Vibrational resonance, allostery, and activation in rhodopsin-like G protein-coupled receptors

G protein-coupled receptors are a large family of membrane proteins activated by a variety of structurally diverse ligands making them highly adaptable signaling molecules. Despite recent advances in the structural biology of this protein family, the mechanism by which ligands induce allosteric changes in protein structure and dynamics for its signaling function remains a mystery. Here, we propose the use of terahertz spectroscopy combined with molecular dynamics simulation and protein evolutionary network modeling to address the mechanism of activation by directly probing the concerted fluctuations of retinal ligand and transmembrane helices in rhodopsin. This approach allows us to examine the role of conformational heterogeneity in the selection and stabilization of specific signaling pathways in the photo-activation of the receptor. We demonstrate that ligand-induced shifts in the conformational equilibrium prompt vibrational resonances in the protein structure that link the dynamics of conserved interactions with fluctuations of the active-state ligand. The connection of vibrational modes creates an allosteric association of coupled fluctuations that forms a coherent signaling pathway from the receptor ligand-binding pocket to the G-protein activation region. Our evolutionary analysis of rhodopsin-like GPCRs suggest that specific allosteric sites play a pivotal role in activating structural fluctuations that allosterically modulate functional signals.

: Network representation the LSFs from the Meta-II rhodopsin MD simulation where the nodes are colored according to the separate network communities of the LSFs from inactive state rhodopsin in Figure 2. The gray nodes highlight residues that were not part of the LSF network of interactions in inactive rhodopsin.

Supplementary FDA: Changes in retinal-rhodopsin pairwise forces and the formation of allosteric communication pathways in rhodopsin (Figures S2 -S6)
In this investigation we have also extended the equilibrium MD simulations of rhodopsin in both the inactive and Meta II state to include force distribution analyses (FDA) 1 . The aim of these studies is to deduce the mechanical stress that is both distributed and propagated within the interior of the receptor due to the retinal interactions that take place within the ligand-binding pocket. And to further comprehend the influence of the retinal dynamics on the global modes of the receptor. A perturbation, such as ligand binding in the receptor structure, would be expected to lead to a shift in the distribution of conformational states across the ensemble. Thus, a return to equilibrium 2 requires a release of the strain energy through a series of propagating structural deformations. In general the fluctuations associated with the release of strain in proteins tend to be smaller-scale, conformational rearrangements rather than large-scale protein conformational changes. Moreover, the pathways for strain release 3 have been conjectured to be closely connected with the formation of major allosteric propagation pathways in proteins and enzymes. Therefore to grasp the nature of the network of correlated protein fluctuations that arise in response to the retinal in rhodopsin we have conducted PCA on the residue averaged pair-wise forces in in both the dark and active-state receptor. Hence, the interpretation of the propagation pathways uncovered from FDA relies on the observations from force-PCA analyses.
In Figs. S2-S3 we find that the retinal force on the receptor in the dark state and Meta II differs somewhat significantly. The force from the retinal in the dark-state is distributed more extensively on the receptor structure and also slightly more aggregated in the extracellular region when contrasted with Meta II. On the other hand, the Meta II receptor ligand-induced forces have less of an influence on the overall structure of the receptor yet the magnitude of the force-induced interactions is higher and concentrated primarily in the immediate vicinity of the retinal C9-and C13-methyl groups. From the MD simulations, we are able to establish a network of interactions that propagate internal strain from the ligand-binding site to the rest of the receptor structure via subtle, structural fluctuations. In the calculation of the pair-wise forces in the dark-state, we find that the retinal interaction with the receptor promotes two distinct mechanisms of force propagation that lead to conformational rearrangements within the receptor interior (Figs. S4a -c). The major pathway (PC1) in Fig. S4 involves a torsional compression of the retinal-ligand binding pocket that is primarily due to the force on residues Glu113 and Gly114 from the oscillation of the Schiff base linkage on helix 3 and from the force on Arg177 that mediates stability of the retinal in the dark-state of the receptor. The ligand-induced force on Glu113 and Gly114 is disseminated through the receptor as a torsional oscillation that promotes fluctuations of Gly89 -90 on helix 2 and Gly120 on helix 3.
Analogously, the force on Arg177 induces oscillations in the β3 loop of extracellular loop 2 (EL2) that creates a counter-torque from that which is produced from the retinal force on residues 113 and 114. Hence, the propagation of internal stress reveals a network of correlated fluctuations that induces a receptor-wide torque-induced rotational motion that resembles the dominant PCA mode uncovered from the MD simulation of the dark-state receptor in Fig. S4d.
A minor force-induced propagation pathway (PC2) in the dark-state receptor is also uncovered in Fig. S4b. In this case, a transient fluctuation of the retinal intermittently modifies the ligand-receptor interaction such that the interaction with the C9-methyl group of the retinal has a much stronger interaction with Gly120 and Gly121. The fluctuationinduced modification in ligand-receptor interactions also creates a counter torque centered at Gly174. Together the retinal-induced correlated structural fluctuations are translated as an elongation motion that extends from the ligand-binding pocket into the direction of the G-protein binding, which consequently slightly alters the packing in the receptor hydrophobic core.
The retinal-induced forced in Meta II only reveals one major pathway of signal propagation (Fig. S5). The interaction with the retinal polyene tail induces prominent forces in residues lining the C9-methyl group, namely Leu119 -Glu122. The fluctuation-induced interaction also modifies the receptor interactions near the β-ionine ring. The oscillation of the ring makes close contact with Tyr268 inducing a counter torque centered at Gly270. Similar to the minor signal propagation pathway uncovered in the dark state receptor in Fig. S4b, the retinal-induced force creates an elongation torsion that extends in this case from the Nterminus up to the G-protein coupling region. Specifically, the torsional oscillation of residues 119 -122 on helix 3 creates a correlated set a structural fluctuations that couples regions of the N-terminus, the CL2 loop between helices 3 and 4, and the C-terminus. The force-induced torsional oscillation centered at Gly270 modifies the dynamical fluctuations in intracellular regions of helix 5 as well as the CL3 loop separating helices 5 and 6. In this case (when contrasted with PC2 in the dark-state receptor) we also observe a more substantial altering of the hydrophobic packing in the receptor in the regions separating helices 3 and 6 that accompany the helical rearrangements. In fact we observe an overall "softening" of backbone motion in the global fluctuations of Meta II (Figs. S6a-b) that is due to the mechanical strain of force propagation from the retinal to the G-protein region that disrupts the packing of the receptor hydrophobic core and at the same time potentially enhances the affinity for the G-protein. The signal is carried via a network of correlated (inplane) side-chain fluctuations that are distinct from those observed in the dark-state receptor (Fig. S6c) and the overall induced motion strongly resembles the dominant PCA mode uncovered from the MD simulation of Meta II (Fig. S5c).
It is interesting to note that experimentally we observe no prominent vibrational modes in the light-state receptor in the ≤ 100 cm -1 region of the THz spectrum yet the MD simulation results suggest that there should be large-amplitude modes in that frequency region due to collective oscillations of both side-chain and backbone atoms (or a coupling of side-chain and backbone motions). On interesting thing to consider is that the strength of the infrared absorption is directly associated with the change in dipole moment. Restricted rotational oscillations or torsions create large changes in dipole moments; hence these types of motions are very prominent in the THz spectrum. For instance, we have associated the peaks at ~ 80 cm -1 and 65 cm -1 (Figs. 3a-b, Figs. S6a-b) with collective oscillations that are associated with a global hinge torsion that takes place in the dark-state of the receptor. These types of motions would be expected to prominent in the experimental spectrum and we find that they are (Fig. 3a). The in-plane fluctuations (between 30 -40 cm -1 ) arising from the retinal-induced structural fluctuations in Meta II (Fig. 3b and Figs. S6a-c) would probably not create large changes in dipole moments. Hence, it is likely that their presence would not be dominant in the low-frequency region of the experimental spectrum. Although the computational analyses that we have conducted suggest that their role in the active receptor dynamics is significant.

