Ab Initio Study of 13C NMR Chemical Shifts for the Chromophores of

Author to whom all correspondence should be addressed. † Tokyo Institute of Technology. ‡ Cray Research Japan Ltd. X Abstract published in AdVance...
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J. Phys. Chem. 1996, 100, 1957-1964

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Ab Initio Study of 13C NMR Chemical Shifts for the Chromophores of Rhodopsin and Bacteriorhodopsin. 2. Comprehensive Analysis of the 13C Chemical Shifts of Protonated all-trans-Retinylidene Schiff Base Minoru Sakurai,*,† Mitsuhito Wada,† Yoshio Inoue,† Yusuke Tamura,‡ and Yoichi Watanabe‡ Department of Biomolecular Engineering, Tokyo Institute of Technology, 4259 Nagatsuta-cho, Midori-ku, Yokohama 226, Japan, and Cray Research Japan Ltd., 13-3 Ichiban-cho, Chiyoda-ku, Tokyo 102, Japan ReceiVed: August 2, 1995; In Final Form: October 12, 1995X

Theoretical analysis was performed for the 13C chemical shifts of the retinal chromophore in bacteriorhodopsin (bR) by means of ab initio NMR shielding calculation, based on the localized orbital/local origin method. In order to comprehensively investigate the correlation between the 13C chemical shieldings of the unsaturated carbons and physicochemical perturbations relating to the spectral tuning of bacteriorhodopsin, the following three factors are taken into account in the present calculation: (1) change in strength of the hydrogen bonding between protonated retinylidene Schiff base and its counterion, (2) conformational changes about single bonds of the conjugated chain, and (3) electrostatic interactions between the Schiff base and electric dipoles. On the basis of these calculations, we successfully find a molecular model for which the shielding calculation almost completely reproduces the observed chemical shift data for the chromophore of bR.

Introduction Bacteriorhodopsin (bR), found in the purple membrane of Halobacterium halobium, acts as a light-driven proton pump.1a-d The light-adapted form of the pigment possesses an all-transretinal covalently bound via a protonated Schiff base linkage with Lys216 of an apoprotein, bacterioopsin.1a-d The all-trans to 13-cis isomerization of the chromophore upon illumination is followed by the cyclic photoreaction, resulting in transfer of the Schiff base proton to the extracellular side.1a-d Similarly, rhodopsin (Rh) present in the rod cell of retina possesses a 11cis-retinal prosthetic group and is responsible for the initial stage of vertebrate dim-light vision.1b-g In spite of the basic difference of biological function, bR has also attracted much attention in the study of visual photochemistry due to the structural resemblance to Rh. An unusual optical property is observed for bR as well as Rh. The absorption maxima of the protonated retinylidene Schiff base appears at 440 nm in methanol, whereas bR and bovine Rh absorb maximally at 568 and 498 nm, respectively.2 Such spectral regulation has been of major interest for many years in the photobiology of the retinal proteins. This red shift of bR, so-called “opsin shift”,2 has been supposed to be originated mainly from (1) a weakened interaction (or increased separation) between the positively charged Schiff base and its counterion relative to the case of model compounds3 and (2) recovering of the conjugation between the C5dC6 double bond and the rest of the chain owing to a conformational change about the C6-C7 single bond.4 For bR, it has been suggested that the complete explanation of the opsin shift requires an additional third factor:5 (3) electrostatic interaction between the ionone ring and the external point charge(s) originating in amino acid residue(s).5 Figure 1 shows the chemical shift difference between alltrans-retinylidenebutylamine chloride and the light-adapted form of bR (bR568) obtained in a series of experiments of Griffin’s group.6-9 The data would reflect the conformational change * Author to whom all correspondence should be addressed. † Tokyo Institute of Technology. ‡ Cray Research Japan Ltd. X Abstract published in AdVance ACS Abstracts, January 1, 1996.

