cAMP binding to closed pacemaker ion channels is cooperative

Significance

Cooperativity of ligand binding has fascinated researchers for almost a century. For the HCN pacemaker channels, intricate binding cooperativity was already documented in the context of voltage-dependent activation. In contrast, for non-activated channels, there are conflicting reports on whether binding-cooperativity exists or not. While ensemble measurements in native cell membranes reported cooperativity, single-molecule measurements with detergent-solubilized channels reported no cooperativity. Here, we combine the advantages of both approaches, the accuracy of single-molecule measurements with the physiological relevance of a native cell membrane surrounding the channels. With this, we show that binding cooperativity already exists in non-activated HCN channels.

Abstract

The cooperative action of the subunits in oligomeric receptors enables fine-tuning of receptor activation, as demonstrated for the regulation of voltage-activated HCN pacemaker ion channels by relating cAMP binding to channel activation in ensemble signals. HCN channels generate electric rhythmicity in specialized brain neurons and cardiomyocytes. There is conflicting evidence on whether binding cooperativity does exist independent of channel activation or not, as recently reported for detergent-solubilized receptors positioned in zero-mode waveguides. Here, we show positive cooperativity in ligand binding to closed HCN2 channels in native cell membranes by following the binding of individual fluorescence-labeled cAMP molecules. Kinetic modeling reveals that the affinity of the still empty binding sites rises with increased degree of occupation and that the transition of the channel to a flip state is promoted accordingly. We conclude that ligand binding to the subunits in closed HCN2 channels not pre-activated by voltage is already cooperative. Hence, cooperativity is not causally linked to channel activation by voltage. Our analysis also shows that single-molecule binding measurements at equilibrium can quantify cooperativity in ligand binding to receptors in native membranes.

Hyperpolarization-activated cyclic nucleotide-modulated (HCN-)channels (1, 2) are nonspecific cation channels that belong to the superfamily of six-transmembrane domain voltage-gated channels (3–5). The obligatory activation stimulus of these channels is a sufficiently negative membrane voltage (6). In addition, the binding of the second messenger cAMP to the four available intracellular cyclic nucleotide-binding domains (CNBDs), one in each subunit, modulates activation by both shifting activation to less negative voltages and accelerating the activation speed (7).

The concentration–activation relationship of HCN2 channels with cAMP can be approximated by a Hill function with Hill coefficients exceeding unity (8), indicating a cooperative effect of cAMP binding on activation. Combined current and binding measurements in ensembles of channels by confocal patch-clamp fluorometry (cPCF) (9) suggested cooperativity with the sequence positive–negative–positive (10, 11) for activated channels. This cooperativity might emerge from a combination of events from ligand binding to channel activation or from activation only by a reciprocal feedback from activation to ligand binding (8).

Results from cPCF measurements on ligand binding to closed and not voltage pre-activated HCN2 channels in patches with ensembles of channels required Hill coefficients larger than unity (12, 13), ruling out independent and supporting cooperative binding to the subunits. In contrast, a recent single-molecule binding study reported that cAMP binds independently to all four subunits in both non-activated HCN1 and HCN2 channels (14). These authors performed single-molecule binding measurements with a fluorescent cAMP derivative to detergent-solubilized receptors positioned in zero-mode waveguides (ZMWs). Their results indicate that only hyperpolarization-induced channel activation, but not cAMP binding alone, evokes relevant cooperative interaction of the subunits. This contradicts previous ensemble data on non-activated channels for which Hill coefficients exceeded unity, indicating cooperative binding (12, 13). Further, these experiments suggested the existence of a flip state following the binding as previously reported (12).

