Solid-State Deuterium NMR Spectroscopy of Rhodopsin

Abstract

Rhodopsin is a prototype for the large Family A of G-protein–coupled receptors (GPCRs). These proteins regulate many signaling processes, and more than 35% of human pharmaceuticals are targeted against diseases related to dysfunctions of GPCR pathways. Membrane proteins such as GPCRs are challenging to crystallize for X-ray studies. In addition, their effective molar masses in detergent solutions push the limits for solution NMR spectroscopy. By contrast, solid-state NMR allows both the structure and dynamics of membrane proteins to be investigated in a natural lipid bilayer environment. Here, we describe solid-state ²H NMR methods for investigating structural and dynamical changes of the retinylidene cofactor of the GPCR rhodopsin upon photoillumination. Rhodopsin was regenerated with retinal containing ²H-labeled C5-, C9-, or C13-methyl groups. The receptor was recombined with phospholipid membranes, which were aligned on planar glass slides. The angular dependences of the ²H NMR spectra and the corresponding relaxation rates were measured for rhodopsin in the dark and in the cryo-trapped, preactive Meta-I and active Meta-II states. Analysis of the ²H NMR lineshapes using a static uniaxial distribution yields orientational restraints for the retinylidene conformation when bound to the protein. Solid-state ²H NMR relaxation data provide additional information on the motion of the bound cofactor. The structural and dynamical changes of retinal reveal how its functional groups (methyl groups and the β-ionone ring) affect rhodopsin light activation, and illustrate the opportunities of solid-state ²H NMR spectroscopy in studying membrane proteins.

Membrane proteins comprise about one-third of the human genome and are responsible for regulating a variety of crucial cellular functions. Transport of proteins, small molecules, and ions across the membrane, reception of external stimuli and cellular signaling, membrane enzyme activity, and involvement in immune system function are among the crucial roles played by membrane proteins. Their location within biological membranes presents the greatest challenge limiting the techniques that can be used for studying such proteins [1]. For instance, the large size of the membrane proteins makes it difficult to use solution NMR spectroscopy; and growing high-quality membrane protein crystals as required for X-ray crystallographic studies is problematic. Advanced magnetic resonance techniques such as solid-state NMR spectroscopy thus become necessary for studying membrane proteins in a native-like lipid bilayer environment. Here, we present an application of solid-state NMR methods to membrane proteins using the visual receptor rhodopsin as the example.

Rhodopsin is the G-protein–coupled receptor responsible for the scotopic (dim light) vision of vertebrates. The chromophore 11-cis retinal acts as an inverse agonist, and locks the rhodopsin in the dark-state conformation. Following light absorption, it isomerizes to the all-trans form, releasing two ionic locks and rearranging hydrogen bonds that lead to movements of the transmembrane helices of the protein, yielding active rhodopsin. Clearly, the retinal chromophore is pivotal for maintaining the rhodopsin structure as well as its function. The temporal sequence of the photointermediates occurring during rhodopsin activation is illustrated in Fig. 1 [2, 3]. Most of these spectroscopically defined photointermediates are yet to be fully characterized, due to their transient nature, and they are trapped under various conditions such as temperature, pH, and lipid composition. The cognate G-protein of rhodopsin, transducin (G_t), is activated by the Meta-II state. The equilibrium between the inactive Meta-I and the active Meta-II species depends on hydration, pH, and the lipid bilayer composition, allowing these metastable species to be studied by varying the above conditions. Magnetic resonance methods such as electron paramagnetic resonance (EPR) [4], solid-state ¹³C NMR [5,6,7,8,9,10,11,12], and solid-state ²H NMR spectroscopy [13,14,15,16,17,18] together with X-ray techniques [19, 20] reveal crucial information about these intermediates in the activation of rhodopsin. Here, we review the use of solid-state ²H NMR spectroscopy to probe the structural and dynamical changes associated with rhodopsin activation in a natural lipid bilayer environment.

Fig. 1

Light activation of rhodopsin involves a time-ordered sequence of photointermediates. The photoillumination of rhodopsin leads to the isomerization of 11-cis retinal to all-trans retinal that in turn triggers changes in the protein structure. Activated rhodopsin occurs through a series of transient intermediates with a lifetime typically orders of magnitude greater than the preceding one. Dark-state rhodopsin goes through photorhodopsin, bathorhodopsin, blue-shifted intermediate (BSI), and lumirhodopsin, leading to equilibrium between inactive Meta-I and active Meta-II. Eventual release of all-trans retinal from Meta-II yields the apoprotein opsin. The active Meta-II form consists of an ensemble of states; Meta-II _a , Meta-II _b , and Meta-II _b H⁺ substates as explained by an ensemble activation mechanism (Ref. [2])

Structural Studies of Rhodopsin Using Solid-State Deuterium NMR Spectroscopy

Site-directed deuterium labeling of the retinal allows one to probe specific groups of the activating ligand. For these experiments, retinal is synthesized with ²H-labeled methyl groups at positions C5, C9, or C13, namely (11-Z-[5-C²H₃]-retinal, 11-Z-[9-C²H₃]-retinal, or 11-Z-[13-C²H₃]-retinal) [17]. The deuterated retinal is incorporated into the binding pocket of opsin. The regenerated rhodopsin is then recombined with synthetic phospholipids to produce a native-like environment to study the structure and dynamics of the chromophore in various states of the receptor [16–18]. Isotopic labeling of each methyl group of 11-cis retinal allows one to probe different regions of the binding cavity, and identify changes during the activation of rhodopsin.

