9 cell InsP₃R in native ER membranes, and found them to be remarkably similar to those of its vertebrate homologues. Among various cell types used for nuclear patch-clamp studies of InsP₃R (COS-7, Xenopus oocyte, DT40, and CHO; our published and unpublished results), functional InsP₃R channels are most frequently and consistently detected using Sf9 cell nuclei, which is distinctly advantageous compared with the other systems in which fewer channels are detected less reliably. We exploited this to demonstrate, for the first time, two important features of InsP₃R channel regulation. First, ligand activation of InsP₃R channel gating inevitably initiates an inactivation mechanism that terminates gating. Second, the number of InsP₃R channels that are recruited to activation is a graded function of ligand concentration.

Functional properties of the endogenous Sf9 InsP₃R

We utilized a nuclear isolation protocol that avoids purification and reconstitution procedures, enabling the InsP₃R channels to remain in their native membrane environment, preserving specific lipid interactions during our experiments. Previously, microsomes obtained from transduced Sf9 cells were used as a source of recombinant InsP₃R in biochemical studies (Cardy et al. 1997) and lipid bilayer reconstitution studies (Tu et al. 2002, 2004; Srikanth et al. 2004). Whereas it was reported in those studies that endogenous Sf9 InsP₃R were not detected biochemically or functionally, the InsP₃ signalling system is present and functional in Sf9 cells (Ross et al. 1994; Knight et al. 2003; Knight & Grigliatti, 2004), and our studies here have revealed that the Sf9-InsP₃R is functionally expressed at a high levels in the outer nuclear membrane of freshly isolated nuclei. The apparent discrepancy may reflect a substantially higher sensitivity of detection of InsP₃R function in patch clamp electrophysiology, enrichment of InsP₃R in the nuclear envelope, or use of antibodies in biochemical studies that only poorly recognized the Sf9 InsP₃R.

Under our experimental conditions, with symmetrical K⁺ as the charge carrier (Mak et al. 1998), the Sf9-InsP₃R channel exhibited a linear current–voltage relation, similar to that observed for nuclear-patched endogenous Xenopus InsP₃R-1, rat cerebellar InsP₃-R (Marchenko et al. 2005) and recombinant rat types 1 and 3 InsP₃R (Mak & Foskett, 1998; Boehning et al. 2001a; Mak et al. 2001); however, the single-channel conductance of ∼480 pS of the Sf9 InsP₃R channel is higher than the ∼360 pS conductance of the vertebrate channels. This may be due to the membrane environment of the Sf9 cell. Alternatively, it may be due to differences at the molecular level between the insect and mammalian InsP₃R pore sequences. Although the amino acid sequence of the Sf9-InsP₃R is not known, all known invertebrate InsP₃R pore selectivity filter sequences (BLAST search: Drosophila, Caenorhabditis elegans, Panulirus, Anopheles, Asterina, Apis, Strongylocentrotus, Aplysia and Tetrahymena) contain a GGIGD motif, whereas the vertebrate sequence is GGVGD. By site-directed mutagenesis of rat InsP₃R-1, it was previously demonstrated that this sequence is involved in ion conductance and selectivity (Boehning et al. 2001b). A mutant mammalian InsP₃R channel with the pore Val replaced with Ile to resemble the invertebrate InsP₃R, had a higher conductance (490 ± 13 pS) (Boehning et al. 2001b), close to that (∼480 pS) of the Sf9-InsP₃R measured here. Thus, other invertebrate InsP₃R channels may also have higher single-channel conductance than their mammalian counterparts. In contrast, the ion permeability selectivity of the Sf9 channel is very similar to that of its mammalian homologs, with the channel cation selective (P_K:P_Cl∼5) with ∼10-fold higher selectivity for Ca²⁺ than K⁺ (Mak & Foskett, 1994, 1998; Mak et al. 2000; Boehning et al. 2001a; Marchenko et al. 2005).

