Kinetics of Ligand-Receptor Interaction Reveals an Induced-Fit Mode of Binding in a Cyclic Nucleotide-Activated Protein

Abstract

Many receptors and ion channels are activated by ligands. One key question concerns the binding mechanism. Does the ligand induce conformational changes in the protein via the induced-fit mechanism? Or does the protein preexist as an ensemble of conformers and the ligand selects the most complementary one, via the conformational selection mechanism? Here, we study ligand binding of a tetrameric cyclic nucleotide-gated channel from Mesorhizobium loti and of its monomeric binding domain (CNBD) using rapid mixing, mutagenesis, and structure-based computational biology. Association rate constants of ∼10⁷ M⁻¹ s⁻¹ are compatible with diffusion-limited binding. Ligand binding to the full-length CNG channel and the isolated CNBD differ, revealing allosteric control of the CNBD by the effector domain. Finally, mutagenesis of allosteric residues affects only the dissociation rate constant, suggesting that binding follows the induced-fit mechanism. This study illustrates the strength of combining mutational, kinetic, and computational approaches to unravel important mechanistic features of ligand binding.

Introduction

Cyclic nucleotides (cAMP and cGMP) are important cellular messengers that control many physiological functions. Signaling occurs when cyclic nucleotides bind to target proteins that share a common cyclic nucleotide-binding domain (CNBD) (1,2). Proteins that carry a CNBD form a small yet important class of signaling proteins, including a bacterial transcription factor CAP (3–6), protein kinases (PKA and PKG) (7–11), the epithelial exchange factor activated by cAMP (EPAC) (12–14), and cyclic nucleotide-regulated ion channels (CNG and HCN channels) (1,2,15,16). The CNBD consists of three major α-helices (A–C) and eight β-strands (β1–β8) that form a flattened β-barrel. The A helix is N-terminal, whereas the B and C helices are C-terminal of the β-barrel. Cyclic nucleotides are bound to the CNBD through a network of polar and nonpolar interactions. Comparison of various CNBD structures in the apo and holo states shows that, on ligand binding, the β-roll is almost invariant, whereas the helical parts show substantial rearrangements (17–19). In particular, when the ligand is bound, the C-terminal C helix is placed like a lid above the binding pocket and, thereby, stabilizes the complex.

Although these structural rearrangements are quite similar in all CNBDs, they are differently relayed to the effector domains that are located either N- or C-terminally of the CNBD. Do the respective effector domains allosterically control the binding properties of the CNBD? Do the effector domains control the residence time of the ligand? What is the mode of binding of CNBDs? Does the conformational change within the CNBDs happens after or before binding of the ligand which refers to the “induced-fit” or the “conformational-selection” mechanism of binding, respectively (20–23) (Fig. 1 a)?

Figure 1.

Kinetics of ligand binding to the CNBD. (a) Schematic representation of a four-state model of protein-ligand binding. Two extreme cases can be distinguished: In proteins following the induced-fit binding mechanism, a loose complex between the ligand and the protein in its ground state (G) is formed in a first step. This encounter complex (GL) isomerizes subsequently into the active conformation (AL). Proteins following the conformational selection type of binding mechanism bind preferably to the active conformation (A). Thereby the equilibrium is shifted toward the active, ligand-bound conformation (AL). (b) Schematic representation of a competition reaction involving a fluorescent (green) and an excess of nonfluorescent (gray) ligand. (c–f) Kinetics of ligand binding to the isolated CNBD. (c) CNBD (2.5 μM), preincubated with 8-NBD-cAMP (1.9 μM), was mixed with various concentrations of cAMP (0.5–1500 μM). A monoexponential function was fitted to the data (gray). (d) CNBD (2.5 μM) was mixed with various concentrations of 8-NBD-cAMP (0.1–10 μM). Equation 5 was fitted to the data (gray). The k_off and ligand and protein concentrations were fixed parameters, whereas the precise protein concentration was determined from the analysis of the steady-state amplitudes in accord with (28). (e) Analysis of steady-state amplitudes of binding as shown in panel d (28) ([CNBD] = 2.0 μM; R² = 0.9963). (f) CNBD (1 μM), loaded with cAMP (1 μM), was mixed with various concentrations of 8-NBD-cAMP (1–400 μM). A monoexponential function was fitted to the data (gray).

Recently, an elegant mutational approach was suggested to distinguish these two extreme cases using allosteric mutants of a protein and compare the respective rate constants of binding to those of the wild-type (24). Consider an allosteric mutation that affects the conformational equilibrium between ground and activated states. If a protein follows the induced-fit mode of binding, the mutation only affects k_off, because the conformational change takes place after ligand binding. If the protein follows the conformational selection mode, the mutation only affects k_on, because the conformational change occurs before ligand binding. The binding mode itself has implications for the temporal behavior of a protein and reflects an important part of the dynamic-personality of a protein (23,26).

Here, using stopped-flow techniques, we study time-resolved ligand binding to the CNBD of a cyclic nucleotide-gated (CNG) channel from Mesorhizobium loti (MlCNG) (27,28). We determine a complete set of rate constants of association and dissociation for the isolated CNBD and the full-length MlCNG channel. In addition, by using a novel computational approach based on transition-path theory (29), we study the association process of cAMP binding to the CNBD. We determine the electrostatic and structural contributions of charged amino acids in the CNBD to the association rate constant. Furthermore, by varying the ionic strength, we examine the electrostatic contribution to the association process. Finally, using allosteric mutants, we demonstrate that binding of cyclic nucleotides follows the induced-fit mode of ligand binding.

