CNBD channels, part of the voltage-gated ion channel superfamily, play pivotal roles in sensory perception, signal transduction, and cellular excitability (Craven and Zagotta, 2006). The CNBD family includes cyclic nucleotide-gated (CNG) channels, which are responsible for visual and olfactory signal transduction, and hyperpolarization-activated cyclic nucleotide-gated (HCN) channels, which regulate the pacemaker activity of the heart (Matulef and Zagotta, 2003; He et al., 2014; Kaupp and Seifert, 2002). Despite their diverse physiological roles, CNBD channels all possess a shared tetrameric structure with four identical or similar subunits surrounding a central ion-conducting pore. Each subunit contains three regions: an N-terminal region, a transmembrane region with a voltage-sensor and pore domain, and a cytosolic C-terminal region that consist of a CNBD plus a C-linker connecting the CNBD to the pore (James and Zagotta, 2018). These channels are activated by the binding of cyclic nucleotides (such as cAMP or cGMP) to the CNBD, which induces conformational changes throughout the protein structure to ultimately open the pore. This ligand-induced allosteric opening is still poorly understood, and questions remain about the structural and energetic changes that occur during this allosteric regulation. In particular, what are the energetics of the conformational changes in individual domains, how are these conformational changes coupled within and between subunits, and how do these processes differ for full and partial agonists?

SthK is a prokaryotic member of the CNBD family from Spirochaeta thermophila, which has considerable sequence and structural similarity to eukaryotic CNBD channels and offers a powerful model for better understanding the allosteric regulation in these channels (Brams et al., 2014). It is easily expressed in E. coli, has established biochemical purification methods, and its physiological properties have been studied with ion flux assays and patch-clamp electrophysiology (Morgan et al., 2019; Schmidpeter et al., 2018). We have also characterized a cysteine-free version of the protein (cfSthK) and found it to behave nearly identically to wild-type channels, making it amenable to thiol-based site-specific labeling (Morgan et al., 2019). As previously shown, binding of cAMP to SthK causes robust channel currents in E. coli spheroplasts (Figure 1A) with a high degree of cooperativity (Figure 1B; Hill slope, h: 2.9±0.2; Morgan et al., 2019). In contrast, cGMP appears to be a poor partial agonist for SthK, and its binding to the same structural pocket is only weakly coupled to conformational changes that increase channel open probability (Figure 1B).

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Excel data for representative electrophysiology traces (Figure 1A) and summary of cyclic nucleotide dose response (Figure 1B).

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X-ray crystallography and cryo-EM structures of SthK reveal notable ligand-induced structural changes throughout the protein, particularly in the CNBD (Kesters et al., 2015; Rheinberger et al., 2018; Gao et al., 2022). These differences include a rotation of the CNBD C-helix towards the β-roll upon binding of cyclic nucleotide. This important conformational change is thought to be coupled to a rearrangement of the C-linker, and ultimately to the opening of the pore. However, structures alone have not been able to fully characterize the energetic landscape of the allosteric regulation, especially in determining the structural heterogeneity within conformational states and the energetics between states.

To link structural information to the mechanism of allostery, we used a simple four-state model to describe the conformational states and energetics in the C-terminal of SthK (Figure 1C). This framework has been used previously to describe allosteric proteins generally and the ligand-binding domains of CNBD channels in particular (DeBerg et al., 2016; Collauto et al., 2017; Colquhoun, 1998; Auerbach, 2003; Aviram et al., 2018; Guo and Zhou, 2016). In this model, the CNBD can exist in either resting or active conformational states, both of which can be ligand free (apo) or ligand bound (holo). Whereas in the absence of ligand the transition from resting to active is unfavorable, the presence of agonist (either full or partial) makes the active state more favorable. The equilibrium constants, and therefore energetics, that describe the transitions between states determine the steady-state fraction of molecules in each given state. Using the four-state energetic model as a framework and an experimental method for determining the fraction of molecules in each state, we can calculate the changes in free energy (ΔG) and differences in energy change (ΔΔG) between the conformational states of the CNBD upon binding of ligands like cAMP and cGMP.