We examined the gating properties of the Sf9-InsP₃R under a wide range of ligand concentrations using experimental conditions similar to those used to study other InsP₃R channels in native ER membranes (Mak et al. 1998; Boehning et al. 2001a). The most fundamental conclusion is that the ligand regulation properties of the insect Sf9-InsP₃R have remarkable similarities to those of the Xenopus type 1 and rat types 1 and 3 channels studied previously (Mak et al. 1998, 2001; Boehning et al. 2001a). Like the vertebrate channels, the Sf9-InsP₃R has a high maximum P_o of 0.7–0.8, and the Sf9 InsP₃R channel P_o has a biphasic dependence on [Ca²⁺]_i, with the ranges of [Ca²⁺]_i over which the channel was activated or inhibited similar to those of the vertebrate channels recorded under similar conditions of [InsP₃] and [ATP]. Also like the vertebrate channels, the Sf9-InsP₃R channel P_o remained at high levels over a broad range of [Ca²⁺]_i, with inhibition by high [Ca²⁺]_i not pronounced until [Ca²⁺]_i > 10 μm in the presence of saturating [InsP₃]. However, inhibition of the Sf9-InsP₃R channel by high [Ca²⁺]_i is less cooperative than the vertebrate InsP₃R isoforms (Mak et al. 2001). Consequently, P_o is already <0.1 in the vertebrate channels at [Ca²⁺]_i= 90 μm, whereas Sf9-InsP₃R P_o is still about 0.2 at [Ca²⁺]_i= 90 μm (Fig. 2B).

The main effect of reducing [InsP₃] to subsaturating levels (∼100 nm) on the Sf9-InsP₃R channel activity was to increase the sensitivity of the channel P_o to inhibition by high [Ca²⁺]_i. In contrast, Ca²⁺ activation was not significantly affected by [InsP₃]. This is highly reminiscent of InsP₃ regulation of endogenous Xenopus InsP₃R-1 (Mak et al. 1998) and recombinant rat InsP₃R-3 (Mak et al. 2001). Nevertheless, the Sf9-InsP₃R has a lower effective sensitivity to InsP₃ and the relief of Ca²⁺ inhibition by InsP₃ has less apparent cooperativity in Sf9-InsP₃R compared with the vertebrate channels (Fig. 2B). Both Sf9-InsP₃R and Xenopus InsP₃R-1 have low channel activity in 10 nm InsP₃, but whereas Xenopus InsP₃R-1 is already fully activated by 100 nm InsP₃, Sf9-InsP₃R responds to InsP₃ over a significantly broader range of concentrations: increasing [InsP₃] from 100 nm to 1 μm gave rise to further relief of Ca²⁺ inhibition of P_o in Sf9-InsP₃R (Fig. 2B).

Finally, the kinetic basis for Sf9-InsP₃R channel activation by InsP₃ and Ca²⁺ involves primarily modulation of t_c. The t_o value remained within a relatively narrow range, whereas t_c varied over an order of magnitude over a range of [Ca²⁺]_i from 50 nm to 90 μm. Thus, the [Ca²⁺]_i dependence of channel t_c is mostly responsible for the channel P_oversus[Ca²⁺]_i relation. This is similar to the effect of [Ca²⁺]_i on the Xenopus InsP₃R-1 and rat InsP₃R-3 channels (Mak et al. 1998, 2001).

The broad similarities of ligand regulation among the Sf9-InsP₃R channel and two types of vertebrate InsP₃R channels suggest that common conserved mechanisms underlie ligand regulation of all InsP₃Rs. A previous study of the Drosophila InsP₃R also concluded that its functional properties were similar to those of mammalian InsP₃Rs (Swatton et al. 2001). The [Ca²⁺]_i and [InsP₃] dependencies of the Sf9-InsP₃R channel activity can be adequately described by an allosteric MWC-based model (Fig. 2C) that accounted for the ligand regulation of the Xenopus InsP₃R-1 and rat InsP₃R-3 channels observed in previous nuclear patch-clamp studies (Mak et al. 2003a). The remarkable functional similarity of Sf9-InsP₃R with the endogenous Xenopus and recombinant rat InsP₃Rs may be a consequence of the high sequence homology among different InsP₃R isoforms from various species.