Material and Methods

Protein preparation

The MlCNG protein was purified as described in Cukkemane et al. (28). Briefly, MlCNG protein was heterologously expressed in Escherichia coli (BL21(DE3) pLysE; Novagen, Darmstadt, Germany). After cell lysis, the insoluble fraction was solubilized in detergent micelles of 20 mM dodecyl maltoside (DM). The His₆-tagged MlCNG was purified by means of a Co²⁺-loaded HiTrap column (GE Healthcare, München, Germany). To remove cAMP that copurifies with MlCNG, the column-bound protein was washed with buffer containing 1 mM 8-(4-Chlorophenylthio) guanosine-3′, 5′-cyclic monophosphate (8-CPT-cGMP; Biolog, Hamburg, Germany) and finally eluted by an imidazole gradient. The MlCNG protein was further purified by gel filtration (Superdex 200 pg 16/60 Hiload from GE Healthcare, in 100 mM KCl, 20 mM Na phosphate, and 5 mM DM, at pH 8.0). The MlCNG proteins elutes at the size of a tetramer. Protein concentration and cAMP content were determined by absorbance measurements (ε₂₈₀ = 47,510 M⁻¹ cm⁻¹ for MlCNG protein; ε₂₆₀/ε₂₈₀ = 0.69 for cAMP-free MlCNG).

CNBD protein was expressed and purified as GST fusion protein as described in Cukkemane et al. (28). After cell lysis, the soluble part was passed over a Glutathione Sepharose 4B column (GE Healthcare) and cleaved from the GST tag by thrombin (16 h, room temperature; GE Healthcare). To remove bound cAMP, the CNBD was denatured and subsequently renatured by rapid dilution and further purified using gel filtration (Superdex 75 pg 16/60 Hiload from GE Healthcare, in 100 mM KCl and 10 mM K phosphate, pH 7.0). Protein concentration and cAMP content were determined by absorbance measurements (ε₂₈₀ = 5500 M⁻¹ cm⁻¹ for CNBD protein; ε₂₆₀/ε₂₈₀ = 0.89 for cAMP-free CNBD).

Kinetic measurements

Kinetic experiments were performed at 20°C with a stopped-flow apparatus (SFM-400; BioLogic, Grenoble, France) equipped with a microcuvette (μFC-08; 0.8 × 0.8 mm). If not otherwise mentioned, proteins were used in respective gel filtration buffers. In all experiments, the mixing ratio was 1:1. The time delay between mixing of the solutions and observation in the cuvette of the instrument (dead-time) was determined using the decline in absorbance (524 nm) of 2,6-dichlorophenolindophenol (500 μM) after mixing with ascorbic acid (25–100 mM) (30); the dead-time was 325 μs at a flow rate of 9.5 mL s⁻¹.

Excitation light from a Xe lamp (150 W, LSB521; LOT-Oriel, Darmstadt, Germany) passed an optical filter (ET 470/40×; Chroma Technology, Bellows Falls, VT); Fluorescence (ET 525/50m; Chroma Technology) was detected by a photomultiplier (H9656-01; Hamamatsu, Hamamatsu City, Japan).

All nucleotides were from Biolog: 8-(2-[7-Nitro-4-benzofurazanyl]aminoethylthio)adenosine-3′; 5′-cyclic monophosphate (8-NBD-cAMP); 8-Bromoguanosine-3′,5′-cyclic monophosphate (8-Br-cGMP); 8-Bromoadenosine-3′,5′-cyclic monophosphate (8-Br-cAMP); and 8-(4-Chlorophenylthio)adenosine-3′,5′-cyclic monophosphate (8-CPT-cAMP).

Data analysis

Data was corrected for the dead-time of the instrument. Fluorescence was corrected for detector offset and for the fluorescence of 8-NBD-cAMP in the absence of protein. The rate constants of binding were derived from corrected fluorescence traces.

Values for k_off were derived from time-resolved competition experiments by fitting the monoexponential function

$$\left[RL\right]={\left[RL\right]}_0\times e^{-k_{\text{app}}t}$$ (1)

to the respective fluorescence traces (RL = receptor-ligand complex; [RL]₀ is the concentration at t = 0). Apparent rate constants (k_app) determined under pseudo-first-order conditions were averaged to yield k_off.

Association rate constants were derived from time-resolved binding experiments. A bimolecular reaction of a receptor R and a ligand L is described by

$$\frac{d\left[RL\right]}{dt}=k_{\text{on}}\left[R\right]\left[L\right]-k_{\text{off}}\left[RL\right],$$ (2)

where k_on and k_off represent the rate constants of association and dissociation, respectively. To solve this equation, we replaced [R] by [R]₀ – [RL] and [L] by [L]₀ – [RL], thus transforming Eq. 2 into Riccati’s equation:

$$\frac{d\left[RL\right]}{dt}=k_{\text{on}}{\left[RL\right]}^2-\left[RL\right]\left(k_{\text{on}}\left[R_0\right]+k_{\text{on}}\left[L_0\right]+k_{\text{off}}\right)+k_{\text{on}}\left[R_0\right]\left[L_0\right].$$ (3)

This differential equation can be solved using the substitution-for-multiple-variables approach and the condition [RL]_{(t = 0)} = 0. The result is

$$\left[RL\right]\left(t\right)=-\frac{{\lambda }_1\times \left[\left(e^{\left({\lambda }_1-{\lambda }_2\right)t}\right)-1\right]}{k_{\text{on}}\times \left[\left(e^{\left({\lambda }_1-{\lambda }_2\right)t}\right)-\frac{{\lambda }_1}{{\lambda }_2}\right]},$$ (4)

wherein

$${\lambda }_{1,2}=-\frac{1}{2}\left(k_{\text{on}}\left[R_0\right]+k_{\text{on}}\left[L_0\right]+k_{\text{off}}\pm \sqrt{{\left(k_{\text{on}}\left[R_0\right]+k_{\text{on}}\left[L_0\right]+k_{\text{off}}\right)}^2-4k_{\text{on}}^2\left[L_0\right]\left[R_0\right]}\right).$$

Because the formation of the receptor-ligand complex is proportional to the fluorescence change, a proportionality factor x was introduced:

$$\Delta F\left(t\right)=\left(-\frac{{\lambda }_1\times \left[\left(e^{\left({\lambda }_1-{\lambda }_2\right)t}\right)-1\right]}{k_{\text{on}}\times \left[\left(e^{\left({\lambda }_1-{\lambda }_2\right)t}\right)-\frac{{\lambda }_1}{{\lambda }_2}\right]}\right)\times x.$$ (5)

Equation 5 was used to fit time-resolved binding data by nonlinear regression. The association rate constant and ligand and protein concentrations are known. The protein concentration was determined by analyzing steady-state fluorescence amplitudes (see Fig. 1 e) (28).