The chemical structure of 11-cis retinal (with the carbon atoms numbered) covalently bound to Lys²⁹⁶ of helix 7 (H7) of rhodopsin is provided in Fig. 2a. Illustrative deuterium NMR spectra of rhodopsin containing retinal with deuterated methyl groups at various positions (C5, C9, and C13) in POPC lipid membranes are shown in Fig. 2b–f. Aqueous dispersions of the recombinant membranes (unaligned) yield powder-type deuterium NMR spectra, where the Pake formula, Eq. (1) as explained in Ref. [21], is used for spectral simulation:

$$ \left|p\left({\xi}_{\pm}\right)\right|\propto \frac{1}{\left|\cos \tilde{\theta}\right|}\propto \frac{1}{\sqrt{1\pm 2{\xi}_{\pm }}} $$

(1)

Fig. 2

Deuterium-labeled 11-cis retinal bound to dark-state rhodopsin in unaligned membranes yields powder-type ²H NMR spectra showing rapid rotation of methyl groups. (a) The 11-cis retinal ligand with the backbone carbon atoms numbered. (b, c) Deuterium NMR spectra of ²H-labeled methyl groups at C5 (yellow) and C13 (red) carbon positions, respectively, of 11-cis retinal in rhodopsin in unaligned POPC lipid membranes (molar ratio 1:50) at T = −100 °C. (d–f) Deuterium NMR spectra of ²H-lableled C9-methyl group of 11-cis retinal bound to rhodopsin in gel-phase POPC lipid membranes at T = −30, −60, and −150 °C, respectively. The continuous-color lines superimposed on the experimental spectra are calculated assuming axial rotations of the methyl groups

In the above formula p(ξ_±) is the probability density, where ξ_± ɛ [∓½, ±1] is the reduced frequency for each of the two spectral branches, and $\tilde{\theta}$ is the overall angle of the C–C²H₃ bond axis to the main B ₀ magnetic field.

Use of the Pake formula and the spectral simulation provide the following information. The motion-averaged ²H NMR lineshapes yield residual quadrupolar couplings (RQCs) of 〈χ_Q〉 = 50.7–52.0 kHz. The occurrence of rapid spinning of the retinylidene methyl groups about their threefold axes is thus established, with rotational correlation times <10⁻⁵ s down to about −160 °C. Methyl-group order parameters of ${S}_{C_3}\approx 0.9$ are measured directly from the RQCs, amounting to ≈15° off-axis fluctuations. The dynamics entail methyl rotations with respect to the unsaturated polyene chain and the β-ionone ring, plus their reorientations within the binding pocket.

By aligning the POPC membranes containing rhodopsin on planar substrates, one can determine the average orientation of the C–C²H₃ bond axis (principal axis of ²H quadrupolar coupling tensor, parallel to methyl threefold axis due to fast spinning) versus the membrane normal frame. The experimental arrangement (Fig. 3) entails a stack of supported membranes including rhodopsin with retinal ²H-labeled at the C5-, C9-, or C13-methyl groups. Rhodopsin is shown by the seven transmembrane helices (Fig. 3). At top right, the retinylidene ligand is depicted to illuminate the structure calculation (Fig. 3). A static uniaxial distribution is assumed, and the orientation θ_B of the C–C²H₃ bond axis to the local membrane frame is established by calculating the ²H NMR lineshape versus the tilt angle θ between the average membrane normal n ₀ and the main magnetic field B ₀ (tilt series). For aligned samples, the simulation parameters entail the C–C²H₃ bond orientation, the residual coupling 〈χ_Q〉, the mosaic spread σ, and the intrinsic line broadening.

Fig. 3

Conformation and orientation of retinylidene ligand of rhodopsin are accessible by solid-state ²H NMR spectroscopy of aligned membranes . Left: schematic depiction of stack of aligned membranes containing rhodopsin within the radiofrequency coil of the NMR spectrometer, showing the geometry relative to the magnetic field. Center: the seven transmembrane helices of rhodopsin are denoted by yellow ribbons, with the N-terminus above (extracellular side) and C-terminus below (cytoplasmic side). Right: for an individual methyl group, θ_B is angle of the C–C²H₃ bond direction to the local bilayer normal n, with a static uniaxial distribution given by the azimuthal angle ϕ. The mosaic spread (alignment disorder) is described by the angle θ^′ of n to the average membrane normal n ₀ , and is uniaxially distributed as given by ϕ′. The tilt angle θ is from n ₀ to the main magnetic field B ₀ about which there is cylindrical symmetry. Finally, θ″ is the angle from n to B ₀ where ϕ″ is the azimuthal angle. The overall angle of the C–C²H₃ bond axis to B ₀ is denoted as $\tilde{\theta}$. Retinal is shown in the flipped all-trans conformation as indicative of the active Meta-II state

Solid-state ²H NMR spectra in the dark state acquired at T = −150 °C are shown (Fig. 4a) for aligned rhodopsin/POPC (1:50) bilayers, with retinal ²H-labeled at the C5-, C9-, or C13-methyl groups, respectively. The results (Fig. 4a) were obtained for the θ = 0° orientation of the membrane normal to the magnetic field B ₀ , where the lineshape is very sensitive to the methyl group orientation (θ_B). Similar experiments were conducted at temperatures of T = −60 and −30 °C. Notably, the solid-state ²H NMR spectra reveal only a minor temperature variation over a broad interval of 120 °C. Theoretical simulations are overlaid on the experimental ²H NMR data, and C–C²H₃ bond orientations of 70 ± 3°, 52 ± 3°, and 68 ± 2° are found for the C5-, C9-, and C13-methyl groups of retinal in the rhodopsin dark state [16]. The data are explained by the average bond orientations and torsion angles of the retinylidene ligand bound to rhodopsin. Accurate bond orientations of the ²H-labeled methyl groups are determined, despite the appreciable alignment disorder (mosaic spread σ = 18–21°). Values for the alignment disorder are greater than in earlier studies of purple membranes containing bacteriorhodopsin [22], which may be due to rhodopsin (M_r = 40 kDa) being a larger molecule, together with the additional extramembranous regions [23]. These values differ from earlier work [24, 25]; yet they correspond well with X-ray studies of single rhodopsin crystals [26, 27].