InsP₃-induced InsP₃R channel inactivation

In single-channel studies, gating activities of Sf9-InsP₃R (the present study) and vertebrate InsP₃R (Mak & Foskett, 1997; Mak et al. 2000; Boehning et al. 2001a) recorded in native ER membranes inevitably abruptly terminate after InsP₃ activation. Whereas the previous vertebrate single-channel studies suggested that the abrupt termination was likely to be due to channel inactivation, it was impossible to rule out non-physiological artefacts associated with patching, for example collisions of the channels with the walls of the glass pipette. However, the present results, by demonstrating both InsP₃ as well as Ca²⁺ dependencies of the channel activity duration, and the reversibility of the activity termination, clearly establish this process as true channel inactivation. Previously, the presence of InsP₃-induced InsP₃R inactivation has been controversial. Pre-exposure of permeabilized hepatocytes to InsP₃ under conditions of constant [Ca²⁺]_i was followed by a time-dependent reduction of InsP₃R-mediated Ca²⁺ release (Hajnóczky & Thomas, 1994, 1997; Dufour et al. 1997; Marchant & Taylor, 1998) as well as transformation of the receptor from a low-affinity active state to a high-affinity, desensitized state (Coquil et al. 1996; Marchant & Taylor, 1998), consistent with InsP₃-mediated InsP₃R inactivation. Biphasic kinetics of Ca²⁺ release rates in intact cells have been observed in many studies (reviewed in Bootman, 1994; Missiaen et al. 1994; Parys et al. 1996; Taylor, 1998), but either inactivation has been ruled out as a mechanism for release termination (Taylor & Potter, 1990; Oldershaw et al. 1992; Hirose & Iino, 1994; Parys et al. 1995; Combettes et al. 1996; Beecroft & Taylor, 1997) or other types of mechanisms have been invoked (reviewed in Bootman, 1994; Missiaen et al. 1994; Parys et al. 1996; Taylor, 1998). In rapid perfusion protocols using isolated microsomes or permeabilized cells that attempted to maintain [InsP₃] and [Ca²⁺]_i constant, transient Ca²⁺ release kinetics indicated that channel inactivation or partial inactivation played a role in the decay of release rates (Champeil et al. 1989; Finch et al. 1991a; Combettes et al. 1994; Wilcox et al. 1996; Dufour et al. 1997; Marchant & Taylor, 1998; Adkins et al. 2000), but questions have been raised regarding the efficacy of maintaining constant conditions in these protocols (Taylor, 1998). Observations of refractory periods following either global (Khodakhah & Ogden, 1995; Carter & Ogden, 1997; Ogden & Capiod, 1997) or more focal (Parker & Ivorra, 1990a; McCarron et al. 2004) InsP₃-mediated Ca²⁺ release in intact cells are also consistent with channel inactivation in intact cells. However, in rapid perfusion and cell studies, it has remained unclear whether release termination or decay is caused by a true intrinsic InsP₃-induced inactivation process, possibly accelerated by high [Ca²⁺]_i, or whether it is due to Ca²⁺-feedback inhibition of channel gating. Furthermore, it has not been established if apparent inactivation as a consequence of pre-exposure to Ca²⁺ before InsP₃ exposure (Parker & Ivorra, 1990a; Payne et al. 1990; Finch et al. 1991b; Combettes et al. 1994; Oancea & Meyer, 1996; Ogden & Capiod, 1997; Swatton & Taylor, 2002; McCarron et al. 2004) is related to apparent inactivation as a result of InsP₃ binding.

