Unitary Ca²⁺ current through recombinant type 3 InsP₃ receptor channels under physiological ionic conditions

Abstract

The ubiquitous inositol 1,4,5-trisphosphate (InsP₃) receptor (InsP₃R) channel, localized primarily in the endoplasmic reticulum (ER) membrane, releases Ca²⁺ into the cytoplasm upon binding InsP₃, generating and modulating intracellular Ca²⁺ signals that regulate numerous physiological processes. Together with the number of channels activated and the open probability of the active channels, the size of the unitary Ca²⁺ current (i_Ca) passing through an open InsP₃R channel determines the amount of Ca²⁺ released from the ER store, and thus the amplitude and the spatial and temporal nature of Ca²⁺ signals generated in response to extracellular stimuli. Despite its significance, i_Ca for InsP₃R channels in physiological ionic conditions has not been directly measured. Here, we report the first measurement of i_Ca through an InsP₃R channel in its native membrane environment under physiological ionic conditions. Nuclear patch clamp electrophysiology with rapid perfusion solution exchanges was used to study the conductance properties of recombinant homotetrameric rat type 3 InsP₃R channels. Within physiological ranges of free Ca²⁺ concentrations in the ER lumen ([Ca²⁺]_ER), free cytoplasmic [Ca²⁺] ([Ca²⁺]_i), and symmetric free [Mg²⁺] ([Mg²⁺]_f), the i_Ca–[Ca²⁺]_ER relation was linear, with no detectable dependence on [Mg²⁺]_f. i_Ca was 0.15 ± 0.01 pA for a filled ER store with 500 µM [Ca²⁺]_ER. The i_Ca–[Ca²⁺]_ER relation suggests that Ca²⁺ released by an InsP₃R channel raises [Ca²⁺]_i near the open channel to ∼13–70 µM, depending on [Ca²⁺]_ER. These measurements have implications for the activities of nearby InsP₃-liganded InsP₃R channels, and they confirm that Ca²⁺ released by an open InsP₃R channel is sufficient to activate neighboring channels at appropriate distances away, promoting Ca²⁺-induced Ca²⁺ release.

INTRODUCTION

Modulating cytoplasmic free Ca²⁺ concentration ([Ca²⁺]_i) is a ubiquitous intracellular signaling pathway that regulates numerous cellular physiological processes, including apoptosis, gene expression, bioenergetics, secretion, immune responses, fertilization, muscle contraction, synaptic transmission, and learning and memory (Clapham, 1995; Berridge et al., 2000; Bootman et al., 2001; Braet et al., 2004; Randriamampita and Trautmann, 2004; Cárdenas et al., 2010b). The inositol 1,4,5-trisphosphate (InsP₃) receptor (InsP₃R), a transmembrane protein localized mainly at the ER in all animal cell types, plays a central role in this [Ca²⁺]_i signaling pathway (Taylor and Richardson, 1991; Bezprozvanny and Ehrlich, 1995; Furuichi and Mikoshiba, 1995; Patterson et al., 2004; Foskett et al., 2007; Joseph and Hajnóczky, 2007). In response to extracellular stimuli, phosphatidylinositol 4,5-bisphosphate in the plasma membrane is hydrolyzed to generate InsP₃ (Berridge, 1993). InsP₃ rapidly diffuses through the cytoplasm to bind to the InsP₃R and activates it as an intracellular Ca²⁺ channel to release Ca²⁺ stored inside the lumen of the ER into the cytoplasm, generating diverse local and global [Ca²⁺]_i signals (Berridge, 1997).

The InsP₃R-mediated Ca²⁺ flux from the ER store in response to various extracellular stimuli is ∝ N_A i_Ca P_o, where N_A is the number of InsP₃R channels activated, i_Ca is the unitary calcium ion current passing through an individual open InsP₃R channel, and P_o is the open probability of the active InsP₃R channels. The amount of Ca²⁺ released, and therefore the amplitude and spatial and temporal nature of the [Ca²⁺]_i signals generated, is directly dependent on i_Ca (Berridge, 1997; Bootman et al., 1997). Furthermore, the P_o of InsP₃R channels is regulated by [Ca²⁺]_i with a biphasic dependence: at low concentrations, Ca²⁺ activates the channel and increases its P_o, whereas at higher concentrations, Ca²⁺ inhibits the channel (Foskett et al., 2007). Consequently, i_Ca also affects indirectly the amount of Ca²⁺ released by regulating the P_o of the activated channel itself, as well as that of nearby surrounding channels. Therefore, the measurement of i_Ca in ionic conditions similar to those that exist physiologically in cells is critical for the understanding of the mechanisms regulating this important signaling pathway.

Although InsP₃R channel activity level (P_o) and the number of channels activated (N_A) under various physiological conditions have been studied previously by electrophysiological methods, especially single-channel nuclear patch clamp experiments in various configurations (Foskett et al., 2007), the unitary Ca²⁺ current (i_Ca) passing through an open InsP₃R channel has not been characterized, primarily as a consequence of technical difficulties. Here, we measured the i_Ca of recombinant homotetrameric rat type 3 InsP₃R channels under physiological ionic conditions and studied its single-channel conductance properties.

MATERIALS AND METHODS

Nucleus isolation and nuclear patch clamp electrophysiology

The generation and maintenance of DT40-KO-r-InsP₃R-3 cells (mutant cells derived from chicken B cells with the endogenous genes for all three InsP₃R isoforms knocked out and then stably transfected to express recombinant rat type 3 InsP₃R) were described in Mak et al. (2005). Nuclear patch clamp experiments were performed using nuclei isolated from DT40-KO-r-InsP₃R-3 cells as described previously (Mak et al., 2005). Excised nuclear membrane patches in the luminal side–out (lum-out) or cytoplasmic side–out (cyto-out) configuration were obtained from isolated nuclei (Mak et al., 2007) using protocols analogous to those used to obtain inside-out or outside-out excised patches in plasma membrane patch clamp experiments. The solution around the excised nuclear membrane patch was rapidly switched multiple times using a solution-switching setup described in Mak et al. (2007).

InsP₃R channel current traces were acquired at room temperature as described previously (Mak et al., 1998), digitized at 5 kHz, and anti-aliasing filtered at 1 kHz. Data analysis and the fitting of channel current–voltage curves were performed using Igor-Pro software. All electrical potentials were measured relative to the bath electrode.

Experimental solution composition

In cyto-out experiments, pipette solutions contained 140 mM KCl, 10 mM HEPES, pH to 7.3 with KOH, 0.5 mM Na₂ATP, and 10 µM InsP₃, with free [Ca²⁺] ([Ca²⁺]_f) buffered to 3 µM by 0.5 mM 5,5′-dibromo 1,2-bis(o-aminophenoxy) ethane-N,N,N’,N’-tetraacetic acid (dibromo BAPTA) and 0.2 mM CaCl₂. Perfusion solutions on the cytoplasmic side of the channel contained 10 mM HEPES, pH to 7.3 with KOH, 0.5 mM Na₂ATP, and either 140 mM KCl with no InsP₃ or 70 mM KCl with 10 µM InsP₃, with [Ca²⁺]_f buffered to 3 µM by 0.5 mM (2-hydroxyethyl) ethylenediaminetriacetate and 0.22 mM CaCl₂ (Mak et al., 2005). InsP₃ and Na₂ATP were included in the pipette solution to confirm that the cyto-out configuration was properly achieved. Because of the presence of InsP₃ and ATP in the pipette solution, observation of InsP₃R channel activity before solution switching would be evidence that the lum-out configuration was erroneously obtained.

