QM/MM Study of the 1 H and 13 C NMR Spectra of the Retinyl Chromophore in Visual Rhodopsin

Transcription

1 QM/MM Study of the 1 H and 13 C NMR Spectra of the Retinyl Chromophore in Visual Rhodopsin José A. Gascón, Eduardo M. Sproviero and Victor S. Batista Department of Chemistry, Yale University, PO Box , New Haven, CT Abstract The 1 H and 13 C Nuclear Magnetic Resonance (NMR) spectra of the retinyl chromophore in rhodopsin are investigated by using Quantum Mechanics/Molecular Mechanics (QM/MM) hybrid methods at the Density Functional Theory (DFT) B3LYP/6-31G*:Amber level, in conjunction with the Gauge Independent Atomic Orbital (GIAO) method for the ab initio Self-Consistent-Field (SCF) calculation of NMR chemical shifts. The study provides a first-principle interpretation of solid-state NMR experiments based on recently developed QM/MM computational models of rhodopsin and bathorhodopsin [Gascón, J.A.; Batista, V.S. (2004) Biophys. J., 87: ]. A detailed analysis of nonbonding interactions responsible for inducing NMR chemical shifts characteristic of the rhodopsin and bathorhodopsin ligand-binding sites is presented, with emphasis on the influence of polar residues in the Extracellular loop II and structural water molecules. The reported results are particularly relevant to the development and validation of atomistic models of prototypical G-protein-coupled receptors which regulate signal transduction across plasma membranes. 1

2 1 Introduction G-Protein-Coupled membrane Receptors (GPCRs) are macro-molecules of great theoretical and experimental interest since they regulate the transduction of signals across plasma membranes from the extracellular environment to the interior of every cell (Ji et al., 1998; Gether and Kobilka, 1998; Meng and Bourne, 2001; Marinissen and Gutkind, 2001). GPCRs are, therefore, important targets for pharmacological intervention (Baldwin et al., 1997). Rhodopsin is a prototypical member of the GPCR family, responsible for initiating the signaling transmission cascade in vertebrate vision (Meng and Bourne, 2001; Hamm, 2001; Ebrey and Koutalos, 2001). It is also the only member of the GPCR family whose structure has been solved at high-resolution. Therefore, rhodopsin is particularly important for advancing our understanding of structure-function relations in GPCRs. In this paper, the 1 H and 13 C NMR spectra of rhodopsin are investigated by using QM/MM hybrid methods at the ONIOM Electronic-Embedding (B3LYP/6-31G*:Amber) level of theory (Maseras and Morokuma, 1995; Svensson et al., 1996; Humbel et al., 1996; Dapprich et al., 1999; Vreven and Morokuma, 2000; Vreven et al., 2001; Vreven and Morokuma, 2003), in conjunction with the Gauge Independent Atomic Orbital (GIAO) method, (Ditchfield, 1974; Wolinski et al., 1990) and high-resolution structural data of bovine visual rhodopsin (Palczewski et al., 2000; Teller et al., 2001). This theoretical study of NMR chemical shifts builds upon QM/MM computational models developed in previous work (Gascon and Batista, 2004), in an effort to advance our understanding of structure-function relations in prototypical GPCRs. The study provides rigorous first-principle interpretations of experimental data founded on analysis of the structural and electronic properties of rhodopsin and bathorhodopsin at the detailed atomistic level. Rhodopsin consists of 348-aa residues and is composed of a bundle of seven transmembrane α-helices surrounding the 11-cis retinyl prosthetic group, a chromophore that is bound to the amino acid residue Lys-296 via a protonated Schiff Base (psb) linkage (Wald, 1968). Rhodopsin is responsible for a signal transduction mechanism, triggered by the light-induced 11-cis/all-trans-isomerization of the retinyl ligand (see Fig. 1), during the primary photochemical event (Wald, 1968; Goldschmidt et al., 1976; Rosenfeld et al., 1977; Honig et al., 1979). The reaction produces bathorhodopsin in the ground electronic state (Schoenlein et al., 1991; Wang et al., 1994), with a high quantum-yield within 200 gs, making it one of the fastest and most efficient photo-reactions in nature (Ji et al., 1998; Gether and Kobilka, 1998; Marinissen and Gutkind, 2001). The formation of the product bathorhodopsin is endothermic and stores approximately 50 % of the photon-energy (Honig et al., 1979; Cooper, 1979a; Cooper, 1979b; Schick et al., 1987). The stored energy is required to promote thermal reactions in the protein bleaching sequence and in the subsequent transducin cycle. The molecular rearrangements responsible for energy storage have been recently investigated by using QM/MM(Molecular Orbitals: Molecular Mechanics) (QM/MM(MO:MM)) hybrid methods in conjunction with high-resolution structures of 2

