Ca2+ permeation in cyclic nucleotide-gated channels

Cyclic nucleotide-gated (CNG) channels conduct Na+, K+ and Ca2+ currents under the control of cGMP and cAMP. Activation of CNG channels leads to depolarization of the membrane voltage and to a concomitant increase of the cytosolic Ca2+ concentration. Several polypeptides were identified that constitute principal and modulatory subunits of CNG channels in both neurons and non-excitable cells, co-assembling to form a variety of heteromeric proteins with distinct biophysical properties. Since the contribution of each channel type to Ca2+ signaling depends on its specific Ca2+ conductance, it is necessary to analyze Ca2+ permeation for each individual channel type. We have analyzed Ca2+ permeation in all principal subunits of vertebrates and for a principal subunit from Drosophila melanogaster. We measured the fractional Ca2+ current over the physiological range of Ca2+ concentrations and found that Ca2+ permeation is determined by subunit composition and modulated by membrane voltage and extracellular pH. Ca2+ permeation is controlled by the Ca2+-binding affinity of the intrapore cation-binding site, which varies profoundly between members of the CNG channel family, and gives rise to a surprising diversity in the ability to generate Ca2+ signals.     

Stoichiometry and arrangement of heteromeric olfactory cyclic nucleotide-gated ion channels

Native cylic nucleotide-gated (CNG) channels are composed of alpha and beta subunits. Olfactory CNG channels were expressed from rat cDNA clones in Xenopus oocytes and studied in inside-out patches. Using tandem dimers composed of linked subunits, we investigated the stoichiometry and arrangement of the alpha and beta subunits. Dimers contained three subunit types: alphawt, betawt, and alpham. The alpham subunit lacks an amino-terminal domain that greatly influences gating, decreasing the apparent affinity of the channel for ligand by 9-fold, making it a reporter for inclusion in the tetramer. Homomeric channels from injection of alphawtalphawt dimers and from alphawt monomers were indistinguishable. Channels from injection of alphawtalpham dimers had apparent affinities 3-fold lower than alphawt homomultimers, suggesting a channel with two alphawt and two alpham subunits. Channels from coinjection of alphawtalphawt and betabeta dimers were indistinguishable from those composed of alpha and beta monomers and shared all of the characteristics of the alpha+beta phenotype of heteromeric channels. Coinjection of alphawtalpham and beta beta dimers yielded channels also of the alpha+beta phenotype but with an apparent affinity 3-fold lower, indicating the presence of alpham in the tetramer and that alpha+beta channels have adjacent alpha-subunits. To distinguish between an alpha-alpha-alpha-beta and an alpha-alpha-beta-beta arrangement, we compared apparent affinities for channels from coinjection of alphawtalphawt and betaalphawt or alphawtalphawt and betaalpham dimers. These channels were indistinguishable. To further argue against an alpha-alpha-alpha-beta arrangement, we quantitatively compared dose-response data for channels from coinjection of alphawtalpham and beta beta dimers to those from alpha and beta monomers. Taken together, our results are most consistent with an alpha-alpha-beta-beta arrangement for the heteromeric olfactory CNG channel.     

Modulation of rod photoreceptor cyclic nucleotide-gated channels by tyrosine phosphorylation

Cyclic nucleotide-gated (CNG) channels in vertebrate photoreceptors are crucial for transducing light-induced changes in cGMP concentration into electrical signals. In this study, we show that both native and exogenously expressed CNG channels from rods are modulated by tyrosine phosphorylation. The cGMP sensitivity of CNG channels, composed of rod alpha-subunits expressed in Xenopus oocytes, gradually increases after excision of inside-out patches from the oocyte membrane. This increase in sensitivity is inhibited by a protein tyrosine phosphatase (PTP) inhibitor and is unaffected by three different Ser/Thr phosphatase inhibitors. Moreover, it is suppressed or reversed by application of ATP but not by a nonhydrolyzable ATP analog. Application of protein tyrosine kinase (PTK) inhibitors causes an increase in cGMP sensitivity, but only in the presence of ATP. Taken together, these results suggest that CNG channels expressed in oocytes are associated with active PTK(s) and PTP(s) that regulate their cGMP sensitivity by changing phosphorylation state. The cGMP sensitivity of native CNG channels from salamander rod outer segments also increases and decreases after incubation with inhibitors of PTP(s) and PTK(s), respectively. These results suggest that rod CNG channels are modulated by tyrosine phosphorylation, which may function as a novel mechanism for regulating the sensitivity of rods to light.     