Prediction of the association rate constant

To determine theoretical diffusional association rate constants of cAMP to wild-type CNBD and its R307A and R307E mutants, we used the transition-path theory approach to calculate association pathways and kinetics (29,31,32). Atomistic NMR coordinates of the CNBD domain were obtained from PDB:2KXL (19). In silico mutants R307A and R307E were created using the mutagenesis tool of the software PyMOL (0.99rc6). The protonation states of amino acids at pH 7 were determined by the software PROPKA (ver. 3.0; see Table S1 in the Supporting Material) (33). Atomic partial charges were assigned using the PDB 2PQR suite (34) with the CHARMM force field as reference. The electrostatic potential of the CNBD was calculated using the adaptive Poisson-Boltzmann solver (35), assuming dielectric constants of ε_P = 4.0 for the protein interior and ε_S = 78.0 for the solvent, an ionic strength of 120 mM, and a temperature of 298.15 K. As joint diffusion constant for protein (D = 110 μm² s⁻¹ (36)) and ligand (D = 440 μm² s⁻¹ (37)), D = 550 μm² s⁻¹ was used.

Finite volume grid points having a minimal distance to protein atoms of <3.2 Å were not taken into account in the final grid. The resulting grids had an average size of 129 × 129 × 129 points with box lengths ranging from 9 Å for distant boxes to 0.55 Å in the vicinity of the protein. For the set of free diffusing cAMP configurations (set A of states), all volume elements whose center is further away than 130 Å from the geometric center of the protein were chosen. The set B of bound/precomplex configurations was chosen to include all volume elements that are within a 2 Å radius of cAMP atoms in the bound configuration.

Results

Kinetics of cyclic nucleotide-binding to the isolated CNBD

The binding kinetics was measured using 8-NBD-cAMP, a fluorescent cAMP analog. Its fluorescence depends on the dielectric environment; fluorescence is low in aqueous solvents and high in a hydrophobic environment prevailing in a binding pocket of a protein (28,38). Thereby, 8-NBD-cAMP reports the association and dissociation of ligands to CNBDs.

To begin, we determined the rate constant of 8-NBD-cAMP dissociation (k_off). The CNBD was preincubated with 8-NBD-cAMP, resulting in a high fluorescence due to the formation of the 8-NBD-cAMP/CNBD complex. Subsequently, the complex was mixed in a stopped-flow apparatus with various cAMP concentrations (Fig. 1 b). The fluorescence declined as nonfluorescent cAMP replaced fluorescent 8-NBD-cAMP (Fig. 1 c). The decline hastened with increasing cAMP concentration. At cAMP concentrations 150-fold larger than that of 8-NBD-cAMP, the fluorescence decline did not accelerate any further, indicating that the rate constant of 8-NBD-cAMP dissociation is rate-limiting. Under these conditions, the apparent rate constant represents k_off (pseudo first-order reaction; k_off = 0.23 s⁻¹). Thus, the residence time (1/k_off) of 8-NBD-cAMP at the binding site is ∼4 s.

The association rate constant (k_on) was determined by recording the time course of the fluorescence increase after mixing of ligand-free protein with 8-NBD-cAMP (Fig. 1 d). The data was analyzed using Eq. 5 (see Material and Methods). To reduce the number of free parameters, the protein concentration was determined independently from steady-state fluorescence amplitudes (Fig. 1 e (28)). The k_on of 8-NBD-cAMP binding is 1.25 × 10⁷ M⁻¹ s⁻¹. The K_D value calculated from rate constants (K_{D, cal} = k_off/k_on = 18.4 nM) agrees well with that determined under equilibrium conditions (K_{D, eq} = 22.0 nM (28)).

Next, we measured the rate constant of cAMP binding to the CNBD (Fig. 1 f). The value for k_off was determined by mixing the preformed cAMP/CNBD complex with increasing 8-NBD-cAMP concentrations. Because nonfluorescent cAMP was replaced by fluorescent 8-NBD-cAMP, the fluorescence increased during the competition reaction. A 20-fold excess of the competing ligand (8-NBD-cAMP) was sufficient to ensure pseudo first-order kinetics. Data analysis yielded a k_off of 1.76 s⁻¹ for cAMP, a value significantly larger compared to 8-NBD-cAMP (0.23 s⁻¹). Thus, the residence time (1/k_off) of cAMP at the receptor is approximately eightfold shorter than for 8-NBD-cAMP (0.57 s vs. 4.35 s).

We calculated k_on of cAMP with k_on = k_off/K_D, using the reported K_D value (28). The association rate constant is 2.60 × 10⁷ M⁻¹ s⁻¹. In addition to extracting rate constants analytically, we used a numerical approach to determine rate constants simultaneously from all experiments using the program DynaFit (39) (see Fig. S1 in the Supporting Material). The results of the analytical and numerical approach are in excellent agreement (Table 1).

Table 1.