The single-channel studies reported here, performed under conditions of constant ligand concentrations and ER luminal conditions, indicate that InsP₃-induced inactivation is an intrinsic property of the single InsP₃R channel. Although the kinetics of apparent inactivation observed in superfusion experiments (Finch et al. 1991b; Combettes et al. 1994; Dufour et al. 1997) and in intact cells in response to photo-release of InsP₃ (Khodakhah & Ogden, 1995) were rapid (<1 s), the inactivation kinetics reported here are slower. However, the kinetics of inactivation for InsP₃R in nuclear patch-clamp studies observed here (T_a∼ 10–100 s) and previously (T_a∼ 20–30 s; Mak & Foskett, 1997), and here in the InsP₃-pre-exposure protocols, are similar to those estimated by ER permeability measurements in permeabilized hepatocytes (Hajnóczky & Thomas, 1994), as well as to the kinetics of InsP₃-induced increases in InsP₃ affinity of an apparently desensitized InsP₃R in cerebellar microsomes (Coquil et al. 1996) (t_½∼15–45 s) and of the transient fast phase of Ca²⁺ release in response to initial exposure to InsP₃ in permeabilized and intact cells (e.g. see Muallem et al. 1989; Meyer & Stryer, 1990; Taylor & Potter, 1990). Of note, InsP₃R inactivation observed in permeabilized hepatocytes (Hajnóczky & Thomas, 1994), which had kinetics similar to those observed in our single channel studies, was shown to account for release termination associated with [Ca²⁺]_i oscillations (Hajnóczky & Thomas, 1997). Together these results suggest that the kinetics of inactivation observed in single-channel studies are of physiological relevance for [Ca²⁺]_i signalling observed in cells. However, it remains unclear whether distinct inactivation kinetics observed in different studies reflects methodological differences, distinct types of inactivation or inhibition, or a physiologically relevant range of kinetics of a common inactivation mechanism.

Our results here demonstrate that the kinetics of single channel inactivation are sensitive to both [InsP₃] and [Ca²⁺]_i. Inactivation was observed for every activated channel, even under conditions of saturating [InsP₃] and very low [Ca²⁺]_i (50 nm). Thus, inactivation appears to be fatefully linked to activation, but the rate of channel inactivation was accelerated at lower [InsP₃] and higher [Ca²⁺]_i, with channel activity duration reduced by over an order of magnitude between 1 and 89 μm Ca²⁺, with average channel duration in 89 μm Ca²⁺ reduced to under 10 s. In addition to ligand concentrations, other factors may also be important in determining channel inactivation kinetics. For example, the rate of channel inactivation of the Xenopus InsP₃R (Mak & Foskett, 1997) was faster than that the Sf9-InsP₃R studied here under identical ligand conditions. Furthermore, the rate of the Sf9-InsP₃R inactivation was faster in the patched membranes than in the InsP₃-pre-exposure protocols. Thus, factors such as membrane tension, membrane lipid composition and associated proteins may also contribute to the rate of InsP₃R channel inactivation. It is interesting that inactivation has not been reported for reconstituted InsP₃R channels recorded in artificial planar bilayer membranes. Our results suggest that inactivation rates of single InsP₃R channels are regulated by ligand concentrations and possibly by additional, including cell-type-specific, factors as well, consistent with a common regulated mechanism of inactivation. Importantly, however, additional studies will be required to determine whether inactivation observed in single channel studies contributes to Ca²⁺ release termination in cells.