Single-molecule detection has become a powerful technique to elucidate details of molecular processes (15, 16) at equilibrium. However, most of single-molecule experiments do not directly follow ligand–receptor interaction though it is the initiating step of most signaling cascades (17). In some studies, ligands were used for continuous reversible labeling in single-molecule tracking (18) and super-resolution microscopy (19). However, single-molecule binding studies are rare, because only few suitable fluorescent agonists are known and the signal-to-noise ratio is limited due to signals from unbound ligands. Single-molecule measurements avoiding the contributions of unbound ligands are only possible at concentrations well below the K_D value of a system (20, 21). However, for small ligands, the time-scale for diffusion through the observation volume and the residence times upon binding differ by several orders of magnitude, effectively blurring the diffusion signal to a quasi-constant background (with corresponding Poisson noise). Several strategies were employed to increase the signal-to-noise ratio:

• 1)Selection of high-affinity systems by mutations or using either natural (22, 23) or engineered (13, 24) ligands with higher affinities to reduce the required concentration.
• 2)Reduction of the detection volume either mechanically (25) or optically, e.g., with total internal reflection Microscopy (TIRFM) (26) or confocal techniques such as fluorescence correlation spectroscopy (FCS) (27, 28) to reduce the number of background fluorophores. A particular case are ZMWs (29) that were successfully used to investigate ligand binding on isolated binding sites (30, 31) or solubilized channels (14). So far, there are only proof-of-concept experiments with ligand binding to native membranes in planar waveguides (32).
• 3)Utilization of brighter fluorophores to reduce relative contributions of the noise (33).

Here, we use a combination of these strategies to enable single-molecule binding measurements: We use a ligand with both increased affinity and brightness (13) compared to previous studies (12, 14) and employed TIRFM to reduce signals from ligands in solution. We follow the binding of single ligands to individual mHCN2 channels embedded in a native membrane. We demonstrate positive cooperativity in ligand binding to these channels, contrasting a recent study in solubilized receptors (14). The consecutive binding steps increase both the ligand affinity of the binding sites and the population of a flip state.

Results

f1cAMP Binds to HCN2 Channels in a Cooperative Manner.

We established a stable HEK293 cell line inducibly expressing N-terminally GFP-tagged HCN2 channels (eGFPmHCN2) under an inducible promoter. The eGFP-HCN2 construct showed voltage activation and ligand modulation comparable to wildtype HCN2 (SI Appendix, Fig. S1A).

The cell-line was used to generate supported membrane sheets with the intracellular side exposed to solution (Fig. 1A): The upper cell membrane was stripped onto plasma-cleaned coverslips using a protocol similar to that of Perez et al. (34). Specific binding of fluorescently labeled cAMP to the GFP-tagged HCN2 channels was confirmed (SI Appendix, Fig. S1B). At controlled low expression (0.2 channels/µm²), the fluorescent ligand f1cAMP (13) allowed for the detection of single-molecule binding to eGFPmHCN2 at concentrations up to 0.5 µM in TIRFM (Fig. 1 B and C).

Fig. 1.

Generation of supported membrane sheets. (A) Supported membrane sheets were generated by using cultured HEK293 cells stably transfected with eGFPmHCN2 and sticking the membrane to cover slips. Coverslips were put upside down onto plasma-cleaned cover slides and pushed down by 5.3 kPa. Coverslips were then removed, leaving the top membrane on the cover slide while the intracellular part was accessible for solutions. (B) TIRF measurements of fluorescent cAMP derivatives and eGFP tags attached to HCN2 channels were performed on supported membranes. Only ligands near the membrane are excited due to the decay of the laser power in the evanescent field. (C) eGFP (Left) and f1cAMP (Right) TIRF recordings of a supported membrane. Individual signals were fitted by a 2D-Gaussian function to ensure evaluation of single molecules.

While the environment of a native membrane excludes artifacts from channel isolation and solubilization, binding of labeled cAMP to endogenous binding sites can distort the measurements. We reduced the potential background by competitive suppression (35–37) of spurious nonspecific binding to endogenous cAMP binding proteins (38–40) (SI Appendix, Fig. S1 C and D) and ruled out diffusional dynamics on the time and length scale of our analysis (SI Appendix, Fig. S2 A–C) or persistent ligand binding (SI Appendix, Supporting Methods and Fig. S2D). This ensured that our experiments report only binding to eGFPmHCN2 channels and not binding to endogenous proteins or diffusional fluctuations.