3 bovine rhodopsin (Gascon and Batista, 2004). There are currently four high-resolution structures of rhodopsin in the literature. The original 2.8 Å structure (PDB identifier 1F88) (Palczewski et al., 2000) was the first highresolution structure of a GPCR and revealed all the major features of the protein previously obtained from a variety of experimental data, including cryomicroscopy (Schertler and Hargrave, 2000). A refined model (PDB identifier 1HZX) (Teller et al., 2001) added some aminoacid residues not identified from the original work. A more recent structure (PDB identifier 1L9h) improved the resolution to 2.6 Å and resolved essential structural components of the chromophore binding site, including two bound-water molecules next to the retinyl chromophore (Okada et al., 2002). Finally, the most recent structure (PDB identifier 1U19), has completely resolved the polypeptide chain at 2.2 Å resolution and has provided further conformational details of the retinyl chromophore (Okada et al., 2004). However, even with these breakthroughs in X-ray spectroscopy, the crystallographic resolution obtained remains insufficient to unequivocally define the parts functionally important to the chromophore binding site (Okada et al., 2004). The reason for this seems to be that the refinement software for X-ray structures does not include parameters for chemically unusual structures such as the twisted extended π-system of the retinyl chromophore, or the carboxylate group of Glu-113 interacting with the delocalized charge in the chromophore. In the absence of an unequivocal X-ray definition of the chromophore-binding site, the orientation and conformation of the psb retinyl chromophore in rhodopsin continue to be the subject of much spectroscopic analysis, including rather heroic efforts in NMR spectroscopy (Shriver et al., 1979; Smith et al., 1990; Smith et al., 1991; Wang et al., 1996; Feng et al., 1997; Gröbner et al., 1998; Creemers et al., 1999; Verdegem et al., 1999; Feng et al., 2000; Gröbner et al., 2000; Verhoeven et al., 2001; Creemers et al., 2002; Carravetta et al., 2004; Crocker et al., 2004), FTIR (Fahmy et al., 1993), and resonance Raman spectroscopy (Eyring et al., 1982; Palings et al., 1987; Lin et al., 1998). However, the interpretation of this wealth of experimental data has yet to provide a fully consistent molecular picture. It is, therefore, essential to combine experimental studies with rigorous first principles computational approaches in order to develop a comprehensive molecular model. Of particular interest is the analysis of the role played by the extracellular loop II (EII) in the interior of the protein and the influence of its polar residues and structural water molecules next to the chromophore. Theoretical studies of rhodopsin have a long history (Warshel and Karplus, 1974; Warshel, 1976; Weiss and Warshel, 1979; Warshel and Barboy, 1982; Birge and Hubbard, 1980; Birge, 1981; Birge and Cooper, 1983; Car and Parrinello, 1985; Schick et al., 1987; Pastore et al., 1991; Tallent et al., 1992; Bifone et al., 1997; Vreven et al., 1997; Garavelli et al., 1998; La Penna et al., 1998; Molteni et al., 1999; Birge and Vought, 2000; Warshel and Chu, 2001; Birge, 2001). Most of these studies were performed long before the high resolution crystallographic structures of rhodopsin were available. The pioneer studies by Warshel and co-workers (Warshel, 1976; Weiss and Warshel, 1979; Warshel and Barboy, 1982), were 3

4 based on the semi-empirical QCFF/PI method for the description of the chromophore while the protein environment was modeled by a surface of closed-packed spheres with adjustable parameters. More recently, the QCFF/PI surfaces were re-calibrated (Warshel and Chu, 2001) to reproduce the trend of ab initio studies of the isolated chromophore (Vreven et al., 1997; Garavelli et al., 1998) but applied only in studies of bacteriorhodopsin (Warshel and Chu, 2001). Birge and co-workers (Birge and Hubbard, 1980; Birge and Cooper, 1983; Tallent et al., 1992) have implemented MNDO/AM1 and INDO-PSDCI procedures to describe the photo-isomerization dynamics in terms of a one-dimensional potential model with an arbitrary rate constant for the dissipation of internal energy. Rigorous molecular models, however, were not possible since the protein structure was not known. The availability of high-resolution X-ray structures, combined with advances in the development of QM/MM hybrid methods (Maseras and Morokuma, 1995; Svensson et al., 1996; Humbel et al., 1996; Dapprich et al., 1999; Vreven and Morokuma, 2000; Vreven et al., 2001), offers a great opportunity to develop rigorous atomistic models that should be fully consistent with experimental data. QM/MM calculations of electronic, vibrational and NMR spectra allow for the validation of these models through direct comparisons with experimental data. High-resolution X-ray structures have already motivated theoretical work focused on the analysis of the geometry and electronic excitation of the retinyl chromophore. The reported studies included calculations based on classical molecular dynamics simulations (Rohrig et al., 2002; Saam et al., 2002; Furutani et al., 2003), ab initio Restricted Hartree Fock (RHF) calculations of reduced-model systems (Yamada et al., 2002; Touw et al., 2004) and QM/MM computations (Sugihara et al., 2002a; Sugihara et al., 2002b; Ferre and Olivucci, 2003; Gascon and Batista, 2004; Okada et al., 2004). The 1 H and 13 C NMR spectra reported in this paper are based on the atomistic computational models of rhodopsin and bathorhodopsin developed in previous work (Gascon and Batista, 2004). The models were obtained by using QM/MM hybrid methods at the ONIOM-EE (TD-B3LYP/6-31G*//B3LYP/6-31G*: Amber) level of theory in conjunction with high-resolution X-ray structures and predicted the energy-storage and electronicexcitation energies for the dark and product states in very good agreement with experimental data. Here, it is shown that such models also predict NMR chemical shifts in very good agreement with solid-state NMR spectra of the retinyl chromophore in the rhodopsin and bathorhodopsin binding sites. In addition to the obvious advance associated with validating prototypical GPCR models, these calculations show that QM/MM geometry optimization of high-resolution structural data provides a rigorous technique which overcomes the limitations of traditional refinement methods, and therefore constitutes a general approach for simulating the spectroscopy of prosthetic groups embedded in biological molecules. To the best of our knowledge, this paper represents the first report on ab initio calculations of 1 H and 13 C NMR chemical shifts of the retinyl chromophore where the influence of the rhodopsin environment is explicitly considered. The paper is organized according to the following sections. Section Computational Mod- 4