A complex protein, such as an ion channel, consists of multiple domains, each of which can undergo conformational changes that are coupled to ligand binding, transmembrane voltage, or the state of a neighboring domain (Horrigan and Aldrich, 2002; Hofmann, 2023). For example, allostery in CNBD channels can be modeled as a cyclic-nucleotide-dependent conformational change in each subunit CNBD that is coupled to a concerted conformational change in the C-linker, which in turn is coupled to a opening conformational change in the pore (Craven and Zagotta, 2006; DeBerg et al., 2016). In this context, to truly understand the allosteric mechanism in CNBD channels, we would need to know ΔG and ΔΔG for each of these domains. Therefore, we need a method that can measure the conformational energetics in each protein domain.

In this study, we utilized our recently described steady-state and time-resolved tmFRET methods to measure the energetics in an isolated C-terminal fragment of SthK (Zagotta et al., 2021; Gordon et al., 2024; Zagotta et al., 2024). In tmFRET, a donor fluorophore is paired with a transition metal ion, such as Cu²⁺, Fe²⁺, or Ru²⁺, as an acceptor. Donor-acceptor pairs can then be incorporated in a protein at different residue positions. As in classical FRET with two fluorophores, the efficiency of energy transferred between the donor fluorophore and acceptor metal ion is steeply distance dependent and can be used as a molecular ruler to measure distances between sites on a protein, and therefore conformational changes (Lakowicz, 2006).

In time-resolved tmFRET, changes in fluorescence lifetimes of the donor fluorophore are quantified to report FRET efficiencies, and therefore molecular distances between the donor and acceptor. The fluorescence lifetime is the time, in nanoseconds, between excitation of the donor fluorophore and emission of a photon (Lakowicz, 2006). Unlike steady-state FRET, time-resolved FRET can provide nanosecond snapshots of the distribution of FRET efficiencies in a sample (Zagotta et al., 2021; Zagotta et al., 2024). In the time-domain, a histogram of photon latencies for the simplest lifetimes appears as a single exponential decay (Figure 1D, black line). FRET resulting from a single donor-acceptor distance also produces lifetimes described by a single exponential decay, but with a time constant that decreases in proportion to the FRET efficiency (Figure 1D, solid green and red lines). However, in the case of two donor-acceptor distances, such as from two protein conformations, the intensity decay will be double exponential, with contributions from both donor-acceptor distances. The average distance of each component and the fraction among components can be determined by fitting the decay with a double-exponential decay model. The fractional contribution of each lifetime represents the prevalence of each distance, and thus conformational state, in the sample population (Figure 1D, green-red dashed lifetime is a mix of 20% solid green and 80% solid red lifetimes; Lakowicz, 2006). Time-resolved tmFRET, therefore, resolves the structural distances and relative abundance of multiple conformational states in a protein sample.

Under physiological conditions, donor-acceptor distances in proteins will typically be heterogeneous and fluorescence lifetime data will reflect this heterogeneity. Thus, we have fit lifetime data with a FRET model that assumes Gaussian distributions of donor-acceptor distances within each state. This heterogeneity can arise from both: (1) backbone and rotameric variations within a given state (the width of each peak, Figure 1E) and (2) differences between conformational states (relative fraction of the resting, black, and active, red, peaks, Figure 1E). Heterogeneity between conformational states reflects the proportion of molecules in the resting and active states of the protein, which can then be used to calculate the free energy difference between the states (ΔG). In this study, we used various donor-acceptor pairs in the CNBD of SthK to measure distance distributions of the C-helix relative to the β-roll in the absence and presence of ligand. Distance distributions were used to determine the energetics for the transitions between conformational states of the four-state model described above. These results provide a more complete understanding of the structural and energetic changes in the CNBD with ligand binding.

We engineered three donor sites for tmFRET experiments into a C-terminal fragment of SthK (SthK_Cterm), comprised of the C-linker and CNBD domains (Kesters et al., 2015). At these sites (359, 361, and 364), we introduced the unnatural amino acid acridon-2-ylalanine (Acd) as a donor fluorophore using amber codon suppression with a previously described tyrosyl tRNA synthetase (Zagotta et al., 2024; Sungwienwong et al., 2017). Incorporation of Acd into stop-codon containing SthK_Cterm constructs occurred only in the presence of both the amino-acyl tRNA synthetase/tRNA plasmid (RS/tRNA) and the Acd amino acid. SDS-PAGE followed by in-gel fluorescence imaging (SthK_Cterm-S361-TAG) indicated that Acd was site-specifically incorporated into our SthK_Cterm constructs and the incorporated product was readily purified for use in tmFRET experiments (Figure 2A).