Summary of rate constants for the CNBD

			CNBD analytically (numerically)	CNBDR307A	CNBDR307E	CNBDK238A analytically	CNBDC331L analytically	CNBDR348A analytically (numerically)
8-NBD-cAMP	kon (107 M−1 s−1)		1.25 ± 0.20	—	—	1.03 ± 0.13	1.25 ± 0.13	1.56 ± 0.04
			(1.30 ± 0.17)	—	—	—	—	(1.60 ± 0.11)
	koff (s−1)		0.23 ± 0.01	—	—	0.48 ± 0.01	0.82 ± 0.01	123 ± 1
			(0.23 ± 0.01)	—	—	—	—	(123 ± 6)
	KD, cal		18.4 nM	—	—	46.6 nM	65.6 nM	7.9 μM
			(17.7 nM)	—	—	—	—	(7.7 μM)
	KD, lit		22.0 nM	—	—	—	—	7.3 μM
cAMP	kon (107 M−1 s−1)		2.60a	—	—	—	—	—
			(2.64 ± 0.39)	—	—	—	—	—
	koff (s−1)		1.76 ± 0.16	—	—	—	—	—
			(1.70 ± 0.02)	—	—	—	—	—
	KD, cal		—	—	—	—	—	—
			(64.4 nM)	—	—	—	—	—
	KD, lit		67.8 nM	—	—	—	—	—
Virtual ligand	−	kon (107 M−1 s−1)	7.0	4.9	2.5	—	—	5.2
	0	kon (107 M−1 s−1)	9.8	—	—	—	—	—
	+	kon (107 M−1 s−1)	12.7	—	—	—	—	—

All values are given as mean ± SD. K_{D, lit} is taken from Cukkemane et al. (28).

^aThe on-rate for cAMP binding to the CNBD could not be derived from experiments by an analytical analysis. Therefore, it was calculated from k_on = k_off/K_D.

The association rate constant depends both on the structure and the charge distribution of the binding site. Because cAMP carries negative charge, we examined the electrostatic contribution to the association process. Is there an attractive electrostatic potential that guides the ligand to the binding site (electrostatic steering (40,41)) or a repulsive potential that slows the association?

We studied the electrostatic contribution by determining the kinetics of ligand binding at different ionic strengths (I) (42). The derived rate constants are given in Fig. 2 a and Table 2. The relation between ionic strength and k_on can be described by a Debye-Hückel-like approximation (43):

$$\ln k_{\text{on}}=\ln k_{\text{on},0}-\frac{U_0}{k_{\text{B}}\cdot T}\times \frac{1}{1+\kappa a}.$$ (6)

The value U₀ is the electrostatic interaction energy in the absence of electrostatic contributions, κ is the Debye-Hückel parameter (κ = I^1/2/0.305), and a is the interaction or encounter radius (a = 1 nm). According to Eq. 6, a plot of lnk_on vs. (1+κa)⁻¹ is a linear relation allowing the extrapolation of k_on to ionic strengths I = ∞ (no electrostatic contribution, k_on,0) and I = 0 (maximal electrostatic contribution, k_on,∞) (Fig. 2 b). U₀ adopts a value of −0.85 kcal mol⁻¹, k_on,0 = 0.6 × 10⁷ M⁻¹ s⁻¹, and k_on,∞ = 2.5 × 10⁷ M⁻¹ s⁻¹ (Table 2). Compared to other proteins (44–47), this is only a minor electrostatic contribution to k_on.

Figure 2.

Electrostatic contributions to the kinetics of ligand binding to the CNBD. (a) Rate constants at different ionic strength (Table 2). (b) Extrapolation of k_on at ionic strengths I = ∞ (k_on,0) and I = 0 (k_on,∞) as described in the main text (κ Debye-Hückel parameter, a interaction or encounter radius). Ionic strength of respective data points (shown in gray). (Red line) Fit of Eq. 6 to the data. (Solid circles) Experimental association rate constants (U₀/(k_BT) = 1.47, U₀ = −0.86 kcal mol⁻¹, k_on,0 = 0.6 × 10⁷ M⁻¹ s⁻¹, and R² = 0.8643). (Open circles) Computed association rate constants (U₀/(k_BT) = −1.07, U₀ = 0.62 kcal mol⁻¹, k_on,0 = 11.3 × 10⁷ M⁻¹ s⁻¹, and R² = 0.9773).

Table 2.

Electrostatic contribution to the kinetics of ligand binding to the CNBD

cAMPb	[I] (mM)	0	21	71	121	221	321	∞
	kon (107 M−1 s−1)	3.9a	5.5	6.2	7.0	7.4	7.8	11.3a
8-NBD-cAMP	kon (107 M−1 s−1)	2.5a	1.53 ± 0.16	1.21 ± 0.11	1.25 ± 0.20	1.05 ± 0.16	0.89 ± 0.07	0.6a
	koff (s−1)	—	0.27 ± 0.01	0.23 ± 0.01	0.23 ± 0.01	0.20 ± 0.01	0.20 ± 0.01	—
	KD, cal	—	17.6 nM	19.0 nM	18.4 nM	19.0 nM	22.5 nM	—
	KD, lit	—	—	—	22.0 nM	—	—	—

All values are given as mean ± SD. K_{D, lit} is taken from (28).

^aExtrapolation as described in the Results.

^bModeled as charged sphere.

A computational model predicts the association rate constant

The experimental k_on values for cAMP and 8-NBD-cAMP (Table 1) are two orders-of-magnitude smaller than the Smoluchowski diffusion limit (4 × 10⁹ M⁻¹ s⁻¹), which we calculated using the diffusion coefficient of cAMP (440 μm² s⁻¹); an estimated diffusion coefficient of the CNBD protein (110 μm² s⁻¹); and an encounter radius of 1 nm (36,37,48–50). We explored why the association process is slowed down. In general, a binding event can be divided into the transport reaction and the chemical reaction (51). We studied which of the two reactions is rate-limiting using a computational model that considers the entire ensemble of association pathways (29).