The same pipette solution was used in lum-out experiments to determine ion permeability ratios of the InsP₃R channel. The perfusion solution used to determine P_K: P_Cl contained 30 mM KCl, 110 mM NMDG chloride, and 10 mM HEPES, pH to 7.3 with NMDG, with [Ca²⁺]_f buffered to 300 nM by 0.5 mM 1,2-bis(o-aminophenoxy) ethane-N,N,N’,N’-tetraacetic acid (BAPTA) and 0.2 mM CaCl₂. The perfusion solution used to determine P_K: P_Na contained 140 mM NaCl and 10 mM HEPES, pH to 7.3 with NaOH. The perfusion solution used to determine P_X: P_K (X = Mg²⁺, Ca²⁺, Sr²⁺, or Ba²⁺) contained 140 mM KCl, 10 mM HEPES, pH to 7.3 with KOH, and 10 mM XCl₂. The perfusion solutions contained no Na₂ATP or Ca²⁺ chelator. No CaCl₂ was added to the perfusion solutions used to determine permeability ratios of Mg²⁺, Sr²⁺, and Ba²⁺ versus K⁺, so free Ca²⁺ in those solutions were from contaminants in the water and salts used to make the solutions. Based on the purity assays of the salts (Sigma-Aldrich) and induction-coupled plasma mass spectrometry assay (Mayo Medical Laboratory) of deionized water samples, [Ca²⁺]_f in those solutions were ∼5–8 µM.

In lum-out experiments to determine the i_Ca through the InsP₃R-3 channel, all solutions contained 10 mM HEPES, pH to 7.3 with KOH. Unless stated otherwise, all solutions used in the same experiment contained the same concentrations of MgCl₂ (0, 0.5, or 1 mM), KCl (140 or 40 mM), and potassium methanesulfonate (KCH₃SO₃; 0 or 100 mM). Pipette solutions also contained 0.5 mM Na₂ATP and 2 or 10 µM InsP₃ to activate the channel to P_o of ∼0.5 (Mak et al., 2001a,b; Vais et al., 2010), with [Ca²⁺]_f buffered to either 70 nM by 0.5 mM BAPTA and 0.06 mM CaCl₂, or to 3 µM by 0.5 mM dibromo BAPTA and 0.2 mM CaCl₂. The same solution (without Na₂ATP or InsP₃) was used as perfusion solution for symmetric ionic conditions. Although [Na⁺] was not symmetric because of the presence of 0.5 mM Na₂ATP only in the pipette solutions, the extra Na⁺ is <1% of the amount of monovalent cations, and its contribution to channel current is negligible. Perfusion solutions used for asymmetric ionic conditions contained 0.3, 1, or 2 mM CaCl₂, with no Ca²⁺ chelator, Na₂ATP, or InsP₃.

[Ca²⁺]_f of <100 µM (buffered by various Ca²⁺ chelators) was confirmed by fluorimetry. [Ca²⁺]_f in solutions without Ca²⁺ chelators was calculated using activity coefficients (see next section).

Evaluating ion permeability ratios

According to the general Goldman-Hodgkin-Katz current equation (Lewis, 1979), the permeability ratio P_Y/P_K for Y, one of the charge-carrying permeant ion species, can be evaluated from the reversal potential (V_rev) of the channel as:

$$\begin{array}{l}{P}_{\text{Y}}:P_{\text{K}}=-{\left(z_{\text{Y}}\right)}^{-2}{\left\{\frac{{\mathrm{[Y}]}_{\text{i}}-{\mathrm{[Y}]}_{\text{o}}\text{exp}\left(-z_{\text{Y}}F{V}_{\text{rev}}/RT\right)}{1-\text{exp}\left(-z_{\text{Y}}F{V}_{\text{rev}}/RT\right)}\right\}}^{-1}\\ {\displaystyle \sum _{\text{X}\ne \text{Y}}}\left\{\left(\frac{P_{\text{X}}}{P_{\text{K}}}\right){\left(z_{\text{X}}\right)}^2\frac{{\mathrm{[X}]}_{\text{i}}-{\mathrm{[X}]}_{\text{o}}\text{exp}\left(-z_{\text{X}}F{V}_{\text{rev}}/RT\right)}{1-\text{exp}\left(-z_{\text{X}}F{V}_{\text{rev}}/RT\right)}\right\},\end{array}$$ (1)

where X represents other permeant ion species present; P_X is the permeability of X through the channel; z_X and z_Y are the valence of X and Y, respectively; [X]_i, [X]_o, [Y]_i, and [Y]_o are the activities of X and Y in the pipette and bath solutions, respectively; F and R are the Faraday and gas constants, respectively; and T is the absolute temperature, provided that all of the P_X/P_K values are known. The activities of all ion species were calculated from activity coefficients, except for [Ca²⁺] < 100 µM, which was determined by fluorimetry.

The activity coefficients of KCl and NaCl were calculated using the Debye-Hückel equation based on data reported by Hamer and Wu (1972). The activity coefficients of CaCl₂ in a 140-mM KCl solution (0.546–0.534 for 0.3–10 mM CaCl₂) were derived by interpolation using data reported by Butler (1968), assuming that CaCl₂ activity coefficients are similar in 140-mM KCl and NaCl solutions. The activity coefficients of CaCl₂ were used for other alkaline earth metal halides (MgCl₂, BaCl₂, and SrCl₂) in solutions with the same concentrations because activity coefficients of the alkaline earth metal halides differ by <5% in concentrations when activity coefficients are ≈0.54 (Goldberg and Nuttall, 1978).

RESULTS

Conductance properties of homotetrameric recombinant rat InsP₃R-3 channels

Although it has been a well-established approach to study the single-channel properties of the InsP₃R channel in its native membrane environment by performing patch clamp electrophysiology on isolated nuclei (Foskett et al., 2007), the molecular composition of the channels observed in many of those studies could not be definitively ascertained. This is because the channels studied were either the endogenous channels (Mak and Foskett, 1994, 1997; Marchenko et al., 2005; Ionescu et al., 2006) with the possibility of different channel isoforms expressed and with possible alternative splicing (Foskett et al., 2007), or recombinant channels expressed in cells with a nonzero level of endogenous InsP₃R expression (Mak et al., 2000; Boehning et al., 2001a), so that heteroligomeric channels of recombinant and endogenous InsP₃Rs could have been formed (Joseph et al., 1995; Mak et al., 2000).

To avoid possible variability that such heterogeneity might introduce, we ensured that only homotetrameric InsP₃R channels with known identical amino acid sequences were studied by using a stably transfected cell line (DT40-KO-r-InsP₃R-3) derived from mutant DT40-InsP₃R-KO cells (Sugawara et al., 1997) that have all endogenous genes for the three InsP₃R isoforms knocked out, with only recombinant rat type 3 InsP₃R (InsP₃R-3) expressed (Mak et al., 2005; Li et al., 2007). During our extensive experience working with this cell line (Mak et al., 2005; Foskett and Mak, 2010), and in hundreds of nuclear membrane patches (in both cyto-out and lum-out configurations), only one kind of channel with a conductance >100 pS in symmetric 140 mM KCl was detected. The identity of these channels as recombinant rat InsP₃R-3 channels was confirmed by their sensitivity to activation by cytoplasmic InsP₃ (Fig. 1 A).

Figure 1.

Current records of homotetrameric recombinant type 3 InsP₃R channels in membrane patches excised from nuclei isolated from DT40-KO-r-InsP₃R-3 cells. (A) Activation by InsP₃ of channels in a cyto-out nuclear membrane patch. Concentrations of InsP₃ and free Ca²⁺ in the perfusion solution on the cytoplasmic side of the channel are indicated by color bars at top. V_app = 30 mV. Channels opened only in the presence of cytoplasmic InsP₃. Gray arrowheads indicate some of the occasions when one of the active channels entered a conductance substate. In this and subsequent current traces, black arrows indicate the membrane current levels when all InsP₃R channels in the membrane patch were closed. (B) Single InsP₃R-3 channel current records observed in different lum-out nuclear patches in symmetric 140 mM KCl and 3 µM [Ca²⁺]_f. Pipette solution contained 10 µM InsP₃. V_app = 40 mV. Gray arrowheads indicate when the channels entered different conductance substates with different conductance values. (C) Representative I-V_app plot for a single InsP₃R-3 channel in the same experimental conditions as in B. V_app was ramped from −25 to 15 mV in 1 s. 20 ramps were analyzed. Data points selected for I_open and I_closed are plotted in green and pink, respectively. Green and red lines represent linear fits to I_open and I_closed data points, respectively.