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Original uncropped protein gel image (Figure 2A).

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Labeled cropped protein gel image (Figure 2A).

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Excel data for size exclusion chromatography (Figure 2D) and mass photometry data (Figure 2E).

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We introduced metal ion acceptor binding sites for tmFRET using cysteine mutations in SthK_Cterm for modification with cysteine-reactive metal chelators (TETAC and phenanthroline maleimide [phenM]) bound to different transition metals (Cu²⁺, Fe²⁺, and Ru²⁺). The three different metal ion-acceptor complexes used in this study, [Cu(TETAC)]²⁺, [Fe(phenM)₃]²⁺, and [Ru(bpy)₂phenM]²⁺, are shown in Figure 2B. The distance dependence of energy transfer between donor and acceptor is described by the Förster equation and is dependent on the overlap between the absorbance spectrum of the acceptor and the emission spectrum of the donor, among other factors (Lakowicz, 2006; Stryer and Haugland, 1967). Paired with Acd, these transition metal acceptor complexes resulted in distances with 50% energy transfer (R₀) of 15.6 Å, 41.8 Å, 43.5 Å for [Cu(TETAC)]²⁺, [Fe(phenM)₃]²⁺, and [Ru(bpy)₂phenM]²⁺, respectively. Thus, with Acd as a donor, these acceptors allowed us to measure both short (10–20Å) and long (25–50Å) distances across SthK_Cterm (Figure 2B; Gordon et al., 2024).

The SthK_Cterm fragment tetramerizes in solution at higher protein concentrations, even though the transmembrane domains are absent. Although the tetrameric structure is the physiologically relevant state for the channel, tetramerization introduces challenges in minimizing the contribution of inter-subunit FRET measurements where only intra-subunit donor-acceptor pairs are desired. Using tmFRET, which is sensitive to relatively short distances, mitigates but does not eliminate this concern. To avoid potential contributions from inter-subunit FRET, Acd-labeled protein was tetramerized with an excess (at least a 3:1 molar ratio) of wild-type SthK_Cterm protein (WT; Figure 2C). WT protein had neither Acd incorporation nor cysteine mutations. This approach ensured that, on average, no more than one Acd-cysteine-containing subunit was present in each tetramer, and our FRET efficiency measurements would be almost exclusively from donor-acceptor pairs within the same subunit.

Tetrameric SthK_Cterm was efficiently separated from monomeric protein using size exclusion chromatography (SEC), where tetrameric protein eluted primarily as a single monodispersed peak at 14 mL, as observed by both absorbance at 280 nm and Acd fluorescence (Figure 2D, closed triangle). We confirmed this large SEC peak corresponded to tetramers of SthK_Cterm using mass photometry, which reported a mass of ~105 kDa, compared to a predicted mass of 101 kDa (Figure 2E). At the low concentrations (~10 nM) used for mass photometry, a second small peak was observed of ~30 kDa, which is below the analytical range for this method. All tmFRET experiments used higher protein concentrations to ensure tetramerization.

Steady-state tmFRET for determining weighted-average distance changes

To resolve the structural changes in tetrameric SthK_Cterm, we characterized steady-state tmFRET using SthK_Cterm-S361Acd-V416C, with a long-distance donor-acceptor pair (Figure 3A), and SthK_Cterm-Q364Acd-R417C, with a shorter distance pair (Figure 3C). We used the metal ion acceptors [Fe(phenM)₃]²⁺ and [Ru(bpy)₂phenM]²⁺ for the long-distance pair and [Cu(TETAC)]²⁺ for the short-distance pair. We measured time courses of Acd fluorescence intensity of the cysteine-containing construct, upon addition of the acceptor, relative to protein without the cysteine mutation, measured separately as a negative control. We plotted the ratio of the normalized fluorescence intensity for the two protein samples as F_Cys/F_{No Cys}. The addition of metal acceptor produced pronounced quenching specifically in the cysteine-containing constructs (Figure 3A, B and C). This fluorescence decrease is indicative of FRET-based quenching of the donor by the metal acceptor, with the FRET efficiency given by E=1- F_Cys/F_{No Cys}. The addition of a saturating concentration of cAMP (160 µM) further increased quenching, indicating a greater FRET efficiency in the presence of agonist compared to the apo state. The increased FRET is consistent with a cAMP-induced decrease in donor-acceptor distance as the C-helix moves towards the β-roll. The dependence of the apparent FRET efficiency change on the cAMP concentration was measured for each donor-acceptor pair, then normalized for comparison and fit with the Hill equation (Figure 3D). The Hill fits obtained from different sites and acceptor metals are in close agreement with one another, suggesting similar binding affinities and that our previous measurements were obtained at saturating concentrations. Additionally, the three Hill fits with slopes, h, of ~1 suggest that the cooperativity observed in full-length channel electrophysiology is not observed in the isolated C-terminal fragment. These steady-state tmFRET results across different donor-acceptor sites and acceptor complexes underscore the large conformational change of the C-helix induced by cAMP.

