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Gating Mechanisms of the Type-1 Inositol Trisphosphate Receptor

Biophysics Department, Faculty of Medicine, University of Medicine and Pharmacy "Carol Davila", Bucharest, Romania

Correspondence: Address reprint requests to Irina Baran, Tel.: 00-40-21-312-5955; E-mail: baran{at}theor1.theory.nipne.ro.

	ABSTRACT

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

 
A large amount of data and observations on inositol 1,4,5-trisphosphate (IP₃) binding to the IP₃ receptor/Ca²⁺ channel, the steady-state activity of the channel, and its inactivation by IP₃ can be explained by assuming one activation and one inhibition module, both allosterically operated by Ca²⁺, IP₃, and ATP, and one adaptation element, driven by IP₃, Ca²⁺, and the interconversion between two possible conformations of the receptor. The adaptation module becomes completely insensitive to a second IP₃ pulse within 80 s. Observed kinetic responses are well reproduced if, in addition, two module open states are rendered inactive by the current charge carrier Mn²⁺. The inactivation time constants are 59 s in the activation, and 0.75 s in the adaptation module. The in vivo open probability of the channel is predicted to be almost in coincidence with the behavior in lipid bilayers for IP₃ levels of 0.2 and 2 µM and one-order-higher at 0.02 µM IP₃, whereas at 180 µM IP₃ the maximal in vivo activity may be 2.5-orders higher than in bilayers and restricted to a narrower Ca²⁺ domain (10 µM-wide versus 100 µM-wide). IP₃ is likely to inhibit channel activity at 120 nM Ca²⁺ in vivo.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

 
Release of Ca²⁺ ions from the endoplasmic reticulum (ER) is essential to many cellular processes (1,2). Calcium is released via the opening of its ER channel, the inositol 1,4,5-trisphosphate receptor (IP₃R), whose complex behavior undergoes marked changes as the receptor is either incorporated into planar lipid bilayers or preserved in its native membrane environment (3–13). The reasons for the extreme variation (reaching as high as 20-fold) found in its peak open-probability are not clear. It is well established, however, that the IP₃R activity is tightly regulated by cytosolic factors such as Ca²⁺, IP₃, and free ATP, but the underlying mechanisms have remained poorly defined and are often confusing. It is not surprising, then, that there is no general consensus among existent models of the IP₃ receptor (4,9,10,14–19), and that even though models (see Refs. 20 and 21 for review) have evolved in explaining increasing amounts of data, the current understanding of the calcium release regulation is still far from complete.

The ER Ca²⁺ channel is recognized as a tetrameric complex that binds IP₃ and Ca²⁺ and is able to promote release of calcium ions into the cytosol. Three IP₃ receptor isoforms are expressed in mammalian cells: IP₃R type-1 (IP₃R1), IP₃R type-2 (IP₃R2), and IP₃R type-3 (IP₃R3). The IP₃R1 sequence contains 2749 amino acids and determines three structurally different parts: a large N-terminal cytoplasmic arm (65–80% of full length), a putative six-membrane-spanning domain near the C-terminus, which contributes to the pore structure; and a short C-terminal cytoplasmic tail (22,23).

IP₃ has been found to bind to the 226–578 residue domain, which is near the NH₂-terminus of each monomer (23,24). Mutational analysis revealed that the IP₃ binding domain contains four segments (indexed here as DS1–4) covering the regions 241–249, 265–269, 504–508, and 568–569, respectively, which are determinant for ligand binding (24). In most biochemical studies IP₃ bound to the receptor with K_d 50 nM and Hill coefficient 1 (4,10,24–29). It has been estimated that in the purified receptor each subunit binds one IP₃ molecule to a single medium affinity site (30), but several recent findings in microsomes, with higher concentrations used of the radioactive ligand, cannot be explained unless a second IP₃ binding site, of low affinity (K_d 10 µM, n_H 1), is present on the IP₃R1 (4) with equal abundance as the 50 nM site (4,10). Meanwhile, a third site with high affinity (K_d 1 nM) appears with extremely low frequency (<1%) in microsomal preparations (4,10), which brings into question its belonging to the IP₃R1 (see below).

Ca²⁺ binds to seven sites residing on the cytoplasmic region of the receptor monomer and to one luminal site (23,31,32). The affinity of the luminal site and that of one cytoplasmic site have been determined (31,32), K_d = 0.3 µM (h = 1) and K_d = 0.8 µM (h = 1), respectively. With constant levels of IP₃, the open probability of the channel depends on cytosolic Ca²⁺ in a bell-shaped manner, which is currently attributed to regulation by two distinct classes of activating and inhibitory Ca²⁺ sites, although some models can reproduce it with the aid of a single Ca²⁺ regulatory site (10). The IP₃R1 sensitivity to activation and inhibition by Ca²⁺ most likely results from the calcium binding sensor (1932–2270 residues in IP₃R1), which may include several Ca²⁺ binding sites (12).

It has been shown that another regulating factor, ATP, affects the activity of the channel (7,8). ATP binds to two-to-three putative sites situated on the regulatory cytoplasmic domain of the IP₃R1 (23,33–36). Initially it has been estimated that in the purified receptor ATP binds to a single high affinity (K_d = 17 µM) site on the monomer (30). Recent studies have proved that the regions 1773–1780 and 2015–2021 of the purified IP₃R1 bind ATP with high (K_d = 1.6 µM) and low affinity, respectively (35,36). The lower affinity site is conserved between IP₃R isoforms. For the type-3 receptor the K_d is 177 µM (35). Binding of ATP can both stimulate and inhibit the receptor, depending on the Ca²⁺ concentration; however, the mechanisms are not clear. A simple, Hill-modified, ATP-dependence of the Ca²⁺ dissociation constant in the activation region (where P_o increases with Ca²⁺, here for Ca²⁺ levels <60 µM) suggests that ATP has a functional K_d of 270 µM and h = 1 (7), whereas in the inhibition region ([Ca²⁺] > 60 µM) an ATP increase from 0 to 500 µM leads to a decrease of the Ca²⁺ dissociation constant from 100 to 50 µM (8). It appears thus that ATP enhances both activation and inhibition of the channel by Ca²⁺.