Averaged over reasonable intervals (>1 s), the rat InsP₃R-3 channel dwells in a main open conductance state >95% of the time it is open, whereas it occasionally exhibits brief substates of lower conductances (Fig. 1, A and B). The substates are not a result of non-InsP₃R channels because in current records showing only one active InsP₃R channel gating, the channel current level dropped to substate levels from the main open state directly without channel closing (Fig. 1 B, arrowheads). Substates have also been observed for other InsP₃R channels (endogenous or recombinant) in other cell systems (Watras et al., 1991; Mak and Foskett, 1997; Mak et al., 2000; Boehning et al., 2001a; Ionescu et al., 2006). To determine the conductance of the main open state of the channel in symmetric 140-mM KCl solutions ([K⁺]_f = [Cl⁻]_f ≈ 104 mM) in the absence of Mg²⁺, currents through excised lum-out membrane patches (I) were recorded as the applied potential (V_app) was ramped (Fig. 1 C). Slope conductance of the channel (g_ch), evaluated as the difference between the slopes of the fits to open- and closed-channel current (I_open and I_closed, respectively) data, was 545 ± 7 pS (n = 16). This and all subsequent open-channel current measurements were not affected by the presence of substates because atypical current data arising from them were excluded when data points were selected for I-V_app fits.

To properly design an experimental approach to measure the i_Ca passing through a single open InsP₃R-3 channel under physiological ionic conditions, it was useful to obtain a maximum estimate of the size of the current using the Goldman-Hodgkin-Katz current equation (Hille, 2001). To obtain such an estimate requires knowledge of the permeability values of all permeant ionic species present. To evaluate the permeabilities of various ions through the InsP₃R-3 channel, I-V_app data were recorded as V_app was ramped during a series of lum-out patch clamp experiments in which the excised membrane patches were exposed to asymmetric ionic conditions (Fig. 2). After correcting for liquid junction potentials (Neher, 1995), the reversal potential (V_rev) of the channel was determined as the V_app at the intersection of the I_open-V_app and I_closed-V_app fits. Permeability ratios for various ions were calculated from V_rev using the general Goldman-Hodgkin-Katz current equation (Eq. 1). The permeability ratio for K⁺ versus Cl⁻ (P_K:P_Cl) was derived using asymmetric ionic solutions containing only two permeant ionic species: K⁺ and Cl⁻ (Fig. 2 A). That value was then used to calculate the permeability ratios of other cations (Mg²⁺, Ca²⁺, as well as Ba²⁺, Sr²⁺, and Na⁺) versus K⁺ from V_rev measured in asymmetric ionic solutions containing three permeant ionic species (Fig. 2, B–F), assuming that P_K:P_Cl is the same in all ionic conditions used. These measurements indicated that P_Ca:P_Sr:P_Ba:P_Mg:P_Na:P_K:P_Cl = (15.2 ± 0.6):(13.2 ± 0.7):(11.8 ± 0.5):(10.2 ± 0.3):(1.24 ± 0.003):1:(0.27 ± 0.01) (n = 3 for each ratio). This same InsP₃R permeability ratio sequence was also observed in other nuclear patch clamp experiments (Mak and Foskett, 1998; Mak et al., 2000; Boehning et al., 2001a; Ionescu et al., 2006).

Figure 2.

Representative I-V_app plots for single InsP₃R-3 channels in excised lum-out nuclear membrane patches under asymmetric ionic conditions used to determine channel permeability ratios for various ions. Compositions of pipette and perfusion solutions are described in Materials and methods. Selected data points for I_open and I_closed are plotted in green and pink, respectively. Red lines are linear fits to I_closed-V_app data points, and green ones are polynomial fits to I_open-V_app data points (linear for B; quadratic for A, E, and F; cubic for C and D). V_rev at the intersection of the I_open-V_app and I_closed-V_app fits are marked by dashed lines and tabulated. (A) Eight V_app ramps in one of four experiments to determine P_K:P_Cl. Junction potential corrected (V_junction) = −9.3 ± 0.4 mV. (B) 15 V_app ramps in one of three experiments to determine P_Na:P_K. V_junction = −1.5 ± 0.2 mV. (C) 10 V_app ramps in one of three experiments to determine P_Mg:P_K. V_junction = −0.7 ± 0.4 mV. (D) 43 V_app ramps in one of three experiments to determine P_Ca:P_K. V_junction = −1.4 ± 0.2 mV. (E) 35 V_app ramps in one of three experiments to determine P_Ba:P_K. V_junction = −2.6 ± 0.3 mV. (F) 16 V_app ramps in one of three experiments to determine P_Sr:P_K. V_junction = −2.2 ± 0.8 mV.

i_Ca through InsP₃R-3 under physiological conditions

Although the InsP₃R channel has a large g_ch in solutions with physiological KCl concentrations, the current measured under those conditions is mostly carried by K⁺ ions driven through the channel by V_app. Because of the absence of a significant voltage across the ER membrane (Beeler et al., 1981; Marhl et al., 1997), Ca²⁺ ions are driven through open InsP₃R channels under physiological conditions by the difference between [Ca²⁺]_f in the ER lumen ([Ca²⁺]_ER) and that in the cytoplasm ([Ca²⁺]_i). [Ca²⁺]_ER observed in various cell types is approximately hundreds of micromolars (Bygrave and Benedetti, 1996; Yu and Hinkle, 2000; Palmer et al., 2004), so there are significantly fewer Ca²⁺ ions than K⁺ ions to carry the current. A simple calculation based on the Goldman-Hodgkin-Katz current equation suggests that, in the absence of transmembrane voltage, with [Ca²⁺]_ER = 1 mM and [Ca²⁺]_i = 70 nM, i_Ca is ∼3 pA for a channel with g_ch = 545 pS in 140 mM KCl and P_Ca:P_K:P_Cl = 15:1:0.27. However, the actual i_Ca is expected to be substantially smaller because divalent cations act as permeant blockers that reduce g_ch (Mak and Foskett, 1998; Mak et al., 2000). Despite their higher permeabilities, divalent cations bind strongly to site(s) in the channel pore so that they pass through the channel significantly more slowly than monovalent cations. In addition, the high [K⁺] in the cytoplasm and ER lumen (∼140 mM) and the relatively weak selectivity of the InsP₃R channel for Ca²⁺ over K⁺ (P_Ca:P_K = 15) make K⁺ a potentially effective competing ion to also reduce i_Ca. i_Ca might be further reduced as a result of competition from free Mg²⁺, which exists at significant levels (∼200 µM–1.1 mM) in both the cytoplasm and ER lumen (Halvorson et al., 1992; Morelle et al., 1994a,b; Silverman et al., 1994; Golding and Golding, 1995; Singh and Wisdom, 1995; Tashiro and Konishi, 1997), and has a permeability similar to that of Ca²⁺ (P_Ca:P_Mg = 1.5).