At each identified mHCN2 channel position, an intensity trajectory was extracted, filtered, and idealized (Fig. 2A). As a model-free approach to detect cooperativity, observed occupancies were compared to the binomial expectations for four independent binding sites (Fig. 2B). For concentrations of 0.3 and 0.5 µM f1cAMP, only the double-liganded state matched the expected fractions. The non-liganded and the highly liganded states with 3 and 4 ligands bound were more abundant where the first liganded state was less abundant than the binomial expectations, contradicting independent binding (14). Only the distribution of equilibrium binding is considered in this analysis. As all models with independent binding sites lead to a constant equilibrium binding probability per binding site (P(1); Eq. 1), the observed stoichiometry will follow a binomial distribution as described by Eq. 2. Thus, model complexity will not affect the outcome of this test for cooperativity. We verify that numerical fluctuation of data generated with a more complex non-cooperative model [a non-cooperative version of model 2 (SI Appendix, Table S2 andFig. S3) does not appear as cooperativity (SI Appendix, Fig. S3)].

Fig. 2.

Recording of binding events and data processing. (A) Raw data traces were smoothened by the Chung–Kennedy Filter. Filtered traces were idealized to the number of bound ligands by the DISC algorithm (41). (B) The proportion of observed states was compared to the expected proportion of non-cooperative binding calculated by Eq. 2. Error bars show SEM. *indicate significant differences (one sample t test, P < 0.05).

To further interpret our results, we approximated microscopic rate constants (Fig. 3 B and C) for the simplest model with four consecutive binding steps (Fig. 3A) and derived equilibrium constants (Fig. 3D). The larger association constants K_A confirm the increased affinity of f1cAMP (13) utilized here compared to the previously used fcAMP (12). The association constants show a non-linear increase along the four binding steps (Fig. 3B), contrasting the almost equal association constants reported by White et al. (14). Thon et al. (12) also observed that K_A varied with ligation state, the data are however not directly comparable due to different model structures and assumptions in their analysis.

Fig. 3.

Kinetic and equilibrium constants calculated for a simple binding reaction. (A) Simplest model with four consecutive binding steps. (B–D) Comparison of present to previously published constants. (B) Microscopic binding rate constants k_on and (C) microscopic dissociation rate constants k_off. (D) Association constants K_A of individual binding steps. (E) Dwell times of isolated single-liganded states at 0.1 µM f1cAMP fitted by a mono- or biexponential function.

Ligand Binding Populates a Flip State.

For the extremely simple model (Fig. 3A, SI Appendix, Tables S2 and S3, model 12), the dissociation rates moderately decrease and the association rates increase with consecutive binding (Fig. 3 B and C and SI Appendix, Table S3, model 12). If one assumes a binding site of defined size and diffusion limited binding (42), a constant association rate constant would be expected. One possible explanation of the observed increase could be that a sequence of transitions (e.g., initial binding followed by a rearrangement of binding mode or protein conformation) is erroneously simplified as a one-step transition in the model.

To test for such an aggregation of transitions, we extracted dwell times of single-liganded states that were both preceded and followed by the non-liganded state as well as empty states preceded and followed by single-liganded states. As a result, dwell times for single-bound ligands, both preceded and followed by non-liganded states, as well as dwell times of the empty channel exhibit two time constants (Fig. 3E and SI Appendix, Fig. S4) for all concentrations. This can be explained by a flip state in both the liganded and empty channel. A flip state was proposed previously only for liganded channels (12, 14).

As the initial simple model (Fig. 3A and SI Appendix, Tables S2 and S3, model 12) cannot explain the observed two time constants, more complex models were considered: to understand the dynamics, we analyzed in total 13 kinetic models (SI Appendix, Table S2). Taking into account both the tetrameric structure with four binding sites and the existence of a flip state, we started the modeling with schemes containing 10 states, five ground states, and five flip states, in a parallel arrangement (SI Appendix, Table S2, model 1). We assumed microscopic reversibility, reducing the number of rate constants per cycle by one. The log-likelihood (LL) value was taken as a measure for the goodness of the fit, the parameter uncertainty (relative SEM) was considered as well (SI Appendix, Table S3).