Subunit interactions in the activation of cyclic nucleotide-gated ion channels

Cyclic nucleotide-gated (CNG) ion channels of retinal photoreceptors and olfactory neurons are multimeric proteins of unknown stoichiometry. To investigate the subunit interactions that occur during CNG channel activation, we have used tandem cDNA constructs of the rod CNG channel to generate heteromultimeric channels composed of wild-type and mutant subunits. We introduced point mutations that affect channel activation: 1) D604M, which alters the relative ability of agonists to promote the allosteric conformational change(s) associated with channel opening, and 2) T560A, which primarily affects the initial binding affinity for cGMP, and to a lesser extent, the allosteric transition. At saturating concentrations of agonist, heteromultimeric channels were intermediate between wild-type and mutant homomultimers in agonist efficacy and apparent affinity for cGMP, cIMP, and cAMP, consistent with a model for the allosteric transition involving a concerted conformational change in all of the channel subunits. Results were also consistent with a model involving independent transitions in two or three, but not one or four, of the channel subunits. The behavior of the heterodimers implies that the channel stoichiometry is some multiple of 2 and is consistent with a tetrameric quaternary structure for the functional channel complex. Steady-state dose-response relations for homomultimeric and heteromultimeric channels were well fit by a Monod, Wyman, and Changeux model with a concerted allosteric opening transition stabilized by binding of agonist.     

Direct interaction between amino- and carboxyl-terminal domains of cyclic nucleotide-gated channels

We have examined domain interactions in the rod cyclic nucleotide-gated ion channel using both physiological and biochemical interaction assays. We have found an interaction between two regions of the channel distant in primary structure, the amino-terminal region and the carboxyl-terminal region containing the cyclic nucleotide-binding (CNB) domain. The interaction in functional channels was detected by the formation of a disulfide bond between cysteine residues at position 35 in the amino-terminal region and 481 in the carboxyl-terminal region. The disulfide bond resulted in channel potentiation, which was due, in part, to an increase in availability of C481 to modification when the channels were open. This state dependence is likely to underlie previously reported potentiation of cyclic nucleotide-gated channels by sulfhydryl-reactive compounds. Polypeptides derived from the amino-terminal and carboxyl-terminal regions were shown to interact, even under conditions which precluded disulfide bond formation. These data argue for a previously unknown, direct interaction between disparate regions of channel sequence.     

Movement of gating machinery during the activation of rod cyclic nucleotide-gated channels

In the visual and olfactory systems, cyclic nucleotide-gated (CNG) ion channels convert stimulus-induced changes in the internal concentrations of cGMP and cAMP into changes in membrane potential. Although it is known that significant activation of these channels requires the binding of three or more molecules of ligand, the detailed molecular mechanism remains obscure. We have probed the structural changes that occur during channel activation by using sulfhydryl-reactive methanethiosulfonate (MTS) reagents and N-ethylmaleimide (NEM). When expressed in Xenopus oocytes, the alpha-subunit of the bovine retinal channel forms homomultimeric channels that are activated by cGMP with a K1/2 of approximately 100 microM. Cyclic AMP, on the other hand, is a very poor activator; a saturating concentration elicits only 1% of the maximum current produced by cGMP. Treatment of excised patches with MTS-ethyltrimethylamine (MTSET) or NEM dramatically potentiated the channel's response to both cyclic nucleotides. After MTSET treatment, the dose-response relation for cGMP was shifted by over two orders of magnitude to lower concentrations. The effect on channel activation by cAMP was even more striking. After modification, the channels were fully activated by cAMP with a K1/2 of approximately 60 microM. This potentiation was abolished by conversion of Cys481 to a nonreactive alanine residue. Potentiation occurred more rapidly in the presence of saturating cGMP, indicating that this region of the channel is more accessible when the channel is open. Cys481 is located in a linker region between the transmembrane and cGMP-binding domains of the channel. These results suggest that this region of the channel undergoes significant movement during the activation process and is critical for coupling ligand binding to pore opening. Potentiation, however, is not mediated by the recently reported interaction between the amino- and carboxy-terminal regions of the alpha-subunit. Deletion of the entire amino-terminal domain had little effect on potentiation by MTSET.     