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Excel data for time courses and dot plots of steady-state FRET efficiencies and dose response (Figure 3A–D).

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In addition to measuring the conformational rearrangement with the full agonist cAMP, we also used the partial agonist cGMP. Like cAMP, cGMP increased quenching by our transition metal labels (i.e. increased FRET); however, the increase was much smaller than that produced by cAMP. As discussed above, cGMP is a poor partial agonist of SthK which elicits only a small fraction of the channel current elicited by cAMP (Figure 1A). The cGMP-induced increase in FRET we observed provides further evidence that cGMP indeed binds to SthK and that cGMP binding causes a conformational change that moves the C-helix closer to the β-roll. These data do not, however, distinguish between (1) cGMP producing a smaller movement relative to cAMP (a distinct state), and (2) cGMP producing the same size movement but with a lower fraction in the active state (different energetics).

At lower protein concentrations, monomeric SthK_C-term protein can be separated from tetrameric protein on SEC. Interestingly, for multiple donor-acceptor sites, steady-state tmFRET measurements consistently revealed higher FRET efficiencies (shorter distances) for monomers than for tetramers, particularly in the apo state (Figure 3—figure supplement 1). These experiments suggest that tetramerization destabilizes the resting-to-active transition of the SthK_C-term protein. For our remaining experiments, we focused on the conformational changes in the tetrameric state of the protein, which is more physiologically relevant.

Predicted in silico distance distributions

To validate the accuracy of tmFRET in determining donor-acceptor distances and ligand-dependent changes in distances, we compared our data to predictions based on structural models. For each donor-acceptor pair, we modelled the donor and acceptor labels on the resting and active static structures of SthK_Cterm (PDB: 7RSH and 4D7T, respectively) to obtain in-silico weighted rotameric ensembles utilizing a previously described python package, chiLife (Figure 4A; Kesters et al., 2015; Gao et al., 2022; Tessmer and Stoll, 2023). We then calculated the distance distributions between every Acd rotamer and every acceptor rotamer for both the resting and the active structures within subunits (intra-subunit) and between all other subunits (inter-subunit; Figure 4B). The inter-subunit distances predicted by chiLife for these sites were longer than 50 Å, contributing less than 15% FRET efficiency to the intra-subunit FRET in either the resting or active states. This inter-subunit FRET is predicted to be negligible in our experiments with added WT SthK_Cterm.

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Excel data for chiLife distance distributions (Figure 4B).

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We compared the intra-subunit chiLife distributions with our measured weighted-average distances predicted from steady-state tmFRET experiments. We calculated the distances from our steady-state FRET experiments using the Förster equation (Stryer and Haugland, 1967) and superimposed them on the distributions from chiLife (Figure 4B, vertical solid black and red lines). Whereas the distance changes based on our tmFRET measurements were generally similar to the structural predictions, the absolute distances differed by as much as 5 Å. Steady-state tmFRET measurements combine several sources of heterogeneity from the protein into a single weighted average, including the presence of mixed populations of resting and active states. An additional source of uncertainty is the labeling efficiency. If, for example, we assume that 10% of the protein sample in steady-state experiments was not labeled with acceptor (e.g. due to cysteine oxidation), the adjusted weighted-average distances from our experimental data become more similar to predicted peak values (vertical dashed black and red lines). Although overall these average distances are close to the expected distances predicted by the structures, a method for measuring the distance distributions would be desirable.

