Quantum Mechanical/Molecular Mechanical Studies on Spectral Tuning Mechanisms of Visual Pigments and Other Photoactive Proteins

Abstract

The protein environments surrounding the retinal tune electronic absorption maximum from 350 to 630 nm. Hybrid quantum mechanical/molecular mechanical (QM/MM) methods can be used in calculating excitation energies of retinal in its native protein environments and in studying the molecular basis of spectral tuning. We hereby review recent QM/MM results on the phototransduction of bovine rhodopsin, bacteriorhodopsin, sensory rhodopsin II, nonretinal photoactive yellow protein and their mutants.

INTRODUCTION

Each retinal protein consists of two building blocks, a protein moiety (opsin) and a covalently bound chromophore (retinal). Rhodopsins (Rh) in vertebrates (1,2) and halobacteria (3) use 11-cis-retinal and all-trans-retinal, respectively, as their chromophores (Figs. 1 and 2). Interacting with different opsins, the identical retinals in various retinal proteins detect a wide range of light from UV to far red (1,2). Sensory rhodopsin II (sRII) of halobacteria (3) and vertebrate Rh (1,2) absorb light maximally (λ_max) at ~500 nm. However, the other halobacterial Rh, e.g. sensory rhodopsin I (sR1), bacteriorhodopsin (bR) and halorhodopsin (hR), have λ_max of 560–590 nm (3). Mutagenesis experiments using retinal proteins of vertebrates (1,2) and bacteria (3,4) show that some amino acids cause significant spectral shifts, but our knowledge on the molecular basis of spectral tuning is still fragmentary.

Figure 1.

The chromophore in (a) vertebrate rhodopsins and (b) bacterial rhodopsins, representing the QM part in QM/MM calculations. Atom numbering in all-trans retinal is the same to that in 11-cis-retinal and thus not shown. When the Schiff base is protonated (deprotonated), the chromophore is called protonated (deprotonated) Schiff-base retinal. The chromophore is bound covalently to a Lys. H_L is the link atom that saturates the bond at the QM/MMborder. In some QM/MM calculations, the QM part is extended more to the Lys residue. Note that orientation of the β–ionone ring is 6-s-cis (6-s-trans) at the C6–C7 bond in the vertebrate (bacterial) rhodopsins. The β–ionone ring is 6-s-cis in the gas-phase all-trans-retinal.

Figure 2.

Seven-transmembrane helices of rhodopsins as taken from the X-ray structure of bovine rhodopsin (pdb code: 1U19). The chromophore is shown with ball and stick model.

Quantum mechanical (QM) methods can describe all chemical properties and processes, but their applicability is limited to a few hundred-atom systems due to their high computational demand. On the other hand, classical molecular mechanical (MM) methods can incorporate conformational complexity of thousands of atoms in biomolecular systems but disregard electrons and hence cannot describe photon absorption process. Hybrid QM/MM methods have been developed to overcome these shortcomings of the two methods. They use a QM method for the region where the chemical process of interest takes place (retinal in Rh) and an MM method for the remaining large portion of protein/solvent environment (opsin) (5,6). QM/MM approaches are thus the method of choice for investigating large biologic systems with high accuracy.

We review the theoretical studies of spectral tuning of retinal proteins and some other photoactive proteins on phototransduction. In particular, we focus on the results of most recent QM/MM studies for the vertical electronic excitation energy from the ground state singlet (S₀) to the first excited singlet electronic state (S₁), which corresponds to the largest λ_max in electronic absorption spectra. QM/MM results on photoemission, NMR and vibrational spectra of retinal proteins will not be considered (7–12). Some photoactive bacterial proteins, such as green fluorescent protein and photoactive yellow protein (PYP), do not contain retinal as the chromophore (7,8); as an example of this class, we shall discuss PYP.

METHODS

Overview of theoretical methods

Theoretical chemistry offers several methods for investigating molecular systems (Fig. 3), which differ in philosophy, accuracy and computational speed. Roughly speaking, the speed of a method is inversely proportional to its accuracy and thus reliability.