0022-3654/96/20100-1957$12.00/0

Figure 1. Plot of the 13C chemical shift difference between bacteriorhodopsin and the chloride salt of all-trans-N-retinylidene-n-butylamine (data taken from refs 9 and 31).

of the retinal chromophore and its interaction with the surrounding environment formed by the protein matrix including dipolar bonds and titrating groups. However, the interpretation of the experimental chemical shifts is still not well-established. For example, the observation of an unusual downfield shift in the C5 shielding may provide the support for the existence of a negatively charged protein residue in the vicinity of C5, and simultaneously, the existence of a positive charge near C7 may be inferred from the chemical shift data for the C5-C7 carbons.8 However, recent NMR and UV/visible studies of a series of retinal analogues implied that the absorption maximum for bR and its C5 chemical shift can be fully explained by a synergistic effect of a combination of the above-mentioned first and second factors without invoking point charges.10,11 Theoretical approaches may be helpful to interpret unambiguously the 13C chemical shifts for bR, because they can provide information about 13C shielding constants even for model compounds which could not be easily synthesized. A wellknown approach is based on the assumption of a linear correlation between experimental chemical shift and π-electron density calculated with a molecular orbital method.12-14 However, such a semiempirical approach seems to have some difficulty in arguing the NMR chemical shift data quantitatively, and it cannot be applied to shielding tensor analysis. An alternative approach is the direct calculation of 13C shielding constants using molecular orbital methods combined with © 1996 American Chemical Society

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theories for NMR shielding. Recently, we have demonstrated that the ab initio shielding calculations, based on Hansen and Bouman’s theory,15-17 provide accurate prediction for the 13C chemical shifts of retinal and its related compounds.18-20 One of the most important findings in our previous study is that the shieldings of the C5 and C8 carbons exhibit periodic changes against the C5dC6sC7dC8 dihedral angle.19 From this, it has been inferred that the chromophore of bR has the planar s-trans conformation about the C6-C7 single bond. This insight has been, however, drawn from the calculation for a model compound whose conjugated system is one isoprene unit shorter than retinal’s, and whose terminal structure is aldehyde, not protonated Schiff base. Rigid confirmation should be given on the basis of calculation for more realistic model compounds. In this study, the 13C shielding calculation is applied to protonated Schiff bases whose conjugated chains have the same number of double bonds as retinal’s. Our main purpose is to comprehensively investigate the correlation between the 13C chemical shifts of the unsaturated carbons and the aforementioned three factors including conformational change about all the single bonds other than the C6-C7 bond. On the basis of these calculations, we successfully find a better molecular model for which the shielding calculation almost completely reproduces the observed chemical shift data for the chromophore of bR. Computational Details

Figure 2. Structures of all-trans-retinal and its analogues.

We used the program RPAC9.021 developed by Hansen and Bouman for ab initio shielding calculations, interfacing to the Gaussian 90 program.22 The computational scheme adopted in this program is based on localized orbital/local origin (LORG) theory,15-17 in which occupied orbitals are localized according to the Foster-Boys criterion.23 Here, we chose the “LORG” localization scheme (not “full LORG” scheme).15 Recently, we have studied in detail what level of basis sets is required to accurately reproduce the 13C chemical shifts of conjugated carbons in retinal and its related compounds.20 According to the results, the 6-31G* or 6-31G** basis sets are required to reproduce the observed data for all the conjugated carbons studied, but even in the 4-31G level of calculation, there is fairly good correlation between the calculated and observed data except for carbonyl and imine carbons. The 4-31G calculation tends to overestimate the chemical shifts of carbons attached to heteroatoms by 5-10 ppm. In CPU time, here the 4-31G basis sets were used for all the shielding calculation. Instead, the data for the imine carbon of Schiff base will not be considered in the subsequent discussion. All the calculated and experimental shieldings were converted to a methane reference, and the positive sign indicates deshielding. The 4-31G//4-31G shieldings for methane shift 222.4 ppm downfield from naked carbon. The experimental shielding for methane shifts 2.1 ppm upfield from tetramethylsilane.24 The geometries of model compounds were optimized by the 4-31G level of calculation, using the Gaussian 92 program.25 Then, for the compounds whose crystal structures have not been published, Pople’s standard parameters26 were used for determining the starting geometries. Unless otherwise noted, we then assumed the trans zigzag framework for the conjugated chain and the anti configuration about the CdN bond. All the calculations were carried out on Cray YMP8E/8128 and C90 supercomputers.