By equating parameters without loss of fit quality and omitting barely used transitions, we derived model 13 (Fig. 4A), featuring, e.g., the plausible assumption of constant k_on for all subunits independent of ligation state (see strategy in SI Appendix, Supporting Methods). This model combined the highest likelihood and lowest uncertainty (SI Appendix, Tables S2 and S3). This model structure assumes a joint flip of all subunits, i.e., it assumes that all subunits transition either into or out of the flip state(s) at the same time. Mechanistically, this might correspond to the proposed rotation of the CNBDs relative to the trans-membrane domain (3). Models enabling individual flips per subunit would require 35 states and either 60 or 80 transitions, with or without binding to the subunits in the flip-states, respectively. Notably, these models either did not enable cooperativity as observed in Fig. 2B (SI Appendix, Table S2, model 10, 11) or did not converge (model-structure as in model 10 or 11 but with each subunit having an independent set of rate constants).

Fig. 4.

Favored model to describe the single binding events. (A) Scheme of model 13. The model consists of four individual binding steps of which each has an own transition to a flip state. In a flip state, additional binding is possible. Due to extremely small rate constants between the non-liganded and the single-liganded flip state, this transition is excluded. Symbols describe subunit properties. (B) Equilibrium association constants (K_A) for binding of ligands in the non-flip (red) and flip state (purple) The affinity constant of a hypothetical binding to the empty flip state was calculated (gray), assuming microscopic reversibility (see text). (C) Equilibrium constants for switching into the flip state depending on the state of receptor occupation. All error bars show SEM.

From the rate constants of the individual steps in model 13, equilibrium association constants, K_A = k_x/k_-x, and equilibrium flip constants, K_F = f_x/f_-x, were calculated. For the ground states, K_A increases in a non-linear fashion from the first to the fourth binding step (Fig. 4B). In the flip state, this K_A increase is even more pronounced; the K_A values are larger for the binding steps 2, 3, and 4 with respect to their counterparts in the ground state by about threefold. Including ligand binding to the empty flipped state worsened the fit, possibly due to a low occurrence of such a transition in the observed time frame. Still, a K_A value can be calculated from microscopic reversibility. Its value is consistent with the trend of the parameters obtained from fitted kinetic parameters (gray point in in Fig. 4B).

Similar to the ground state, K_A stays almost constant for binding step 3 with respect to binding step 2 but almost doubles for binding step 4 with respect to binding step 3. Regarding the flip reaction, the empty and the single-liganded state have about the same K_F value, whereas the binding of the ligands 2, 3, and 4 increases K_F strongly in an approximately exponential fashion (Fig. 4C).

These results show that in channels not pre-activated by voltage, the first binding step is without major effect. In contrast, the second binding step plays a key role for enhancing ligand binding in the third and fourth binding step.

Discussion

We quantified the kinetics of ligand-binding on individual, closed, not voltage pre-activated tetrameric mHCN2 channels, functionally expressed in native cell membranes. We demonstrate that the binding process in these closed channels is cooperative and associated with a molecular flip reaction. While a flip state was proposed previously (12, 14), the occupation of a flip state in the empty channel was not concluded previously. Our results on cooperativity are in contrast to a previous study on single-molecule binding by White et al. (14) but are in line with results on previous macroscopic measurements of ligand binding kinetics in excised patches (12).

To explain the qualitative difference between our data and the reports by White et al., the following aspects should be emphasized: (1) White et al. established the DISC algorithm to analyze data (41), which we adapted to our conditions (SI Appendix, Supporting Methods). (2) In previous studies, the fluorescent cAMP derivative fcAMP (11, 12, 14) (Dy547-AET-cAMP) was used, whereas we used the superior f1cAMP (13) (Cy3B-AHT-cAMP). This compound has an about 2.5 times higher affinity for HCN2 channels and a brighter fluorophore compared to fcAMP (13). This allowed us to use lower ligand concentrations and conventional TIRFM, whereas White et al. used ZMWs. As the measurements have to be performed at high sub-micromolar concentrations with substantial fluorescence background from free ligand in solution, both ZMW and TIRF use evanescence effects to reduce the observation volume. The background contribution from free ligand (http://www.pnas.org/lookup/doi/10.1073/pnas.2315132121#supplementary-materialsSI Appendix, Discussion for estimates) is about one order of magnitude higher in our systems than in in the study by White et al. As result, our data contain more noise but are still sufficiently reliable to resolve single-binding events (SI Appendix, Fig. S5).