Regulation of IP₃R1 activity by IP₃ and Ca²⁺ has been approached with models of increasing complexity. Even though early models (14,37) succeeded in reproducing the biphasic dependence of P_o on Ca²⁺ on the basis of three regulatory sites (one IP₃-, one activating Ca²⁺-, and one inhibitory Ca²⁺ site), the right dependence of P_o on both Ca²⁺ and IP₃ was achieved later, by including a low affinity IP₃ site (4). However, better fit to P_o and open dwell-time data was obtained with a more complex, 125-state model (10), which assumed a single Ca²⁺ regulatory site and two IP₃ sites (of medium and low affinity) in each monomer. The P_o dependence on Ca²⁺ at 2 µM IP₃ can be reproduced as well with different combinations of regulatory sites, as, for example, in the model of Swillens et al. (15,16)—where the assumed regulatory sites are the medium-affinity IP₃, two Ca²⁺ activating sites, and two Ca²⁺ desensitizing sites.

In this article we analyze different sets of published data on IP₃R binding and single channel activity, and show that the stationary activity of the IP₃R type-1 (IP₃R1) in both native and artificial membranes as well as various puzzling properties of the IP₃ binding to the ER membrane can be consistently explained by a unique gating mechanism involving triple allosteric interactions between Ca²⁺, IP₃, and free ATP binding to the channel molecule, but with different receptor sensitivity to particular ligands under different experimental conditions. Nevertheless, since to this end we use exclusively equilibrium data, the IP₃R gating model is then adapted to reproduce channel inactivation in the sustained presence of IP₃. Time trends of channel's open probability after two-pulse IP₃ stimulation can be found closely similar to the experimental ones.

The model assumes that the activity of the Ca²⁺ channel is determined by the opening of three independent gates, each belonging to a certain region of the receptor, termed a module. One module is activated whereas another is inhibited by Ca²⁺. They are therefore called the activation module (AMo) and the inhibition module (IMo), respectively, whereas the remaining module, termed the adaptation module (AdMo), is considered to contribute to channel inactivation. The whole model is constructed on the basis of considering the tetramer receptor as a complex unit, so it describes how IP₃ binds globally to each module, not to the corresponding portion of each monomer within a certain module. That allows us to assume that each module provides a single equivalent IP₃ binding site. Then the Hill coefficient that defines IP₃ binding to such a site gives the mean number of IP₃ molecules that at an instant bind all four monomers at the locus of IP₃ binding in the corresponding module.

Some of the model outputs pertain to the following:

1. The prediction of four IP₃ binding sites on each receptor subunit, presumably located on the DS1–4 segments; three of these sites are implicated in channel gating.
   
2. The modulation by ATP of (IP₃-dependent) channel activation and inhibition by Ca²⁺, effected by ATP binding at two sites on the receptor and allosteric regulation of Ca²⁺ and IP₃ binding.
   
3. The description of Ca²⁺ inhibitory effects on IP₃ binding, comprising alternative effects on affinity or the number of available binding sites.
   
4. The involvement in channel gating of a spontaneous or ligand-induced interconversion between two receptor conformations.
   
5. The description of channel inactivation by IP₃ observed in two-pulse experiments, involving the transient kinetic response to successive IP₃ additions; the rates of spontaneous conformation interchanges are determinant for the timescale of inactivation.
   
6. The prediction of the in vivo steady-state activity of the channel, which shares both similarities and differences with the behavior observed in bilayer experiments.
   

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

 
Analysis of steady-state channel activity
Calculation of channel open probability and open/close dwell-times is done according to a previously published method (18), considering 0.2-ms temporal resolution of single channel recordings (8) in Xenopus oocytes and the IP₃R1 reactions assumed in the present model. In the analysis of data obtained with the channel in lipid bilayers we have not corrected for missed events; however, the resolution therein is better (40 µs; see Ref. 10), and errors should be very small, at least for the open probability (18).

At equilibrium

(1)

where P_ad denotes the probability that the AdMo gate is open, and is assumed to be constant. Here and throughout the article, h denotes Hill coefficient, k is the rate constant, K is the dissociation constant, P_o is the open probability of the channel, P_m is the open gate probability of the m-type module, and [X] is the concentration of the X species. A site's occupancy is valued 1 (or 0) if the ligand is (or is not) bound to that site.

Where not specified, h = 1 for all ATP binding reactions. The rate of IP₃ dissociation is 5 s^–1 (15) unless otherwise stated, whereas the ATP dissociation rate constant is set to 0.05 s^–1 for all ATP sites in the activation module (see Channel Inactivation).

To obtain the equilibrium open gate probability of every module we consider first-order kinetics for all state transitions, using mass balance equations to describe the time variation in state fractions, and the thermodynamical constraints, as

(2)

where is the equilibrium constant of the binding reaction of the n-type ligand L_n (n = 1, 2, or 3, corresponding to L_n IP₃, Ca²⁺ and ATP, respectively) in the m-type module when the occupancies of the other two ligand sites are i and j, respectively, written in the order IP₃, Ca²⁺, and ATP. The on-rates are of the form where is the Hill coefficient of L_n binding to its site in the m-type module, with the other two ligand sites having occupancies i and j, respectively. is the dissociation constant of L_n under the same conditions.

Equilibrium state probabilities are calculated numerically by solving the ordinary differential equations (ODEs) describing kinetics of each state fraction and extracting the solution values in steady state. Within analyses of channel activity at steady state, inactivation is not considered (see Channel Inactivation), so transitions to inactive states in Figs. 1 and 2 are not included in the equations.

View larger version (36K): [in this window] [in a new window]   FIGURE 1  States and transitions within activation and inhibition modules of the IP3R1. Open and shaded circles represent states with open and closed gates, respectively. Ligands bound to the module are marked by symbols inside the circles. Detailed state transitions have common forms in both modules (m act or m inh in the activation and inhibition modules, respectively) and are represented without reference to the gate configuration (open/closed). The state denoted AI in the activation module can enter an inactive form (solid circle) when the charge carrier Mn2+ binds to a inner site of the channel.