Time-resolved tmFRET for determining distance distributions

While steady-state tmFRET shows an average FRET efficiency (and weighted-average distance) for all the molecules in the sample, time-resolved measurements of fluorescence lifetimes can be used to measure distance distributions in the sample. This approach can account for the two forms of heterogeneity in the protein mentioned earlier (within state and between state heterogeneity), as well as protein not labeled with acceptor. Here, we measured fluorescence lifetimes in the frequency-domain, which can obtain distance distributions utilizing the same principles discussed above for time-domain lifetime measurements (Figure 1D). Instead of measuring donor emission photons in response to an impulse of excitation light, lifetimes in the frequency-domain quantify the phase shift (phase delay) and decrease in amplitude of response (modulation ratio) of the donor emission as functions of the modulation frequency of a sinusoidally-varying excitation light (Zagotta et al., 2024).

We first measured the fluorescence lifetime of SthK_Cterm-S361Acd-V416C in the absence of acceptor. The phase delay and modulation ratio as a function of the modulation frequency of the excitation light are shown as gray symbols in the Weber plot of Figure 5A. We fit these data with a model for a single exponential lifetime with a time constant of 17.2±0.01 ns (n=8, Figure 5A, grey curves), comparable but a little longer than values seen previously for Acd (~16 ns; Zagotta et al., 2024; Speight et al., 2013). When [Fe(phenM)₃]²⁺ was added to the protein sample, the average fluorescence lifetime decreased, illustrated by a shift in the phase delay and modulation ratios to higher frequencies in the Weber plot (Figure 5A, black circles). Adding a saturating concentration of cAMP (1.23 mM), further decreased the average lifetime, indicating increased FRET (Figure 5A, red circles). This change in lifetime is consistent with steady-state measurements and reflects a decreased distance between the C-helix and the β-roll. In contrast, adding a saturating concentration of cGMP (1.23 mM) instead of cAMP only moderately decreased the fluorescence lifetime, with phase delay and modulation ratio curves falling closer to the apo conditions (Figure 5A, green circles).

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Excel data for Weber plots, spaghetti plots and summary of Gaussian fit scatter plots (Figure 5A–F).

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To further validate our lifetime measurements using a different acceptor with a different R₀, we repeated these experiments using [Ru(bpy)₂phenM]²⁺ as the acceptor instead of [Fe(phenM)₃]²⁺. [Ru(bpy)₂phenM]²⁺ also decreased the average fluorescence lifetime in all three conditions (apo, cAMP and cGMP) relative to the donor-only lifetime (Figure 5B). As expected from the longer R₀ value for Acd-[Ru(bpy)₂phenM]²⁺ compared to Acd-[Fe(phenM)₃]²⁺, [Ru(bpy)₂phenM]²⁺ produced an even greater shift in phase delays and modulation ratios towards higher frequencies compared to [Fe(phenM)₃]²⁺ (Figures 5B and 6B). Neither [Fe(phenM)₃]²⁺ nor [Ru(bpy)₂phenM]²⁺ produced a change in lifetime for SthK_Cterm-S361Acd (without the cysteine) used as a negative control (Figure 5—figure supplement 1). The decreases in lifetimes of SthK_Cterm-S361Acd-V416C with the metal acceptors and ligands reflect measurable decreases in the donor-acceptor distances (i.e. conformational state) with the addition of cyclic nucleotide, as seen with the steady-state tmFRET measurements.

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Excel data for phasor plot coordinates, Weber plot, spaghetti plot and dot plot for summary of Gaussian fit parameters from global fits (Figure 6A–E).