The model considers both the electrostatic potential of protein and ligand and the structure of the protein. We used the solution structure of the isolated CNBD in the apo form (19). The cAMP molecule was treated as a negatively charged sphere. The calculated k_on was 7.0 × 10⁷ M⁻¹ s⁻¹, i.e., 60-fold smaller than the Smoluchowski approximation, but still threefold larger than the experimental k_on (2.6 × 10⁷ M⁻¹ s⁻¹). The relatively small remaining difference between calculated and experimental rate constants might be attributed to either the structural features of the ligand or the chemical reaction, i.e., removal of water molecules and structural alignment of the binding partners.

Using the computational model, we studied the electrostatics of the protein-ligand interaction in more detail.

We varied the electrostatics by using virtual ligands with different charge. A neutral ligand reveals the effect of structure on the association rate constant. The k_on value is slightly larger for a neutral ligand (9.8 × 10⁷ M⁻¹ s⁻¹) compared to the native ligand. Thus, in the absence of electrostatic interactions, the association process is still slow—indicating that primarily structural constraints are responsible for the small k_on. For a positively charged ligand, the k_on increased further to 12.7 × 10⁷ M⁻¹ s⁻¹ (Fig. 3, a–c, Table 1).

Figure 3.

Two arginine residues contribute to high binding affinity of the CNBD. (a) Interaction of R307 and R348 with cAMP (PDB:2K0G). (b) Electrostatic potential maps of the CNBD (PDB:2KXL) representing the ±0.2 k_BT/e potential. (c) Structural model of apo CNBD (PDB:2KXL). (Left panel) Cartoon of the apo CNBD. R307 and R348 (ball-and-stick model). (Middle panel) Electrostatic potential map. Negative and positive charges (red and blue), respectively. Scale is from −3 k_BT/e to +3 k_BT/e. (Right panel) Streamlines represent the flux of the ligand toward the binding site. The lighter the color, the stronger the flux.

In addition, we performed in silico mutagenesis of a key arginine residue (R307) in the phosphate-binding cassette of the CNBD that is crucial for ligand binding (Fig. 3 a) (28,52). Does this residue co-determine the association rate constant? We calculated k_on for two amino-acid substitutions at this position. Neutralizing the charge by replacing arginine with alanine reduced k_on from 7.0 × 10⁷ M⁻¹ s⁻¹ to 4.9 × 10⁷ M⁻¹ s⁻¹. Inverting the charge by replacing arginine with glutamate, reduced k_on even further to 2.5 × 10⁷ M⁻¹ s⁻¹ (Table 1). This result indicates that although R307 provides the major energetic interaction with the ligand, it only moderately contributes to the association kinetics.

Furthermore, we computed association rate constants for the protein-ligand interaction at different ionic strengths (Table 2, Fig. 2 b, open circles). Values for k_on vary from 5.5 × 10⁷ M⁻¹ s⁻¹ (at an ionic strength of 21 mM) to 7.8 × 10⁷ M⁻¹ s⁻¹ (at an ionic strength of 321 mM). Again, k_on values in the presence and absence of ionic interactions were extrapolated by Eq. 6: k_on,0 = 11.3 × 10⁷ M⁻¹ s⁻¹ and k_on,∞ = 3.9 × 10⁷ M⁻¹ s⁻¹ (Table 2). To conclude, the association rate constant for a neutral ligand (k_on = 9.8 × 10⁷ M⁻¹ s⁻¹) matches k_on,0. The difference between computed and measured rates is always within one order of magnitude, which is the expected computational accuracy. The small existing trend in k_on depending on ionic strength has different directions in simulation and experiment, most likely due to fundamental inaccuracies of the computational charge assignment (see Discussion).

Mutational analysis reveals the mode of cyclic nucleotide-binding

According to Weikl and von Deuster (24), the analysis of allosteric mutants can reveal the binding mode of a ligand-receptor pair. We studied two allosteric mutants, K238A, located between helices A and A′ (Fig. 4 a), and C331L, located at the junction between helices B and C (Fig. 4 b). Both sites are not expected to interfere directly with binding of the ligand. However, they might be involved in the conformational change between resting and activated state. We studied the kinetics of both mutants by stopped-flow experiments. Whereas the association rate constants of both mutants were similar to that of the wild-type (Table 1), the dissociation rate constants differed by ∼2- and 3.5-fold, respectively (Table 1). We conclude that according to the simple four-state model (Fig. 1 a), ligand binding to the CNBD follows an induced-fit mechanism.

Figure 4.

Kinetics of allosteric mutants reveals the binding mode. (a) Kinetics of ligand binding to the isolated CNBD^K238A. Results of the analysis are given in Table 1. (Upper panel) Location of K238 in the CNBD. (Middle panel) CNBD^K238A (2 μM), preincubated with 8-NBD-cAMP (1.5 μM), was mixed with various cAMP concentrations (2.5–1500 μM). A monoexponential function was fitted to the data (gray). (Lower panel) CNBD^K238A (2.5 μM) was mixed with various concentrations of 8-NBD-cAMP (0.1–5 μM). Equation 5 was fitted to the data (gray). The k_off and the ligand and protein concentrations were fixed parameters; the protein concentration was determined from the analysis of the steady-state amplitudes in accord with Fig. S2a (28). (b) Same as panel a for CNBD^C331L. (Upper panel) Location of C331L in the CNBD. (Middle panel) CNBD^C331L (2.5 μM), preincubated with 8-NBD-cAMP (2 μM), was mixed with various cAMP concentrations (2.5–1500 μM). (Lower panel) CNBD^C331L (2.5 μM) was mixed with various 8-NBD-cAMP concentrations (0.1–5 μM). The k_off and the ligand and protein concentrations were fixed parameters; the protein concentration was determined from the analysis of the steady-state amplitudes in accord with Fig. S2b (28).