Inactivation versus inhibition

Because the curves that describe the transient kinetics of Ca²⁺ release observed in cells and rapid perfusion experiments are reminiscent of the biphasic curves that describe the [Ca²⁺]_i dependencies of steady-state channel P_o, there has been a tendency in the literature to equate the two and to account for release termination by effects of high [Ca²⁺]_i on single-channel gating activity. Consequently, the terms ‘inhibition’ and ‘inactivation’ and ‘partial inactivation’ have sometimes been used to refer to similar phenomena. However, as pointed out (Sneyd et al. 2004), the bell-shaped or otherwise biphasic shape of the steady state P_oversus[Ca²⁺]_i curve has ‘very little, if anything’, to do with the fact that the InsP₃R exhibits complex rapid kinetic behaviours. Our single-channel studies of Sf9-InsP₃R demonstrate that channel inactivation occurs over all [Ca²⁺]_i studied, with the rate of inactivation not necessarily correlated with channel P_o. Of note, it was previously observed that Xenopus oocyte InsP₃R channels that lack high [Ca²⁺]_i inhibition of channel P_o (as a result of an experimental manoeuvre) nevertheless still inactivated (Mak et al. 2003b). Thus, InsP₃R inhibition by high [Ca²⁺]_i, and InsP₃-induced inactivation of the InsP₃R, are distinct processes. The [Ca²⁺]_i dependencies of channel P_o inhibition and inactivation are likely to be mediated by distinct Ca²⁺-binding sites, as discussed in more detail below. Consequently, we propose that the term ‘inhibition’ be used to refer to the effects of high [Ca²⁺]_i on steady-state channel P_o, whereas ‘inactivation’ be used to refer to the time-dependent loss of the capacity of the channel to open even in the presence of constant [InsP₃] and [Ca²⁺]_i.

Ligand stimulation by both InsP₃R channel recruitment and activation

We found that the average number of channels activated in a membrane patch (N_A) depends on the strength of ligand activation. N_A had a biphasic dependence on [Ca²⁺]_i, and was smaller when InsP₃ was reduced to suboptimal concentrations over the entire range of [Ca²⁺] examined (Fig. 3C). These differences in N_A cannot be explained by underestimation of the number of channels when P_o was low, since the channel current records were long enough for N_A to be accurately determined. Notably, the ligand concentration dependencies of P_o and N_A are similar. Thus, the product N_AP_o is a sensitive function of both [Ca²⁺]_i and [InsP₃] (Fig. 3D), and N_AP_o quantitatively accounts for the magnitude of the Ca²⁺ flux associated with InsP₃-mediated [Ca²⁺]_i signals in cells (eqn (2)) because channel conductance is constant. Our single-channel results therefore suggest that the magnitudes of InsP₃R-mediated Ca²⁺ signals in cells are determined by both channel recruitment as well as single-channel activity.

The observed ligand dependence of the number of channels that become recruited into the activated state is unexpected. Because the channels were observed for tens of seconds during their exposure to the ligands, graded channel recruitment cannot be accounted for by stochastic probabilities of ligand binding to the channels. Thus, it was anticipated that the entire channel population in a membrane patch would always become engaged, albeit to different levels of activity (P_o) depending on the strength of ligand stimulation. The graded recruitment of the number of activated channels seemingly implies that the InsP₃R channels in Sf9 cell nuclei have heterogeneous sensitivities to both [InsP₃] and [Ca²⁺]_i. Nevertheless, it seems unlikely that heterogeneous ligand sensitivity exists among the channels. InsP₃R isoform diversity cannot be involved since no invertebrate has been demonstrated to express more than one InsP₃R isoform. Furthermore, it is unlikely that heterogeneous covalent modifications could account for the observed graded responsiveness to such a wide range of both ligands in nuclei from different batches of cells. In addition, possible local determinants of channel activity such as luminal [Ca²⁺] or channel density can be ruled out in the system studied here.

A qualitative model that accounts for ligand dependencies of channel recruitment and inactivation