Another major difference lies in the sample preparation and, consequently, in the molecular environment of the channels: White et al. (14) solubilized and purified the channels into artificial detergent micelles, whereas we studied the binding in native cell membranes. While micelles contain only one protein, the mHCN2 channel, our native membrane contains also other proteins potentially binding f1cAMP. To minimize inclusion of binding to these, we employed two strategies: i) We utilized eGFP-tagged channels and only evaluated binding signals with point-spread-function (PSF) like shapes that where closely colocalized to the PSF-shaped eGFP signal. ii) We reduced the influence of endogenous binding sites (35, 36, 40) by adding a mixture of selective competitive inhibitors (SI Appendix, Supporting Methods) (37–39). The functionality of the mHCN2 channels was not altered by these inhibitors (SI Appendix, Fig. S1E). Assuming that the observed flip states in our and White et al.’s work represent the same molecular transition, we suggest that the functional difference between our results and those of White et al., cooperativity versus non-cooperativity in ligand binding, arises predominantly from the different molecular environment of the channel.

It should also be emphasized that influences of the membrane composition on either the structure or function of membrane proteins is a well-known phenomenon. For example, Cao et al. (43) showed for mGlu2 receptors that the interaction between membrane-forming lipids and the receptor is required for function. With regard to HCN channels, Fürst and D’Avanzo (44) reported that altering the cholesterol content in the membrane severely influenced both activation and deactivation kinetics as well as current density in cells. They also discussed an effect of cholesterol on cooperativity. As White et al. (14) had to optimize the detergent conditions to obtain stable sample preparations for different HCN-isoforms, which always included a steroidal detergent, a similar effect could have been present. More recently, an effect of lipid environment on the rearrangement of the voltage sensor upon activation was reported for HCN4 but not HCN1, demonstrating the sensitivity of pacemaker channels to their lipid environment (45).

A wealth of new knowledge, mainly structural from cryo-EM, is generated from detergent-solubilized channels (3). However, the discrepancy between the data by White et al. (14) and the data presented here is a cautionary tale on how far the channel properties are potentially altered in detergent micelles or depend on factors present in native membranes. Still, careful variation of detergent composition can increase the understanding of ion channels, as by enabling the recording of different functional states (46).

To quantify the mode of cooperativity, we fitted a series of kinetic models and subsequently adopted the following three assumptions: 1) Binding rates to ground-state channel subunits were set to be equal after accounting for stoichiometry. 2) Rates of entering the flip state were linked to increase the accuracy of the determined parameters while off-rates were kept independent to account for possible ligand–protein interactions stabilizing the flip state. 3) Binding to neighboring subunits was not distinguished from that to opposite subunits and among the neighboring subunits, also not between the right and the left neighbor. We assume that this is justified as no respective difference was reported for channel activation in mutated concatamers (47). With these assumptions the best model was chosen based on the certainty of the estimated parameters and the LL. Binding rates were comparable to values published for related isolated binding sites (48). All our models featured an increase of affinity with increased number of already occupied subunits. Such an affinity dependence on the number of occupied subunits is the hallmark of cooperativity in oligomeric proteins.

In conclusion, our data demonstrate that the subunits in closed, not voltage pre-activated HCN2 channels act in a cooperative fashion when ligands bind to the four binding sites and that this cooperative action of the subunits is associated with the transition to a flip state. In general, this indicates that cooperativity emerges already upon ligand-binding and does not require activation of the channel pore.

Materials and Methods

Chemicals.