In addition, we studied the rate constants of a mutant (R348A) in the C helix of the CNBD. R348 interacts with the purine ring of the cyclic nucleotide, thus forming part of the binding site. Replacing R348 with alanine decreases the binding affinity roughly 300-fold (28) (Table 1). We were interested in this mutant, because movement of the C helix toward the ligand represents one of the major conformational rearrangements after ligand binding (17–19,53). We compared the kinetics of wild-type (Fig. 1) and R348A CNBDs (Fig. 5). Again, the association rate constants of the mutant and the wild-type are virtually identical (1.56 × 10⁷ M⁻¹ s⁻¹ vs. 1.25 × 10⁷ M⁻¹ s⁻¹, Table 1). In contrast, the dissociation rate constant is increased by more than two orders of magnitude in the mutant (123 s⁻¹ vs. 0.23 s⁻¹).

Figure 5.

The low-affinity mutant CNBD^R348A. (a) Cartoon of the in silico mutant CNBD^R348A. (b) Time-resolved binding experiment with CNBD^R348A (5 μM) mixed with various concentrations of 8-NBD-cAMP (0.2–20 μM). Only 0.2–4.2 μM quantities of 8-NBD-cAMP were considered for the analysis. Equation 5 was fitted to the data (gray). The k_on and k_off were extracted from this data set. Analysis of steady-state amplitudes allowed us to assess the precise protein concentration (see Fig. S2c) (28). This concentration was used as a fixed parameter in the kinetic analysis. (c) Electrostatic potential map. Negative (red) and positive (blue) charges. Scale is from −3 k_BT/e to +3 k_BT/e. (d) Streamlines represent the flux of the ligand toward the binding site. The lighter the color, the stronger the flux.

Therefore, the large change in the k_off constant is responsible for the lower affinity of the CNBD^R348A mutant (Table 1). We studied by circular dichroism spectroscopy whether the conformational changes observed in the CNBD protein still occur in the R348A mutant. The changes in the circular dichroism spectra upon cAMP binding are much smaller in the mutant compared to the wild-type CNBD (see Fig. S3), indicating that, in the mutant, the apo conformation predominates in the structural ensembles. Conformational changes, if they occur, are only short-lived. We also calculated k_on for the R348A mutant by analyzing the transition path of cAMP (Fig. 5, c and d). The association rate constants of mutant and wild-type CNBDs are very similar (5.2 × 10⁷ M⁻¹ s⁻¹ vs. 7.0 × 10⁷ M⁻¹ s⁻¹), confirming the experimental result.

Taken together, the results of the allosteric mutants and the kinetic behavior of the R348A mutant illustrate the mechanism of cAMP binding: The ligand binds to the apo CNBD and induces a conformational change involving a movement of the C helix that closes like a lid over the CNBD. R348 then forms a favorable interaction with cAMP that strongly stabilizes the bound conformation.

Kinetics of ligand binding to the CNBD in the full-length channel

The K_D values of ligand-binding to the isolated CNBD and the full-length channel are virtually identical (28). We sought an explanation for this surprising result by studying the binding kinetics of the full-length channel (Fig. 6). The MlCNG channel protein solubilized in detergent micelles was incubated with 8-NBD-cAMP to form the ligand-receptor complex. Subsequently, k_off of 8-NBD-cAMP binding was assessed by mixing the complex with cAMP or other nonfluorescent cNMP analogs (8-Br-cGMP, 8-Br-cAMP, or 8-CPT-cAMP) (Fig. 6 a). The competing ligands were used in at least 500-fold excess, i.e., pseudo first-order conditions were ensured. In contrast to the isolated CNBD, the fit of the fluorescence decay requires two exponentials rather than one (Fig. 6 a inset; see Fig. S4). The rate constant of the major (86%) slow component is well defined (0.070 s⁻¹) (Fig. 6 b), whereas the minor (14%) faster component (0.47 s⁻¹) shows a large fluctuation margin (Fig. 6 b, Table 3, and see Fig. S2). Neither component is identical to k_off of the isolated CNBD.

Figure 6.

Kinetics of ligand binding to the full-length, solubilized MlCNG protein. (a) MlCNG (2.5 μM), loaded with 8-NBD-cAMP (1 μM), was mixed with various concentrations of cAMP (0.5–2 mM: blue, 1.25 mM; red, 2.5 mM), 8-Br-cGMP (1.25–6 mM: light green, 3 mM; pink, 6 mM), 8-Br-cAMP (1.25–6 mM: dark green, 6 mM), or 8-pCPT-cAMP (0.5–2.5 mM: yellow, 2.5 mM). (Inset) A biexponential function (red) was fitted to the data (black; 2.5 μM MlCNG, 1 μM 8-NBD-cAMP, 2.5 mM cAMP). (b) Analysis of fast and slow rate constants and their relative amplitudes. (c) The MlCNG protein (2.5 μM) was mixed with 8-NBD-cAMP (0.1–5 μM). Equation 5 was fitted to the data (gray). Furthermore, analysis of steady-state amplitudes allowed us to assess the precise protein concentration. The equation can be found in Cukkemane et al. (28). This concentration was used as a fixed parameter in the kinetic analysis. (d) Analysis of steady-state amplitudes of binding (28) as shown in panel c to derive the protein concentration ([MlCNG] = 1.5 μM; R² = 0.9908).

Table 3.