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To obtain distance distributions and average distances that reflect individual conformational states, we fit our lifetime data to a previously described model that assumes each ligand condition (apo, cAMP, and cGMP) is described by a single Gaussian distribution of distances (parameters in Figure 5—figure supplement 2; Zagotta et al., 2021). The [Fe(phenM)₃]²⁺ and [Ru(bpy)₂phenM]²⁺ time-resolved tmFRET datasets for each ligand condition were individually fit using this lifetime model (solid and dashed curves, Figure 5A and B; Zagotta et al., 2021; Zagotta et al., 2024). The average distances ($\overline{r}$) and standard deviations ($\sigma$) of the Gaussian distance distributions from these fits are shown for [Fe(phenM)₃]²⁺ and for [Ru(bpy)₂phenM]²⁺ as spaghetti plots experiments in Figure 5C and D, respectively. Overlayed on the spaghetti plots are the distance distributions for the resting and active states predicted using chiLife (dashed curves). The $\overline{r}$ and $\sigma$ of the lifetime model from individual experiments for apo, cAMP and cGMP are summarized in Figure 5E and F. Average Gaussian distances measured from experiments for apo and cAMP using both [Fe(phenM)₃]²⁺ (apo=39.6 Å, cAMP=29.4 Å) and [Ru(bpy)₂phenM]²⁺ (apo=40.1 Å, cAMP=29.4 Å) agreed remarkably well with the chiLife predictions and with each other despite the difference in R₀ between [Fe(phenM)₃]²⁺ and [Ru(bpy)₂phenM]²⁺. Interestingly, the cGMP data had an $\overline{r}$ distance between the apo and cAMP $\overline{r}$ values and had a much wider $\sigma$, spanning a distance range of the apo and cAMP Gaussians combined.

While this lifetime model, with a single average distance for each ligand condition, fits the time-resolved tmFRET data well, it seems likely that there might be more than one conformational state (resting and active) present for each ligand condition (DeBerg et al., 2016). As our four-state model suggests, each liganded condition (apo, cAMP, and cGMP) should be comprised of a mixture of resting and active conformational states at varying proportions. For example, the wide cGMP Gaussian positioned between those of the apo and cAMP distributions might reflect the sum of two Gaussians, one with a longer average distance (resting conformation) and one with a shorter average distance (active conformation). The larger apo state $\sigma$ compared to the chiLife prediction could also be due to the presence of a small fraction of the active state, even without ligand. Determining the fractional occupancy among the resting and active states in the apo, cAMP and cGMP conditions would provide energetic information about the transition between resting and active SthK_Cterm in the different conditions.

Changes in energetics with salt concentrations

We were surprised by the high probability of being in the active state for cGMP (A₂=0.34) indicated by the sum of Gaussian fits (Figure 6E), especially when electrophysiology shows a much lower open probability with cGMP (Figure 1A). Although this difference might be due to intrinsic energetic differences between our fragment SthK_Cterm construct and the full-length channel, it could also arise, in part, from the high ionic conditions (500 mM) used in our lifetime experiments compared with physiological ionic concentrations used in electrophysiology experiments. Known inter-subunit C-terminal salt bridge interactions could be destabilized by increased ionic strength and, previously, it was observed that higher ionic strength eliminated tetramerization in HCN1 C-terminal fragments (Morgan et al., 2019; Lolicato et al., 2011; Craven and Zagotta, 2004). However, we found no difference in elution volume for SEC experiments performed with SthK_Cterm-S361Acd-V416C using 150 mM instead of 500 mM KCl, indicating that the oligomerization state was the same under both experimental conditions (Figure 7A).

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Excel data for size exclusion chromatography traces, Weber plot, and dot plots for summary of Gaussian fit parameters from global fits (Figure 7A–D).

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To test whether the high ionic strength of our experiments contributed to the high A₂ for cGMP, we repeated the above lifetime experiments with a more physiological salt concentration (150 mM KCl). We made new time-resolved tmFRET measurements with SthK_Cterm-S361Acd-V416C in lower ionic conditions, for both the [Fe(phenM)₃]²⁺ and [Ru(bpy)₂phenM]²⁺ acceptors across apo, cAMP, and cGMP conditions. Comparison of [Fe(phenM)₃]²⁺ lifetime data in the two different ionic conditions are shown in the representative Weber plot in Figure 7B. While the apo and cAMP data appeared to be equivalent between 150 and 500 mM KCl, the cGMP data were different between the conditions. When an additional 300 mM KCl was added to protein samples in 150 mM KCl after cGMP application, the phase delay and modulation ratio approached the same lifetimes as the 500 mM KCl cGMP condition (Figure 7B, dark green circle), recapitulating the 500 mM KCl data set. We then globally fit the 150 mM KCl data across [Fe(phenM)₃]²⁺ and [Ru(bpy)₂phenM]²⁺ acceptors for apo, cAMP, and cGMP conditions with the sum of two Gaussians (Figure 7C) and found that the average distances, $\overline{r}$, and standard deviations, $\sigma$, were nearly identical to those at 500 mM KCl (Figure 7D). The A₂ from cGMP fits decreased in 150 mM KCl compared to 500 mM KCl indicating that a decrease in ionic concentration made activation by cGMP less favorable (ΔΔG_cGMP=–0.47 kcal/mol, ΔΔΔG_{cGMP KCl}=0.35 kcal/mol). In the absence of ligand, A₂ was unchanged between the two ionic concentrations (Figure 7D), indicating that the increased ionic strength effected only the active conformation in the presence of cGMP. Since activation is already very favorable in the presence of cAMP, we could not determine if ionic strength also effected ΔΔG_cAMP. These results suggest that ionic strength might specifically affect an electrostatic interaction between CNBD and the cyclic nucleotide during the activation transition.