A simple qualitative kinetic scheme (Fig. 5) involving channel sequestration can account for the observed ligand-dependent channel recruitment without invoking intrinsic channel heterogeneity. The model assumes that InsP₃R channels can become sequestered in a non-active S state by the binding of Ca²⁺ to a sequestration site. In the absence of InsP₃, the regular closed C state of the channel is in equilibrium with the S state, with the C state being favoured (Fig. 5A). When the channel is exposed to InsP₃, InsP₃ binding to the channel enables the channel to enter activated A states (including the A* state in which the channel is open to conduct ion flux, and the closed A′ state). A competition ensues in which the probability of the channel becoming activated, which depends on [Ca²⁺]_i according to the previously developed MWC-based allosteric model (Mak et al. 2003a), is countered by the probability of the channel becoming sequestered into the non-active S state (Fig. 5B). Ca²⁺ concentrations that favour activation of the InsP₃R channel (optimal [Ca²⁺]_i) decrease the chance of the channel being sequestered before activation, increasing N_A; in contrast, suboptimal [Ca²⁺]_i (subactivating [Ca²⁺]_i or high inhibitory [Ca²⁺]_i) that are less favourable for channel activation increase the chance that the channel is sequestered into the S state and therefore reduce N_A. Consequently, the [Ca²⁺]_i dependence of N_A is biphasic and similar to the [Ca²⁺]_i dependence of channel P_o under all [InsP₃]. Once an InsP₃-bound channel enters the S state, it is stabilized there because the affinities of its InsP₃-binding sites and the sequestration Ca²⁺-binding sites are so high that it cannot escape from that state in the continuous presence of InsP₃. For any particular [Ca²⁺]_i, N_A is lower in subsaturating [InsP₃] than saturating [InsP₃] because lower [InsP₃] allows more channels to be siphoned off into the S state by Ca²⁺ binding to the sequestration site before InsP₃ can bind to the channel. Subsequent binding of InsP₃ to the channel stabilizes it in the S state.

Figure 5. Schematic diagram of a model to account for ligand dependencies of graded InsP₃R channel recruitment and InsP₃-induced inactivation.

A, C, S and I represent activated, closed, sequestered and inactivated InsP₃R channel states, respectively. Subscripts indicate state of InsP₃-binding. The InsP₃R channel states are connected by arrows, with triangular arrowheads representing Ca²⁺ and InsP₃ binding to the channel as indicated. ○, Ca²⁺ binding to sequestration site; §, Ca²⁺ binding to inactivation site. A bigger arrowhead indicates the side of the reaction or transition that the equilibrium favours. Reactions or transitions with thicker arrow shafts have higher rates. The activated InsP₃-bound A state can gate between channel open (A*) and closed (A′) conformations through ligand-independent transitions represented by arrows with chevron arrowheads. Equilibrium between InsP₃R channels in C and A states is represented by the open arrow marked with MWC, discussed in detail in (Mak et al. 2003a). See text for a full description of the model.

According to this scheme, termination of channel activity due to inactivation is caused by the channel going from the closed activated state (A′ state) to an inactive I state as the result of Ca²⁺ binding to an inactivation site (Fig. 5C). Because the channel only enters the I state from the A′ state, conditions that reduce channel P_o (high inhibitory [Ca²⁺]_i and subsaturating [InsP₃]) increase the chance that the channel is in A′ state, and therefore accelerate channel inactivation. In subactivating [Ca²⁺]_i, channel P_o is low but channel inactivation is not accelerated because this effect is countered by the reduction of the rate of Ca²⁺ binding to the inactivation site due to lower [Ca²⁺]_i. Like the S state, the channel in the I state has high affinities for InsP₃ and for Ca²⁺ in the inactivation site, which prevents the channel from escaping from the I state for as long as InsP₃ is present. Recovery from inactivation is only possible by InsP₃ dissociation as InsP₃ is removed. This accounts for the observed reversibility from inactivation upon wash-out of InsP₃ (Figs 4 and 5).

There are obvious similarities in the properties of channel sequestration, which results in a certain fraction of available InsP₃R channels not being activated despite the continuous presence of InsP₃, and channel inactivation, which results in InsP₃-induced termination of channel activity. In both processes, the InsP₃R channel ends up in a state from which it cannot escape in the continuous presence of InsP₃. Both processes are regulated by [InsP₃] and [Ca²⁺]_i. And, in our scheme, both processes involve Ca²⁺ binding to the InsP₃R channel. However, the time scales of the two processes are very different. Channel sequestration must occur on a time scale shorter than the activation of the InsP₃R channel after it is exposed to InsP₃, within ∼1–5 s (from the time the patch pipette makes contact with the membrane and the channels in the isolated membrane patch are exposed to InsP₃, to the time when the gigaohm seal forms to allow recording of channel currents). In contrast, channel inactivation occurs at least an order of magnitude slower, ∼20–100 s. Therefore, it is likely that sequestration and inactivation are distinct processes, involving two distinct Ca²⁺-binding sites.