Fig. 4

Retinal structure in rhodopsin dark state and preactive Meta-I state is established by solid-state ²H NMR spectroscopy. (a) Solid-state ²H NMR spectra for 11-cis retinal in dark state of rhodopsin provide methyl bond orientations and disorder in aligned membranes. Examples of ²H NMR spectra are shown for 11-Z-[5-C²H₃]-retinylidene rhodopsin, 11-Z-[9-C²H₃]-retinylidene rhodopsin, and 11-Z-[13-C²H₃]-retinylidene rhodopsin, respectively. Data are included for rhodopsin/POPC bilayers (1:50) at θ = 0° alignment of membrane normal to the main magnetic field B ₀ at pH = 7 and T = −150 °C. (b) Illustration of simple three-plane model with dihedral twisting solely about C6–C7 and C12–C13 bonds. The retinal conformation is indicated by three planes of unsaturation (designated A, B, C). (c) Extended three-plane model with added pretwisting about C11=C12 double bond. (d) Solid-state ²H NMR spectra are shown of retinal in preactive Meta-I state for θ = 0° orientation of membrane normal to B ₀ at pH 7 and T = −150 or −100 °C. (e) Orientations of methyl groups and electronic transition dipole moment define orientations of the planes of unsaturation; two of the four possible solutions are indicated in each case. (f) Examples of possible structures for retinylidene ligand with Schiff base linkage to Lys²⁹⁶ of rhodopsin. Note that different ²H NMR structures for retinylidene ligand are distinguished using rotational resonance ¹³C NMR carbon–carbon distances (see text). The extracellular side of rhodopsin is above and the cytoplasmic side below (Adapted with permission from Ref. [15])

Deuterium NMR Lineshapes

A simple analytical model can then be introduced (Fig. 4) for establishing the retinal conformation when bound to rhodopsin. Three planes of unsaturation are assumed, encompassing the β-ionone ring and the polyene chain to either side of the C12–C13 bond [16, 18, 28,29,30]. Relative orientations of the pairs of ²H-labeled methyl groups are used for calculating the effective dihedral angles for the various planes of unsaturation. By conducting studies of aligned samples, the ²H NMR data allow one to establish the orientation of the retinal cofactor bound to rhodopsin. Each molecular plane (here designated A, B, or C) is defined by two vectors, and thus two angular constraints are required to specify its orientation in space. The three planes have two bonds in common; hence, a total of four independent parameters (i.e., degrees of freedom) must be introduced to define the structure of the retinal molecule within its binding cavity. Because experimental data for the C1R,S methyl groups are currently unavailable, the electronic transition dipole moment of the retinylidene chromophore obtained from linear dichroism measurements can be used as a fourth orientational restraint [31,32,33,34].

It follows that the torsion angles χ_i,k between the A, B, and C planes are given by [16]:

$$ {\chi}_{i,k}={\cos}^{-1}\left(\frac{\cos {\theta}_i\cos {\theta}_{\mathrm{B}}^{\left(i,k\right)}-\cos {\theta}_{\mathrm{B}}^{(i)}}{\sin {\theta}_i\sin {\theta}_{\mathrm{B}}^{\left(i,k\right)}}\right)-{\cos}^{-1}\left(\frac{\cos {\theta}_k\cos {\theta}_{\mathrm{B}}^{\left(i,k\right)}-\cos {\theta}_{\mathrm{B}}^{(k)}}{\sin {\theta}_k\sin {\theta}_{\mathrm{B}}^{\left(i,k\right)}}\right) $$

(2)

In the above formula, ${\theta}_{\mathrm{B}}^{(i)}$ and ${\theta}_{\mathrm{B}}^{(k)}$ designate the orientations to the local membrane normal n of the various methyl groups within the consecutive planes. In addition, θ _i and θ _k are the angles of the two methyl axes to the C _i –C _k bond whose torsion angle is χ_i,k as in the case of the C6–C7 or the C12–C13 bond. Note that the C _i –C _k bond angle to the local membrane normal is ${\theta}_{\mathrm{B}}^{\left(i,k\right)}$ and is obtained from the C9-methyl orientation, plus the transition dipole moment. For the torsion angles between the A, B, or C planes, multiple solutions are found (and multiple retinal geometries), which correspond to a single set of experimental methyl bond orientations. A total of 64 combinations for the relative orientations of the A, B, and C planes are possible for retinal bound to rhodopsin, giving 128 possible retinal configurations with the even parity taken into account (e.g., up and down orientation of the magnetic field cannot be distinguished). What is more, circular dichroism (CD) data [29, 35] and carbon–carbon distances obtained from rotational resonance solid-state ¹³C NMR studies [12, 36] can be introduced. It is then possible to obtain a simple physical result, in analogy to solution NMR spectroscopy.