5 els describes the preparation of computational models of the 11-cis retinyl chromophore in rhodopsin and in chloroform solution. Section QM/MM Method outlines the computational approach, including a description of the ONIOM hybrid methods for computations of 1 H and 13 C NMR chemical shifts according to the GIAO method. Section Results presents the computational results organized in five subsections: Subsection Rhodopsin 1 H NMR reports the computed 1 H NMR chemical shifts of rhodopsin and the comparison to solidstate NMR data. This subsection also reports the 1 H NMR chemical shifts of the psb 11-cis retinyl chromophore in chloroform solution and their comparison with corresponding experimental data. Subsection C6-C7 Bond Conformation discusses the conformation of the retinyl chromophore, with emphasis on the 6s-cis and 6s-trans configurations about the C6-C7 single bond. Subsection Rhodopsin 13 C NMR reports 13 C NMR chemical shifts of the 11-cis retinyl chromophore in rhodopsin and in chloroform solution as well as the corresponding comparisons to experimental data. Subsection Bathorhodopsin 13 C NMR compares the computed 13 C NMR chemical shifts of the all-trans retinyl chromophore in bathorhodopsin to readily available solid-state NMR data. Finally, subsection Comparative Structural Analysis compares the rhodopsin computational model investigated in this paper to other structures of bovine visual rhodopsin available in the literature. The final section summarizes the computational findings and concludes. 2 Computational Models Rhodopsin: The computational models of rhodopsin are prepared according to previous work (Gascon and Batista, 2004), and are based on the refinement of the crystal structure of bovine rhodopsin (Protein Data Bank (PDB) accession code 1F88, monomer A), solved at 2.8 Å resolution (Palczewski et al., 2000). Starting from the 1F88 PDB crystal structures, hydrogen atoms are added by using the molecular modeling program TINKER (Ponder, 2001). The protonation of all titratable groups is standard. The rhodopsin cavity is set neutral, consistent with experiment results (Fahmy et al., 1993). The Schiff-base linkage between Lys-296 and the chromophore bears a net positive charge NH(+), compensated by the Glu-113 negative counter-ion, forming a salt-bridge (Sakmar et al., 1989; Zhukovsky and Oprian, 1989). Amino acids Glu-122, Asp-83 and Glu-181, all within the protein core, are assumed to be neutral, as indicated by FTIR experiments (Fahmy et al., 1993) and UV-vis spectroscopic measurements of site-directed mutants (Yan et al., 2002). Finally, the regular ends of the protein and the artificial ends due to the missing or incomplete amino acids from the X-ray structures are capped with NH + 3 and CO 2. The model system in the present calculations contains 5170 atoms with a total charge of +4e. Model systems based on the crystal structure with PDB accession code 1L9H, monomer A, solved at 2.6 Å resolution (Okada et al., 2002) have also been prepared. A crucial difference between the 1F88 and 1L9H crystal structures is the presence of two water molecules 5

6 next to the retinyl chromophore in the 1L9H structure, not observed at the lower resolution. These two water molecules are included in the computational model investigated in this paper, since they are important to the stabilization of the chromophore inside the protein cavity (Gascon and Batista, 2004). Specifically, the computational model shows that these two water molecules participate in an extended hydrogen-bonding network (see Fig. 2), that involves both water molecules and polar residues Glu-181, Cys-187, Ser-186 and Glu-113. This structural feature associated with EII in the interior of the protein is consistent with a recently proposed counter-ion switch mechanism for a subsequent step in the rhodopsin photo-bleaching sequence (Birge and Knox, 2003; Yan et al., 2003). psb model: In order to compare the changes in the NMR spectroscopy of the retinyl chromophore inside the protein with a prototypical chromophore in solution (i.e., the opsin effects on NMR chemical shifts), computational models of the 11-cis- retinyl- propyliniumchloride complex in chloroform solution are also constructed. These changes are also compared to experimental data (Shriver et al., 1979). The psb complex is constructed by geometry optimization at the DFT B3LYP/6-31G* level of theory, embedded in a Polarizable Continuum Model (PCM) solvent (ɛ sol = 4.9). Figure 3 shows the optimized configuration of the complex, where the chloride ion is located in the C=NH+ plane at 2.09 Å from the proton of the Schiff-Base linkage. For future reference, Fig. 3 labels the carbon atoms along the polyene chain. 3 QM/MM Method The QM/MM(MO:MM) calculations reported in this paper are based on the ONIOM two-layer hydrogen link-atom scheme (Maseras and Morokuma, 1995; Svensson et al., 1996; Humbel et al., 1996; Dapprich et al., 1999; Vreven and Morokuma, 2000; Vreven et al., 2001; Vreven and Morokuma, 2003). The full-system of 5170 atoms is partitioned into two layers by imposing a frontier at the C δ -C ɛ bond of the Lys-296 side chain (i.e., two bonds beyond the C-NH(+) linkage). The Quantum-Mechanical (QM) layer includes 48 atoms of the retinyl chromophore, five atoms of Lys-296 (NH +,CH 2 ) and a link hydrogen atom that saturates the extra valence of the terminal -C-H 2 at the boundary. While a QM layer that includes only the retinyl chromophore is sufficient to describe the optimum geometry of the system, as well as conformational changes due to 11-cis/all-trans isomerization, the analysis of numerical convergency with respect to the size of the QM layer indicates that precise calculations of 1 H and 13 C NMR chemical shifts require a more extended QM layer. Thus we have explicitly considered in the QM layer amino acid residues with significant steric interactions with the chromophore, or nearby residues containing aromatic rings, including Trp-265, Tyr-268, Ser-186, Cys-187 and Gly-188. Inclusion of these residues results in an extended QM layer with 80 additional atoms, including 6 link hydrogen atoms placed a the C-N bond connecting these five residues with their neighbors. The remainder of the protein 6