Figure 3.

Methods for investigating molecular systems.

In general, wave function-based ab initio QM methods are the most accurate and the most time-consuming. The Hartree-Fock (HF) method, which does not incorporate any electron correlation (13,14), is the simplest and the least accurate ab initio level. To include electron correlation effects, many post-HF ab initio methods based on HF wave function (called single-reference methods) have also been developed (13,14). The simplest perturbational post-HF method MP2 improves the HF geometries and energies significantly (13,14). The coupled cluster ab initio calculations at the CCSD(T) level seem to give the most reliable results among single-reference methods (15). For more complicated multireference systems, complete active space self-consistent field (CASSCF) calculations followed by complete active space with second-order perturbation theory (CASPT2), multireference configuration interaction (MRCI) and several other simplified methods (spectroscopy-oriented configuration interaction [SORCI], symmetry adapted cluster configuration interaction [SACCI] etc.) have been devised (13,14).

In density functional theory (DFT), the energy and all other molecular properties are derived from the electron density, which is obtained by a single determinantal auxiliary wave function (Kohn-Sham formalism) (13,16). In DFT, electron correlation is incorporated through the exchange-correlation energy terms (13,16). Hybrid exchange-correlation functionals like B3LYP are often preferred over the gradient-corrected (GGA: BLYP, BP86, etc.) and local density functionals (LDA) (13,16). Needless to say, the accuracy of DFT results depends strongly on the selected functionals and basis sets. Computational demand for DFT is much smaller than the correlated ab initio calculations. To calculate electronic spectra (16), the ground state HF and DFT results must be extended by time dependent (TD) theory to excited states (e.g. TD-HF and TD-DFT).

In semiempirical QM methods, many terms in the ab initio formalism are neglected and many others are taken from experiment or calibrated against reliable experimental or theoretical data, which speed up the calculations (17).

In MM methods, electrons are disregarded and the nuclear structure of a molecular system is calculated using force fields, whose functions and parameters are derived from experiments and/or appropriate QM calculations (5,13). The MM methods are thus faster but less reliable than the QM methods. Their computational speed allows the sampling of conformational space of several thousand atoms by molecular dynamics (MD) or Monte Carlo (MC) simulations.

In QM/MM methods, the interaction between QM and MM parts can be computed with several schemes (6,18). In the simplest mechanical embedding (ME) scheme, the electrostatic interactions between the two layers are computed at theMMlevel. In the electronic embedding (EE) scheme, the fixed MM point charges are included in the one-electron QM Hamiltonian. Hence, the QM/MM interaction includes both electrostatic contribution and polarization of the QM wave function by the surrounding MM charges. Unless stated otherwise, the QM/MM calculations considered in this review were performed with the EE scheme. The covalent bonds cut at the QM/MM border, are generally saturated with hydrogen link atoms redistributing or deleting neighboring MM charges (18), which give competitive results with more sophisticated frozen density approaches (19). Starting coordinates of QM/MM studies generally belong to protonated and solvated X-ray structures subjected to some initial pure classical MM geometry optimizations and/or MD simulations. In the absence of X-ray structures, the amino acid sequence of the proteins can be used to construct three-dimensional structures by homology modeling.

Performance of various methods for retinal geometry

Geometry optimization of the entire retinal (Fig. 1) is too demanding with highlevel correlated ab initio methods. Hence, gas-phase QM-only calculations of reduced systems (20–22), e.g. polyene chains with different lengths and an NH₂ ⁺ terminal (+1 charged systems with missing β-ionone ring that correspond to protonated Schiff-base retinal, PSBR, Fig. 1), have been performed to assess the performance of various methods for retinal geometry. These calculations show that HF (no electron correlation) and CASSCF (incorporating only nondynamic correlation) methods overestimate the single/double bond length alternation (BLA) pattern obtained with MP2, B3LYP and CASPT2, incorporating both nondynamical (static) and dynamical correlations. For neutral polyene chains that correspond to deprotonated Schiff-base retinal (SBR), dynamical correlation is less influential to the single/double BLA pattern (20–22).