To measure i_Ca, we monitored the transmembrane current I through excised lum-out nuclear membrane patches containing a single active InsP₃R channel. The capability to switch the perfusion solutions around the excised patch was used to minimize systematic measurement errors by calibrating the patch clamp setup for each individual experiment. The lum-out membrane patch was first exposed to a perfusion solution with the same ionic composition as the pipette solution (symmetric ionic conditions). I-V_app data were recorded with V_app ramped from −20 to 10 mV, and data points for I_open-V_app and I_closed-V_app were fitted linearly (Fig. 3 A). With no permeant ion concentration gradient across the excised nuclear membrane patch, the current passing through the InsP₃R channel (I_open–I_closed) and the leak current across the nuclear membrane patch (I_closed) must both be zero when V_app = 0. Thus, the intersection of the I_open-V_app and I_closed-V_app lines established the zero-current level for the patch clamp current recording system during each experiment (Fig. 3 B).

Figure 3.

Measuring i_Ca in physiological ionic conditions. (A) Linear fits (green and red lines) to selected I_open and I_closed data (plotted in green and pink, respectively) from 25 V_app ramps recorded from an excised lum-out nuclear membrane patch containing one active InsP₃R channel under symmetric ionic conditions, with pipette and perfusion solutions containing 140 mM KCl, 0.5 mM MgCl₂, and 3 µM [Ca²⁺]_f. Pipette solution contained 2 µM InsP₃. (B) Graph of the fitted I_open-V_app and I_closed-V_app lines in the I-V_app region marked by the black rectangle in A. Zero-current level (black dotted line) established at the intersection of the I-V_app fits at V_app = 0 (marked by orange arrowhead). (C) Linear fits to I_open and I_closed data (same convention as in A) from 25 V_app ramps recorded for the same membrane patch under asymmetric ionic conditions, with perfusion solution containing 2 mM CaCl₂. I and V_app ranges in A and C are the same. (D) Graph of the fitted I-V_app lines in the same I-V_app region with the same zero-current level as in B. V_app = 0 (marked by orange arrowhead) at the intersection of the I_closed-V_app line and zero-current level. i_Ca is I_open at V_app = 0 (marked by blue arrow).

The perfusion solution was then switched to one with higher [Ca²⁺]_f (asymmetric ionic conditions). Higher [Ca²⁺]_ER reduced both the InsP₃R g_ch, as a result of an increase in permeant divalent cation block, and the leak conductance (Fig. 3 C). However, the zero-current level of the recording system was not affected by the perfusion solution switch. For the leak current (I_closed) through the excised membrane patch, V_rev = 0 because there are no significant concentration differences for the major ionic components in the pipette and perfusion solutions, K⁺ and Cl⁻, which have significantly higher mobility across the membrane than divalent cations (Beeler et al., 1981; Marhl et al., 1997). Therefore, V_app = 0 at the point where I_closed = 0 (Fig. 3 D). The open-channel current (I_open) at V_app = 0 is driven only by the [Ca²⁺]_f gradient across the channel (Δ[Ca²⁺] = [Ca²⁺]_ER−[Ca²⁺_i]) and therefore is i_Ca (Fig. 3 D).

We first measured i_Ca in symmetric 140 mM KCl with no Mg²⁺. To cover the range of reported [Ca²⁺]_ER (Bygrave and Benedetti, 1996; Yu and Hinkle, 2000; Palmer et al., 2004), the luminal side of the excised membrane patch was exposed to perfusion solutions with [Ca²⁺]_f = 160 µM, 550 µM, and 1.1 mM. [Ca²⁺]_i in the pipette solution was fixed at 3 µM to keep channel P_o high. The observed magnitude of i_Ca was well described by a linear relation with Δ[Ca²⁺] (Fig. 4), as predicted by the Goldman-Hodgkin-Katz current equation. However, the value for P_Ca (1.5 × 10⁻¹⁸ m³s⁻¹) derived from the slope of the i_Ca versus Δ[Ca²⁺] line is an order of magnitude smaller than that (1.5 × 10⁻¹⁷ m³s⁻¹) estimated using g_ch in 140 mM KCl and the measured permeability ratios of P_Ca:P_K:P_Cl. This discrepancy results from interactions between the channel and the permeant ions (K⁺ and Ca²⁺) and among permeant ions in the channel that are not considered in the Goldman-Hodgkin-Katz equation.

Figure 4.

i_Ca’s through the InsP₃R channel under various asymmetric ionic conditions. Error bars show SEM. The number of measurements performed for each ionic condition is tabulated next to the corresponding data point. The line is the linear fit to the data points in 140 mM KCl, 0 mM [Mg²⁺]_f, and 3 µM [Ca²⁺]_i, with slope of 0.30 ± 0.02 pA/mM.

To assess the effect on i_Ca of physiological concentrations of free Mg²⁺, ranging from 200 µM to 1.1 mM in both the cytoplasm and ER lumen (Halvorson et al., 1992; Morelle et al., 1994a,b; Silverman et al., 1994; Golding and Golding, 1995; Singh and Wisdom, 1995; Tashiro and Konishi, 1997), we measured i_Ca in symmetric 270 or 550 µM [Mg²⁺]_f with [Ca²⁺]_i = 3 µM and [Ca²⁺]_ER = 550 µM or 1.1 mM. Interestingly, i_Ca observed in the presence of physiological [Mg²⁺]_f was not significantly different from i_Ca measured in 0 [Mg²⁺]_f (Fig. 4).

Under normal physiological conditions, [Ca²⁺]_ER is significantly higher than [Ca²⁺]_i, so i_Ca should have little dependence on [Ca²⁺]_i. Indeed, we observed no statistical difference between i_Ca for [Ca²⁺]_i at resting (70 nM) and activating (3 µM) levels (Fig. 4).

Free chloride ion concentration [Cl⁻]_f is significantly lower than [K⁺]_f in the cytoplasm as a result of the Gibbs-Donnan effect of negative charges in cytoplasmic proteins (Foskett, 1990). To verify if physiological cytoplasmic [Cl⁻]_f significantly affects i_Ca, we measured i_Ca with pipette and perfusion solutions containing symmetric 100 mM potassium methanesulfonate (KCH₃SO₃), 40 mM KCl ([K⁺]_f ≈ 104 mM, [Cl⁻]_f ≈ 30 mM), and 270 µM [Mg²⁺]_f, with [Ca²⁺]_i = 3 µM and [Ca²⁺]_ER = 550 µM or 1.1 mM. Again, i_Ca observed was not significantly different from that observed in 140 mM KCl (Fig. 4), indicating that i_Ca is to a large extent independent of [Cl⁻]_f under physiological ionic conditions. Interestingly, g_ch = 293 ± 4 pS in symmetric 270 µM [Mg²⁺]_f and 30 mM [Cl⁻]_f, the same as that observed in symmetric 270 µM [Mg²⁺]_f and 104 mM [Cl⁻]_f (292 ± 5 pS). This correspondence probably arises because decreasing [Cl⁻]_f reduces Cl⁻ current through the channel and also reduces Cl⁻ competition with K⁺ to move through the channel, with the two opposing effects on InsP₃R g_ch cancelling each other out.

These results indicate that, in physiological ionic conditions, with symmetric 104 mM [K⁺]_f, 30–104 mM [Cl⁻]_f, 0–550 µM [Mg²⁺]_f, 70 nM to 3 µM [Ca²⁺]_i, the i_Ca for rat homotetrameric type 3 InsP₃R channel in native ER membrane is (0.30 ± 0.02 pA mM⁻¹) × [Ca²⁺]_ER. This is equivalent to having an asymptotic Ca²⁺ slope conductance (g_ch as V_app in the ER relative to the cytoplasm→∞) of (23.4 ± 1.6 pS mM⁻¹) × [Ca²⁺]_ER. For a filled store with 500 µM [Ca²⁺]_ER, i_Ca = 0.15 ± 0.01 pA and the asymptotic Ca²⁺ slope conductance is 11.7 ± 0.8 pS.