7 defines the Molecular-Mechanics (MM) layer. The total energy of the system E is obtained according to the so-called ONIOM Electronic- Embedding (ONIOM-EE) approach, which combines three independent calculations as follows, E = E MM,full + E QM,red ẼMM,red, (1) where E MM,full is the energy of the full-system computed at the molecular-mechanics level of theory; E QM,red is the energy of the reduced-system computed at the quantum-mechanics level of theory; and ẼMM,red is the energy of the reduced-system computed at the molecularmechanics (MM) level of theory. Note that Electrostatic interactions between the two layers are included in the calculation of both E QM,red and ẼMM,red at the quantum mechanical and molecular mechanics levels, respectively. Therefore, the electrostatic interactions included at the MM level in both terms ẼMM,red and ẼMM,full cancel and the resulting quantum mechanical description includes the polarization of the reduced system induced by the surrounding protein environment. All calculations reported in this paper involve a description of the MM layer as modeled by the standard Amber force field (Cornell et al., 1995). The distribution of atomic charges in the retinyl chromophore is based on the ElectroStatic-Potential (ESP) atomic-charges, obtained at the ONIOM-EE (B3LYP/6-31G*: Amber) level of theory by using Gaussian03 (Frisch et al., 2003). Shielding constants (i.e., chemical shifts) are obtained according to the GIAO method at the DFT ONIOM-EE (B3LYP/6-31G*: Amber) level of theory. Details concerning the calculation of shielding constants have already been extensively reviewed in the literature (Helgaker et al., 1999). In order to facilitate the comparison to experimental values of shielding constants, often reported relative to various different internal or external references, ab initio chemical shifts are reported relative to the reference value of shielding constant that minimizes the overall root mean squared deviation between the ab initio and experimental NMR spectra. All chemical shifts are expressed as usual in parts per million (ppm). Therefore, a chemical shift at δ ppm indicates that the nucleus responsible for the signal is magnetically unshielded relative to the reference and requires a magnetic field δ millionths less than the field needed by the reference to produce resonance. 4 Results 4.1 Rhodopsin 1 H NMR Table 1 (columns 2 and 3) and Fig. 4 compare the calculated 1 H NMR chemical shifts of the 11-cis-retinyl chromophore in rhodopsin and the chemical shifts of the 11-cis- retinyl propylinium- chloride complex in chloroform solution with their corresponding experimental 1 H NMR chemical shifts. The remarkable agreement between ab initio and experimental values indicates that the computational models are able to reproduce the 1 H NMR spec- 7