shielding calculation and the other compounds are ones whose experimental data are cited in the subsequent sections. Although N-retinylidene-n-butylamine may be a proper model for the chromophores of bR, the major part of this study was pursued by using analogues 1a and 1b, where the n-butyl group is replaced by an ethyl group. We have already confirmed that such a structural truncation does not exert a significant effect on the isotropic chemical shifts and the principal values of the shielding tensor of the conjugated carbons (within 1 ppm).20 In addition, the ionone ring was replaced by a CH3CHdCH group, giving analogue 1c. We have also confirmed that for the C9 to N atoms, such a structural modification hardly affects both isotropic shieldings (within 1 ppm) and principal values. When the isotropic shieldings of the C5 to C8 atoms were compared with the observed data for PSB 2c, the correlation coefficient was 0.84.27 We used a chloride anion as the counterion of protonated Schiff base, although a carboxylate ion may be a better model of Asp85 and/or Asp212, which is (are) likely to be the counterion of the chromophore in bR.28-30 This replacement is required from the following facts. In the step of geometry optimization, the proton attached to the Schiff base is abstracted by a carboxylate ion, leaving both components neutral. The use of chloride prevents the occurrence of such a proton abstraction. PSBs 4 and 5 were used to examine the effect of demethylation at C1 on the shieldings of the conjugated carbons. The computational procedures obtaining the structure of PSB 4 were as follows. First, the dihedral angle about C5dC6sC7dC8 was determined to be 59.0° by optimizing the structure of PSB 2c, which has a ionone ring. Next, all the geometrical parameters of PSB 4 were optimized with the above dihedral fixed to be 59.0°. Similar procedures were carried out to determine the structures of PSB 5.

Selection of Model Compounds

Results

The model compounds studied here are shown in Figure 2, where compounds 1a-c, 4, and 5 were actually used in the

Reliability of the Shielding Calculation. In general, to check the reliability and limitation of the 13C shielding calcula-

Chromophores of Rhodopsin and Bacteriorhodopsin

Figure 3. Comparison of the calculated (b) and experimental (O) chemical shifts for the unsaturated carbon of (a) USB and (b) PSB, together with the difference (c) between PSB and USB (experimental data taken from ref 31). For compounds 1a and 1b, the C5dC6sC7dC8 dihedral angle (φ6-7) was set to be 60° (skewed 6-s-cis form), and the other geometrical parameters were optimized. In the case of PSB 1b, the resulting distance between the Schiff base nitrogen and a chloride anion (rN-Cl) was 3.0 Å.

tions, it is desirable that the principal values of shielding tensors are compared between the calculated values and the corresponding experimental data. Unfortunately, the principal values have not been reported for the 13C shielding tensors of the conjugated carbons of retinylidene Schiff bases. Here the isotropic shieldings were used for comparison. Parts a and b of Figure 3 indicate the calculated data for USB 1a and PSB 1b and the solid-state NMR data for USB 2a and PSB 2b.31,32 The calculated chemical shieldings are in good agreement with the experimental ones: the correlation coefficients except for C15 are 0.86 and 0.96 for USB and PSB, respectively. Figure 3c shows the chemical shift difference between USB and PSB. The calculation reproduces well the characteristic zigzag pattern: the largest downfield shift is found at C13, and the magnitudes of the downfield shifts in the odd-numbered carbons decrease with an increase in distance from the Schiff base terminal. Consequently, it is confirmed that the shielding calculation used is sufficiently accurate for analyzing the chemical shifts of USB and PSB, although we have already obtained a similar conclusion through application of the calculation to all-trans-retinal with full atomic representation.19 Effects of Counterion on the 13C Shieldings. In order to examine the effect of Coulombic interactions between the protonated Schiff base and its counterion, the position of a chloride ion was consecutively changed along the N-H bond on the conjugated plane of PSB 1b. For each case, the geometry was optimized with a constraint of fixing the distance (rN-Cl) between the Schiff base nitrogen and the chloride anion. In Figure 4, the 13C isotropic shieldings of PSB 1b are plotted against the distance rN-Cl. The shieldings of C9, C11, and C13 shift downfield with an increase in rN-Cl, whereas no apparent

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Figure 4. Isotropic chemical shifts for the unsaturated carbons of PSB 1b calculated as a function of the length rN-Cl.