Tetracaine reports a conformational change in the pore of cyclic nucleotide-gated channels

Local anesthetics are a diverse group of clinically useful compounds that act as pore blockers of both voltage- and cyclic nucleotide-gated (CNG) ion channels. We used the local anesthetic tetracaine to probe the nature of the conformational change that occurs in the pore of CNG channels during the opening allosteric transition. When applied to the intracellular side of wild-type rod CNG channels expressed in Xenopus oocytes from the alpha subunit, the local anesthetic tetracaine exhibits state-dependent block, binding with much higher affinity to closed states than to open states. Here we show that neutralization of a glutamic acid in the conserved P region (E363G) eliminated this state dependence of tetracaine block. Tetracaine blocked E363G channels with the same effectiveness at high concentrations of cGMP, when the channel spent more time open, and at low concentrations of cGMP, when the channel spent more time closed. In addition, Ni2+, which promotes the opening allosteric transition, decreased the effectiveness of tetracaine block of wild-type but not E363G channels. Similar results were obtained in a chimeric CNG channel that exhibits a more favorable opening allosteric transition. These results suggest that E363 is accessible to internal tetracaine in the closed but not the open configuration of the pore and that the conformational change that accompanies channel opening includes a change in the conformation or accessibility of E363.     

Molecular cloning of a putative cyclic nucleotide-gated ion channel cDNA from Limulus polyphemus

Cyclic nucleotide-gated channels have been proposed to mediate the electrical response to light in the ventral photoreceptor cells of the horseshoe crab, Limulus polyphemus. However, a cyclic nucleotide-gated channel has not been identified from Limulus. We have cloned a putative full-length cyclic nucleotide-gated channel cDNA by screening cDNA libraries constructed from Limulus brain using a probe developed from Limulus ventral eye nerves. The putative full-length cDNA was derived from two overlapping partial cDNA clones. The open reading frame encodes 905 amino acids; the sequence shows 44% identity to that of the alpha subunit of the bovine rod cyclic GMP-gated channel over the region containing the transmembrane domains and the cyclic nucleotide binding domain. This Limulus channel has a novel C-terminal region of approximately 200 amino acids, containing three putative Src homology domain 3 binding motifs and a putative coiled-coil domain. The possibility that this cloned channel is the same as that detected previously in excised patches from the photoreceptive membrane of Limulus ventral photoreceptors is discussed in terms of its sequence and its expression in the ventral eye nerves.     

Perfusion system components release agents that distort functional properties of rod cyclic nucleotide-gated ion channels

In switching from studying native cyclic nucleotide-gated (CNG) ion channels in rod cells to studying the corresponding cloned channels expressed in Xenopus oocytes, we changed our perfusion system to a more efficient one. This change involved replacing culture flasks and a small plexiglass/glass chamber with plastic syringes, metal needles, and plastic petri dishes. We now report that these new perfusion system components release agents that distort or obscure measured functional properties of rod CNG channels. The magnitude and time course of appearance of the artifacts vary widely among individual components (e.g. from syringe to syringe). The effects most resemble voltage-dependent block of the channels, giving a decrease in current at positive potentials, and producing distortions of the kinetics and voltage dependence of channel activation.     

Three amino acids in the C-linker are major determinants of gating in cyclic nucleotide-gated channels

The activation of cyclic nucleotide-gated (CNG) channels is a complex process comprising the initial ligand binding and a consecutive allosteric transition from a closed to an open configuration. The cone and olfactory CNG channels differ considerably in cyclic nucleotide affinity and efficacy. In each channel, the cyclic nucleotide-binding site is connected to the last transmembrane segment of the channel by a linker peptide (C-linker) of approximately 90 amino acids. Here we report that replacement of three amino acids in the cone C-linker by the corresponding amino acids of the olfactory channel (I439V, D481A and D494S) profoundly enhanced the cAMP efficacy and increased the affinities for cAMP and cGMP. Unlike the wild-type cone channel, the mutated channel exhibited similar single-channel kinetics for both cGMP and cAMP, explaining the increase in cAMP efficacy. We thus conclude that the identified amino acids are major determinants of channel gating.     