Roughly speaking, the computed C–C bond lengths are directly proportional to the weight of HF exchange in the density functionals (23). B3LYP (20% HF exchange) reproduces CASPT2 geometry for the charged system (see above), but pure LDA and GGA functionals (no HF exchange) underestimate C–C bond lengths. For example, C–C bond lengths estimated by BP86 (no HF exchange) are smaller than those estimated by B3LYP (20% HF exchange) for the neutral polyene chains. However, B3LYP and BP86 geometries for the charged polyene chain systems are almost the same contrary to the correlational expectation (22).

Polyene chain bond lengths calculated by the semiempirical MNDO, AM1 and PM3 methods differ from those calculated by the B3LYP method significantly (24). The semiempirical DFTB method is parameterized to obtain BP86 geometry (25), and reproduces BP86 geometry of PSBR for the polyene chain, and thus B3LYP geometry (see above) (24). The computational speed of DFTB allows for long proper QM/MM MD simulations to sample the conformational space of PSBR.

There is no reliable reference (experimental or theoretical correlated high-level ab initio) data to assess the performance of HF, CASSCF, DFT and semiempirical methods for the dihedral twist angle of the β-ionone ring (C4–C5–C6–C7, Fig. 1). The twist angle computed with these methods is different to each other (23,24).

In conclusion, CASPT2 geometry optimizations are prohibitively demanding for the entire PSBR. B3LYP, BP86 and DFTB methods, in decreasing order of computational demand, give reasonable polyene chain geometries for PSBR and thus their geometries can be used for electronic excitation energy calculations. For deprotonated SBR, the geometries of DFTB and pure density functionals like BP86 should not be used to calculate excitation energies, leaving B3LYP as a cost-effective method.

SPECTRAL TUNING BY PROTEIN ENVIRONMENTS OF RHODOPSINS

As the absorption maximum is tuned by the protein environments, chromophore-only models are not appropriate to discuss the performance of the methods for calculating vertical excitation energies. The presence of the β-ionone ring in the QM part is essential to calculate proper excitation energies of retinal proteins (9,23,26). The incorporation of dynamical correlation in the QM method corrects excitation energies at least by 100 nm (9,26). Hence, we shall consider neither the results obtained in the absence of the β-ionone ring nor those obtained by HF and CASSCF methods. SORCI and SORCI/MM calculations reviewed were performed with the SV(P) basis set. Unless stated otherwise, the basis set used in the other QM/MM calculations is 6-31G* and the QM part of the QM/MM calculations includes only retinal (Fig. 1).

BOVINE RHODOPSIN

Geometry of 11-cis-retinal

At present, there are no reliable MM parameters for 11-cis-retinal in the standard X-ray refinement softwares. Hence, geometry parameters of the 11-cis-retinal and the neighboring Glu113 have large differences among the available X-ray structures (27). Although some QM/MM X-ray refinement methods that incorporate raw crystallographic data into a QM method have been developed (28,29), they have not been applied to retinal proteins, still continuing some debates on the geometry of the active sites of Rh. This highlights the importance of QM/MM calculations in obtaining the chromophore structure in the protein environment.

Orientation of the β-ionone ring is 6-s-cis at the C6–C7 bond (Fig. 1) in all X-ray structures (27). NMR results, however, predict different orientations—6-s-trans (30,31), 6-s-cis (32–34), a mixture of 6-s-cis (74%) and 6-s-trans (26%) (35). The 6-s-trans geometry is more stable at the semiempirical MNDO-CI level (36), but the protein pocket tolerates both conformations with energetic preference to 6-s-cis conformation at the B3LYP/AMBER level (11). Moreover, experimental NMR parameters agree better with the calculated ones for the 6-s-cis conformation at the B3LYP/AMBER level (11). These results suggest that 6-s-trans conformation will appear only very rarely during protein dynamics.