View larger version (34K): [in this window] [in a new window]   FIGURE 2  The adaptation module of the IP3R1 is operated by IP3, Ca2+ and the interconversion between two possible conformations, C1 and C2, with open and, respectively, closed gates. The state AdI is rendered inactive (solid circle) when Mn2+ (or K+) binds to an inner site of the channel.

When analyzing the single channel data of Mak et al. (6–9), two distinct values are obtained for each measured quantity, _o, namely, P_o (mean open time), and _c (mean close time). The actual value corresponds to the real value, which would be obtained if all the events were recorded (i.e., time resolution _d = 0), whereas the apparent value corresponds to the measured value, obtained with _d = 0.2 ms. The difference between the two values reflects errors in discriminating open from closed channel events, which determine part of the events to be missed during recordings. The kinetic parameters derived from fit to these data (presented in Table 1, column CA-nm) are the only rate constants appearing in the calculation of _o and _c at steady state (see Appendix 2 in Ref. 18).

View larger version (11K): [in this window] [in a new window]   FIGURE 8  The IP3 dependence of the IP3R1 open probability exhibited by channels incorporated in lipid bilayers, with 0.16 µM Ca2+ and 500 µM ATP on the cytosolic side. Data shown as open and solid circles are from two different experiments performed under the same conditions; see Refs. 4 and 10, respectively.

View larger version (29K): [in this window] [in a new window]   FIGURE 3  The [Ca2+]cyt dependence of the IP3R1 open probability in the presence of 500 µM or 0 ATP, exhibited by channels within nuclear membranes of Xenopus oocytes. Curves are theoretical fits to the data and predictions for IP3 concentrations other than those used in experiments. Values next to curves represent IP3 concentrations in nM, unless otherwise specified. In the upper panel, data from Ref. 6 are represented as solid triangles, solid squares, open circles, solid circles, and open triangles, corresponding to 10 nM, 20 ± 3 nM, 33 ± 6 nM, 100 nM, and 10 µM IP3, respectively. The second and third datasets are to be confronted with the two regions delimited by dashed lines (squares to the 17–23 region, open circles to the 27–39 domain), to correct for variations in the IP3 level. In the lower panel, open and solid circles represent data of Mak et al. (8), obtained with 0 ATP, and 33 nM or 10 µM IP3, respectively.

View larger version (18K): [in this window] [in a new window]   FIGURE 4  Model fit to data of Mak et al. (6,8) obtained with the channel in the nuclear membrane, and 10 µM IP3 and 500 µM ATP on the cytosolic side. Dashed and solid lines characterize actual and apparent values, respectively, of the quantity represented in each graph.

View larger version (15K): [in this window] [in a new window]   FIGURE 5  Model fit to data of Mak et al. (8) obtained with 10 µM IP3 and 0 ATP on the cytosolic side. Other details as in Fig. 4.

View larger version (18K): [in this window] [in a new window]   FIGURE 6  Number of events during 1000 single-channel recordings. Point values and error bars are calculated with the use of open and close time data of Mak et al. (6,8) obtained with the channel in the nuclear membrane, 10 µM IP3, and 0 or 0.5 mM ATP on the cytosolic side of the channel. Dashed and solid lines represent actual and apparent numbers of events, respectively.

View larger version (22K): [in this window] [in a new window]   FIGURE 11  Simulated inactivation of the IP3R1 in the continuous presence of IP3R. The Mn2+ content in the stores, expressed in arbitrary units in the upper panel, corresponds, from the lower to the upper trace, to preincubation with IP3 for 0, 20, and 180 s, respectively. Here t = 0 is the moment of Mn2+ addition, coincident with application of the second IP3 pulse. Lower panels depict kinetics of open gate probability in each IP3R1 module before and after addition of IP3. The first IP3 pulse initiates at t = 0. The second IP3 pulse is applied at t = 20 and 180 s, respectively.

View larger version (11K): [in this window] [in a new window]   FIGURE 12  Kinetics of channel inactivation depends on the time of preincubation with IP3. On the ordinate it is represented the time to half-maximum of the Mn2+ content trace obtained after preincubation with IP3 for the duration represented on the abscissa. The data are from Hajnoczky and Thomas (38); solid line is obtained by model calculation.

View larger version (14K): [in this window] [in a new window]   FIGURE 13  Predicted in vivo channel open probability at 500 µM ATP. Calculation is done according to the 3M-model, using parameter values defined in Table 1, last column. Numbers next to each curve represent IP3 concentration, in µM.

View larger version (20K): [in this window] [in a new window]   FIGURE 9  The IP3 binding to cerebellum membranes at different [Ca2+]cyt and two different temperatures. Data are from Moraru et al. (10) and correspond, in the upper panel, to 0 (solid circles), 0.1 µM (open circles), 0.5 µM (triangles), and 10 µM (squares) Ca2+, respectively. In the lower panel, open and solid circles are data obtained with 0 and 10 µM Ca2+, respectively.

The highest number of data was provided by experiments performed with Xenopus oocytes. The informative data on the dependence of IP₃R1 inhibition on ATP are quite few; however, we estimated that the inhibition module is saturated by ATP at 0.5 mM. In particular, from our findings, ATP binding to the activation module results to have low affinity. Therefore the nominal InMo-dissociation constant K_{ATP, 10} is fixed at the 17 µM value of the high affinity site (30). We first fit the model to the data obtained at 10 µM IP₃, including P_o, open-, and close-dwell-times (6,8). At this level, inhibition is maximal (6,9), meaning that the inhibition module is saturated with IP₃. We obtain the parameters indexed with superscripts (||) in the column CA-nm of Table 1. For the ATP dependence of receptor activation, P_o is approximated to P_act x P_ad since the inhibition module has, effectively, no Ca²⁺ bound. Then the rest of the parameters defining binding of ATP to the activation module (labeled with () in Table 1) are estimated from fit to other data (7). The three remaining parameter values (indexed with () in Table 1) are extracted from fit of IP₃ and Ca²⁺ dependencies of the P_o (6,8,9). Parameters labeled with (¶) in the adaptation module are estimated exclusively from dwell-time information. The procedure is repeated for 0 ATP-data.