Summary of rate constants for the full-length mlCNG channel

		MlCNG channel		MlCNG channel
		Analytically—CNG buffer		Analytically—CNBD-like buffer
		Major (86%)	Minor (14%)	Major (80%)	Minor (20%)
8-NBD-cAMP	kon (107 M−1 s−1)	0.50 ± 0.12		0.50 ± 0.10
	koff (s−1)	0.070 ± 0.008	0.47 ± 0.27	0.060 ± 0.015	0.43 ± 0.29
	KD, cal	14.0 nM	94.0 nM	12.0 nM	86.0 nM
	KD, lit	15.9 nM	—	—	—

CNBD-like buffer is CNBD gel filtration buffer with 5 mM DM. All values are given as mean ± SD. K_{D, lit} is taken from Cukkemane et al. (28).

The association rate constant was determined by rapidly mixing the MlCNG channel protein with 8-NBD-cAMP. Only a single component is observed and k_on, calculated according to Eq. 5, is 0.5 × 10⁷ M⁻¹ s⁻¹, even lower than that of the isolated CNBD (Fig. 6 c). The association rate constant and the major component of k_off precisely predict the K_D value determined for the full-length channel under equilibrium conditions (K_{D, cal} = 14.0 nM; K_{D, eq} = 15.9 nM). Moreover, the equilibrium amplitudes of the time-resolved binding signal are well described by a simple binding isotherm (Fig. 6 d). Thus, the second component is not observed under equilibrium conditions.

Because experiments with the MlCNG channel and the CNBD were done in different buffers, we repeated the experiments with the MlCNG protein in a CNBD-like buffer supplemented with 5 mM DM to solubilize the MlCNG in detergent micelles. The results for the two different buffers are very similar (Table 3, and see Fig. S5). We also recorded the rates for the MlCNG protein with cAMP. The derived dissociation rate constant(s) only provides an upper estimate, because the inner filter effect of the competing ligand prevented a more precise characterization (see Fig. S6). According to this data set, k_off is smaller than 0.2 s⁻¹ (see Fig. S6). The respective estimated k_on is 0.3 × 10⁷ M⁻¹ s⁻¹. Both rate constants are significantly smaller than those of the isolated CNBD.

The observation that the full-length channel exhibits two different dissociation rate constants is not straightforward to interpret, because functional studies of the MlCNG channel are sparse (54). Whether gating rearrangements take place in the detergent-solubilized channel is not known. Therefore we cannot correlate the kinetic data with channel gating. One interpretation could be that the different rate constants reflect different activation states of the channel. Alternatively, a small fraction of the solubilized MlCNG might exist in an impaired conformation. Future work is necessary to distinguish between the two interpretations.

Discussion

Here, we studied the kinetics and mode of ligand binding for a CNBD. We gained several insights into the activation mechanism of CNBDs and observed indications for an allosteric control of the CNBD by the transmembrane region of the MlCNG.

Allosteric control of the CNBD by the transmembrane region of the MlCNG channel

Studying equilibrium binding, we gained similar K_D values for the MlCNG channel (15.9 nM) and the isolated CNBD (22.0 nM) (28). This finding is unexpected, because the energetic requirements for gating of the pore are absent in the isolated CNBD. Here, we provide an explanation for this surprising result. The respective rate constants of binding and unbinding are considerably smaller for the full-length channel compared to the isolated CNBD; however, their ratios (i.e., the K_D values) become fortuitously similar. Our kinetic data supports the idea that the binding sites in the full-length CNG channel and the isolated CNBD are structurally distinct. Thus, both proteins have their own dynamic-personality. The association rate constant in the full-length channel is probably slowed down, because the tetrameric channel embedded in a detergent micelle has a higher molecular mass than the monomeric CNBD. As a consequence, the diffusion constant is smaller than that of the nonsolubilized CNBD (55). The smaller k_off constant indicates an allosteric control of the CNBD by the pore or the transmembrane region, because it is independent of diffusion.

A slower k_off, as observed here for the MlCNG channel, could be physiologically important. It implies a longer residence time of the ligand at the binding site, i.e., in the absence of desensitization, the channel could stay open for a longer time (56,57). Most likely, the structures of the isolated CNBD and the CNBD in the channel are somewhat different. When tethered to the membrane-spanning part of the channel, CNBDs might interact with each other, as proposed for HCN channels (58), or they might be sensitive to the activation state of the transmembrane region of the protein. Due to the lack of functional data for MlCNG, we can only speculate about the underlying reasons by comparison with related channels that have been functionally characterized. One example is a mutation (T369S) located within the selectivity filter of the CNGA3 channel of photoreceptors. This mutation, although remote from the CNBD, lowers the ligand sensitivity almost fivefold (59), suggesting that changes in the pore structure propagate to the CNBD. Another example is the intimate coupling of voltage gating and cAMP modulation in HCN2 channels. Activation of HCN2 by hyperpolarization increases the sensitivity of the binding domain for cAMP, whereas during depolarization, the cAMP sensitivity decreases (60).

If binding sites in a tetramer become nonequivalent due to allosteric interaction of subunits, several distinct dissociation rate constants are expected. In fact, for the full-length channel, two distinct dissociation rate constants are observed that differ by approximately sevenfold. We can only speculate about the significance of this finding. The two components might reflect dissociation of ligands from different activation states in the tetramer, arguing for allosteric control of binding by other regions in the channel. Alternatively, in detergent solution, the channel protein might be slightly inhomogeneous. The large dispersion of the minor component could indicate such an inhomogeneity.

Classical CNG channels form heteromers composed of distinct subunits that are cooperatively activated by ligands (1,2). Although the binding constants for individual subunits in a heteromer have not yet been determined, models suggest both positive and negative cooperativity of binding (61). It will be interesting to study the kinetics of ligand binding in classical CNG channels whose binding sites might be nonequivalent due to heteromeric composition and cooperativity among subunits.