According to these procedures, the angle between planes B and C is established using Eq. (2) to be χ_9,13 = +150 ± 4° (+147 ± 4°) (Fig. 4b). The two values correspond to a C11=C12–C13 bond angle of 120 or 130°, respectively [15]. Note also that distortion of the C11=C12–C13 bond angle from ideal orbital geometry may take place due to steric hindrance of the C13-methyl group with the retinal hydrogen H10, or it may be induced by the rhodopsin binding pocket. Considering next the β-ionone ring, introducing positional restraints for the C8-to-C18 and C8-to-C16/C17 distances from solid-state ¹³C NMR [36] plus the chirality known from CD studies [35], the C6–C7 dihedral angle of χ_5,9 = −65 ± 6° is the physical solution. It represents a negatively twisted 6-s-cis conformation (Fig. 4b). To further specify the 11-cis-retinylidene structure derived from solid-state ²H NMR, it was inserted into the binding pocket of the rhodopsin X-ray structure (resolution of 2.2 Å; PDB accession code 1U19) [27]. The Schiff base end of retinal was superimposed with the Lys²⁹⁶ nitrogen, keeping the C12 to C15 carbon atoms near to the X-ray coordinates. Even so, a simple three-plane model did not fit into the binding pocket, because of the multiple steric clashes of retinal with the Tyr¹⁷⁸ and Cys¹⁸⁷ side chains of extracellular loop E2, as well as Met²⁰⁷, Tyr²⁶⁸, and Ala²⁹² in helices H5, H6, and H7, respectively. To resolve this difficulty, an additional twist of the C11=C12 bond of the polyene chain was assumed [16, 37]. Adopting an extended three-plane model, the C11=C12 dihedral angle was established by fitting the C10-to-C20 and C11-to-C20 distances to ¹³C NMR rotational resonance data [12]. As a result, the C11=C12 torsion angle was found to be −25 ± 10° and the C12–C13 torsion angle 176 ± 6°, where the twist is predominantly localized to the C11=C12 bond. Note that the C10-to-C20 and C11-to-C20 distances are less sensitive to the C11=C12 torsion angle. The structure deduced for retinal (Fig. 4c) in this way corresponds to the rhodopsin N-terminus at the top (extracellular side), and the C-terminus at the bottom (cytoplasmic side).

To summarize at this point using solid-state ²H NMR spectroscopy, the structural studies reveal twisting of the retinal chromophore when bound to rhodopsin in the dark state. This finding is in accord with other biophysical studies [18, 26, 29, 30, 34, 36,37,38,39,40,41,42,43,44,45] and is key to understanding its photoreaction dynamics [46,47,48,49]. Of notable significance for rhodopsin is the torsional twisting about the C11=C12 double bond, together with the twist of the β-ionone ring [30]. The finding of a nonplanar structure of the retinal ligand is consistent with the presence of hydrogen-out-of-plane (HOOP) modes in resonance Raman [47, 49,50,51] and FTIR [40] spectroscopies and with circular dichroism (CD) studies [29, 38, 42, 43]. All of these features are significant to explaining how release of the photonic energy is used to initiate visual signaling by rhodopsin in the natural photoreceptor membranes [16, 29, 31, 36].

In a manner similar to the above studies, the Meta-I state can also be cryo-trapped in planar-supported bilayers to determine the changes in the retinal conformation and orientation induced by light absorption. Solid-state ²H NMR spectra acquired at −100 °C for macroscopically aligned POPC membranes at θ = 0° tilt angle allow comparison of the dark state (Fig. 4a–c) to the Meta-I state (Fig. 4d–f). For the bound retinylidene ligand, the greatest differences are found for the C9–C²H₃ group, with smaller variations for the C5–C²H₃ and C13–C²H₃ groups (Fig. 4d). These differences in the ²H NMR spectra manifest the bond orientation θ_B as well as the alignment disorder (mosaic spread σ). In the preactive Meta-I state, orientations are determined for the C5-, C9-, and C13-methyl groups θ_B of 72 ± 4°, 53 ± 3°, and 59 ± 3°, respectively. Because of the larger mosaic spread of Meta-I (σ = 22–25°) versus dark-state rhodopsin (σ = 18–21°), the ²H NMR spectra for the C9-methyl differ, although the bond orientations are similar (Fig. 4d). In contrast, for the C13-methyl group, a smaller spectral difference is evident with a larger change in bond orientation. Analogous to dark-state rhodopsin, the solid-state ²H NMR spectra establish that the retinylidene methyl substituents have rapid threefold rotation, with order parameters for off-axial motions of ≈0.9 within the Meta-I binding cavity (Fig. 4d).

Theoretical simulation of the solid-state ²H NMR spectra [21] provides the methyl group angles, which together with the electronic transition dipole moment define the orientations of the molecular fragments. The fragments are then assembled to yield to the retinal structure when bound to the protein. Examples (two for each plane) show that multiple solutions are possible for the retinal structure (Fig. 4e). By use of Eq. (2), and including experimental rotational resonance ¹³C NMR data [12] for the C10-to-C20 and C11-to-C20 carbon distances, the torsion angle between the B and C planes of χ_9/13 = ±173 ± 4° is found. An almost fully relaxed all-trans conformation occurs in the preactive Meta-I state [11, 12]. What is more, solutions for the β-ionone ring of χ_5/9 = ±32 and ±57° are found as two possibilities. For the Meta-I state, the region of the polyene chain with the C13-methyl group rotates about the С11=С12 double bond toward the membrane extracellular side. Evidently, the polyene chain becomes straightened, whereby the β-ionone ring is displaced along the retinal axis toward helix H5. The calculated Meta-I structures are further restrained by placing them into the dark-state rhodopsin X-ray structure [27]. Assuming the shape of the retinal binding cavity in Meta-I resembles the dark state, most of the retinal structures were eliminated because of the different position of the β-ionone ring in the binding pocket. The exception is the retinal structure with χ_5/9 = −32° and χ_9/13 = 173° (left of Fig. 4f) and the structure with χ_5/9 = 32° and χ_9/13 = −173° obtained by reflection (mirror symmetry transformation) in a vertical plane. Even so, the first structure fits best within the binding cavity, the only close contact being with the side chain of Trp²⁶⁵. By contrast, the mirror structure makes close contacts with the side groups of Glu¹²², Trp²⁶⁵, Tyr²⁶⁸, and Ala²⁹², and thus it is less probable.