Molecular and pharmacological analysis of cyclic nucleotide-gated channel function in the central nervous system

Most functional studies of cyclic nucleotide-gated (CNG) channels have been confined to photoreceptors and olfactory epithelium, in which CNG channels are abundant and easy to study. The widespread distribution of CNG channels in tissues throughout the body has only recently been recognized and the functions of this channel family in many of these tissues remain largely unknown. The molecular biological and pharmacological properties of the CNG channel family are summarized in order to put in context studies aimed at probing CNG channel functions in these tissues using pharmacological and genetic methods. Compounds have now been identified that are useful in distinguishing CNG channel activated pathways from cAMP/cGMP dependent-protein kinases or other pathways. The ways in which these interact with CNG channels are understood and this knowledge is leading to the identification of more potent and more specific CNG channel subtype-specific agonists or antagonists. Recent molecular and genetic analyses have identified novel roles of CNG channels in neuronal development and plasticity in both invertebrates and vertebrates. Targeting CNG channels via specific drugs and genetic manipulation (such as knockout mice) will permit better understanding of the role of CNG channels in both basic and higher orders of brain function.     

A state-independent interaction between ligand and a conserved arginine residue in cyclic nucleotide-gated channels reveals a functional polarity of the cyclic nucleotide binding site

Activation of cyclic nucleotide-gated channels is thought to involve two distinct steps: a recognition event in which a ligand binds to the channel and a conformational change that both opens the channel and increases the affinity of the channel for an agonist. Sequence similarity with the cyclic nucleotide-binding sites of cAMP- and cGMP-dependent protein kinases and the bacterial catabolite activating protein (CAP) suggests that the channel ligand binding site consists of a beta-roll and three alpha-helices. Recent evidence has demonstrated that the third (or C) alpha-helix moves relative to the agonist upon channel activation, forming additional favorable contacts with the purine ring. Here we ask if channel activation also involves structural changes in the beta-roll by investigating the contribution of a conserved arginine residue that, in CAP and the kinases, forms an important ionic interaction with the cyclized phosphate of the bound ligand. Mutations that conserve, neutralize, or reverse the charge on this arginine decreased the apparent affinity for ligand over four orders of magnitude but had little effect on the ability of bound ligand to open the channel. These data indicate that the cyclized phosphate of the nucleotide approaches to within 2-4 A of the arginine, forming a favorable ionic bond that is largely unaltered upon activation. Thus, the binding site appears to be polarized into two distinct structural and functional domains: the beta-roll stabilizes the ligand in a state-independent manner, whereas the C-helix selectively stabilizes the ligand in the open state of the channel. It is likely that these distinct contributions of the nucleotide/C-helix and nucleotide/beta-roll interactions may also be a general feature of the mechanism of activation of other cyclic nucleotide-binding proteins.     

Molecular determinants of a Ca2+-binding site in the pore of cyclic nucleotide-gated channels: S5/S6 segments control affinity of intrapore glutamates

Cyclic nucleotide-gated (CNG) channels play an important role in Ca2+ signaling in many cells. CNG channels from various tissues differ profoundly in their Ca2+ permeation properties. Using the voltage-dependent Ca2+ blockage of monovalent current in wild-type channels, chimeric constructs and point mutants, we have identified structural elements that determine the distinctively different interaction of Ca2+ with CNG channels from rod and cone photoreceptors and olfactory neurons. Segments S5 and S6 and the extracellular linkers flanking the pore region are the only structural elements that account for the differences between channels. Ca2+ blockage is strongly modulated by external pH. The different pH dependence of blockage suggests that the pKa of intrapore glutamates and their protonation pattern differ among channels. The results support the hypothesis that the S5-pore-S6 module, by providing a characteristic electrostatic environment, determines the protonation state of pore glutamates and thereby controls Ca2+ affinity and permeation in each channel type.     

Three residues predicted by molecular modeling to interact with the purine moiety alter ligand binding and channel gating in cyclic nucleotide-gated channels

Cytoplasmic cAMP and cGMP are soluble cellular messengers that directly activate cyclic nucleotide-gated (CNG) channels. These channels mediate sensory transduction in photoreceptors and olfactory neurons. The closely related CNG channels in these cell types have different nucleotide activation profiles, and we have investigated the molecular basis of their nucleotide selectivity properties. Previously, we predicted that the purine moiety of the nucleotide interacts with residues F533, K596, and D604 (bovine rod alpha CNG channel subunit sequences) of the nucleotide binding domain. In this study, we replaced these three residues with the corresponding residues of the bovine olfactory CNG channel. Mutations at each position altered the nucleotide activation of the rod CNG channels. In a mutant where K596 was replaced with arginine, cAMP-activated currents were enhanced 8-12-fold, suggesting that residue 596 influences channel gating. Thermodynamic cycle analysis of the data showed that (1) the residues are energetically coupled and (2) energetic coupling exists between the potentiating effects of Ni2+ and the replacement of F533 with tyrosine. These data suggest that changes in one of the residues alter the purine contacts with the other residues and that F533 communicates with the C-linker region of the channel involved in Ni2+ potentiation.     