8 troscopy of the chromophore in both the rhodopsin and solution environments, including the significant differences in chemical shifts between the more unshielded H atoms attached to sp 2 carbon atoms in the C7-C15 segment (σ P = 6 7 ppm range) and the more protected sp 3 carbon atoms (σ C = ppm range) in the methyl-substituent groups and the β-ionone ring. Table 1 (column 4) and Fig. 5 present the theoretical and experimental values of changes in the chromophore 1 H NMR chemical-shifts, σ H = σrhod H σh sol, due to the influence of the rhodopsin environment on 1 H NMR chemical shifts (i.e., the opsin effects on 1 H NMR chemical shifts). In semiquantitative agreement with the experimental data, the ab initio calculations predict that the most significant influence of the protein environment is to unshield H atoms in the C11-C14 segment, while nearby residues partially shield protons in the β-ionone ring, including H-4 and H-18. The theoretical predictions, however, underestimate changes in chemical shifts of H-15 and H-20 probably due to the oversimplified description provided by the reaction field of the PCM dielectric solvent, as indicated by the numerical deviations in Table 1 (column 3). In order to elucidate the fundamental interactions responsible for magnetically unshielding H atoms in the C11-C14 segment, the 1 H NMR spectrum has also been computed after zeroing the atomic charges of Wat2a and nearby polar residues, including amino acid residues in EII. The resulting opsin effects on the complete set of 1 H NMR chemical shifts is shown by the solid circles in Fig. 5. Obviously, these results indicate that EII and Wat2a are most responsible for the influence of the protein environment on the chemical shifts of H atoms in the C11-C14 segment. 4.2 C6-C7 Bond Conformation The configuration about the C6-C7 single bond of the 11-cis retinyl chromophore defines the orientation of the β-ionone ring relative to the polyene chain. The QM/MM computational models reported in this paper, as well as in previous work (Gascon and Batista, 2004), support the 6s-cis form with substantial negative ( 44 ) twist of the C6-C7 bond. All other dihedral angles along the polyene chain have been reported earlier (Gascon and Batista, 2004). The conformation of the C6-C7 bond, however, has been a subject of debate in the literature (Smith et al., 1990; Gröbner et al., 2000; Birge, 2001; Creemers et al., 2002). In particular, NMR studies by Watts and co-workers (Gröbner et al., 2000), as well as theoretical work by Birge and co-workers (Birge, 2001), concluded that the chromophore geometry is 6s-trans at the C6-C7 bond and not the 6s-cis assumed from earlier optical and other NMR studies (Smith et al., 1987; Smith et al., 1990; Tan et al., 1997; Jäger et al., 1997; Buss et al., 1998; Creemers et al., 2002). This section analyzes the non-trivial questions of whether the 6s-trans configuration is energetically accessible, whether the 1 H NMR chemical shifts of the 11-cis-retinyl chromophore in rhodopsin are affected by the 6s-cis/6s-trans configurational change of the C6-C7 8

9 bond and which of the two 1 H NMR spectra agrees better with experiments. In order to address these questions, computational models of the 6s-trans isomer were constructed by geometry relaxation of the system after cis/trans rotation of the β-ionone ring around the C6-C7 bond. It is found that the resulting 6s-trans structure, obtained at the ONIOM Electronic-Embedding (B3LYP/6-31G*:Amber) level of theory is more stable than the 6scis isomer by about 6 kcal/mol. However, the 1 H NMR chemical-shifts of the 6s-trans isomer compare much less favorably to experiments than those of the 6s-cis isomer, as shown in Fig. 6. Figure 6 compares the opsin effects on the 1 H NMR chemical-shifts of the 6s-trans chromophore ( σ H = σrhod H σh sol ) to the corresponding experimental values for rhodopsin. This figure shows that the 6s-trans isomer compares less favorably to experiments than the 6s-cis isomer (see Fig. 5). It is, therefore, concluded that the 6s-cis/6s-trans configurational change significantly affects the 1 H NMR chemical-shifts of the chromophore and that the 6scis isomer is the most likely structure in the dark state of rhodopsin, although the 6s-trans isomer is energetically more stable than the 6s-cis isomer. These results are consistent with recent NMR studies (Creemers et al., 2002) and with the analysis of the recently resolved X-ray structure at 2.2 Å resolution (Okada et al., 2004), but disagree with earlier studies (Gröbner et al., 2000; Birge, 2001). 4.3 Rhodopsin 13 C NMR Table 2 (columns 2 and 3) and Fig. 7 compare the calculated and experimental 13 C NMR chemical shifts of the 11-cis-retinyl chromophore in rhodopsin and the corresponding chemical shifts of the 11-cis- retinyl propylinium- chloride complex in chloroform solution. Fig. 7 also shows the ESP atomic charges of carbon atoms with sp 2 hybridization along the polyene chain. The agreement between ab initio and experimental values of chemical shifts indicates that the computational models are able to reproduce the 13 C NMR spectroscopy of the chromophore in both the rhodopsin and solution environments, including the significant difference in chemical shifts between the unshielded carbon atoms with sp 2 hybridization in the C7-C15 segment (σ C = ppm range) and the more protected sp 3 carbon atoms (σ C = ppm range). A common feature of both 13 C NMR spectra, shown in Fig. 7, is the zigzag alternation of chemical shifts in the segment C9-C15 of the polyene chain (i.e., C15, C13, C11 and C9 have maximum values while C14, C12, C10 are minima). Note that the alternation is observed in both the psb retinyl chromophore in rhodopsin (upper panel) and in solution (lower panel). Such an alternation pattern is partially correlated with a corresponding alternation of atomic charges along the polyene chain (see solid circles in Fig. 7, representing the ESP atomic charges of carbon atoms with sp 2 hybridization along the polyene chain). Note that such a correlation between atomic charge and bond alternation, however, vanishes in the C5-C8 segment where out-of-the-plane dihedral-angle distortions can be as large as 44 9