QM/MM calculations on bovine Rh (11,27,37–40; A. Altun, S. Yokoyama and K. Morokuma, unpublished data) reveal three characteristics—(1) the bonds along the polyene chain show a clear single/double BLA pattern for a neutral retinal, e.g. deprotonated SBR; (2) delocalization of the positive charge of PSBR through the polyene chain reduces BLA; and (3) polarization of the PSBR by the protein environment makes BLA more pronounced. B3LYP/MM bond lengths of the polarized PSBR (11,27,39; A. Altun, S. Yokoyama and K. Morokuma, unpublished data) agree with recent high-resolution double-quantum solid-state NMR results (41) within the experimental error (±0.025 Å).

Effect of BLA on the first excitation energy

Total charge of the PSBR in both all-trans and 11-cis-retinals is mainly distributed to C¹⁵–NH₂ moiety and carbon atoms that have one methyl substituent (C13, C9 and C5) (42; A. Altun, S. Yokoyama and K. Morokuma, unpublished data). The protein environment modulates the electron-drawing ability of the methyl groups and thus the charge distribution within the chromophore (electronic polarization) (A. Altun, S. Yokoyama and K. Morokuma, unpublished data). The more electron drawing group is placed near these methyl groups, the less polyene chain of PSBR possesses positive charge, or vice versa. The decreased (increased) positive charge along the polyene chain means decreased (increased) BLA or stretching (A. Altun, S. Yokoyama and K. Morokuma, unpublished data). The energy gradient of the S₁ surface at the Franck-Condon point correlates positively with the stretching coordinate of the retinal (43). Hence, the first excitation energy is shifted to red (blue) with the decreased (increased) BLA. Average BLA has a linear correlation with the first excitation energy as long as there is a H-bond between 11-cis-retinal and Glu113 for bovine Rh and its mutants (A. Altun, S. Yokoyama and K. Morokuma, unpublished data). Hence, the QM method used to optimize the polyene chain should be able to give correct BLA for calculating accurate excitation energies.

Methods for calculation of excitation energies

The 11-cis-retinal in bovine Rh has a λ_max of 500 nm (1,2). QM/MM vertical excitation energy calculations at CASPT2/MM (9,44), SACCI/AMBER (39), aug-MCQDPT2/EFP (40) and TD-B3LYP/AMBER (11,39; A. Altun, S. Yokoyama and K. Morokuma, unpublished data) levels reproduce the experimental value of PSB 11-cis-retinal in bovine Rh within ±20 nm (Table 1). The choice of fixed charge model of the protein environment (Mulliken, CHARMM, ANO, etc.) influences the computed first excitation energy significantly (44). Protein contribution to the first excitation energy is also affected strongly by the choice of QM method. For example, while the protein environment shifts the first excitation energy by ca 300 nm at the SACCI/AMBER level, the shift is ~10 nm at TD-B3LYP/AMBER level on the same geometry (39). Although the amounts of protein contributions are different, the first excitation energy is estimated reasonably well in all of these QM/MM studies (500 ± 20 nm, Table 1). Certainly, more careful analyses are needed to assess the effects of QM and MM methods, QM/MM interaction schemes, basis sets and the QM regions on the excitation energies by using the same system setup.

Table 1.

The first excitation energy (nm) calculated in different QM/MM studies.

Excitation energy method	Optimized geometry	Embedding scheme	Initial PDB (resolution in Å)	Excitation energy (nm)
CASPT2/AMBER (9)	CASSCF/AMBER	EE	1F88 (2.8)	479
CASPT2/ANO† (44)	DFTB	EE	1U19 (2.2)	502
TD-B3LYP/AMBER (11)	B3LYP/AMBER	EE	1HZX (2.8)	481
TD-B3LYP/AMBER‡	B3LYP/AMBER	EE	1U19 (2.2)	503
TD-B3LYP/AMBER‡§	B3LYP/AMBER	ME	1U19 (2.2)	504
TD-BLYP/AMBER‡	BLYP/AMBER	EE	1U19 (2.2)	572
TD-B3LYP/AMBER (39)||	B3LYP/AMBER	EE	1L9H (2.6)	508 (492)
SACCI/AMBER (39)||	B3LYP/AMBER	EE	1L9H (2.6)	601 (506)
Aug-MCQDPT2/EFP (40)¶	PBE0/AMBER	EFP	1HZX (2.8)	515