Cloning and characterization of an olfactory cyclic nucleotide-gated channel expressed in mouse heart

Regulation of ionic currents in the heart is partly achieved by signaling cascades which alter intracellular levels of cyclic nucleotides. Changes in cyclic nucleotide levels can regulate channels either directly, like the direct binding of cAMP to the i(f) channel in pacemaker tissues, or indirectly through phosphorylation of channels by cAMP-dependent, or cGMP-dependent protein kinases. These types of regulation generally alter the voltage sensitivities of channels. A class of voltage-insensitive channels, first discovered in retinal rods and olfactory neurons, were recently identified in the heart. These channels are opened by the direct binding of cyclic nucleotides, providing a means of regulating ionic currents outside the influence of membrane voltage. Since different isoforms have different affinities for cAMP and cGMP, it is important to determine which isoforms are expressed in heart in order to predict their roles in heart function. We have cloned the olfactory channel from mouse heart, and find that although the message is very rare, Western blot analysis indicates the olfactory channel protein is stable in heart sarcolemma. Our data also suggest the olfactory channel protein forms homomeric channels in the heart since other isoforms or splice variants were not detected either by PCR amplification or by RNase protection. In addition, we have isolated and sequenced the mouse olfactory cyclic nucleotide-gated channel gene, and show the genomic organization is remarkably similar to that found in the human retinal channel gene. Part of this work was presented in abstract form.     

Extracellular proton alters the divalent cation binding affinity in a cyclic nucleotide-gated channel pore

The effects of zolpidem on the two forms of recombinant human GABAA receptors (alpha1beta2gamma2s and alpha3beta2gamma2s) at different temperatures were functionally investigated, using the whole-cell patch recording configuration. In both forms, zolpidem potentiated the response to GABA in a concentration-dependent manner. At 16 degrees C, the apparent dissociation constant (KD) values for the alpha1beta2gamma2s and alpha3beta2gamma2s forms were 3.7 x 10(-8) and 5.6 x 10(-7) M, respectively. When the temperature was increased to 36 degrees C, the KD values for the alpha1beta2gamma2s and alpha3beta2gamma2s forms were 2.1 x 10(-7) and 1.5 x 10(-6) M, respectively. Although the affinity ratio was reduced from 15.1 to 7.1-fold the selectivity of zolpidem for the alpha1beta2gamma2s still remained at 36 degrees C.     

An isoform of the rod photoreceptor cyclic nucleotide-gated channel beta subunit expressed in olfactory neurons

Sensory transduction in olfactory neurons involves the activation of a cyclic nucleotide-gated (CNG) channel by cAMP. Previous studies identified a CNG channel alpha subunit (CNG2) and a beta subunit (CNG5), which when heterologously expressed form a channel with properties similar but not identical to those of native olfactory neurons. We have cloned a new type of CNG channel beta subunit (CNG4. 3) from rat olfactory epithelium. CNG4.3 derives from the same gene as the rod photoreceptor beta subunit (CNG4.1) but lacks the long, glutamic acid-rich domain found in the N terminus of CNG4.1. Northern blot and in situ hybridization revealed that CNG4.3 is expressed specifically in olfactory neurons. Expression of CNG4.3 in human embryonic kidney 293 cells did not lead to detectable currents. Coexpression of CNG4.3 with CNG2 induced a current with significantly increased sensitivity for cAMP whereas cGMP affinity was not altered. Additionally, CNG4.3 weakened the outward rectification of the current in the presence of extracellular Ca2+, decreased the relative permeability for Ca2+, and enhanced the sensitivity for L-cis diltiazem. Upon coexpression of CNG2, CNG4.3, and CNG5, a conductance with a cAMP sensitivity greater than that of either the CNG2/CNG4.3 or the CNG2/CNG5 channel and near that of native olfactory channel was observed. Our data suggest that CNG4.3 forms a subunit of the native olfactory CNG channel. The expression of various CNG4 isoforms in retina and olfactory epithelium indicates that the CNG4 subunit may be necessary for normal function of both photoreceptor and olfactory CNG channels.     