Supplementary Signal propagation and GSFs: Signal propagation and global fluctuations in Meta II (Figure S8)
A mapping of the LSFs (localized structural fluctuations) with the GSFs (global structural fluctuations) from the MD simulation allows us to investigate the relationship (overlap) between the local conformational fluctuations taking place in the receptor and the global, collective motions (as seen in Fig. S5c) that accompany activation. We find that the change in interactions surrounding the retinal β-ionine ring during activation moves it closer to the extracellular side where it has closer contact with residues in helix 4 (particularly Cys167 -Ala169). The new interactions create a long-distance collective torsion that links the helix 4 residues with residues in the N-terminus (Pro23 -Glu25) and provides the necessary space for the helix 6 outward rotation and the CL3 loop connecting helices 5 and 6. The changes in retinal interactions in the active-state of the receptor also modify contacts with residues that regulate interhelical packing within the retinal ligandbinding pocket. Particularly, the global elongation torsion of Meta II alters the tertiary contacts of residues involved with conserved water-mediated interactions in helices 1 and 2 such as Gly51, Phe52, Thr92, and Thr93. The modifications in the tertiary contacts 4 in the receptor hydrophobic core are a necessary precursor for signal propagation and are a consequence of the counterion switch from Glu113 to Glu181 in the active-state receptor. The global elongation torsion is also coupled with localized fluctuations that move the signal from the retinal ligand-binding pocket out toward the G-protein coupled region. Specifically, residues in EL1 -EL3 and the N-terminus are correlated with the dynamics of residues in helix 7 (Ala292 -Phe293, Met308 -Lys311) in the global torsion. The   Nodes represent a specific amino acid and edges represent the lines between the nodes. The rainbow coloring of the nodes characterizes the degree to which a given amino acid takes part in the MI network (denoting coevolution propensity). Red nodes have a high MI value and blue nodes a low MI value. The size of the nodes in this case corresponds to the conservation of the amino acid from the MSA. The reference structure for the MSA is bovine rhodopsin (opsd_bovin) with pdb ID 1u19.

Force Distribution Analysis (FDA)
A modified version of Gromacs 4.5.3 was used to write out the pair-wise forces 1 , , between each residue pair i and j. Forces include contributions from the electrostatic and van der Waals interactions involving the retinal and rhodopsin that are calculated below a certain cut-off distance. These non-bonded pairwise forces of the residue pairs in close proximity comprise a force-propagation network involving short-range to medium-range connections that are averaged over the simulation time. The averaged forces were saved every 10 ps and convergence was reached when an equilibrium value for the forces was attained. The stored forces were written out as force trajectories and the average of those forces were used later for further analysis in R (https://www.r-project.org/) as well as visualization in VMD (http://www.ks.uiuc.edu/Research/vmd/). Covariance matrices and principal component analyses (PCA) were used on the averaged residue forces to identify correlated changes in the pair-wise forces in both the dark-and Meta II state of rhodopsin. Eigenvalues and eigenvectors were calculated by diagonalizing the covariance matrix, and eigenvectors were sorted in descending order of their eigenvalue. In each case, > 80% of the variance was described in either the top two or top PCA mode in the dark-and Meta II state, respectively. The modes of fluctuation were visualized by calculating a trajectory along either the first two eigenvectors in the dark-state or the first eigenvector in the Meta II state.