In this study, we measured both steady-state and time-resolved tmFRET for a C-terminal fragment of SthK and interpreted the data using a four-state allosteric model. This approach allowed us to acquire structural information and energetics of the conformational change of the C-helix under different ligand and experimental conditions. Our findings revealed a small presence of the active state in the absence of ligand, while saturating concentrations of cAMP exhibited energetics consistent with that of a full agonist by strongly shifting occupancy into the active state. In contrast, saturating concentrations of cGMP demonstrated characteristics of a partial agonist, eliciting a lower fraction of the same active conformation observed with cAMP. Furthermore, our results demonstrated the impact of both oligomerization and ionic strength on the energetics of the conformational change of isolated SthK_Cterm.

Our ability to recover structural information in the form of average distance, $\overline{r}$, and standard deviation of distances, $\sigma$, from time-resolved tmFRET indicates that this approach is superior to weighted-average steady-state distance measurements alone. The average distance values obtained from lifetime measurements closely matched the distances predicted by chiLife, indicating that the characterized states likely correspond to the observed resting and active states in existing X-ray and cryo-EM structures (Kesters et al., 2015; Gao et al., 2022). Whereas the active state’s standard deviation (${\sigma }_2$) closely aligned and was slightly narrower than the chiLife predictions, the resting state’s standard deviation (${\sigma }_1$) was larger than chiLife predictions, even with the global fitting approach. This indicates a broad structural heterogeneity in the resting state that cannot be explained by the rotamer clouds of the labels alone, such as heterogeneity in the position of the C-helix backbone, which is consistent with several past experimental observations (Rheinberger et al., 2018; Taraska et al., 2009; Matulef and Zagotta, 2002). Overall, time-resolved tmFRET reliably provides valuable, although sparse, structural insights, especially in cases of heterogeneity where current structural methods are limited.

In addition to the heterogeneity within a given conformational state, time-resolved tmFRET allowed us to obtain the heterogeneity between conformational states (A₂) and thus energetics of state transitions in our four-state model. We determined the distribution between these four conformational states by employing a model comprising the sum of two Gaussian distributions, and globally fitting data across distinct acceptors and ligand conditions. This analysis allowed us to quantify the changes in free energy (ΔG) describing our four-state model. Additionally, we were able to calculate the ΔΔG for each ligand, which represents the free energy imparted by the ligand to drive the conformational change of the CNBD. Although we assumed a model with only two stable conformational states, this may not capture all the stable states in the CNBD. Even if the conformational distributions assumed here were oversimplified, our time-resolved tmFRET approach still allowed for a deeper understanding of the allostery in the C-terminal of SthK.

There are some complications with our time-resolved tmFRET approach that should be considered in future applications. (1) Donor and acceptor sites for tmFRET were carefully selected for solvent accessibility, but it is possible that the introduction of Acd and metal acceptor altered the energetics compared to WT SthK_Cterm. (2) Incomplete labeling in our protein samples introduces a fraction of donor-only molecules, which are not captured in steady-state measurements but are estimated in our lifetime fits. We have previously shown that there is some degree of correlation among parameters in our FRET model, particularly between the fraction of donor-only and the standard deviation of the Gaussians (Zagotta et al., 2024). As a result, it is important to ensure a low contribution (<15%) from the donor-only fraction, and this fraction should be validated by independent methods. (3) Although parameters all reliably converged to ${\chi }^2$ minimized values in our global fits, some parameters were more identifiable than others (Figure 6—figure supplement 2). (4) Both the single Gaussian distribution model and the sum of two Gaussian distributions model yielded minimized ${\chi }^2$ s and excellent fits; however, our results do not conclusively favor one lifetime model over the other. Whereas the single Gaussian distribution fits contain fewer assumptions, the sum of two Gaussian global fits contain fewer free parameters across the multiple acceptors and conditions. We believe that the assumptions in the four-state model and sum of two Gaussians fitting are reasonable based on both previous experiments and theoretical considerations (Morgan et al., 2019; DeBerg et al., 2016; Zagotta et al., 2024).