Drugs affecting phospholipase C-mediated signal transduction block the olfactory cyclic nucleotide-gated current of adult zebrafish

Amino acid and bile salt odorants are detected by zebrafish with relatively independent odorant receptors, but the transduction cascade(s) subsequently activated by these odorants remains unknown. Electro-olfactogram recording methods were used to determine the effects of two drugs, reported to affect phospholipase C (PLC)/inositol tripohsphate (IP3)-mediated olfactory transduction in other vertebrate species, on amino acid and bile salt-evoked responses. At the appropriate concentrations, either an IP3-gated channel blocker, ruthenium red (0.01-0.1 microM), or a PLC inhibitor, neomycin (50 microM), reduced amino-acid-evoked responses to a significantly greater extent than bile salt-evoked responses. Excised patch recording techniques were used to measure the affects of these drugs on second-messenger-activated currents. Ruthenium red and neomycin are both effective blockers of the olfactory cyclic nucleotide-gated (CNG) current. Both drugs blocked the CNG channel in a voltage-dependent and reversible manner. No IP3-activated currents could be recorded. The differential effects of ruthenium red and neomycin on odor-evoked responses suggest the activation of multiple transduction cascades. The nonspecific actions of these drugs on odor-activated transduction pathways and our inability to record an IP3-activated current do not permit the conclusion that zebrafish, like other fish species, use a PLC/IP3-mediated transduction cascade in the detection of odorants.     

Synaptic transmission and hippocampal long-term potentiation in olfactory cyclic nucleotide-gated channel type 1 null mouse

Field potential recording was used to investigate properties of synaptic transmission and long-term potentiation (LTP) at Schaffer collateral-CA1 synapses in both hippocampal slices of mutant mice in which the alpha-subunit of the olfactory cyclic nucleotide-gated channel (alpha3/OCNC)1 was rendered null and also in slices prepared from their wild-type (Wt) littermates. Several measures of basal synaptic transmission were unaltered in the OCNC1 knockout (KO), including maximum field excitatory postsynaptic potential (fEPSP) slope, maximum fEPSP and fiber volley amplitude, and the function relating fiber volley amplitude to fEPSP slope and paired-pulse facilitation. When a high-frequency stimulation protocol was used to induce LTP, similar responses were seen in both groups [KO: 1 min, 299 +/- 50% (mean +/- SE), 60 min, 123 +/- 10%; Wt: 1 min, 287 +/- 63%; 60 min, 132 +/- 19%). However, on theta-burst stimulation, the initial amplitude of LTP was smaller (1 min after induction, 147 +/- 16% of baseline) and the response decayed faster in the OCNC1 KO (60 min, 127 +/- 18%) than in Wt (1 min, 200 +/- 14%; 60 min, 169 +/- 19%). Analysis of waveforms evoked by LTP-inducing tetanic stimuli revealed a similar difference between groups. The development of potentiation throughout the tetanic stimulus was similar in OCNC1 KO and Wt mice when high-frequency stimulation was used, but OCNC1 KO mice showed a significant decrease when compared with Wt mice receiving theta-burst stimulation. These results suggest that activation of cyclic nucleotide-gated channels may contribute to the induction of LTP by weaker, more physiological stimuli, possibly via Ca2+ influx.     

Constraining ligand-binding site stoichiometry suggests that a cyclic nucleotide-gated channel is composed of two functional dimers

Cyclic nucleotide-gated ion channels are composed of four pore-forming subunits. Binding of cyclic nucleotide to a site in the intracellular carboxyl terminus of each subunit leads to channel activation. Since there are four subunits, four binding events are possible. In this study, we investigate the effects of individual binding events on activation by studying channels containing one, two, three, or four functional binding sites. The binding of a single ligand significantly increases opening, although four ligands are required for full activation. The data are inconsistent with models in which the four subunits activate in a single concerted step (Monod-Wyman-Changeux model) or in four independent steps (Hodgkin-Huxley model). Instead, the four subunits may associate and activate as two independent dimers.