Figure 5. Molecular configuration of the water-containing model.

shifts are observed for carbons distant from the Schiff base linkage and for the even-numbered carbons. The shieldings of C9, C11, and C13 shift downfield by 1.3, 2.3, and 6.5 ppm, respectively, when the value of rN-Cl changes slightly from 3.0 to 3.5. It is worth noting that the shielding of C13 most sensitively changes against the charge separation. This finding is consistent with results from solution-state NMR measurements.34 For example, the chemical shift differences between the trifluoroacetate salt of N-(11-cis-retinylidene)propylimine and the hydrochloride salt of the same imine are 1.5, 1.7, and 3.9 ppm for the C9, C11, and C13 carbons, respectively.33 Since trifluoroacetate anion is more bulky than chloride anion, these data show a result of weakening of the electrostatic interaction between the Schiff base and the counterion. It has been widely accepted that some water molecules exist inside bR.34-40 From the resonance Raman studies of the CdN stretching band of the chromophore, it has been suggested that one water molecule is hydrogen-bonded to the Schiff base in bR.34 Here a water-containing model was made by applying geometry optimization to a system including PSB 1b and one water molecule. As shown in Figure 5, the water molecule is hydrogen-bonded to both the Schiff base and its counterion,

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Figure 6. Calculated chemical shift difference between the watercontaining model and PSB 1b.

Figure 7. Isotropic chemical shifts for the C5 and C8 of PSB 1c calculated as a function of the angle φ6-7.

which is not directly hydrogen-bonded to the Schiff base. Figure 6 shows the chemical shift difference between the watercontaining model and PSB 1b, with a chloride ion located at 3.0 from the Schiff base. The resulting shift pattern is similar to that induced by increasing the Schiff base-counterion separation in the water-lacking model (Figure 4). Thus, the water simply acts as a spacer without causing any unique shielding changes to the conjugated carbons. Effects of Single-Bond Rotations on the 13C Shieldings. In Figure 7, the 13C isotropic shieldings for PSB 1c are plotted against the rotation angle φ6-7. For the planar 6-s-cis conformation, the angle φ6-7 was taken to be 0°. The shieldings of C5, C6, C7, C8, and C9 change with the value of φ6-7, whereas no apparent angular dependence is found in the carbons distant from the C6-C7 bond (data not shown). One of the most striking findings is that the shieldings of C5 and C8 exhibit clear periodic dependence on the angle φ6-7. In Figure 8, the principal values for the C5 shielding tensor are plotted against the angle φ6-7. It is evident that the σ22 and σ33 elements dominantly contribute to the periodic angular dependence of the C5 shielding. Similar results were obtained for the C8 shielding tensors (data not shown). In both isotropic shielding and principal values, the behavior of the C5 and C8 of PSB 1c is essentially similar to that of the corresponding carbons of retinal analogue 6 which was intensively studied in our previous report.19 It is thus concluded that the periodicity is independent of the existence of the ionone ring and of the length of the conjugated chain. It may be safely said that the conjugated polyene compounds share this property. Therefore, the origin of periodicity is attributed to the recovering and breaking of the conjugated plane, as described in detail in the previous study.19

Figure 8. Principal components of the shielding tensor for C5 of PSB 1c calculated as a function of the angle φ6-7.

Comparison between the calculated and experimental data for the effects of the C6-C7 rotation is shown in Figure 9, where the calculated data were obtained by taking the difference in chemical shifts between PSB 1d in a skewed form (φ6-7 ) 90°) and that in a planar 6-s-trans form (φ6-7 ) 180°) , and the experimental data indicate the chemical shift difference between 2d and 3 in the solution state.10 The analogue 2d is assumed to have a skewed conformation about the C6-C7 bond due to the steric hindrances between H8 and C16 or between H8 and the two methyl groups attached to C1,10 whereas the analogue 3 is supposed to take the planar 6-s-trans conformation as a result of the 1,1-demethylation.10 Thus, both calculated and observed data would reflect the conformational change in going from a skewed 6-s form to the planar 6-s-trans form. It is, however, expected that the demethylation gives nonnegligible contribution to the shielding difference between 2d and 3a. The net effect of demethylation could be extracted by subtracting the shieldings for compound 4 from those for compound 5. The experimental data were corrected using this result (solid line in Figure 9b). Clearly, the calculated chemical shift difference is in better agreement with the corrected experimental data. The effect of rotation around the other single bonds is shown in Figure 10, where the data indicate the chemical shift change arising from rotation of each single bond by 30°. The shieldings of carbons near the rotated bond are mainly affected; the torsion around the C8-C9 bond leads to a downfield shift for the C10 shielding by 1.6 ppm; the torsion around the C12-C13 bond causes an upfield shift for the C13 shielding by ca. 1.4 ppm. In the case of C14-C15 bond, the C13 shielding again largely shifts downfield, similar to the counterion effect as

Chromophores of Rhodopsin and Bacteriorhodopsin

Figure 9. Chemical shift changes in going from a skewed to a planar 6-s-trans form of a retinal Schiff base. (a) Calculated value is obtained by subtracting the chemical shifts of 1c at φ6-7 ) 90° from those of 1c at φ6-7 ) 180°. (b) Experimental values (b) are obtained by subtracting the chemical shifts of 2a from those of 3a and are corrected for the effect of demethylation as described in the text. The expeirmental value without the correction (×) is also indicated in the dashed line (experimental data taken from ref 10).