Retinal Molecular Dynamics and Solid-State ²H NMR Relaxation

Turning next to the retinal dynamics, in Fig. 5 the experimental ²H NMR relaxation experiments are summarized for rhodopsin in the dark state. Arrhenius-type plots of both the T_1Z relaxation times and T_1Q relaxation times are shown versus reciprocal temperature, for those methyl groups of the bound retinal crucial to its function. One can perceive that the structural fluctuations of retinal in the dark state are unaltered by phase transitions of the lipids or by the freezing of water. The retinal cofactor is deeply buried within the receptor core (Fig. 3), and hence the relaxation data can be smoothly extrapolated to physiological temperature. For the retinylidene C5-Me group (Fig. 5a, b), a clear minimum in T_1Z is seen at −120 °C and for T_1Q at −135 °C. By contrast, for the C9- and C13-Me groups, the T_1Z and T_1Q minima occur at much lower temperatures, outside the measured range (Fig. 5c, d) [52]. According to these results, site-specific differences exist in the dynamics of the retinylidene methyl groups when bound to rhodopsin, despite that the order parameters show little variation.

Fig. 5

Solid-state ²H NMR relaxation uncovers site-specific differences in the mobility of the retinal ligand of rhodopsin. Spin-lattice (T_1Z) and quadrupolar-order (T_1Q) relaxation times are graphed against reciprocal temperature for rhodopsin in the dark state in POPC membranes (1:50 molar ratio). (a, b) Retinal ²H-labeled at the C5-methyl group, (c) the C9-methyl group, and (d) the C13-methyl group. Experimental T_1Z and T_1Q times were fit using analytical models for molecular dynamics [52, 53]: axial threefold jump model (rate constant k, solid lines); and continuous rotational diffusion model (coefficients D_|| and D_⊥ with solid lines for D_⊥ = 0 and dashed lines for D_⊥ = D_||). Variations in the rates of methyl spinning are seen for the retinylidene ligand of dark-state rhodopsin in a membrane environment (Adapted with permission from Ref. [52])

As discussed above, for slower motions, the T_1Z and T_1Q minima occur at higher temperature (to the left). Conversely, for faster motions, the minima occur at lower temperature (to the right) [13]. At a given minimum, the effective correlation time τ _c is matched to the Larmor (resonance) frequency ω₀ by τ _c ≈ 1/ω₀ = 13 ns. Moreover, the correlation times are less at higher temperatures, as observed for the different retinylidene methyl groups. The comparatively short T_1Z and T_1Q relaxation times for the C5-Me group indicate a mainly 6-s-cis conformation of the β-ionone ring [18], in contrast to 6-s-trans. (For a 6-s-cis conformation, the nonbonded (1,7) interactions with hydrogen H8 would give slower spinning of the C5-Me group versus (1,6) interactions with hydrogen H7 in the 6-s-trans conformation.) What is more, the polyene C9- and C13-methyl groups have longer T_1Z times. They indicate greater mobility, because of the weak noncovalent interactions within the retinal ligand, and with the adjacent amino acid residues.

Generalized Model-Free Analysis for Nuclear Spin Relaxation Rates

At the initial stage, our approach [53] is evidently model free, because we directly measure the RQCs and derived C–C²H₃ order parameters, plus the corresponding R_1Z relaxation rates. In the next level of analysis, the theory of nuclear spin relaxation is introduced to investigate the molecular dynamics [53]. Experimentally, the nuclear spin-lattice relaxation rates depend on thermal motions of the C–²H bond (electric field gradient, EFG tensor) near the ω₀ resonance frequency, and read [53]:

$$ {R}_{1\mathrm{Z}}=1/{T}_{1\mathrm{Z}}=\frac{3}{4}{\pi}^2{\chi}_{\mathrm{Q}}^2\left[{J}_1\left({\omega}_0\right)+4{J}_2\left(2{\omega}_0\right)\right] $$

(3)

and

$$ {R}_{1\mathrm{Q}}=1/{T}_{1\mathrm{Q}}=\frac{9}{4}{\pi}^2{\chi}_{\mathrm{Q}}^2{J}_1\left({\omega}_0\right) $$

(4)

In the above expressions, T_1Z is the relaxation time for Zeeman order and T_1Q is that for quadrupolar order; χ_Q is the quadrupolar coupling constant; and ω₀ is the nuclear resonance (Larmor) frequency. The spectral densities of motion are denoted by J₁(ω₀) and J₂(2ω₀) and describe the power of the fluctuations at ω₀ and twice ω₀. A simple physical picture is that matching of the power spectrum of the fluctuations to the Zeeman energy level gap drives the transitions between states of different nuclear spin angular momentum [53].