10 (Gascon and Batista, 2004). Table 2 (column 4) and Fig. 8 compare the theoretical and experimental values of changes in the chromophore 13 C NMR chemical-shifts, σ C = σrhod C σc sol, due to the influence of the rhodopsin environment (i.e., the opsin effects on 13 C NMR chemical shifts). Considering that the reported experimental errors of 13 C NMR chemical shifts can be as large as ± 1 ppm (Creemers et al., 2002; Smith et al., 1990), the overall semiquantitative agreement with experimental data is remarkable. The theoretical predictions, however, seem to underestimate the changes in the chemical shifts of C17 and C20, due to an overestimation of the chemical shifts of the corresponding methyl-substituent groups in rhodopsin, as indicated by the numerical deviations in Table 2 (column 2). These results predict that the protein environment partially unshields all C atoms in the polyene chain but C5. Table 3 presents the quantitative analysis of the electrostatic influence of the nearby amino acid residues on the 13 C NMR chemical shifts of the retinyl chromophore. Individual contributions are estimated as the difference in chemical shifts after and before zeroing the atomic charges of the specific residue. For clarity, only the residues with the largest upfield and downfield effects are listed. Table 3 thus identifies the specific residues responsible for producing the most significant influence, indicating that nearby residues can be responsible for σ C as large as ± 3 ppm of carbon atoms in the conjugate π-system (i.e., carbon atoms with sp 2 hybridization). In contrast, the chemical shifts of carbon atoms with sp 3 hybridization, (e.g., carbon atoms in methyl-substituent groups) are not as significantly affected by nearby residues (e.g., σ C < 1 ppm). The upfield of σ C at C5 has been the subject of recent discussion in the literature and has been assigned to the interaction between C5 and the carboxylic group of Glu-122 (Creemers et al., 2002). The calculations reported in this paper, however, indicate that the electrostatic influence of Glu-122 is negligible when such a residue is protonated as suggested by FTIR experiments (Fahmy et al., 1993). Instead, Table 3 shows that the most important upfield effect on C5 is due to Trp-265, with an upfield of -2.0 ppm. This effect, however, is almost completely canceled by the downfield of 1.8 ppm due to Asp-190. It is, therefore, concluded that the net upfield of σ C at C5 is not necessarily determined by the nearby residue with the largest upfield contribution but rather by the overall polarization of the π-system, predominantly modulated by the counter-ion Glu-113. In order to analyze the electrostatic contributions of EII and Wat2a to the 13 C NMR chemical shifts, the spectrum has been recomputed after zeroing the atomic charges of amino acid residues in EII and Wat2a. The resulting opsin effects on the complete set of 13 C NMR chemical shifts is shown by the solid circles in Fig. 8. These results indicate that the electrostatic influence of EII and Wat2a affects the overall 13 C NMR spectrum but does not fully account for the overall unshielding effect due to the protein environment. 10

11 4.4 Bathorhodopsin 13 C NMR The QM/MM analysis of molecular rearrangements due to the primary photochemical event in rhodopsin indicated that during such an event the φ(c11-c12) dihedral angle changes from 11 in the 11-cis isomer to 161 in the all-trans product, where the preferential sense of rotation along negative angles is determined by steric interactions between Ala-117 and the polyene chain at the C13 position (Gascon and Batista, 2004). The isomerization also induces torsion of the polyene chain due to other steric constraints in the binding pocket and stretching of the salt-bridge between the protonated Schiff-base and the Glu- 113 counterion. The stretching of the salt-bridge involves reorientation of the polarized bonds, localizing part of the net positive charge at the Schiff-base linkage, a process that is stabilized by the formation of a hydrogen bond between the protonated Schiff-base and Wat2b (Gascon and Batista, 2004). The resulting all-trans molecular structure has been validated by directly comparing the endothermicity of the cis/trans isomerization with calorimetry measurements as well as the S 0 S 1 electronic-excitation energies for the dark and product states to readily available spectroscopic data. Table 4 (second column) and Fig. 9 (upper panel) present the calculated 13 C NMR chemical shifts of the all-trans-retinyl chromophore in bathorhodopsin. Table 4 and Fig. 9 also show the experimental 13 C NMR chemical shifts of bathorhodopsin, available only for C8, C10, C11, C12, C13, C14, C15 (Smith et al., 1991). In addition, Table 4 (third column) and Fig. 9 (lower panel) present the theoretical and experimental values of changes in the chromophore 13 C NMR chemical-shifts, σ C = σbatho C σc rhod, due to the 11-cis/all-trans isomerization. The comparison shows good qualitative agreement between calculations and existing experimental data. However, a complete and systematic comparison would require a more comprehensive set of experimental data. Considering the long-standing interest in this system we anticipate that these results will stimulate the development of further experimental work. 4.5 Comparative Structural Analysis After the computational studies reported in the previous sections were completed, the latest refinement of the rhodopsin crystal structure was published at 2.2 Å resolution (Okada et al., 2004), together with a QM/MM structural analysis based on the Self-Consistent Charge Density Functional Tight Binding (SCC-DFTB) method (Elstner et al., 1998) and the CHARMM force field (MacKerell et al., 1998). Therefore, it is of interest to compare the structural properties of the rhodopsin computational model analyzed in this paper to the recently published molecular structures. Table 5 and Fig. 10 compare the chromophore bond-lengths in readily available X- ray structures and the QM/MM computational models, including the 1F88, 1HZX, 1L9H and 1U19 X-ray structures, the QM/MM-MD (SCC-DFTB:CHARMM) structure (Okada 11