Because of the lack of sufficient data, some of the parameter values are shared among other sets, especially and or and which are taken from the Xenopus set, whereas is dissipated from the CA-lb set. The consistency of the results validates this option. In analyses of IP₃ binding, P_ad and are each tested on two values, obtained with the sets CA-lb or In, and the best fit is kept. Where not specified, certain values of Table 1 copy the most reliable value among columns. If such a value does not provide reasonable fit, it is treated as a variable. The same principle applies also for various K- and h-parameters characterizing a certain ligand in AMo and IMo, within every single column of the table. All these simplify the fitting to a reasonable number of parameters. For example, with the fit in Figs. 4 and 5, eight and five parameters are estimated, respectively; in this particular case, the fitting is performed in two stages. First, the best fit is obtained separately for each set of data. Then, the common parameters are varied in a common range covering the values already obtained, and the best parallel fit is selected. With these values, the fitting moves forward to the data on the modulation by IP₃ of the P_o values Ca²⁺ dependencies at 0 or 0.5 mM ATP. From the fit shown in Fig. 3 (upper panel), three parameter values are determined. The fit of the data in Fig. 3 (lower panel) and related dwell-time data at 33 nM IP₃ (8) (not shown) provides two other parameter values. For other data presented in Figs. 7 and 10, twelve and, respectively, six variable parameters are required. Fig. 9 (upper and lower panels) is obtained with 10- and six-parameter fits, respectively.

View larger version (13K): [in this window] [in a new window]   FIGURE 7  The [Ca2+]cyt dependence of the IP3R1 open probability at 500 µM ATP, exhibited by channels incorporated in lipid bilayers. Data, taken from Kaftan et al. (4) and Moraru et al. (10), and shown as solid and open circles, squares, and triangles, are obtained with 10, 20, 200 nM, and 180 µM IP3, respectively. Theoretical curves are obtained with the present model.

View larger version (11K): [in this window] [in a new window]   FIGURE 10  The IP3 binding to cerebellum membranes at different [Ca2+]cyt. Data (from Ref. 29) correspond to 2 nM (open circles) and 1.1 µM (solid circles) Ca2+, respectively.

IP₃ bound to the receptor is calculated by summing the products of the following terms, each one corresponding to a certain class of IP₃ binding sites: site abundance, apparent number of IP₃ molecules bound to the IP₃ sites of the respective site class, and receptor concentration. The apparent number of IP₃ molecules bound to a certain module is determined by summing the fraction of each IP₃ bound-state within that module, times the Hill coefficient of IP₃ binding to the respective state. Site abundances are denoted n_A, n_I, n_Ad, and n_hi in the lowest row of Table 1 and correspond to the IP₃ sites located on the activation, inhibition, and adaptation modules, and, respectively, to the high-affinity IP₃ site existent in the respective microsome preparation. For each of the activation, inhibition, and adaptation modules the fraction of states with bound IP₃ equals the sum of the steady-state probabilities corresponding to the module being in one of the four possible states with the IP₃ site occupied. The IP₃-bound state fraction of the high-affinity site is computed as The receptor concentration is calculated such that the same apparent K_d values are obtained as derived from the original Scatchard plots (10,29).

Simulation of channel inactivation
The time variation of P_o after IP₃ stimulation is calculated numerically by solving the kinetic equations (ODEs) corresponding to the reactions in each module, followed by multiplication of all three open gate probabilities at every instant. Inactivation of a certain state is equated by subtracting from the ODE right-hand side a term of the form f_st/_st, where f_st is the instantaneous fraction of that state and _st its inactivation time constant.

The cytosolic conditions are fixed by levels of 2 mM ATP and 300 nM Ca²⁺, and the time constant for IP₃ degradation is _IP3 = 12 min (calculated from data in Ref. 38). Addition of 7.5 µM IP₃ takes place firstly at t₁ = 0 and then at a specified moment after the first pulse. The IP₃ concentration varies according to the equation

(3)

where the rate of IP₃ addition is r = 7.5 µM/t in the time interval (t_a,t_a + t) starting with the moment t_a of IP₃ addition, and r = 0 otherwise. The time of IP₃ addition is t = 1 s; however values t <1 s lead to similar results. The basal IP₃ production rate r_b = [IP₃]_b/_IP3 with the basal level of IP₃ set to [IP₃]_b = 1 nM.

The variation in the Mn²⁺ content inside the stores is obtained by considering the same constant value of the single channel current for all the IP₃Rs. The rate of Mn²⁺ increase is given by the Mn²⁺ current through the membrane, which is proportional to the open probability of the IP₃Rs. Each Mn²⁺ profile is then obtained, in arbitrary units, by integrating P_o over time after the moment of Mn²⁺ addition, which is specified for each trace. It is assumed that quenching of fura-2 fluorescence by Mn²⁺ (obtained experimentally) is proportional to the Mn²⁺ content (calculated by model simulation), so both traces should have identical time courses. On some simulated traces a Gaussian noise is superimposed with standard deviation chosen so as to yield a noise magnitude similar to that observed experimentally in the fluorescence signal (38).

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

 
Model construction
We proposed previously (18) a model, and we have found it was the minimal one, to describe P_o, _o, and _c dependence on Ca²⁺ at saturating levels of IP₃ (10 µM), as well as both ATP- and Ca²⁺-dependence of P_o in the activation region. The model was defined with three 4-state modules that drive independent gates responsible for activation/inhibition/inactivation of the channel. Here we improve that model to describe more data and reproduce the P_o, _o, and _c dependence on Ca²⁺, IP₃, and ATP, as well as the IP₃ binding characteristics and the inactivation of the channel.