Block of InsP₃R channel conduction by permeant divalent cations

Another indication of the inadequacy of the Goldman-Hodgkin-Katz equation to describe ionic flow through the InsP₃R channel is the substantial reduction of g_ch by Ca²⁺ or Mg²⁺ (in millimolar concentrations) on the luminal or cytoplasmic side of the channel, despite their high permeability ratios (Fig. 5A). Similar partial reduction of g_ch by permeant divalent cations (Mg²⁺, Ca²⁺, and Ba²⁺) was observed in endogenous type 1 InsP₃R channels in Xenopus laevis oocyte nuclear membrane (Mak and Foskett, 1998) and recombinant type 1 InsP₃R channels in the plasma membrane of DT40-KO-r-InsP₃R-1 cells (Dellis et al., 2006). This reduction suggests that movement of divalent cations through the InsP₃R channel is substantially slowed down by strong interactions between the ions and the pore, causing temporary block of ion flow through the channel (Hille, 2001). The channel conductance g_ch at the reversal potential V_rev was systematically evaluated in experiments performed to measure i_Ca in the presence of 3 µM, 160 µM, 550 µM, and 1.1 mM [Ca²⁺]_ER, and symmetric 0, 270 µM and 550 µM [Mg²⁺]_f. Channel blocking effects of Ca²⁺ and Mg²⁺ were not mutually exclusive, as the addition of Mg²⁺ further reduced g_ch already suppressed by Ca²⁺, and vice versa (Fig. 5 A). The observed reduction of g_ch by Ca²⁺ could be described by an empirical saturating partial inhibition equation:

$$g_{\text{ch}}\left({\left[{\text{Ca}}^{2+}\right]}_{\text{ER}}\right)=\left(g_{\mathrm{\infty }\text{CaER}}{\left[{\text{Ca}}^{2+}\right]}_{\text{ER}}+g_0{K}_{\text{CaER}}\right)/\left(K_{\text{CaER}}+{\left[{\text{Ca}}^{2+}\right]}_{\text{ER}}\right),$$ (2)

where g₀ is the channel slope conductance at 0 [Ca²⁺]_ER, g_∞CaER is the channel slope conductance at saturating [Ca²⁺]_ER, and K_CaER is the half-maximal blocking [Ca²⁺]_ER. g₀, g_∞CaER, and K_CaER have different values in different [Mg²⁺]_f (corresponding to the different curves in Fig. 5 A). In the absence of Mg²⁺ (Fig. 5 A, red curve), K_CaER = 210 ± 20 µM, g_∞CaER = 82 ± 8 pS, and g₀ is 545 pS, the channel slope conductance with no divalent cations.

Figure 5.

Slope conductance of an InsP₃R-3 channel at V_rev in symmetric 140-mM KCl solutions with various divalent cation concentrations. SEM for all data points are shown as error bars, some of which are smaller than the size of the symbols. The number of measurements performed for each ionic condition is tabulated next to the corresponding data point in the same color. The same symbols in the same color are used for the same set of data points plotted in the different graphs. (A) g_ch versus [Ca²⁺]_ER in the presence of various symmetric [Mg²⁺]_f as tabulated. Curves are fits to g_ch data by the empirical inhibition equation (Eq. 2), with different K_CaER for various [Mg²⁺]_f. The red curve is for g_ch in 0 [Mg²⁺]_f. (B) g_ch versus concentrations of divalent cations in the cytoplasmic or luminal side of the channel as tabulated. The purple curve is described by Eq. 3, and the red one is described by Eq. 2. (C) g_ch versus equivalent divalent cation concentrations [X²⁺]_eq = [Ca²⁺]_ER + 0.5 × ([Mg²⁺]_i + [Mg²⁺]_ER) for various combinations of [Ca²⁺]_ER, [Mg²⁺]_ER, and [Mg²⁺]_i as tabulated. The red curve is described by Eq. 5.

To compare the capacities of Mg²⁺ and Ca²⁺ to block the channel, we measured g_ch with various [Mg²⁺]_ER, in 0 [Mg²⁺]_i and symmetric 3 µM [Ca²⁺]_f (Fig. 5 B, purple open squares). g_ch data could be fitted using an equation similar to Eq. 2:

$$g_{\text{ch}}\left({\left[{\text{Mg}}^{2+}\right]}_{\text{ER}}\right)=\left(g_{\mathrm{\infty }\text{MgER}}{\left[{\text{Mg}}^{2+}\right]}_{\text{ER}}+g_0{K}_{\text{MgER}}\right)/\left(K_{\text{MgER}}+{\left[{\text{Mg}}^{2+}\right]}_{\text{ER}}\right).$$ (3)

Eq. 3 describes the purple curve in Fig. 5, with g₀ again being the channel conductance in the absence of divalent cations (545 pS). Interestingly, g_∞MgER = 81 ± 5 pS is very similar to g_∞CaER, suggesting that Ca²⁺ and Mg²⁺ are equally efficacious in blocking the InsP₃R channel. Furthermore, K_MgER = 410 ± 20 µM, which is ≈ 2 × K_CaER, suggesting that the affinity for Ca²⁺ of the site in the channel responsible for blockage by luminal divalent cations is twice that for Mg²⁺; i.e., Mg²⁺ is half as potent in blocking the InsP₃R channel as Ca²⁺.

Although inhibition of InsP₃R gating by high [Ca²⁺]_i (>20 µM) (Mak et al., 2001b) prevents comparison of the effectiveness of Ca²⁺ from the cytoplasmic and luminal sides to block permeation, the effectiveness of Mg²⁺ to block permeation from either side of the channel can be compared because physiological [Mg²⁺]_i has no significant effect on channel gating (Mak et al., 1999). g_ch observed in 0.55 mM [Mg²⁺]_i and 0 [Mg²⁺]_ER (Fig. 5 B, magenta filled square) was the same as that in 0 [Mg²⁺]_i and 0.55 mM [Mg²⁺]_ER. This indicates that Mg²⁺ blocks the InsP₃R channel with equal potency from either side. Thus, the site responsible for permeant divalent cation block is probably located inside the pore along the ion permeation pathway, with cations from either side of the channel having similar access to the site.

The data for g_ch in symmetric [Mg²⁺]_f (Fig. 5 B, black crosses) fall on the curve described by Eq. 2 (Fig. 5 B, red curve), so that

$$g_{\text{ch}}\left({\left[{\text{Mg}}^{2+}\right]}_{\text{sym}}\right)=\left(g_{\mathrm{\infty }\text{CaER}}{\left[{\text{Mg}}^{2+}\right]}_{\text{sym}}+g_0{K}_{\text{CaER}}\right)/\left(K_{\text{CaER}}+{\left[{\text{Mg}}^{2+}\right]}_{\text{sym}}\right).$$