12 et al., 2004) and the QM/MM ONIOM-EE (B3LYP:AMBER) rhodopsin model (Gascon and Batista, 2004) considered in this paper. The comparison includes bond-lengths along the polyene chain and the salt-bridge between the protonated Schiff-base and the negative counter-ion Glu-113. All distances but those in the last two columns are averaged over both monomers. The comparison shows that the rhodopsin computational model investigated in this work is fully consistent with the QM/MM-MD (SCC-DFTB:CHARMM) structure (Okada et al., 2004). However, when QM/MM models are compared to X-ray structures, both computational models show a weaker alternation of CC bond-lengths along the polyene chain (see zigzag of red triangles in Fig. 10), although in partial agreement with the chromophore bond lengths predicted by a recent double-quantum solid state NMR study (see last column of Table 5 and open circles in Fig. 10) (Carravetta et al., 2004). Furthermore, both QM/MM models predict a shorter distance N(Lys-296)-O(Glu-113) between the Schiff-base linkage and the counterion Glu-113. The structural differences between X-ray and QM/MM structures seem to result from inadequate parametrization of the software which interprets the X-ray data, specially when dealing with chemically unusual structures, including the twisted and extended π-system and the carboxylate group interacting with the delocalized charge of the extended chromophore. In addition, the X-ray structures show a larger dispersion of values in crystallographic bond-lengths and C11-C12 dihedral angles. The latter ranges from 36 in the 1U19 crystal structure (Okada et al., 2004) to 1 in 1F88, 8 in 1HZX, and 0 in 1L9H. In contrast, the ONIOM-EE and SCC-DFTB QM/MM models have a smaller dispersion and predict the C11-C12 dihedral angle to be 11 (Gascon and Batista, 2004) and 18 ± 9 (Okada et al., 2004), respectively, in reasonable agreement with the value 13 suggested by an earlier molecular dynamics simulations study (Saam et al., 2002). An important difference between the QM/MM-MD (SCC-DFTB:CHARMM) structure (Okada et al., 2004) and the QM/MM ONIOM-EE (B3LYP:AMBER) rhodopsin model analyzed in this paper (Gascon and Batista, 2004) concerns the assignment of interactions responsible for twisting the extended π-system. The QM/MM ONIOM-EE model predicts that the torque responsible for the C11-C12 dihedral twist is mainly due to steric interactions between the methyl-group of Ala-117 and the polyene chain at the C13 position (Gascon and Batista, 2004). These results are obtained from an analysis of the decomposition of forces acting on the chromophore at its equilibrium configuration in the binding site. In contrast, Okada et al suggest from simple inspection of the neighboring residues, that the C11-C12 negative twist must be due to interactions with the Trp-265 residue (Okada et al., 2004). The reduction of bond-length alternation near the Schiff-base linkage has been attributed to partial delocalization of the net positive charge in the psb (Carravetta et al., 2004), since the delocalization of positive charge is expected to weaken the corresponding CC doublebonds. In order to analyze the extent of positive charge delocalization along the polyene chain, the distribution of electronic density has been computed after and before protona- 12

13 tion of the retinyl chromophore in the rhodopsin binding site. Figure 11 (upper panel) shows iso-surfaces of electronic density difference, obtained at the ONIOM-EE (B3LYP/6-31g*:AMBER) level, after and before protonation of the chromophore in its equilibrium configuration. Note that the presence of the proton at the Schiff-linkage induces electronic charge redistribution, driving electronic density from the polyene chain toward the NH+ bond (see red iso-surface). As a consequence, a partial positive charge (green iso-surface) is injected in the polyene chain according to an alternating pattern i.e., the decrease of electronic density (or delocalization of positive charge) is represented by the green iso-surface. It is shown that the positive charge is partially delocalized in the segment C9-C15, N z (Lys- 296), and C ɛ. Indeed, such a delocalization of positive charge, with significant amplitude at C15 and C13 and minimum at C14, directly correlates with the 13 C NMR chemical-shifts shown in Fig. 7. In order to investigate whether the underlying delocalization of positive charge is influenced by nearby polar residues in EII and Wat2a, the electronic density difference after and before protonation of the chromophore has been recomputed but after zeroing all atomic charges in EII and Wat2a (see Fig. 11 (lower panel)). The comparison between the upper and lower panels of Fig. 11 shows that the electrostatic influence of EII and Wat2a accounts for small changes in the delocalization of positive charge along the polyene chain. Note that switching off the atomic charges of EII and Wat2a enhances the alternating pattern of charge distribution and extends the delocalization throughout the polyene chain (i.e., see significant amplitude at C7). These results therefore partially agree a recent solid-state NMR study (Carravetta et al., 2004), where EII and Wat2a were thought to influence the delocalization of positive charge. However, our results do not support the assesment, in that study, that the positive charge is being pulled away from the Schiff-base linkage. Rather than pulling positive charge away from the linkage, toward the C12 atom, the electrostatic influence of EII and Wat2a concentrates the positive charge next to the Schiff-base linkage within the C9-C15 segment although with negligible amplitude on C12 (i.e., note that in the absence of such electrostatic interactions the positive charge is more delocalized along the entire π-system). It has also been suggested that the influence of EII and Wat2a should also reduce of bond-length alternation near the Schiff-base linkage (Carravetta et al., 2004). In contrast, the re-optimization of rhodopsin at the ONIOM-EE (B3LYP/6-31g*:AMBER) level after zeroing all atomic charges in the EII and Wat2a indicates that the absence of electrostatic interactions with EII and Wat2a does not significantly alter the bond-length alternation pattern along the polyene chain. These results will be reported in a future publication together with a Natural Bond Orbital (NBO) analysis of resonance structures responsible for the redistribution of charges along the polyene chain. 13