J. Phys. Chem., Vol. 100, No. 5, 1996 1961 that the electron exchange between the HCl and the conjugated system is negligibly small. First, the HCl was located as indicated in Figure 11a: the chloride and hydrogen atoms of HCl are placed above the C5 and C6, respectively, and the H-Cl bond is directed parallel to the C5dC6 double bond. In this case, the dipole field mainly affects the shieldings of C5 and C6. The C5 and C6 shieldings shift downfield by 6.3 ppm and upfield by 2.8 ppm, respectively, accompanied by a small upfield shift (1.4 ppm) of the C8 resonance. Similar results are also obtained for two cases as illustrated in Figure 11c and e, where the H-Cl bond is directed parallel to the C7dC8 or C9dC10 double bond, respectively. On the other hand, no striking influence is found on all the carbon shieldings when the H-Cl bond is placed parallel to the single bond, as illustrated in Figure 11b and d, or when it is orientated perpendicular to the conjugated plane, as illustrated in Figure 11g. In order to further check the effect of dipolar field on the 13C shieldings, two HCl molecules were simultaneously located above the C5dC6 and C7dC8 double bonds (Figure 12a). The calculated chemical shift difference is indicated in the solid line. The broken line represents the sum of chemical shift differences for the two separate models, models where a single HCl molecule is located above the C5dC6 or C7dC8. The broken line is nearly identical with the solid line. Similarly, for the case where two HCl molecules are located above the C5dC6 and C9dC10 double bonds, the broken line is again nearly identical with the solid line. Thus, it is reasonable to conclude that the effect of dipolar field has an additive property. Discussion

Figure 10. Calculated chemical shift changes for PSB 1b induced by rotation around each single bond by 30° from the planar trans conformation.

described above. However, the torsion around the C14-C15 single bond is not expected to occur because the torsional potential barrier is larger than those of the other C-C single bonds.41 Effect of Dipolar Electric Field on the 13C Shieldings. According to an external charge model,5 an ion pair is placed above the ionone ring. In order to test this model, we used hydrogen chloride as a model of aprotein dipole. Hereafter, the term “HCl” is used to distinguish this hydrogen chloride molecule from the proton donor of the Schiff base. We systematically located HCl above the conjugated plane of PSB 1b with keeping the chloride counterion at 3.0 Å from the nitrogen along the N-H bond and calculated the chemical shift difference relative to chloride salt of PSB 1b without a perturbation from the HCl dipole. The position of chloride of HCl is set at 3.2 Å apart from the conjugated plane so that PSB 1b and the HCl are in van der Waals contact with each other. For such a model, the Mulliken population analysis indicated

Interpretation of 13C Shieldings of bR. The above results indicate the way in which the 13C shieldings of the conjugated carbons are affected by the individual structural or electrostatic perturbation believed to be responsible for the spectral tuning of bR. On the basis of this information, we attempt to deduce the structure and local electrostatic environments of the bR retinal chromophore. The chloride salt of all-trans-retinal PSB with n-butylamine is an appropriate reference compound for analyzing the chemical shifts of bR (Figure 1). Unfortunately, the crystal structure of this compound has not been published, but its key geometries can be estimated as follows. First, it can be assumed that the C6-C7 bond takes a skewed conformation on the basis of the X-ray structure of all-trans-retinal32 and of the data for the C5 and C8 shieldings. In our previous study,19 it was proposed that the value of σC8-C5, obtained by subtracting the value of the C5 shielding from that of the C8 one, can be used to estimate the twist angle of the C6-C7 bond (φ6-7). The σC8-C5 for the reference compound is 12.0 ppm, indicating that the φ6-7 angle is 80-100°, corresponding to a skewed 6-s form. Second, the distance between the Schiff base nitrogen and the chloride counterion can be estimated to be 3.0 Å from the optimized structure of the complex of the Schiff base 1b. We start from the separate consideration of the following two factors: that is, the Schiff base-counterion interaction and a conformational change about the C6-C7 bond. The effect of the first factor may be examined by introducing a hypothetical process in which the rN-Cl distance is elongated from 3.0 to 3.5 Å along the N-H bond. The resulting chemical shift changes calculated for PSB 1b are plotted in Figure 13a. Comparing this with Figure 1, it is evident that the calculation reproduces well the characteristic shielding pattern near the Schiff base terminal, especially a large downfield shift on C13 (5.2 ppm). This indicates that the Schiff base-counterion