Using g_∞CaER = g_∞MgER = g_∞, and K_CaER = 0.5 K_MgER,

$$g_{\text{ch}}\left({\left[{\text{Mg}}^{2+}\right]}_{\text{sym}}\right)=\frac{g_{\mathrm{\infty }}\left\{{\left[{\text{Mg}}^{2+}\right]}_{\text{ER}}+{\left[{\text{Mg}}^{2+}\right]}_{\mathrm{i}}\right\}+g_0{K}_{\text{MgER}}}{K_{\text{MgER}}+\left\{{\left[{\text{Mg}}^{2+}\right]}_{\text{ER}}+{\left[{\text{Mg}}^{2+}\right]}_{\mathrm{i}}\right\}},$$ (4)

suggesting that contributions to channel block by Mg²⁺ on either side can be combined by simply summing the [Mg²⁺]_f on the two sides as if all the Mg²⁺ was on one side. This relation can even be extended to include [Ca²⁺]_ER. g_ch data observed in various combinations of [Ca²⁺]_ER, [Mg²⁺]_i, and [Mg²⁺]_ER (whether [Mg²⁺]_i = [Mg²⁺]_ER or not), when plotted against the equivalent divalent ion concentrations [X²⁺]_eq defined as {[Ca²⁺]_ER +0.5×([Mg²⁺]_ER + [Mg²⁺]_i)}, are all well fitted by a curve similar to that described by Eq. 2 (Fig. 5 C, red curve); i.e.,

$$\begin{array}{l}{g}_{\text{ch}}\left({\left[{\text{Ca}}^{2+}\right]}_{\text{ER}},{\left[{\text{Mg}}^{2+}\right]}_{\text{ER}},{\left[{\text{Mg}}^{2+}\right]}_{\text{i}}\right)\\ =\frac{g_{\mathrm{\infty }}\left\{{\left[{\text{Ca}}^{2+}\right]}_{\text{ER}}+0.5\times \left({\left[{\text{Mg}}^{2+}\right]}_{\text{ER}}+{\left[{\text{Mg}}^{2+}\right]}_{\text{i}}\right)\right\}+g_0{K}_{\text{CaER}}}{K_{\text{CaER}}+\left\{{\left[{\text{Ca}}^{2+}\right]}_{\text{ER}}+0.5\times \left({\left[{\text{Mg}}^{2+}\right]}_{\text{ER}}+{\left[{\text{Mg}}^{2+}\right]}_{\text{i}}\right)\right\}}\\ =\frac{g_{\mathrm{\infty }}{\left[{\text{X}}^{2+}\right]}_{\text{eq}}+g_0{K}_{\text{CaER}}}{K_{\text{CaER}}+{\left[{\text{X}}^{2+}\right]}_{\text{eq}}}.\end{array}$$ (5)

This result strongly indicates that channel block by different permeant divalent cations is caused by binding to a unique, saturable site in the ion permeation pathway that is equally accessible from either side of the channel, with an affinity for Ca²⁺ twice that for Mg²⁺. This site is probably located at or near the selectivity filter of the channel where the channel pore size is most restricted.

DISCUSSION

Magnitude of i_Ca through the InsP₃R channel in physiological ionic conditions

In this study, the conduction properties of a homotetrameric recombinant rat InsP₃R-3 channel were examined under various ionic conditions, especially under physiological monovalent and divalent ion concentrations. Under physiological ranges of [K⁺]_f, [Cl⁻]_f, [Mg²⁺]_f, [Ca²⁺]_i, and [Ca²⁺]_ER, i_Ca through an open InsP₃R channel depends only on [Ca²⁺]_ER with a linear relation. i_Ca = 0.15 ± 0.01 pA for a filled ER store with 500 µM [Ca²⁺]_ER. This value is compatible with the magnitude of Ca²⁺ flux estimated by the imaging of Ca²⁺ release events (puffs) of 0.4–2.5 pA (Sun et al., 1998) and 0.12–0.95 pA (Bruno et al., 2010) in Xenopus oocytes, where multiple active InsP₃R channels were involved in generating a puff. The value is also in reasonable agreement with the values for i_Ca estimated from Ca²⁺ release events (blips and puffs): ∼0.4 pA (Shuai et al., 2006) and ∼0.1 pA (Bruno et al., 2010) for endogenous InsP₃R-1 in Xenopus oocytes, and ∼0.05 pA i_Ca estimated for endogenous InsP₃R-1 channels in human neuroblastoma SH-SY5Y cells (Smith and Parker, 2009). Accordingly, our experimental approach, with the advantages of observing Ca²⁺ currents with single-channel resolution and rigorous control of ionic conditions on both sides of the channel, appears to accurately reflect the physiological behavior of InsP₃R channels in intact cells. Furthermore, our measured value of i_Ca is comparable to the i_Ca of 0.1 pA (Swillens et al., 1999), 0.07 pA (Thul and Falcke, 2004), and 0.2 pA (Shuai et al., 2008), assumed in various efforts to numerically simulate Ca²⁺ release through InsP₃R channels, thus providing experimental support for the validity of those modeling efforts.

i_Ca for InsP₃R measured here is comparable to but smaller than those determined for RYR channels, the other major family of intracellular Ca²⁺ release channels. i_Ca driven by 500 µM [Ca²⁺]_ER through purified amphibian type 1 RYR (RYR1) and mammalian type 2 RYR (RYR2) channels reconstituted in artificial lipid bilayers was estimated to be 0.26 and 0.27 pA, respectively, in the presence of symmetric 150 mM KCl and 1 mM MgCl₂ (Kettlun et al., 2003). Under similar ionic conditions (140 mM KCl and 1 mM MgCl₂), i_Ca through an open rat InsP₃R-3 channel is 0.15 pA. However, as discussed in more detail below, if the lipid environment impinges on the conductance properties of the release channels, a comparison of the i_Ca may not yet be possible because i_Ca measurements for the two channel types were obtained in different membrane environments.

InsP₃R channel conductance

g_ch of various InsP₃R channel isoforms in symmetric 140 mM KCl has been observed, mainly by nuclear patch clamp experiments (Mak and Foskett, 1998; Mak et al., 2000; Boehning et al., 2001a; Ionescu et al., 2006; Betzenhauser et al., 2009), to be comparable to but smaller than those for RYR channels reconstituted into lipid bilayers under the same KCl concentration: ≈750 pS for RYR1 (Wang et al., 2005) and 740 pS for RYR2 (Lindsay et al., 1991). Comparisons of primary sequences of different InsP₃R isoforms from various species with those of RYR isoforms reveal that a conserved sequence GGGXGDX (amino acid residues 2545–2551 in rat InsP₃R-1 SI⁺ SII⁺ isoform [Mignery et al., 1990] and 2472–2478 in rat InsP₃R-3 [Blondel et al., 1993]; X stands for I or V) between putative transmembrane helices 5 and 6 in the InsP₃R pore-forming domain is highly homologous to the sequence GGGIGDE (amino acid residues 4895–4901 in human RYR1 [Fujii et al., 1991] and 4824–4830 in human RYR2 [Zorzato et al., 1990]), which is conserved in all three RYR isoforms. Site-directed mutagenesis in the homologous RYR sequence alters the conductance properties of RYR channels (Zhao et al., 1999; Gao et al., 2000; Du et al., 2001; Chen et al., 2002; Wang et al., 2005), suggesting that those amino acids lie in or near the selectivity filter that determines, at least in part, the conductance of the RYR channel. Point mutations in the corresponding sequence in the rat InsP₃R-1 also altered its conductance properties (Boehning et al., 2001b). A mutation changing the GGGVGDV sequence to GGGIGDV made it more similar to that of the RYR and increased InsP₃R channel conductance (Boehning et al., 2001b). Conversely, GGGIGDE to GGGVGDE (Gao et al., 2000) and GGGIGDE to GGGIGDQ (Wang et al., 2005) substitutions in the RYR sequence generated channels with reduced conductance. Furthermore, invertebrate InsP₃R isoforms have a GGGIGDI sequence (Yoshikawa et al., 1992; Baylis et al., 1999; Iwasaki et al., 2002) that resembles the RYR sequence and have a higher single-channel conductance (477 ± 3 pS; Ionescu et al., 2006) than the vertebrate isoforms (360 – 390 pS; Mak and Foskett, 1998; Mak et al., 2000; Boehning et al., 2001a; Betzenhauser et al., 2009), which have a GGGVGDX sequence. Collectively, these observations strongly suggest that the GGGXGDX sequence in InsP₃R is close to or forms part of the selectivity filter in the tetrameric channel, and is therefore a major factor that determines the conductance properties of InsP₃R channels. However, mutagenesis suggests that amino acids outside the GGGXGDX sequence also play a role in determining the conductance of the InsP₃R (unpublished data) and RYR (Gao et al., 2000; Du et al., 2001; Xu et al., 2006) channels, possibly through electrostatic effects to concentrate ions in the channel.