The general theory of NMR relaxation [53] can then be applied to analyze in greater detail the molecular dynamics of retinal bound to rhodopsin. Generalized model-free (GMF) analysis [53] describes how the irreducible spectral densities J _m (ω) depend on the average methyl angle to the magnetic field, plus the mean-square amplitudes and rates of the motions. The spectral densities are given by:

$$ {J}_m\left(\omega \right)=\sum \limits_{r,q}{\left|{D}_{0r}^{(2)}\left({\Omega}_{\mathrm{PI}}\right)\right|}^2\left[\left\langle {\left|{D}_{rq}^{(2)}\left({\Omega}_{\mathrm{IM}}\right)\right|}^2\right\rangle -{\left|\left\langle {D}_{rq}^{(2)}\left({\Omega}_{\mathrm{IM}}\right)\right\rangle \right|}^2{\delta}_{r0}{\delta}_{q0}\right]{j}_{rq}^{(2)}\left(\omega \right){\left|{D}_{qm}^{(2)}\left({\Omega}_{\mathrm{ML}}\right)\right|}^2 $$

(5)

where ω = mω₀ and m = 1,2 [54]. Here, D⁽²⁾(Ω _ij ) indicates the second-rank Wigner rotation matrix, and Ω _ij  ≡ (α _ij , β _ij , γ _ij ) are the Euler angles [53] for the relative orientations of the coordinate systems {i, j} ≡ {P, I, M, L} under consideration (see Fig. 3). In this notation P is the principal axis system for the electric field gradient tensor of the C–²H bond, I specifies the instantaneous orientation of the methyl group, M the average orientation, and L the laboratory (B ₀ ) axis system. Notably, the mean-square amplitudes are contained in the angular brackets and denote a time-ensemble average. The corresponding reduced spectral densities are indicated by ${j}_{rq}^{(2)}\left(\omega \right)=2{\tau}_{rq}/\left(1+{\omega}^2{\tau_{rq}}^2\right)$, where τ _rq are the rotational correlation times.

In the case of either membrane proteins [55] or lipids, using the GMF approach, the mean-square amplitudes are quantified by the segmental order parameters, and the rates by the motional correlation times [53]. For example, for a methyl group with Euler angles Ω_PI = (0°, 70.5°, 0°), assuming ideal geometry, an effective coupling constant of ${\chi}_{\mathrm{Q}}^{\mathrm{eff}}={\chi}_{\mathrm{Q}}{D}_{00}^{(2)}\left({\Omega}_{\mathrm{PI}}\right)=\hbox{--} \frac{1}{3}{\chi}_{\mathrm{Q}}$ is obtained. The order parameter of the threefold axis describes the off-axial fluctuations, and it is defined by ${S}_{C_3}=\frac{1}{2}\left\langle 3{\cos}^2{\beta}_{\mathrm{IM}}\hbox{--} 1\right\rangle$, where β_IM is the angle of the methyl orientation at any instant to its average value. Further theoretical analysis entails the introduction of a motional model [53, 56] to explain the fluctuations.

Applying the above formalism to rhodopsin, the T_1Z times can be analyzed using either a 3-site jump model or a continuous diffusion model for rotation of the retinylidene methyl groups [53]. For N-fold jumps with a rate constant k about a single axis, the correlation times are [54, 56] 1/τ _rq  → 1/τ _r  = 4ksin²(πr/N) leading to 1/τ _r = 3k for a methyl group. Alternatively, the limit of rotational diffusion about an axis can be considered. For continuous diffusion within a potential of mean torque [57], the rotational correlation times read:

$$ 1/{\tau}_{rq}={\mu}_{rq}{D}_{\perp }/\left[\left\langle {\left|{D}_{rq}^{(2)}\left({\Omega}_{\mathrm{IM}}\right)\right|}^2\right\rangle -{\left|\left\langle {D}_{rq}^{(2)}\left({\Omega}_{\mathrm{IM}}\right)\right\rangle \right|}^2{\delta}_{r0}{\delta}_{q0}\right]+\left({D}_{\mid \mid}\hbox{--} {D}_{\perp}\right){r}^2 $$

(6)

Here, the symbols D_∣∣ and D_⊥ indicate the axial and off-axial diffusion coefficients for methyl rotation; and the moments μ _rq and mean-squared moduli $\left\langle {\left|{D}_{rq}^{(2)}\left({\Omega}_{\mathrm{IM}}\right)\right|}^2\right\rangle$ depend on both second- and fourth-rank order parameters [57]. For a strong-collision approximation, the correlation times are those of a rigid rotor [53]: 1/τ _rq  → 1/τ _r  = 6D_⊥ + (D_∣∣ − D_⊥)r². The limit of continuous diffusion, e.g., for diffusion about a single axis, 1/τ _r  = D_∥r² giving the results in Refs. [53, 56]. Finally, application of transition-state theory indicates the correlation times are inversely related to A exp(−E_a/RT), where A is the pre-exponential factor (k₀ or D₀) and E_a is the activation barrier (energy) for methyl rotation. For a rotational diffusion model D_∣∣ = D_0∣∣ exp(–E_a∣∣/RT) and D_⊥ = D_0⊥ exp(–E_a⊥/RT) and analogously for a threefold jump model [13, 53, 54, 57].

Retinal Dynamics in Inactive and Active Rhodopsin

As a next step, one is able to use NMR relaxation to investigate the changes in the dynamics of the retinal ligand of rhodopsin that occur upon light absorption. Compared to the dark state, pronounced T_1Z differences are found in the Meta-I and Meta-II states that encapsulate the light-induced changes in the retinylidene dynamics (Fig. 6). The short T_1Z relaxation times measured for the C5-methyl group in the dark state (Fig. 6a) indicate the β-ionone ring has a predominantly 6-s-cis conformation [13, 37], as opposed to 6-s-trans for bacteriorhodopsin [58]. Evidently [59], the β-ionone ring retains nearly the same local environment, and is not strongly affected by transitions among the dark, Meta-I, and Meta-II states (Fig. 6b, c) [37]. A shifting of the T_1Z minimum for the C5-methyl to lower temperatures in Meta-II (Fig. 6c) indicates a reduction in the local correlation time, e.g., due to lowering E_a by changing the C6–C7 torsional angle and/or enhancing the ring mobility. For the functionally critical C9-Me group [60], a striking change in T_1Z is evident in the Meta-I and Meta-II states, due to an increase in E_a for methyl spinning within the rhodopsin-binding pocket. What is more, similar E_a barriers of the C9- and C13-methyl groups upon 11-cis to all-trans isomerization are plausible, because they are on the same side of the retinal polyene chain (Figs. 6b, c).