^†Geometry optimization of the full system was performed with the DFTB method. The excitation energies were then calculated by including the 11-cis-retinal and Glu113 in the QM system and representing the remaining protein environment with point charges. This method raises a problem regarding the type of charges that will be used in QM/MM interaction term during excitation energy calculations. When using ANO charges derived from B3LYP/6-31G** density, the gas-phase CASPT2 excitation energy of the 11-cis-retinal and Glu113 system at the protein geometry (486 nm) redshifts by 16 nm. However, the calculated shifts are 20 and −7 nm with Mulliken and CHARMM charges, respectively. As the geometry used is not optimized with any of these charge sets, reliability of these calculated shifts is not clear. TD-B3LYP/AMBER calculation at B3LYP/AMBER geometry (38) shows that the protein environment (excluding Glu113) has no overall effect on the first excitation energy. SACCI/AMBER (39) and Aug-MCQDPT2/EFP (40) studies find that the effects of counterions and the remaining protein parts on the λ_max-shift are more than ±100 nm.

^‡A. Altun, S. Yokoyama and K. Morokuma (unpublished data).

^§Standard ME calculations do not consider the change in QM charges upon excitation and thus in electrostatic energy. Hence, the standard calculations correspond to excitation energies of the QM part in the gas phase. The contribution of electrostatic interaction between QMandMM parts to the first excitation energy (30 nm) was included in this study calculating ground and excited state charges.

^||The QM/MM calculations (39) were performed using the D95(d) basis set. In these calculations, the QM part extends to C_γ of Lys296 at the Schiff-base terminal. When this retinal-only QM part (out of parenthesis) is extended to the carboxylic group of Glu113 and its H-bonding water (in parenthesis), the first excitation energy decreases by 16 (95) nm in TD-B3LYP/MM (SACCI/MM) calculations. TD-B3LYP/MM studies (‡) show that the first excitation energy is only affected by 5 nm when Glu113 is included in the QM region. The difference in QM effect of Glu113 in both studies is small and can be attributed to the differences in the QM region, basis set and QM/MM method.

^¶The QM/MM calculations were performed using the cc-pVDZ basis set. PBE/cc-pVDZ charges of each amino acid in the gas phase were used to calculate electrostatic interaction energy (effective fragment potential model, EFP). The QM region extends to the C_ε atom of Lys296, parts of Glu113 and Glu181 and three water molecules around them. Glu113 and Glu181 decrease the excitation energy by ca 200 nm in the gas-phase QM-only calculations. The remaining protein environment increases the excitation energy by ca 125 nm.

TD-BLYP/AMBER calculations overestimate the first excitation energy by at least 50 nm (A. Altun, S. Yokoyama and K. Morokuma, unpublished data), indicating that pure density functionals are not well balanced in evaluating electronic spectra. For PSBR, the geometries obtained using DFTB/AMBER and B3LYP/AMBER calculations are almost the same and thus the TD-B3LYP/AMBER excitation energies calculated at these geometries are similar (38), in agreement with gas-phase chromophore-only calculations (24). This confirms further that the semiempirical DFTB method is a very effective fast geometry optimization tool for PSBR.

Almost all QM/MM studies incorporate polarization of the QM part by environmental residues but ignore polarization of the protein environment by QM charges. QM/MM excitation energies and spectral shifts resulting from mutations on bovine Rh obtained ignoring environmental polarization agree with experimental results reasonably well (9,11,39,40,44; A. Altun, S. Yokoyama and K. Morokuma, unpublished data). Hence, environmental polarization is not expected to affect electronic spectra of bovine Rh significantly.