It is important to stress the major idea of the modeling procedure. Such an empirical formulation of the P_o dependence with Ca²⁺ and IP₃ as found to describe the data in Xenopus oocytes (6,7) can be explained by at least three independent gates, of which two depend, at steady state, on Ca²⁺ and IP₃ concentrations whereas the others do not. To simplify the model, we consider only three such gates that act independently, leading to channel activity only when all of them are simultaneously open. For each gate-associated module now we introduce molecular mechanisms able to explain various experimental observations. The state-transition diagram of each module is constructed as the simplest state-configuration that agrees with all of the findings taken into account.

The activation module of the IP₃ receptor is responsible for the stimulation of channel in the low-domain of cytosolic calcium concentrations, where the inhibitory effect of Ca²⁺ is absent. The module is operated by Ca²⁺ and ATP (18) as one can readily deduce from direct observation of the P_o, _o, and _c data obtained with the channel in the outer nuclear membrane of Xenopus oocytes (6,7). The dwell-time data in conjunction with the P_o-data can only be explained by allosteric regulation of the activation module by Ca²⁺ and ATP (18), which requires at least four states of the module. Interestingly, with the receptor reconstituted into lipid bilayers (4,10) the activation module appears also to be IP₃-regulated since with 20 nM IP₃ the IP₃R1 activity in the activation region is 10-fold reduced as with 200 nM or higher IP₃ concentrations. Although the data in the former set is not sufficient to evidence that feature (as seen in Fig. 3 here, it is not clear from the data whether AMo is sensitive to variations in IP₃ in the Xenopus nuclear membrane), we collect both observations and draw the conclusion that gating in the activation module is allosterically controlled by IP₃, Ca²⁺, and ATP.

To make this statement one has to assume that the gating mechanisms are the same in both membrane systems and the resulting differences in channel behavior are purely quantitative. In fact this is exactly the basic rationale of the article, for we intended to see whether the variability observed in different data can be explained by considering the same molecular processes and, if so, to find the quantitative differences in ligand affinities and Hill coefficients associated to each data set obtained under different experimental conditions. One major observed discrepancy, which is discussed in this section, comes from the observation that under closely similar conditions on the cytosolic side of the receptor the maximal activity of the channel appears to vary 20-fold in the two different membrane systems mentioned before. Other sources of variability will be addressed in the next sections.

So, the state-structure of the activation module is defined with allosteric regulation by IP₃, Ca²⁺, and ATP, and the corresponding state-transition diagram is shown in Fig. 1.

Upon further raising cytosolic [Ca²⁺], the channel becomes increasingly inhibited. In this region, the behavior is dominated by the inhibition module, which is less active, whereas the activation gate may remain continuously open. As the data indicate (4,5–8,10), IP₃ is an important modulator of the calcium inhibitory effect (18). The inhibition module can therefore exist in one of at least four states. We characterize this module better than in our previous work (18), with more recent results on IP₃R1 regulation by ATP (8) included in the present analysis. These data require ATP to modulate channel inhibition by Ca²⁺. Taken together, all the data mentioned above point to the existence of three regulatory sites within IMo, namely one ATP, one IP₃, and one Ca²⁺ binding site, and a similar state distribution within AMo and IMo (see Fig. 1) derives naturally after a summary inspection of the P_o data. The difference is that Ca²⁺ binding in the AMo opens the AMo gate; Ca²⁺ binding in the IMo closes the IMo gate; ATP binding in the AMo stimulates opening of the AMo gate by Ca²⁺; and ATP binding in the IMo reduces opening of the IMo gate by Ca²⁺.

The two modules are not sufficient to reproduce the observed behavior of the channel, since with appropriate Ca²⁺ levels both gates virtually remain continuously open (the open gate probability in both modules is 1). Therefore, to obtain agreement with experimental data in both cases (native and artificial membranes), including P_o, _o, and _c data, the model is constrained to include one other regulatory module, the adaptation module, characterized by constant (i.e., Ca²⁺, IP₃, and ATP-independent) and subunitary steady-state probability of the open gate, P_ad. It follows then that P_ad represents the maximal open probability of the channel reached at steady state.

The model predicts that the Ca²⁺, IP₃ and ATP dependence of channel's activity at equilibrium is determined by the AMo and IMo modules only. However, we found that the model established in the simplest possible form (see below) is not able to simulate several observed features related to the inactivation of the channel by Ca²⁺ and IP₃. In vivo kinetic studies on Ca²⁺ release indicate that after double IP₃ pulse delivery to Xenopus oocytes, the second release event gets weaker if the interval between pulses is successively increased up to 30 s, and the process occurs with a half-time of 10 s. For a 30-s interval, the inhibition of the release is 80% relative to the case of simultaneous IP₃ delivery. Metabolism of IP₃ is slow both in Xenopus oocytes (half-life 60 s, see Ref. 39) and in permeabilized hepatocytes (half-life 12 min., calculated from the data of Ref. 38), so it is more likely that the observed release inhibition is due to a ligand-induced inactivation of the IP₃R1 rather than IP₃ degradation, as suggested by Callamaras and Parker (39). In favor of this, other measurements (5) of the IP₃R1 activity in the nuclear membrane of the oocyte evidenced an inactivation process at the receptor level, with a time constant of 30 s (discussed later, in Channel Inactivation). Calcium release events after IP₃ photolysis in Xenopus oocytes (40) show IP₃-dependent time courses that are similar (17) to those obtained from superfusion of ⁴⁵Ca-loaded hepatic microsomes (41). In these and other similar (42) cases the release is fast, at variance with the slow channel inactivation detected in hepatocytes, where the unwanted effects of the cytosolic and luminal Ca²⁺ dynamics on the ion permeation properties were avoided by eliminating the Ca²⁺ fluxes (38). The type-2 IP₃ receptor (IP₃R2) is the major expressed subtype in hepatocytes, with 80% abundance (43). In this cell type the Ca²⁺ channel is subjected to an IP₃- and Ca²⁺-dependent slow inactivation (38), and channel inhibition reaches 70% after preincubation with 7.5 µM IP₃ for 30 s.