Chemicals were purchased and used with no further purification: 8-pCPT-2’OMe-cAMP (Biolog LSI GmbH & Co KG), Trolox, Piclamilast, Glucose oxidase, Catalase, Glucose, Poly-L-Lysin (Merck KGaA), ht31 was synthesized on demand (Genosphere Biotechnologies), and Cy3B-AHT-cAMP was synthesized in house as described previously (13).

Generation of the Stable Cell-Line.

The cell line Flp-In-T-REx-293 eGFP-mHCN2 (RRID: CVCL_D4B1) contains an inducible promoter (Flp-In-T-REx 293; Invitrogen #R78007) and was cultured in minimum essential medium [MEM, (Thermo Fisher Scientific)] supplemented with 10% fetal calf serum (BioWest), non-essential amino acids (Gibco, Thermo Fisher Scientific) and antibiotics according to the manufacturer's instructions. It was generated by transfecting Flp-In-T-REx 293 cells using the calcium phosphate method with a mixture of plasmids (0.5 µg eGFPmHCN2 and 1.5 µg pOG44). After hygromycin B treatment, stable clones were selected and cultured until a passage number of approximately 20. eGFPmHCN2 contains an eGFP linked by a 6-amino acids linker (SDPNST) to mHCN2 (49).

Membrane Preparation.

For single-molecule measurements, cells were plated on cover slips (13 mm diameter, #1–0.15 mm thickness, Menzel Gläser) in 24-well plates. Cover slips were coated with poly-L-lysin before use (0.1 mg/mL poly-L-lysine solution for 2 h followed by multiple washes with media). Per cover slip, 200 µL of resuspended cells (500 cells/µL) culture was added. Cells were allowed to settle a day before induction of protein expression with media supplemented with 0.2 µg/mL tetracycline (Sigma-Aldrich). Cells were used 2 to 48 h after induction. Coverslips with cells were washed three times with sterile filtered PBS (300 µL). Cover slides (25 mm diameter, #1–0.15 mm thickness, Menzel Gläser), prior to usage cleaned by Zepto Plasma cleaner (Diener Electronics), were mounted in Attofluor imaging chambers (Thermo Fisher Scientific). Cover slips were inverted onto plasma-cleaned cover slides with 20 µL PBS in-between the glasses. Additional weight (0.7 N, generating 5.3 kPa) was put onto the coverslips for 5 min. After taking off the weight, the upper coverslip was removed using an EDSYN LP200 Pixter Pen-Vac pneumatic forceps (EDSYN Inc.) leaving supported membrane attached to the lower, plasma-cleaned cover slide. The cover slide with the attached membrane was washed three additional times with sterile filtered PBS. A solution of 100 µM ht31 in sterile filtered PBS was added and removed after 5 min. The membranes were subsequently washed three times with sterile filtered PBS. Afterward, membranes were incubated with a solution of f1cAMP (Cy3B-AHT-cAMP) (13), competitive inhibitors for membrane-associated cAMP binding proteins (65 µM 8-pCPT-2’OMe-cAMP, 100 µM Piclamilast), an oxygen scavenger system (165 U/mL Glucose oxidase, 2,170 U/mL Catalase, 0.4 w% Glucose), and 2 mM Trolox. The system was allowed to equilibrate for 5 min before imaging.

Single-Molecule Microscopy.

Measurements were performed on a Nikon Eclipse Ti inverse microscope using an Apochromat 1.49/100× oil objective (Nikon Europe B.V.) with Immersol^TM 518F (Zeiss). After localizing the membranes with Nikon Intensilight lamp, the system was switched into TIRF-mode. Data were recorded by an Andor iXon 888 Ultra camera (Oxford Instruments) equipped with an LS-OC optomask (Cairn Research Ltd.) controlled with NIS-Elements AR 5.02.02. Single-molecule recordings were performed in a 256 × 256 pixel ROI in the camera’s isolated cop mode. Movies of 10,000 frames (exposure time 10 ms, ≈88 fps, 115 s) of the cAMP signal were followed by movies of 3,000 frames (exposure time 40 ms; ≈25 fps; 75 s) of the eGFPs signal. Excitation and emission were filtered using appropriate filter sets (AHF Analysentechnik AG): eGFP-excitation: 472/30 Brighline HC, dichroic: zt 488 RDC, emission: 515/30 BrightLine HC (Semrock); f1cAMP: dichroic: ZT543rdc, emission: 596/83 BrightLine HC. eGFP was excited by a Stradus® 488-150 VORTRAN Laser (LASER TECHNOLOGY, INC./Frankfurt Laser Company). Fluorescent f1cAMP derivatives were excited by a 100 mW MLL-III-543/1 ~ 100 mW laser (Changchun New Industries Optoelectronics Tech. Co.). Lasers were dimmed and controlled by an AOTF included in the Nikon Laser Box LU4A.