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Figure 12. Chemical shift difference induced by the double-site location of HCl’s in PSB 1b. (a) the solid line (b) indicates the calculated chemical shift change for PSB 1b induced by the dipolar field of two HCl molecules simultaneously located above the C5dC6 and C7dC8 double bonds. The molecular configuration used is illustrated in the right-hand side of the plot. The dashed (×) line indicates the sum of chemical shift differences for the two separate model, a model where a single HCl molecule is located above the C5dC6 or C7dC8 of PSB 1b. (b) Two HCl molecules are simultaneously located above the C5dC6 and C9dC10 double bonds. The symbols b and × are used in a manner similar to the case of a.

Figure 13. Effects of a weakened Schiff base-counterion interaction and a rotation around the C6-C7 single bond. (a) Calculated chemical shift difference between PSB 1b with a chloride ion at 3.0 Å and with that at 3.5 Å. (b) Calculated chemical shift difference between PSB 1c in a skewed form (φ6-7 ) 90°) and that in a planar 6-s-trans form (φ6-7 ) 180°).

Figure 11. Chemical shift changes between the complex (PSB 1b + HCl) and PSB 1b. The corresponding molecular configuration for each complex is illustrated in the right-hand side of the plot.

interaction in bR is appreciably weakened compared with the reference. Figure 13b shows the data for the chemical shift changes of PSB 1d induced by a conformational transition on

going from a skewed 6-s form (φ6-7 ) 90°) to a planar 6-strans form (φ6-7 ) 180°). Such a shielding pattern is very similar to that for carbons near the ionone ring (C5 to C9) observed in bR, suggesting that the chromophore of bR takes a nearly planar 6-s-trans conformation about the C6-C7 single bond. This result is consistent with that of our previous work19 and other spectroscopic studies.4,42-44 Figure 14a shows a combining effect of the two perturbations of interest. The major part of the observed data was reproduced by the calculation. It can be thus concluded that the dominat factors, responsible for the shielding diffrences between the reference and the bR chromophore, are a weak Schiff base-counterion interaction and a 6-s-trans conformation.6-11,45

Chromophores of Rhodopsin and Bacteriorhodopsin

Figure 14. Synergistic effects. (a) Filled circle indicates the sum of the chemical shift difference indicated in Figures 13a and b. Open circle indicates difference in chemical shifts observed between bR and PSB 2b. (b) Filled circle indicates the sum of the chemical shift differences indicates in Figures 11a, 13a, and b. Open circle is the same as in a (experimental data taken from refs 9 and 31).

However, the unusual downfield shift of C5 (16.1 ppm)9 may appear to be not fully reproduced by the above combining effect alone; the C5 resonance shifts downfield only by 8.7 ppm. The residual downfield shift (7.4 ppm ) 16.1-8.7 ppm) may be induced by an electrostatic perturbation from a dipole near the ionone group. Figure 14b indicates the calculated chemical shift difference induced by the combination of the three factors including the dipolar group near the ionone ring, which is located as shown in Figure 11a. Judging from the present calculation, the 13C shielding data for bR are better fitted by addition of the effect of dipolar field. According to a recent molecular dynamics study of bR, the C6-C7, C10-C11, and C12-C13 single bonds are twisted from the planar s-trans form by 15°, 15°, and 30°, respectively.41 It is of importance to examine whether these torsions are a major contributor for changing the chemical shifts of the conjugated carbons. First, as can be seen from Figure 7, the C5 and C8 shieldings are expected to undergo no apparent shifts by such a degree of rotation of the C6-C7 bond, although they should have maximal sensitivity to this structural perturbation. Second, the rotation of the C10-C11 bond scarcely affects the shieldings of all the unsaturated carbons (Figure 10b), indicating that this rotation is not the major contributor responsible for the abnormal chemical shift in bR. Third, as the C12-C13 bond becomes twisted, the C13 shielding should shift upfield (Figure 10c). Consequently, this rotation contributes to the C13 shielding so as to cancel out the shifts induced by weakening the Schiff base-counterion interaction. If one takes into account this effect, the calculated data would be rather improved. Therefore, even if the chromophore in bR takes a distorted framework for the conjugated system, the above conclusion should not be significantly affected. Local Environment of the bR Chromophore. As described above, the presence of dipolar field located near the ionone ring is required to better reproduce all the chemical shifts observed for the unsaturated carbons of the chromophore of bR568. And the dipole may be directed parallel to the C5dC6 bond, and its positive and negative charges may be located near C5 and C6, respectively. This is basically consistent with the original