Kinetics of association can be predicted by transition-path theory

For the isolated CNBD, k_on adopts a value of 1.25 × 10⁷ M⁻¹ s⁻¹ for the fluorescent cAMP analog and 2.60 × 10⁷ M⁻¹ s⁻¹ for cAMP. These values are similar to those determined for EPAC using another fluorescent ligand (0.6–1 × 10⁷ M⁻¹ s⁻¹) (38). The k_on for both the isolated CNBD and the full-length channel is two orders-of-magnitude smaller than predicted, if the diffusion according to Smoluchowski happened to be rate-limiting (49,50,62). Such large discrepancies have been noted quite frequently, and have mostly been attributed to the simplicity of the model (62). For example, the Smoluchowski approximation treats binding partners as uniformly reactive spheres and, evidently, the discrepancies are due to this simplification. Therefore, more ambitious geometries were considered that result in more realistic rate constants (50). Only recently, a computational model was introduced that, based on high-resolution structures, systematically analyses the full ensemble of possible association pathways (29). This computational model predicts the experimental association rate constants with great precision and, therefore, shows that the observed association rate constants of ligand binding to the CNBD are largely diffusion-limited. The residual difference between theoretical and experimental values might be accounted for by treating cAMP as a sphere or neglecting its solvation (63).

The association rate has only a minor electrostatic component

Electrostatics affects the association rate constant in a weak manner. The k_on is enhanced only fourfold by electrostatic steering, which is very little compared to other binding reactions (45–47): A strong electrostatic steering might increase k_on up to 60,000-fold as observed for the interaction of barnase and barstar (44). The computational model agrees with experimental results in that the effect of ionic strength on k_on is small. However, the computational model predicts an opposite trend compared to experiment, where k_on increases with ionic strength. This difference might be explained by inaccuracies in the definition of atomic charges in the computational model. The protonation state in the computer model was assigned based on the calculated pK_a values shown in Table S1. We have validated that protonation of the sole histidine (H 323) does not significantly affect the result. However, the protonation state of each residue cannot be characterized by a single pK_a value, but depends on the momentary conformation and the protonation states of all other residues.

As of this writing, it is impossible to model such a complex scenario with precision to achieve an order-of-magnitude agreement between the computed and measured rates. Regarding the CNBD, we conclude that k_on is primarily limited by geometric constraints imposed by the CNBD structure, although there is also a small electrostatic contribution. To visualize the charge distribution, we plotted the electrostatic iso-surfaces of the wild-type CNBD at ±0.2 kT/e (Fig. 3 b) resulting from charged residues located on the surface of the CNBD. The binding site is indicated by an arrow. It is immediately apparent that, on top of the mouth of the binding site, there exists a cluster of negatively charged residues producing a repulsive potential. However, adjacent to this cluster, there exists a region with positively charged residues that will attract the cAMP molecule. The weak effect of electrostatics suggests that the negative and positive patches almost counterbalance each other.

Binding mode revealed

Mutational analysis is a simple and general approach to unravel the binding mode. The observation that two allosteric mutations, kinetically, have an effect exclusively on the dissociation rate constants, suggests that cAMP binding proceeds along an induced-fit mechanism (24). This conclusion is supported by the NMR solution structure of the apo and holo states of the CNBD. For each of these states, only a single conformation is observed (19,53). Thus, our study shows that mutagenesis combined with kinetic techniques provides a simple, yet powerful tool to disclose the binding mode.

The induced-fit mechanism allows some insight regarding the activation of the CNBD: In the apo form, only the ground-state (G) of the CNBD is observed. After the initial contact with its ligand, i.e., during formation of the encounter complex, the CNBD undergoes the structural transition to the active conformation (AL). The conformational changes upon cAMP binding along the induced-fit mechanism can be viewed as a type of switch that allows tight control of the effector domain (Fig. 1 a). Effector domains are located either N- or C-terminally of the CNBD on the same polypeptide and are structurally and functionally as diverse as a pore region, a catalytic kinase domain, or a DNA-binding domain. Considering this diversity, how general is the induced-fit mechanism, and how tight is the regulation of effector domains by cyclic nucleotides?

For the CAP protein, a picture has emerged that is as simple and clear as for the MlCNG channel (64–66). The apo and the holo forms of dimeric CAP and its isolated CNBD both exist in a single conformation (64). Moreover, protein motions, in the microsecond-to-millisecond range required for structural transitions between conformers, are suppressed in the apo form (64,65), demonstrating that activation of CAP also proceeds along an induced-fit mechanism. Interestingly, the negative cooperativity observed for the binding of a second cAMP to CAP is due to strongly enhanced structural dynamics, i.e., entropic contributions rather than a change in the mean three-dimensional structure. CNG channel activation involves both positive and negative cooperativity of binding (61). Considering that ligand binding in CAP and CNG channels proceeds along an induced-fit mechanism, negative cooperativity in CNG channels might be governed by entropic contributions as well.

The situation for EPAC appears to be more complex. In NMR spectra of a truncated EPAC construct in the apo form, some residues display chemical shifts similar to those of the active holo form, arguing for a conformational-selection mechanism (67). Moreover, NMR studies reveal substantial dynamics in the microscond time-range, consistent with transitions between different conformers of the apo form. These residues are predominantly located in the N-terminal helical bundle; however, N- or C-terminal segments are known for their enhanced flexibility (19). Also, the full-length apo form is inactive (18), arguing for a tight regulation of the effector domain, i.e., the active conformers in the apo form are not populated.

We show that cAMP binding follows an induced-fit mechanism. This offers the unique opportunity to identify the sequence and time-course of conformational rearrangements that occur after ligand recognition. Techniques that allow spatio-temporal resolution of conformational events are, e.g., infrared spectroscopy (68) and electron paramagnetic resonance spectroscopy (69). These techniques might provide a first glimpse at the conformational landscape of the dynamic binding event.