A number of previous studies have measured the energetics of allostery in CNBD channels; however, interpreting our results within the context of these previous studies presents challenges. These studies have utilized various different CNBD channels where the energetics, including even the ligand specificity, are very different (Morgan et al., 2019; DeBerg et al., 2016; Collauto et al., 2017; Craven and Zagotta, 2004; Puljung et al., 2014; Evans et al., 2020; Goldschen-Ohm et al., 2016; Pfleger et al., 2021; Craven et al., 2008; Kondapuram et al., 2022). For example, in CNGA1 channels from rod photoreceptors, cGMP is a full agonist, and cAMP is a weak partial agonist, while in SthK the agonist specificity is reversed (Brams et al., 2014; Morgan et al., 2019; Gordon and Zagotta, 1995; Varnum et al., 1995). In addition, most of these previous studies have been limited to electrophysiology, which measures the open probability of the pore. Without additional information, the open probability provides only an indirect measurement of the energetics of other domains like the ligand-binding domain. While double electron-electron resonance spectroscopy (DEER; DeBerg et al., 2016; Collauto et al., 2017; Puljung et al., 2014; Evans et al., 2020) and single-molecule fluorescence studies (Gao et al., 2022; Goldschen-Ohm et al., 2016; Goldschen-Ohm et al., 2017) offer the potential to measure the energetics of individual domains, these methods have not yet been applied to the SthK CNBD. Interestingly, DEER spectroscopy on the HCN2 CNBD fragment revealed a mixture of resting and active states in cAMP (DeBerg et al., 2016), whereas we observed in the SthK CNBD fragment a more favorable transition in cAMP. These differences might be due to either inherent differences in the energetics between the C-terminal domains of SthK and HCN2, or the different experimental conditions used, such as the monomeric protein used in the DEER studies vs the tetrameric C-terminal domain studied here. Although their energetics may differ, all CNBD channels studied to date appear to undergo an allosteric transition of the CNBD where the binding of cyclic nucleotide promotes a movement of the C-helix relative to the β-roll that is coupled indirectly to the opening of the pore.

For simplicity, here we used the C-terminal fragment of SthK instead of the full-length channel. The relationship between the energetics of the C-terminal fragment and the full-length channel is likely complex and requires further study. For example, coupling of the conformational changes in the individual CNBDs to a concerted opening of the pore is expected to alter both the ΔG for the CNBD transition and the cooperativity of the transitions between subunits. This coupling would also make the ΔΔG measured in the pore by electrophysiology smaller than the ΔΔG we measured in the CNBD. If the conformational change in the CNBD is the same in the fragment and full-length channel, as suggested by structural studies (Kesters et al., 2015; Gao et al., 2022), we could use our measured ΔΔG from the fragment, together with measurements from the full-length channel, to develop a full allosteric model of the intact channel.

Source data files have been included with the final manuscript. Code used for data analysis has been posted to GitHub, (copy archived at Zagotta, 2021).

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Author details

1. Pierce Eggan

   Department of Physiology and Biophysics, University of Washington, Seattle, United States

   Contribution

   Conceptualization, Data curation, Formal analysis, Investigation, Visualization, Methodology, Writing – original draft, Writing – review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-6134-4569

2. Sharona E Gordon

   Department of Physiology and Biophysics, University of Washington, Seattle, United States

   Contribution

   Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Visualization, Methodology, Writing – original draft, Writing – review and editing

   For correspondence

   seg@uw.edu

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-0914-3361

3. William N Zagotta

   Department of Physiology and Biophysics, University of Washington, Seattle, United States

   Contribution

   Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Visualization, Methodology, Writing – original draft, Writing – review and editing

   For correspondence

   zagotta@uw.edu

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-7631-8168

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