Single-Molecule Analysis.

Time trajectories of single molecules binding and unbinding were extracted and processed using MATLAB 2020b (Mathworks). Background and drift were removed by subtracting a median filtered movie (Kernel: 9 × 9 × 3). Single molecules were identified by iteratively selecting subsequent signal maxima in a maximal intensity projection of the background-subtracted movie and fitting a 2D Gaussian to 5 × 5 pixel around the maxima. Positions with fit results showing half axes wider than 2 pixels were rejected. The process was repeated at the same location for the eGFP-Signal. Due to the worse signal-to-noise ratio in the eGFP signal, leading to poorer fits, fits with half axes exceeding 3.3 pixels were rejected. If both the f1cAMP signal and the eGFP signal were present at the same position, the sum of a 3 × 3 area around the original location was used as time trace corresponding to binding signal at individual mHCN2-channel. Traces were filtered by Chung–Kennedy filter with p, M, and N being 40, 10, and [4 8 16 32] (50, 51). Only traces showing stepwise changes in average intensity (f1cAMP) and stepwise photo-bleaching with four or less steps were included in further analysis. Sparse and unusually bright one- or two-frame events were removed by a five-point median filter. Traces were then idealized using a modified version of the DISC algorithm (41) (SI Appendix, Supporting Methods, Adaptation of DISC: Algorithm). All idealized traces were inspected by eye following idealization. Accepted traces accumulated to 1.6 × 10⁴ s of measurements across approximately 150 mHCN2 channels at f1cAMP concentrations of 0.1, 0.3, and 0.5 µM. From these traces, the population of liganded states, the average binding probability and dwell times were extracted:

From observed states the average probability of a ligand binding to a subunit, P(1), was calculated using

$$\begin{array}{c}P\left(1\right)=\frac{N\left(1\right)+2N\left(2\right)+3N\left(3\right)+4N\left(4\right)}{4(N\left(0\right)+N\left(1\right)+N\left(2\right)+N\left(3\right)+N\left(4\right))},\hfill \end{array}$$ [1]

with N(x) being the number of frames spent in with x ligands bound. P(1) was used to calculate the expected binomial distribution according to:

$$F\left(x\right)=\left(\genfrac{}{}{0.0pt}{}{4}{x}\right)P{\left(1\right)}^x{\left(1-P\left(1\right)\right)}^{4-x},$$ [2]

with F(x) being the expected fraction of x ligands bound.

Dwell times of single-liganded channels that were preceded and followed by states in which no ligand was bound were extracted and binned in a histogram. Mono- and biexponential distributions were fitted to the data according to ${Y = A}_1{e}^{-\frac{x}{{\tau }_1}}$ (monoexponential) or $Y=A_1{e}^{-\frac{x}{{\tau }_1}} {+ A}_2{e}^{-\frac{x}{{\tau }_2}}$ (biexponential). Dwell times of non-liganded channels that were preceded and followed by single-liganded states were treated the same way.

Modeling.

Models (SI Appendix, Table S2) were optimized globally over all concentrations using maximum idealized point optimization (52) as implemented in QuB (53) and the DISC-idealized traces as data. The quality of optimization was evaluated by ranking the maximum likelihood and relative errors of the parameters.

Supplementary Material

Appendix 01 (PDF)

Data, Materials, and Software Availability

Evaluation routine data have been deposited in Open Science Framework (54). Microscopy data is impractical for deposition due to size, the raw data are shared upon reasonable request.