Given these and other similarities (e.g., the dual effect of cytosolic calcium on the open probability) between type-1 and type-2 receptors, we assume that the ligand-dependence of channel inactivation is common to both forms. To strengthen this choice, we observe that:

1. Both IP₃R1 and IP₃R2 exhibit intrinsic inactivation.
   
2. The fraction of IP₃R2 in hepatocytes is 0.8 of total IP₃Rs.
   
3. In hepatocytes the intrinsic IP₃Rs inactivation displays, depending on the preincubation time, one or two exponential components of equal weights.
   

We were not able to fully explain inactivation assuming that gating dynamics of the adaptation module are independent of Ca²⁺ and IP₃ (not shown). We have reasoned then that the adaptation element has to contribute as well to channel inactivation, and is therefore considered to be driven by Ca²⁺ and IP₃ binding reactions, yet yielding in steady state a constant (i.e., not dependent on Ca²⁺, IP₃, and ATP concentrations) open probability of the adaptation gate.

We consider that the adaptation module has a two-ligand (namely Ca²⁺ and IP₃) pattern, constrained by two experimental observations:

1. The channel recovers from inactivation after IP₃ removal or Ca²⁺ buffering (38).
   
2. In lipid bilayers the two components of the open dwell-time distribution appear to vary with the Ca²⁺ concentration (10).
   

Based on these observations, we obtain the transition- and state-configuration in the two-ligand (IP₃ and Ca²⁺) AdMo module as presented in Fig. 2. It is assumed that every time IP₃ or Ca²⁺ bind to, or dissociate from their AdMo sites, the module changes conformation, and, in addition, there is an auto-switch mode determined by spontaneous conversion between two possible conformations (C1 and C2) of the receptor. This particular combination between an autonomous change mode and the existence of only two possible conformations ensures that the exact adaptation requirement is always met, with no need to unnaturally force the respective transition rates. With the present module structure we obtain (not shown) that indeed the equilibrium open gate probability does not depend on IP₃ and Ca²⁺ concentrations, and neither does the apparent affinity of either ligand.

It will be certainly difficult to test such a molecular description of the adaptation module. However, the fact that it can reproduce IP₃R inactivation, whose mechanisms are unknown at present, makes it a good starting point and, corroborated by several other observations discussed below, lends support for other experiments designed to clarify the nature of inactivation. Recent findings on the three-dimensional structure of the IP₃R1 indicate (23,46) that the receptor presents two different conformations, which viewed from the top have either a square- or a windmill-like appearance (S- and W-conformations). The second conformation is favored at high Ca²⁺ concentration. However, it is not induced exclusively by Ca²⁺ binding to the receptor, since even in the absence of Ca²⁺ (and IP₃, too) the ratio of states W/S is 0.5 (this supports our hypothesis on the spontaneous conversion mode). There are two possible reasons for this behavior. One is that Ca²⁺ is an allosteric factor that is affecting the rate of the IP₃R structural changes. The other one is that the same state conversion, S-to-W, can be performed in two different ways: induced by Ca²⁺ binding or through a Ca²⁺-independent step. The first scenario applied to the adaptation module involves that the equilibrium open gate probability depends on Ca²⁺ concentration. Therefore, our model agrees with the second possibility. The Ca²⁺-independent step is considered as a spontaneous state conversion, which can take place even in the absence of the ligands. The main assumption here is that Ca²⁺, by binding to the adaptation module in either S/W conformation, acts as a molecular switch and triggers irreversibly a mechanism that destabilizes the respective conformation, which then changes rapidly. In this two-step process (Ca²⁺ binding-conformation change) Ca²⁺ binding is the rate limiting step, so the reaction scheme in Fig. 2 can apply. Conversely, Ca²⁺ dissociation from the adaptation module switches off the activated mechanism and the receptor resumes its initial configuration. The same mechanism is introduced for IP₃, too, and is incorporated into the same module, because the roles of IP₃ and Ca²⁺ in IP₃R inactivation are interdependent (38).

There are two other possible limitations of the adaptation modeling approach. The first is that the effect of 1 or 10 µM IP₃ on the receptor conformation was undetectable (23). However, the possibility that IP₃ binding to the adaptation module or the IP₃ effect itself on the receptor conformation could be affected during the respective experimental maneuvers cannot be neglected, and that would explain why such an effect was not observed. A second apparent discrepancy between our model and the data is the observed increase, up to approximately six, of the windmill/square-state ratio in the presence of calcium (23), whereas, according to our model, this ratio should remain constant at equilibrium. A plausible explanation would be that equilibrium was not yet reached at the moment of image recording, and the W/S ratio increase was observed during the transitory regime in the activation module, which develops after calcium application. Existent evidence supporting this idea is the fact that the rapidness of the practical procedures, from receptor purification to application onto the carbon grids for electron microscopy, is critical for the detection of the Ca²⁺-dependent structural changes (23). This means that images recorded after a sufficiently long time indicate that the W/S ratio is unchanged whether calcium (or IP₃) is present or not, and that would be an important confirmation of the model prediction. This point is also strengthened by the finding of one other group (47), which established in the absence of calcium a pinwheel-like structure of the IP₃R, which is more similar (23) to the windmill-like aspect of the receptor top-view, found to predominate when calcium is present. It has been suggested (23) that in the respective study the receptor has been locked in that state during purification, freezing, and thawing. Nevertheless, it seems highly improbable that all of the IP₃Rs in the sample preparation be locked in the same open state at an early stage of the experiment. Alternatively, the differences between various experimental strategies used in these experiments (e.g., different purification methods, different detergents, or different pH) can determine apparent discrepancies between results, and this issue has been discussed (47). It is therefore possible that the equilibrium W/S ratio, which, according to our model, should be the same in either the absence or the presence of calcium, depends with high sensitivity on the actual experimental conditions. Further diversity is evident at higher pH (8.3), where the IP₃R1 appears with a flowerlike structure (22) in the absence of calcium. This is consistent with the square-shaped reconstituted image obtained by Hamada and collaborators (23), but the structural details in the side view of the three-dimensional map are different (23).