J. Phys. Chem., Vol. 100, No. 5, 1996 1963 conclusion drawn from the NMR studies by Griffin and coworkers,5b although there are some differences in details concerning the position of the dipole. A possible candidate for this dipole may be protonated Asp115.46 If helix D is rotated by 60-90° from the orientation found in the Henderson model,28 then the carboxyl group can be placed near the ionone ring.2b The site-directed mutagenesis studied reveals that the replacements of Asp115 with Asn, Glu, and Ala induce a blue shift in λmax by a few nanometers,47 suggesting that Asp115 may be responsible for the opsin shift. Trp189, located near the ionone ring in the Henderson model,28 is also another possible candidate.2b In order to support this idea, we calculated the dipole moments of acetic acid and indole, which are side-chain analogues of protonated Asp and Trp, respectively. The calculation was carried out using the 4-31 G basis sets, and the resultant values were 1.90 D for both molecules, in good agreement with the dipole moment (1.88 D) of HCl. Therefore, HCl is a better analogue of these amino acids, and the above conclusion does not depend on which amino acid is an actual perturbator of the bR chromophore. Recent NMR and UV/visible studies of various Schiff base analogues have suggested that the anomalous downfield shift of the C5 resonance (144.8 ppm) and λmax in bR568 could be explained only by the synergistic effect of a weak Schiff basecounterion interaction and a 6-s-trans conformation.10,11 For example, PSB 3 is appropriate as a model for bR because it lacks the 1,1-dimethyl group, thus allowing the chromophore to take an planar 6-s-trans conformation in solution. In addition, the introduction of positive charge close to the Schiff base results in an extremely weakened interaction between the Schiff base and its counterion. Eventualy, the values of the C5 shielding (145.7 ppm) and λmax (574 nm) for PSB 3 were comparable to those for bR568.10 However, even with the successful reproduction of the C5 shielding, the C9, C11, and C13 resonances were significantly downfield shifted relative to those for bR568. Albeck et al. suggested that this unfavorable result may be improved on the assumption that a positive charge is located in the vicinity of C7-C9 and proposed protonated Arg82 as a possible candidate for this charge source.10 In conclusion, it seems to be reasonably accepted that in addition to a weak Schiff base-counterion interaction and a 6-s-trans conformation, the third factor is required to completely rationalize the 13C shieldings of the bR chromophore. The molecular model proposed here satisfactorily accounted for the 13C shieldings of the conjugated carbons of the bR chromophore. However, we do not neccessarily think that this model is a unique one for the active site of bR, the evidence of which would not be provided only by considering the NMR data for the chromophore. Rather, the significance of this study is that the calculation clarified the effect of the individual perturbator, relating the opsin shift of bR, on the 13C shieldings of the conjugated carbons. In particular, it is of great importance that dipolar fields additively influence the 13C shieldings, and each effect is localized on the nearby carbons. This would provide invaluable information for constructing a more realistic model of the active site of bR in the future. The opsin shift of the bR absorption is now under investigation using the current theoretical framework (the RPA method). References and Notes (1) See for reviews: (a) Lanyi, J. K. Biochem. Biophys. Acta 1993, 1183, 241-261. (b) Birge, R. R. Annu. ReV. Phys. Chem. 1990, 41, 683733. (c) Birge, R. R. Biochem. Biophys. Acta 1990, 1016, 293-327. (d) Siebert, F. Stud. Org. Chem. 1990, 40, 756-792. (e) Nathans, J. Biochemistry 1992, 31, 4923-4931. (f) Khorana, H. G. J. Biol. Chem. 1986, 267, 1-4. (g) Khorana, H. G. Ann. N. Y. Acad. Sci. 1986, 471, 272-288.

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