14 5 Conclusions We have investigated the 1 H and 13 C NMR spectra of the retinyl chromophore in rhodopsin by using QM/MM hybrid methods at the DFT (B3LYP/6-31G*:Amber) level in conjunction with the GIAO method for ab initio SCF calculations of NMR chemical shifts. We have shown that computational models of rhodopsin, developed by QM/MM geometry optimization of high-resolution X-ray structural data, are able to reproduce the 1 H NMR and 13 C NMR spectra of the retinyl chromophore in very good agreement with recent solidstate NMR measurements, in addition to reproducing the electronic spectroscopy as shown in previous work (Gascon and Batista, 2004). Furthermore, we have also shown that the computational methodology is able to reproduce the NMR spectroscopy of the chromophore in solution as well as the changes in the chromophore chemical shifts due to 11-cis/all-trans isomerization in the rhodopsin environment. These results are particularly relevant to the validation of detailed atomistic models of rhodopsin (Gascon and Batista, 2004), a prototypical GPCR which regulates signal transduction across plasma membranes. In addition to the obvious advance associated with establishing GPCR atomistic models, these calculations show that the QM/MM geometry optimization of high-resolution structural data provides a rigorous technique that overcomes the limitations of traditional refinement methods and a general approach to simulate the spectroscopy of prosthetic groups embedded in biological molecules. We have computationally shown that the 6s-cis/6s-trans configurational change, about the C6-C7 single bond of the 11-cis retinyl chromophore, significantly affects the 1 H NMR chemical-shifts of the chromophore. We found that our computational models predict the 6s-cis isomer to be the most likely structure in the dark state of rhodopsin, although the 6s-trans isomer is energetically slightly more stable. These results are consistent with recent NMR experimental studies (Creemers et al., 2002) and with the QM/MM analysis of the most recently resolved X-ray structure (Okada et al., 2004). We have shown that the QM/MM computational models reveal significant alternation of bond-lengths in the C5-C9 segment of the polyene chain. Such a bond-length alternation pattern becomes weaker along the π-system near the Schiff-base linkage, in partial agreement with the chromophore bond-lengths predicted by a recent double-quantum solid state NMR study (Carravetta et al., 2004). We have shown that the quantitative QM/MM analysis of delocalization of positive charge does not support a model where the EII and Wat2a significantly stabilize a partial positive away from the Schiff-base linkage, on C12 (Carravetta et al., 2004). In contrast, the results reported in this paper show that the partially injected positive charge remains delocalized in the C9-C15 N z (Lys-296) and C ɛ atoms, with very small density on C12. Rather than shifting the positive charge away from the linkage toward C12, EII and Wat2a concentrate the otherwise more delocalized positive charge next to the Schiff-base linkage within the C9-C15 segment. 14

15 We found that the 1 H NMR chemical shifts are considerably more sensitive than the 13 C NMR chemical shifts to changes in the chromophore environment (e.g., from solution to the protein environment). In particular, the 1 H NMR spectra is found to be significantly influenced by nearby polar residues in EII and residues with aromatic rings (e.g., Trp-265, and Tyr-268). Reliable QM/MM calculations of chemical shifts thus require including these residues in the QM layer, predicting that site specific mutations of any of these residues would produce a large effect on the observed 1 H NMR spectroscopy of the chromophore in rhodopsin. 6 Acknowledgment V.S.B. acknowledges supercomputer time from the National Energy Research Scientific Computing (NERSC) Center and financial support from Research Corporation, Research Innovation Award # RI0702, a Petroleum Research Fund Award from the American Chemical Society PRF # G6, a junior faculty award from the F. Warren Hellman Family, the National Science Foundation (NSF) Career Program Award CHE # , the NSF Nanoscale Exploratory Research (NER) Award ECS # and start-up package funds from the Provost s office at Yale University. The authors are very grateful to Mr. Sabas Abuabara for proof-reading the manuscript. References Baldwin, J., Schertler, G., and Unger, V. (1997). An alpha-carbon template for the transmembrane helices in the rhodopsin family of G-protein- coupled receptors. J. Mol. Biol., 272: Bifone, A., de Groot, H. J. M., and Buda, F. (1997). Energy storage in the primary photoproduct of vision. J. Phys. Chem. B, 101: Birge, R. (1981). Photophysics of light transduction in rhodopsin and bacteriorhodopsin. Annu. Rev. Biophys. Bioeng., 10: Birge, R. (2001). Conformation and orientation of the retinyl chromophore in rhodopsin: A critical evaluation of recent NMR data on the basis of theoretical calculations results in a minimum energy structure consistent with all experimental data. Biochemistry, 40: Birge, R. and Cooper, T. (1983). Energy-storage in the primary step of the photocycle of bacteriorhodopsin. Biophys. J., 42:61. 15

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24 11-cis-rhodopsin fs all-trans bathorodopsin NH-Lys NH-Lys Figure 1: 24

25 W265 A117 K296 Y268 wat2b wat2a E181 E113 C187 S186 Figure 2: 25