Channel activity at steady state
The high dimension of the present IP₃R1 model system (8³ total states, with 4³ open states) can be easily reconciled with the small number, namely 2, of distinct open time components detected experimentally (5,8,10). Using rate constant values given in Table 1, column CA-nm, for the transitions within the AMo and IMo, one obtains a two-component open-time histogram with 0.5 mM ATP if IP₃ and Ca²⁺ binding/dissociation are much slower than the rates of spontaneous conformation change, which are high in this case. As one can see later on, with one other data set (see Channel Inactivation) the conformational modifications appear to be very slow. However, the transition rates may be modified during reconstitution (45) or may vary from one system to another (17), so we obtain two distinguishable open time constants similar to those reported in each case (5,8,10), with appropriate kinetic parameters given in Table 1.

In this way, with the three-module (3M-) IP₃R1 model the dependence of the channel open probability and dwell-times on all three cytosolic factors, IP₃, Ca²⁺, and ATP, can be accurately reproduced with parameter values given in Table 1. Fit of the model to the various data on steady-state channel activity is presented in Figs. 3–8.

Moreover, the ATP stimulation of P_o in the activation domain is obtained (not shown) closely similar to the fit in Fig. 5 of our previous article (18), where data from Xenopus oocytes were used (8). The dominant ATP binding reaction leading to this effect is effected within the AMo with an estimated affinity (given by K_d = 160–190 µM, h = 1.2–1.4) similar to the one (K_d = 270 µM, h = 1) reported before (7) in Xenopus, whereas in bilayers the affinity for ATP of cerebellar IP₃R1 (10) appears 2.5 times higher (K_d = 50 µM, h = 1) than obtained from functional characterization of the rat IP₃R1 expressed in Sf9 cells and reconstituted into planar lipid bilayers (K_d = 130 µM, h = 1) (11,12). In the activation module we obtain that ATP increases the Ca²⁺ affinity: from K_d = 0.55 µM at 0 ATP one goes to K_d = 10 nM at saturating ATP in both types of membranes. Given the lack of data, the AMo sensitivity to IP₃ in oocyte membranes is not well defined (it is not clear whether IP₃-K_d is constant or is increased by ATP), but the data obtained with bilayers indicate that ATP increases IP₃ affinity from K_d = 210 nM at 0 ATP to K_d = 50 nM at saturating ATP.

Within the inhibition module, surprisingly, the 3M-model predicts a very high cooperativity (h = 6, higher than h = 4 ± 0.5 obtained by Mak et al., see Ref. 6, with a biphasic Hill equation) of IP₃ in binding its IMo site in oocyte nuclear membranes, as compared to the low value (h = 1.5 ± 0.3) obtained with the receptor reconstituted into bilayers. Similarly, in the same native environment, Ca²⁺ shows high cooperativity (h = 4, as obtained by Mak et al., see Refs. 7 and 8) in binding to its IMo site at saturating IP₃ levels, but exhibits reduced cooperativity (h = 1.35 ± 0.15) in bilayers, though its affinity is the same. Interestingly, at saturating levels of ATP, Ca²⁺ inhibits IP₃ binding, leading, in bilayers, to a variation from K_d = 52.5 nM in the absence of calcium, to K_d = 121 µM at high levels of calcium, whereas the corresponding variation in nuclear membranes is from K_d = 17 nM to K_d = 165 nM. Reciprocally, Ca²⁺ binding is strongly affected by IP₃, and its K_d at saturating ATP varies from 0.09 µM in the absence of IP₃ to 52 µM at high IP₃ in both membranes, but the Hill coefficient changes in different ways. Finally, the effects of ATP are less dramatic on both IP₃ and Ca²⁺ within the inhibition module.

Since the cytosolic conditions are closely similar in those studies, the differences obtained in the receptor sensitivity to each ligand might be induced by a luminal factor, loss of an accessory protein and/or by alteration of the protein-protein/protein-lipid interactions associated to the membrane.

At the end of this section, it should be mentioned that the model fits into the P_o, _o, and _c data if there are only one AMo and one IMo per channel molecule, whereas on the regulation of the adaptation module the equilibrium data analyzed so far do not impose any restriction except that, at steady state, the open gate probability is constant.

IP₃ binding to the ER membrane
Calcium has been reported to induce almost complete reduction of IP₃ binding to cerebellum membranes at pH 8.3 (29,48), to cause partial—up to 70% at pH 7.35 (10), and up to 50% at pH 7.0 (29)—inhibition under more physiological conditions, or to have no effect on IP₃ binding to the purified receptor (25). The inhibition was initially found to be apparent only, and was associated to the activation of an endogenous phospholipase C that produces competitive IP₃ (49) but this scenario was contradicted by subsequent determinations under different conditions (10). In some studies an effective inhibition resulted exclusively from a Ca²⁺-mediated decrease of the apparent affinity of the receptor for IP₃ (10,26,50), whereas Cardy et al. (29) found the mechanism to be a reduction in the maximal number of IP₃ binding sites with no change in the affinity for IP₃ or the Hill coefficient.

For comparison, in hepatocytes, cytosolic Ca²⁺ increases the affinity of the receptors (mostly IP₃R2) for IP₃ (51), whereas in RINm5F cells, which express predominantly the type-3 IP₃R (42), there is no effect at 0.1 mM (42) or 1 mM (29) Ca²⁺. However, there is a maximum increase of 100% in IP₃ binding at 500 nM Ca²⁺ (29) and a complex regulation by calcium of the number of exposed IP₃ binding sites and the affinity for IP₃.