Other factors also appear to contribute to the channel conductance properties. Different single-channel conductances have been observed for the same recombinant InsP₃R-1 isoform expressed in DT40-InsP₃R-KO cells, depending on whether it was localized in the outer nuclear membrane (373 ± 2 pS; Betzenhauser et al., 2009) or the plasma membrane (214 ± 17 pS; Dellis et al., 2006). Moreover, the conductance of the homotetrameric recombinant InsP₃R-3 channel expressed in the outer nuclear envelope of DT40-KO-r-InsP₃R-3 cells measured here (545 ± 7 pS) is nearly 50% larger than that observed for the same recombinant InsP₃R-3 channel expressed in the outer nuclear envelope of Xenopus oocytes (370 ± 8 pS; Mak et al., 2000). Conductance values (∼125 and 200 pS) smaller than the one we observed here were reported for the same channel in the same location from the same cell type (Taufiq-Ur-Rahman et al., 2009), but those smaller and variable conductances were likely a result of heavy contamination by Mg²⁺ of the Na₂ATP used (Rahman and Taylor, 2009). The conductance of the r-InsP₃R-3 channels in the outer nuclear membrane of DT40-KO-r-InsP₃R-3 cells is even larger than that for the invertebrate InsP₃R (477 ± 3 pS; Ionescu et al., 2006), despite the more RYR-like putative selectivity filter sequence of the latter. Because all of these patch clamp studies of various InsP₃R channels were all performed in symmetric 140 mM KCl ([K⁺]_f = 104 mM), these observations suggest that besides the primary sequences of the InsP₃R, other factor(s)—lipid environment, interacting proteins or peptides, etc., that are different in various expression systems (outer nuclear membrane vs. plasma membrane; DT40-KO-r-InsP₃R-3 nucleus vs. Xenopus oocyte nucleus)—can affect the conductance of InsP₃R channels substantially.

The factors that cause the differences of the InsP₃R-3 g_ch observed in the same rigorously controlled ionic conditions (symmetric 140 mM KCl) in different cellular locations and different cells may also affect the size of i_Ca through InsP₃R-3 channels in those contexts. Because ours is the first measurement of i_Ca through an InsP₃R channel under physiological ionic conditions, how i_Ca correlates with g_ch in various cell systems cannot be clearly gauged until similar measurements are made in different systems. It should be pointed out that although the ionic conditions ([Ca²⁺]_ER, [Mg²⁺]_f, [K⁺], and [Cl⁻]) under which i_Ca was measured in this study were physiological or near-physiological, the ionic conditions under which g_ch in symmetric 140 mM KCl were measured (in this study and all published reports) were nonphysiological because of the absence of divalent cations, especially Mg²⁺, on either side of the channels. It is possible that the observed variability of g_ch is a result of the use of nonphysiological ionic conditions, as a study on the effects of divalent cations on InsP₃R g_ch suggested (Mak and Foskett, 1998). This issue can be clarified with more direct measurements of i_Ca for other InsP₃R channels in different cell systems. At this point, the applicability of the i_Ca of homotetrameric type 3 InsP₃R channels in DT40-KO-r-InsP₃R-3 cells to other InsP₃R channels and cell types should be considered judiciously with recognition of its potential limits. However, this first direct measurement is of significant value for improving our understanding of the mechanisms of InsP₃R-mediated Ca²⁺ release and for modeling efforts to simulate Ca²⁺ signaling.

Selective permeant ion block of the InsP₃R channel by Mg²⁺

Physiological [Mg²⁺]_f (200 µM–1.1 mM in both the cytoplasm and ER lumen) substantially reduced g_ch of the InsP₃R channel in symmetric 140-mM KCl solutions (Fig. 5) by acting as a permeant blocking cation. This indicates that under physiological conditions, Mg²⁺ significantly affects the passage of K⁺ through the InsP₃R channel pore. Accordingly, it is not immediately obvious why i_Ca was not measurably different in the presence or absence of physiological [Mg²⁺]_f (Fig. 4). Similarly, i_Ca’s passing through RYR channels under physiological (∼500 µM) [Ca²⁺]_ER (Chen et al., 2003; Kettlun et al., 2003; Gillespie and Fill, 2008) were not significantly affected by the presence or absence of 1 mM MgCl₂.

Because of the lack, to date, of a quantitative model to describe the conductance properties of the InsP₃R channel pore, we attempt to explain qualitatively the apparently contradicting observations by using models developed to account for conductance properties of RYR channels, which have a putative selectivity filter sequence, and therefore structure, highly homologous to those of InsP₃R channels.

In a barrier model that describes the RYR channel as a single-ion occupancy channel with four energy barriers in the selectivity filter (Tinker et al., 1992), the channel is blocked when any cation enters the vacant selectivity filter because the channel cannot accommodate two cations simultaneously. Despite higher permeability of Mg²⁺ than K⁺, because [K⁺]_f in the cytoplasm and ER lumen is about two orders of magnitude higher than [Mg²⁺]_f, K⁺ is likely to be the major permeant blocker of i_Ca through the InsP₃R channel. Furthermore, because of the higher affinity of Ca²⁺ for the selectivity filter relative to that of Mg²⁺, as revealed by its more potent reduction of InsP₃R g_ch (Fig. 5), the energy released as Ca²⁺ enters the channel selectivity filter from the luminal side can compensate for the energy required to push an occupying Mg²⁺ out the cytoplasmic side, especially if the Mg²⁺ is bound to the side energy well close to the cytoplasmic end of the filter. Thus, it is possible that the i_Ca through the InsP₃R channel is already significantly suppressed by physiological [K⁺]_f, such that Mg²⁺, with lower affinity for the selectivity filter than Ca²⁺, cannot reduce the magnitude of i_Ca further by a detectable amount.

In Poisson-Nernst Planck models with (Gillespie et al., 2005) and without (Chen et al., 1997, 2003) density function theory, a cation-selective channel is described as one with a constricted selectivity filter region containing negative charges from acidic amino side chains or carbonyl backbones. Cations move through the pore by electrodiffusion under electrical and concentration gradients, interacting with the channel both electrostatically and chemically. According to these models, concentrations of cations in the selectivity filter of the RYR/InsP₃R channel are higher than those in the bulk solutions because of the permanent negative charges from the Asp (in GGGXGDX in InsP₃R) or Asp and Glu (GGGIGDE in RYR) located in or near the selectivity filter of the channel. This concentrating effect is stronger for Ca²⁺ and Mg²⁺ than for K⁺ because of the more negative chemical potentials of Ca²⁺ and Mg²⁺ in the selectivity filter as a result of either chemical interactions between the divalent cations and the channel (Chen et al., 2003), or because of the smaller ionic radii and therefore smaller excluded volumes and higher charge densities of Ca²⁺ and Mg²⁺ (Gillespie, 2008). The high divalent cation concentration in or near the selectivity filter in turn lowers [K⁺] there as a result of electrostatic repulsion between the cations (Chen et al., 2003; Gillespie et al., 2005; Gillespie, 2008). This can cause the observed reduction of g_ch by physiological concentrations of Mg²⁺ or Ca²⁺. In InsP₃R channels, the conserved sequence GGGXGDX in or near the selectivity filter has fewer acidic residues than the corresponding sequence GGGIGDE for the RYR channels. This may reduce the permanent negative charge density in the InsP₃R channel selectivity filter relative to that for the RYR channel and consequently weaken the electrostatic interaction between the selectivity filter and the cations (Gillespie et al., 2005), making the effect of the more negative chemical potential of Ca²⁺ than Mg²⁺ in the filter even more prominent in the InsP₃R than RYR, as indicated by the substantial higher potency of Ca²⁺ than Mg²⁺ to reduce InsP₃R g_ch (Fig. 5). High [Ca²⁺]_f in the InsP₃R selectivity filter will suppress entry of Mg²⁺ through electrostatic repulsion. With only physiological [Mg²⁺]_f in the bulk solution around the channel, there may not be enough Mg²⁺ in the filter to significantly impede the flux of Ca²⁺.