This simple qualitative modelling of our single-channel results indicates that InsP₃-induced channel inactivation (I states in Fig. 5) from active conformations may play a role in terminating Ca²⁺ release. Here, we now propose that channel sequestration before it releases Ca²⁺, plays a role in tuning the number of release channels involved in responses in cells. Interestingly, this model is reminiscent of a kinetic model developed by Sneyd & Dufour (2002), that closely followed the ideas of Taylor (Marchant & Taylor, 1997; Adkins & Taylor, 1999), to account for Ca²⁺ release kinetics from hepatic microsomes, and of another kinetic model developed by Dawson et al. (2003) that was adapted from a kinetic scheme of ryanodine receptor adaptation (Sachs et al. 1995). In both kinetic models, inactivated InsP₃R states were also accessible from either open or closed channel states. Although our simple model cannot predict transient kinetic features, and the two kinetic models either did not or could not account well for steady-state single-channel data, it is interesting that the model here, based primarily on equilibria among channel conformations that accounts for steady-state single-channel activities, has a similar transition diagram with one based on rate constants of ligand binding reactions that accounts for dynamic Ca²⁺ release by a population of InsP₃R channels. Future studies of the rapid kinetic responses of single InsP₃R channels to step changes in ligand concentrations may provide data necessary to extend the insights derived from models of steady-state channel gating to understanding kinetic features that underlie dynamic [Ca²⁺]_i signals in cells.

Physiological implications of InsP₃R channel recruitment

An intriguing aspect of InsP₃R-mediated Ca²⁺ release is that it can be graded in response to incremental levels of extracellular agonist or [InsP₃]. Many mechanisms that have been proposed to account for graded release invoke heterogeneity of either the Ca²⁺ stores or the release channels. Thus, different Ca²⁺ stores with distinct sensitivities to InsP₃ (Muallem et al. 1989; Kindman & Meyer, 1993) or different densities of InsP₃R channels (Meyer & Stryer, 1990; Hirose & Iino, 1994) have been proposed to account for graded Ca²⁺ release. Alternately, it was hypothesized that graded responses are due to progressive recruitment of independent, so-called elementary release units within a continuous Ca²⁺ store, including Ca²⁺ puffs and sparks (Berridge, 1997). Although it has been suggested that InsP₃ or Ca²⁺ might regulate the stochastic probability of triggering an InsP₃R-mediated Ca²⁺ release event (Yao et al. 1995; Horne & Meyer, 1997), localized Ca²⁺ release events are observed from ‘eager sites’ even under conditions of uniform cytoplasmic [InsP₃] and [Ca²⁺] (Yao et al. 1995), suggesting apparent heterogeneity of InsP₃ sensitivity among release sites. As pointed out in (Bootman & Berridge, 1995), a key issue to account for graded Ca²⁺ release is to understand the mechanisms involved in ‘progressive recruitment’ of local release events.

The results of the present study now suggest one possible mechanism that does not require channel or store heterogeneity. We observed that single InsP₃R channels are recruited into active conformations as a graded function of stimulus intensity, in a uniform population of InsP₃R channels in membrane patches with apparent constant channel density and luminal conditions, ruling out factors invoked in many previously proposed mechanisms. Indeed, our results strongly suggest that graded recruitment of channels is an intrinsic property of the InsP₃R channel itself, consistent with graded Ca²⁺ release having been observed in vesicles containing purified InsP₃R protein (Ferris et al. 1992; Hirota et al. 1995) and in a wide variety of cell types (Bootman, 1994; Missiaen et al. 1994; Parys et al. 1996; Taylor, 1998).