We found that our gating model is able to integrate even such contradictory data of IP₃ binding. Here we discuss only IP₃ binding properties of the type-1 IP₃R. Best model fit to the data are shown in Figs. 9 and 10. To obtain consistency with the results of Kaftan et al. (4) and Moraru et al. (10), the high (K_d 1 nM) and low (K_d 10 µM) affinity IP₃ sites (4) are included in determinations related to their data. However, since the type-1 is the most frequent (95–99%) isoform of cerebellar IP₃Rs (52), it is likely that the 1 nM affinity site actually belongs to the other isoforms of the receptor, so that its low (1%) abundance (see Refs. 4 and 10; see also this article, Table 1, here) might simply reflect their low expression level found in microsome preparations. Nevertheless, the consistent contribution of the low affinity site in microsomes (4) indicates clearly that the 10 µM site is located on the IP₃R1, and we will include it in proportion 1:1:1:1 with respect to the three regulatory IP₃ sites of the model. Its affinity does not vary with temperature (4), so the corresponding K_d is set to 10 µM in both calculations based on the two sets of data obtained at 0°C and 22°C, respectively.

Interestingly, the IP₃ affinity for the its IMo-site in lipid bilayers at 22°C appears close to that detected in microsomes at 0°C, not 22°C as expected, suggesting an increased molecular rigidity of the receptor in planar bilayers, or the interaction between the channel and an accessory protein in fractionated membranes, interaction that might become effective at higher temperatures. We also notice that the channel with IP₃ and ATP bound to their sites in the inhibition module has an extremely low affinity (52 µM) of the inhibitory Ca²⁺ site in all preparations at 22°C, as compared to the medium affinity (0.8 ± 0.1 µM) found at 0°C.

At saturating levels of ATP the activation module appears desensitized to IP₃ in cerebellum microsomes at room temperature, with a 50-fold lower affinity for IP₃ than in bilayers. The most dramatic effect of increasing the temperature in microsomes is the 10-fold decrease in IP₃ affinity for its AdMo site with ATP bound to the module, as well as for its IMo site in the absence of Ca²⁺; at saturating levels of Ca²⁺ and ATP the IMo IP₃ site is largely desensitized at 22°C (K_d = 11 mM), as also happens with the receptor in bilayers.

Cardy et al. (29) found that Ca²⁺ regulates, presumably through the intermediate of an accessory protein, the interconversion between two conformations of the receptor, one with high affinity for IP₃ (K_d 10 nM) and the other one having the IP₃ site either occluded or of extremely low affinity. Consistent with this mechanism, our fit to the data (shown in Fig. 10) results in a virtually inaccessible IP₃ site (K_d = 31 mM) within the inhibition module when the Ca²⁺ site is occupied. For comparison, at saturating [Ca²⁺], IP₃ binds with medium affinity to the channel molecule in Xenopus nuclear membranes, whereas the IP₃ affinity in the absence of calcium is similar to that obtained from channel recordings in Xenopus nuclei, but with Hill coefficient consistently different (1 as compared to 6). However, Ca²⁺ affinity for the IMo site appears to be identical in both experiments. As for the activation module, IP₃ appears to increase channel's affinity for Ca²⁺, which is of the same order as obtained with the other data sets, and reciprocally, Ca²⁺ increases the affinity for IP₃, which however appears one-order-higher than in the other experiments, possibly reflecting the effect of the high pH.

At high ATP and in the absence of calcium, IP₃ binds with similar affinity to AMo and IMo; it appears then that IP₃ binds to a unique class of sites. At increasing [Ca²⁺], however, the dominant feature is determined by Ca²⁺ depressing IP₃ binding to its IMo site, whereas the AMo IP₃ site contributes with an increase in the apparent affinity for IP₃ of the channel molecule. For instance, at 22°C in the presence of ATP (see Table 1, column B-II) there is no IP₃ bound in the inactivation module faced to saturating calcium, but the receptor appears to bind IP₃ with low affinity (K_d = 2 µM in the activation module). Extrapolation of the curves in the lower panel of Fig. 9 evidences the corresponding reduction in the maximal binding sites (not shown) which is similar to the phenomenon reported under different conditions (2°C in absence of ATP). In fact, this situation is evident also under reconstitution of the receptor in lipid bilayers (see Table 1, column CA-lb), where, at high levels of Ca²⁺ and ATP, the inhibition module has an extremely low affinity for IP₃. These results provide indirect evidence that the mechanism proposed by Cardy et al. (29) can manifest even with different microsomal preparations, and show that when one single parameter (temperature; see Table 1, columns B-II and B-III) is modified between experiments otherwise similar, the resulting variations in ligand binding may lead to the interpretation with apparently different mechanisms.

In all of the cases discussed in this section, the summated contribution of the three IP₃ binding sites predicted by the model to belong each to a single gating module looks similar to the contribution of an apparently unique class of sites. As seen also from the values determined by model fit, all the three sites are of similar, i.e., medium (100 nM) apparent affinities. We propose that each IP₃R1 monomer has four IP₃ binding sites (one of low affinity, three of medium affinity), presumably located in the four determinant segments of the IP₃ binding domain, which are known to contain conserved basic residues that interact with the phosphate groups of IP₃ (24). Except the case of the Xenopus IP₃ receptor, the obtained n_H 1 for all the three modules indicate that binding of one molecule of IP₃ to a certain site on a monomer prevents binding to a related site on any other subunit. In Xenopus, n_H = 6 indicates that six molecules bind cooperatively to the inhibition module of the receptor. Presumably, two IP₃ molecules bind three of the four monomers at the IMo site location each, and binding is highly cooperative. The prediction can be tested by binding assessment on Xenopus nuclear membranes.

It is likely that the low affinity (K_d = 10 µM) site resides on one of the two IP₃ binding determinant segments of the IP₃R1 which are closer to the C-terminal (DS3, DS4), since the GST protein fused to the 341–604 fragment of the receptor obtained from cerebellar microsomes binds IP₃ with similar affinity (K_d = 4.7 µM) (27). Additionally, breakup of the IP₃ binding core into two fragments (F1, 226–317 and F2, 346–604) by mild trypsin digestion does not alter the capacity for IP₃, the specificity or affinity of the receptor evaluated for the medium-affinity binding component (27