Fig. 6.

Solid-state ²H NMR relaxation reveals striking differences in retinal mobility during rhodopsin activation. Spin-lattice (T_1Z) relaxation times of retinylidene methyl groups were determined in (a) the dark state, (b) the Meta-I state, and (c) the active Meta-II state from T = −30 to −160 °C. Methyl dynamics were theoretically interpreted using an axial threefold jump model or a continuous diffusion model with coefficients D_|| (for rotation about the C₃ axis) and D_⊥ (for off-axial reorientation). In (a–c), theoretical fits are for an axial threefold jump model or a continuous rotational diffusion model with D_⊥ = 0 shown by solid lines. Dashed lines are for continuous diffusion with D_⊥ = D_||. In (b), theoretical fits for the C5-methyl group in Meta-I assume either two conformers with different bond orientations and axial diffusion coefficients (solid line), or one conformer with anisotropic methyl diffusion constants (D_|| ≠ D_⊥) (dashed line). The results show that photoactivation of rhodopsin yields selective relaxation enhancement for C9-methyl group rotations due to nonbonded interactions of the retinal ligand with the protein (Adapted with permission from Ref. [13])

Application of transition state theory allows the NMR relaxation rates to be quantified in terms of the activation barriers for the motions, together with the corresponding pre-exponential factors. Using transition state theory, large site-specific differences are found in the pre-exponential factors and activation barriers (E_a) (Fig. 7). For the C5-methyl substituent of the β-ionone ring (E_a = 10–15 kJ mol⁻¹), the barrier values exceed those of the other methyl groups in dark, Meta-I, and Meta-II states. For the C5-methyl group of the retinylidene ligand, the relatively high activation energy E_a (calculated from the slope of the temperature dependences of the T_1Z and T_1Q relaxation times) of ≈12 kJ mol⁻¹ is usual for methyl rotations in organic solids. Steric hindrance can occur because of nonbonded, intraretinal interactions with the polyene H8 hydrogen, and/or steric clashes with amino acid residues within the binding cavity, e.g., Glu¹²² or possibly Trp²⁶⁵. By contrast, the notably low E_a value (barrier) for the C9-methyl is most likely due to compensation of intraretinal steric interactions, as discussed below.

Fig. 7

Analysis of NMR relaxation data reveals site-specific dynamics of retinal underlying rhodopsin activation. The results illustrate how solid-state ²H NMR relaxation probes the local energy landscape of retinal bound to rhodopsin. (a) Schematic methyl torsional potentials in dark state showing how the low activation barrier for C9-Me is due to antiphase (1,6) interactions with hydrogen atoms H7 and H11. (b, c) Potentials for C13- and C5-Me groups include nonbonded (1,7) interactions with hydrogen atoms H10 and H8, and reveal the energy barrier for fluctuations of the C5-methyl group is largest. (d) Summary of findings for the dark, Meta-I, and Meta-II states, respectively [15]. Methyl rotation is formulated as axial threefold jumps (rate constant k) or instead continuous diffusion (coefficients D_|| and D_⊥). The pre-exponential factor is denoted by either k₀ for threefold axial jumps or D₀ for continuous diffusion; and E_a is the barrier height (activation energy). Results are shown for the diffusion model for η_D ≡ D_∣∣/D_⊥ = 1 (in front) and D_⊥ = 0 (in back). For the C5-methyl of the β-ionone ring in Meta-I, both axial (||) and off-axial (⊥) motions are included with η_D ≠ 1, or instead a two-conformer model with both positive (+) and negative (−) C5=C6–C7=C8 dihedral angles and D_⊥ = 0. Note that local roughness of the potential energy landscape corresponds to site-specific variations in barriers for methyl spinning of the retinylidene ligand of rhodopsin (Adapted with permission from Refs. [15, 37])

Quantum mechanical calculations for retinal model compounds [61, 62] confirm that the vanishingly small barrier to rotation of the C9-methyl group (E_a = 2 kJ mol⁻¹ in the dark state) (Fig. 7a) is due to nonbonded (1,6) interactions with hydrogen atoms H7 and H11 of the polyene chain (see Fig. 1). In Fig. 7a, a simple explanation of why the C9-methyl group of retinal has a smaller activation energy than expected from quantum mechanical calculations for typical organic compounds is given [37, 61]. Hydrogen atoms H7 and H11 of the polyene chain have intraretinal (1,6) interactions that are approximated by a threefold rotational potential. These rotational potentials are in antiphase due to periodic eclipsing interactions; that is to say, they are offset by ≈60° giving a shallow resultant potential (Fig. 7a). Within the binding cavity, interactions with other residues are comparatively weak, because the C9-methyl is located in the space between Tyr²⁶⁸ and Thr¹¹⁸ in the crystal structure. By contrast, for the C13-methyl group near the protonated Schiff base (PSB) end of retinal (Fig. 7b), and the C5-methyl group of the β-ionone ring at the opposite end (Fig. 7c), the mobility is less because of nonbonded (1,7) interactions with hydrogens H10 and H8, respectively. For the C13-methyl group, the intermediate E_a barrier may be due to steric interactions with retinal hydrogen H10, and possibly Tyr²⁶⁸ as well.