It was previously proposed that high-[Ca²⁺]_i feedback inhibition of InsP₃R gating, tuned by [InsP₃], could provide a mechanism to grade release with stimulus intensity (Mak et al. 1998). Because high [Ca²⁺]_i inhibits InsP₃R channel gating by stabilizing the channel closed state (Fig. 2D) (Mak et al. 1998, 2001), Ca²⁺ release by one InsP₃R channel can feed back to stabilize the closed channel state of other channels in the immediate proximity, preventing them from opening. Because InsP₃ decreases the sensitivity of the channel to high [Ca²⁺]_i inhibition (Mak et al. 1998, 2001), this could be a mechanism to grade the number of release channels activated, and consequently the amount of Ca²⁺ released. Thus, two distinct mechanisms exist that can grade the number of InsP₃R channels that become activated in response to InsP₃, one intrinsic to the channel itself mediated by sequestration processes revealed in this study, and another involving communication among channels by released Ca²⁺-mediated inhibition. Both mechanisms enable the initial rate of Ca²⁺ release to be tuned to the strength of ligand activation even in a homogenous population of channels. In addition, the activities of the recruited channels (P_o) are also tuned to the strength of ligand activation. Simultaneous multiple channel recruitment and gating activation mechanisms enables Ca²⁺ release to be regulated by [InsP₃] in a highly cooperative manner. It has been suggested that graded recruitment of release events involves the progressive recruitment of more signalling units that individually release Ca²⁺ in an all-or-none manner (Bootman & Berridge, 1995; Horne & Meyer, 1997). However, our single-channel results would suggest that both the recruitment of release sites (by channel recruitment) as well as the activity of each site (by P_o effects on the activated channels and by recruitment of additional channels at each site through CICR) are graded functions of stimulus intensity, in agreement with imaging observations in oocytes (Callamaras & Parker, 1998; Sun et al. 1998) and HeLa cells (Thomas et al. 1998). Importantly, both features appear to be intrinsic to the InsP₃R channel itself.

Graded recruitment of channels and inactivation of activated channels can provide a mechanism to account for quantal Ca²⁺ release observed in many studies. Our single-channel results are reminiscent of InsP₃-induced incremental inactivation observed in permeabilized hepatocytes, in which pre-exposure to submaximal [InsP₃] reduced the responses to subsequent higher [InsP₃] in direct proportion to the amount of release induced by the pre-exposure to InsP₃ (Hajnóczky & Thomas, 1994). Our results can account for this observation by recruitment of only a fraction of the total channel population by submaximal [InsP₃] and subsequent inactivation of those recruited activated channels. However, our model cannot account for the InsP₃ responsiveness of the remaining channels. Similarly, whereas our model can explain why sustained exposure to submaximal levels of agonists can only mobilize a fraction of total releasable Ca²⁺ in a cell, it cannot account for observations that subsequently increasing [InsP₃] can release more Ca²⁺, thereby enabling Ca²⁺ stores to act as increment detectors of stimuli (Muallem et al. 1989; Meyer & Stryer, 1990; Bootman, 1994; Parys et al. 1996). Increment detection (Meyer & Stryer, 1990), unlike inactivation, enables the channels to retain full responsiveness to InsP₃, whereas our proposed model of quantal Ca²⁺ release relies on inactivation from both open and closed channel states. Nevertheless, it is important to note that our model here is a simplified one, in particular because it largely ignores the tetrameric structure of the channel. It is possible that a more detailed scheme that accounted for ligand binding to each of the four monomers in a tetrameric channel could provide richer behaviours, for example to enable channels in inactivated states to retain the capacity to escape to open channel states in response to higher [InsP₃]. Alternately, it is possible that factors not intrinsic to the channel, such as heterogeneous Ca²⁺ stores and InsP₃R channels, luminal Ca²⁺ regulation, and InsP₃R channel heterogeneity and density, play a role in enabling Ca²⁺ release to exhibit properties of increment detection. Thus, until studies have been performed that demonstrate that increment detection is a property of single InsP₃R channels, development of more complicated models is unwarranted.