[Ca²⁺]_i at various distances from an open InsP₃R channel as a result of i_Ca

The size of i_Ca through an open InsP₃R channel in the ER membrane obviously directly affects the [Ca²⁺]_i immediately surrounding it. Measurement of i_Ca in physiological ionic conditions now enables us to estimate the [Ca²⁺]_i in the vicinity of an open InsP₃R. For the estimation, the channel pore can be treated as a point source in a semi-infinite region (Smith, 1996). Within short distances from the open-channel pore (<15 nm), the concentrations and Ca²⁺-binding rates of endogenous cytoplasmic Ca²⁺ buffers are too low to significantly affect the local [Ca²⁺]_i. Thus, local [Ca²⁺]_i in the immediate vicinity of the open channel is mainly determined by the equilibrium between Ca²⁺ flux through the channel and diffusion of unbound Ca²⁺ through the cytosol, and can be estimated with reasonable accuracy as

$${\left[{\text{Ca}}^{2+}\right]}_{\text{i}}\left(r\right)\approx [i_{\text{Ca}}/(z_{\text{Ca}}F2\pi Dr\left)\right]\approx 1.1\times {\left[{\text{Ca}}^{2+}\right]}_{\text{ER}}\hspace{0.17em}\text{nm}/r,$$ (6)

where r is the distance from the channel pore, D is the diffusion coefficient for Ca²⁺ in the cytoplasm with no buffering, and z_Ca and F are as defined in Eq. 1 (Smith, 1996; Neher, 1998), using the value of i_Ca measured here and D ≈ 225 µm²s⁻¹ (Allbritton et al., 1992). According to cryo-electron microscopy (Jiang et al., 2002; da Fonseca et al., 2003; Hamada et al., 2003; Serysheva et al., 2003; Sato et al., 2004; Wolfram et al., 2010) and electron microscopy (Cárdenas et al., 2010a) measurements, the radius of a tetrameric InsP₃R channel in a plane perpendicular to the axis of the channel pore is ∼10–12 nm. There is no structural information concerning the locations of various Ca²⁺-binding sites in the channel relative to the pore, but it is reasonable to assume that the distance between the sites and the pore is <10–12 nm. Using 8 nm as an estimate of the distance between the channel pore and the activating and inhibitory Ca²⁺-binding sites of the channel, within the physiological range of [Ca²⁺]_ER (100–500 µM), [Ca²⁺]_i is sensed by the channel; i.e., [Ca²⁺]_i (8 nm) ≈ 14 – 69 µM (Fig. 6). This [Ca²⁺]_i level is reached within a short time (microsecond) after the opening of the channel (Neher, 1998). With a filled ER store, [Ca²⁺]_i (8 nm) is high enough that even at saturating [InsP₃], P_o of the open channel itself is significantly inhibited for most InsP₃R isoforms that have been studied in single-channel experiments (Foskett et al., 2007). This can provide negative feedback to terminate the Ca²⁺ release. On the other hand, when the ER store is partially depleted, Ca²⁺ released by the InsP₃R channel may not be sufficient to raise [Ca²⁺]_i high enough to suppress activity of the releasing channel to terminate the Ca²⁺ release.

Figure 6.

Spatial profiles of [Ca²⁺]_i at various distances from an open InsP₃R channel for different [Ca²⁺]_ER with different cytoplasmic Ca²⁺-buffering capacities. [Ca²⁺]_i was calculated using Eq. 7 with characteristic length λ = 55 and 440 nm for strong and weak cytoplasmic Ca²⁺ buffering, respectively.

Farther away from the channel pore, [Ca²⁺]_i is strongly affected by cytoplasmic Ca²⁺ buffers. Estimates of concentrations and Ca²⁺-binding rates of endogenous Ca²⁺ buffer(s) (B_T and k_on, respectively) vary widely (Wagner and Keizer, 1994; Smith et al., 1996; Falcke, 2003; Shuai et al., 2008), so only a first-order estimate of [Ca²⁺]_i(r) is feasible for a general case. For simplicity, so that [Ca²⁺]_i(r) can be evaluated analytically, the excess buffer approximation is assumed (Smith, 1996) for our rough estimation, so

$${\left[{\text{Ca}}^{2+}\right]}_{\text{i}}\left(r\right)\approx [i_{\text{Ca}}/(z_{\text{Ca}}F2\pi Dr)]\hspace{0.17em}\text{exp}(-r/\lambda ),$$ (7)

where λ, the characteristic length, is (D/k_onB_T)^1/2. From parameters used in Wagner and Keizer (1994), Smith et al. (1996), and Falcke (2003), we determined a high and low estimate for λ as 440 and 55 nm, respectively, and estimated the range of [Ca²⁺]_i(r) using Eq. 7 (Fig. 6).

For r > 200 nm, [Ca²⁺]_i(r) calculated from the two estimates for λ differs by over two orders of magnitude (Fig. 6), and it is no longer meaningful to consider [Ca²⁺]_i(r) for a general case. More specific values for k_on and B_T are needed to give a better evaluation of [Ca²⁺]_i.

From our estimation, it is clear that as [Ca²⁺]_i(r) decreases for larger r, there is a range of r within which the Ca²⁺ released by an open InsP₃R channel can activate a neighboring channel at that distance away, as long as [InsP₃] is sufficiently elevated, for all InsP₃Rs studied (Foskett et al., 2007). Thus, the magnitude of i_Ca observed confirms that CICR can be a mechanism to couple neighboring InsP₃R channels to coordinate concerted Ca²⁺ release by multiple channels to generate various intracellular Ca²⁺ signals.

In this simple consideration, the [Ca²⁺]_i profile was estimated around an open channel with P_o = 1. In reality, the amount of Ca²⁺ moving through the releasing channel depends not only on i_Ca, but also on the stochastic gating of the releasing channel, which is dynamically regulated by the local [InsP₃] and [Ca²⁺]_i (Foskett et al., 2007), which in turn are affected by Ca²⁺ released by the releasing channel and any neighboring active channels. Furthermore, the activation of an InsP₃R channel by CICR is a complex dynamic process regulated by stochastic binding and unbinding of InsP₃ and Ca²⁺ to activating and inhibitory sites, which are affected not only by local [Ca²⁺]_i, but also by the on- and off-rates of the sites that can be allosterically coupled (Atri et al., 1993; Tang et al., 1996; Kaftan et al., 1997; Moraru et al., 1999; Dawson et al., 2003; Mak et al., 2003). To properly take into consideration all of these complicated factors affecting the regulation of Ca²⁺ signaling, quantitative kinetic modeling (De Young and Keizer, 1992; Swillens et al., 1994, 1998, 1999; Dupont and Swillens, 1996; Tang et al., 1996; Falcke et al., 2000; Sneyd and Falcke, 2005; Swaminathan et al., 2009) using the right parameters, of which i_Ca is a critical one, is necessary.

In summary, we have described the first direct electrophysiological measurements of the i_Ca’s driven by physiological [Ca²⁺] gradients across single InsP₃R channels in a native ER membrane environment under physiological ionic conditions. These measurements will enable more accurate evaluations of the amount of Ca²⁺ released in a fundamental Ca²⁺ release event mediated by a single InsP₃R channel, contribute to a better estimation of the coupling between the activities of neighboring InsP₃R channels through CICR, and provide insights to improve future understanding and modeling of intracellular Ca²⁺ signals.