Following light-induced isomerization of the bound retinal ligand, the most pronounced changes entail the polyene chain of retinal, rather than the β-ionone ring. In the sequence, dark to Meta-I to Meta-II, there is a systematic increase in the activation energy barrier (E_a) for the C9-methyl of the polyene chain, together with an opposite decrease for the C13-methyl substituent (Fig. 7d). For example, the activation barrier for the C9-methyl group rotation is increased about twofold; hence, its rotational dynamics become slower. Surprisingly, however, the C9-methyl group – which is essential to rhodopsin function [60] – remains as a dynamical hotspot. Following 11-cis to trans isomerization (Fig. 1), the (1,6) interactions of the C13-methyl group occur with both polyene hydrogens H11 and H15; hence, the C13-methyl barrier (E_a = 3–5 kJ mol⁻¹) becomes similar to the C9-methyl barrier in the Meta-I and Meta-II states (Fig. 7d). Perhaps most striking, the C5-methyl barrier stays almost unchanged up to the active Meta-II state (Fig. 7d), in agreement with a mainly 6-s-cis conformation of the β-ionone ring [13, 37].

Challenges Ahead: Molecular Mechanism of Rhodopsin Activation

Obviously, many important details of the activation mechanism of rhodopsin in a natural membrane environment remain unsolved. Because the secondary and tertiary structures of the Rhodopsin (Family A) GPCRs are similar, the local interactions are expected to be crucially important for targeted drug design. For rhodopsin, despite that several X-ray crystal structures including Meta-II-like structures are available, the orientation of the chromophore is still uncertain. What is more, there is a controversy between X-ray and solid-state ¹³C NMR results. Notably, the retinal conformation in the active Meta-II state needs to be established with a high degree of certainty [63, 64]. The molecular dynamics of the retinal ligand and the rhodopsin overall structure in the activation mechanism are very important in the receptor activation, and probably other GPCRs as well. For studying GPCRs, a combination of different techniques is salutary, including molecular simulation methods that connect snapshots provided by X-ray and NMR studies of rhodopsin [52, 64], both in crystals as well as a natural lipid membrane environment.

Our current understanding of rhodopsin activation by retinal [13, 37] (Fig. 8) allows us to propose how local (ps–ns) motions of the ligand initiate the large-scale (ms) functional protein motions (Fig. 8a) [65–67]. In the inactive dark state, the low energy barrier to rotations of the C9-methyl group signifies a lack of steric clashes, because it occupies a slot between Tyr²⁶⁸ and Thr¹¹⁸. The C9-methyl group acts effectively as a hinge point for retinal isomerization, causing the C13-methyl and the C=NH⁺ groups to change their positions upon light activation (Fig. 8a). In the Meta-I NMR structure of retinal [13, 15, 16, 37], rotation of the C13-methyl shifts the β₄ strand of the E2 loop upward to the extracellular (e) side (Fig. 8b). A hydrogen-bonding network involving TM helices H4–H6 is disrupted, as implied by a decrease in the rotational barrier (E_a) for the C13-methyl group. At the other end of the retinal ligand, the β-ionone ring is shifted toward the helix H5. A closer packing for the C5-methyl is suggested by the comparatively high E_a value in the Meta-I state (Fig. 7d). The first ionic lock of the retinylidene PSB on helix H7 with its complex counterion due to Glu¹¹³ (H3) and Glu¹⁸¹ (E2) is broken by internal proton transfer from the PSB to Glu¹¹³ in Meta-II. Elongation of retinal displaces the β-ionone ring away from Trp²⁶⁵ (H6) toward the H5–H6 helical interface [37, 63]. Initial tilting of helix H6 away from the H1–H4 helical core is accompanied by restructuring of helix H5, bringing Tyr²²³ closer to Arg¹³⁵ and Gly²³¹ near to Glu²⁴⁷ (Fig. 8c) [66]. This destabilizes the second ionic lock involving Glu¹³⁴ and Arg¹³⁵ of the conserved E(D)RY sequence of helix H3 plus Glu²⁴⁷ of helix H6 [66], transiently exposing the recognition sites for transducin (G_t) on the cytoplasmic face (c-side) (Fig. 8c) [67]. In the above model, rhodopsin activation entails collective movements of transmembrane helices H5 and H6, together with the cytoplasmic loops in the Meta-I to Meta-II equilibrium. The reversible helix fluctuations [65, 67] happen at kHz frequencies, matching the catalytic turnover rate for G_t binding and activation by rhodopsin [68]. Receptor activation thus entails a fluctuating equilibrium among states and substates on the energy landscape [13, 37]. A key question for future research is whether one can quantitatively trap a single activated rhodopsin species, or whether the receptor activation requires the dynamics of a conformational ensemble unlocked by photoisomerization of the retinal ligand.

Fig. 8.

Proposed activation mechanism for rhodopsin in membranes based on solid-state NMR [13] and X-ray [19] data. The extracellular side of rhodopsin is above and the cytoplasmic side below. (a) Isomerization of retinal (red) displaces the extracellular E2 loop toward the membrane surface (e-side). (b) Elongation of transmembrane helix H5 and tilting of helix H6 away from the H1–H4 helical core opens a binding cleft for the G-protein transducin. (c) Fluctuations of transmembrane helices H5 and H6 of rhodopsin occur in conjunction with exposing recognition sites on the opposing cytoplasmic membrane surface (c-side) for transducin (G_t) in the catalytic activation mechanism (Adapted with permission from Ref. [13])