Protonation state of 11-cis-retinal

When protonated Glu113 forms a H-bond with deprotonated SBR or there is a H-bonding water molecule between deprotonated SBR and Glu113, B3LYP/AMBER studies show that bovine Rh has a λ_max of 430 nm (Table 2). When both SBR and Glu113 are deprotonated and there is no H-bonding water molecule between them, it becomes 380 nm. The λ_max of 500 nm is reproduced only when PSBR forms a H-bond with deprotonated Glu113, as some experiments (45–49) suggest. The large difference between the computed first excitation energies of PSBR and SBR clearly excludes the possibility of deprotonated SB 11-cis-retinal in Rh.

Table 2.

Effects of the protein environment on the first excitation energy (nm) at the TD-B3LYP/AMBER level (A. Altun, S. Yokoyama and K. Morokuma, unpublished data).

		ME geometry			EE geometry
	Retinal protonation (experiment)	Bare retinal*	+Electrostatics	+Electronic polarization	+Geometry relaxation due to electronic polarization	=The resulting first excitation energy (spectral shift)
WT	PSBR (500)	535	−31	+1	−2	503 (0)
	SBR† (−)	400	−1	+13	+17	429 (−74)
	SBR‡ (−)	399	−33	+16	−2	380 (−123)
E113Q§	PSBR (496)	536	−15	+5	+4	530 (27)
	SBR (384)	398	−8	+7	+12	409 (−94)
E122Q	PSBR|| (480)	533	−30	−6	−5	492 (−11)
	PSBR¶ (−)	544	−35	+3	+2	514 (11)
G90D	PSBR# (483)	544	−51	−3	−15	475 (−28)
	PSBR** (−)	544	−43	+2	−1	502 (−1)
E181Q	PSBR (502)	541	−42	+2	−2	499 (−4)

^*The TD-B3LYP first excitation energy for the isolated chromophore from B3LYP/AMBER optimized geometry with ME scheme.

^†With protonated Glu113.

^‡With deprotonated Glu113.

^§Gln112 whose NH₂ moiety is oriented toward one of the methyl groups attached to C1 atom of the chromophore.

^||Gln112 whose O=C–NH₂ plane is rotated by ca 90° compared with that in footnote§.

^¶With Gln113 whose side-chain NH₂ (carbonyl O) moiety is oriented toward its backbone carbonyl O (Schiff-base N).

^#With deprotonated Asp90.

^**With protonated Asp90.

The source of opsin shift

The chromophores in organic solvents and gas phase are all-trans-retinal and have λ_max of 450 nm (50) and 610 nm (51), respectively. As noted earlier, the 11-cis-retinal in bovine Rh has a λ_max of 500 nm (1,2). Hence, solvent and protein (opsin) decrease the λ_max. The λ_max of 11-cis PSBR calculated on the gas-phase geometry is 528 nm at the TD-B3LYP level (B3LYP geometry) (A. Altun, S. Yokoyama and K. Morokuma, unpublished data) and 534 nm at the CASPT2 level (CASSCF geometry) (52). When it is optimized at the B3LYP/AMBER level considering only the electrostatic effect of the protein environment (ME scheme), gas-phase TD-B3LYP excitation energy of isolated PSBR is 535 nm (A. Altun, S. Yokoyama and K. Morokuma, unpublished data). Hence, geometrical changes induced by protein electrostatics have a small effect on the excitation energy (<10 nm). Electrostatic interaction energy between the 11-cis PSBR and protein environment changes upon electronic excitation because the charge distributions within the 11-cis PSBR are different for the ground and excited states. The change in the electrostatic energy decreases the first excitation energy of PSBR by ~30 nm (535 → 504 nm, Table 2) at the B3LYP/AMBER level (38). This blueshift is mainly caused by the H-bond interaction between 11-cis-retinal and Glu113, as revealed in TD-B3LYP/AMBER calculations in which the charges on Glu113 are turned off (A. Altun, S. Yokoyama and K. Morokuma, unpublished data). The effect of other amino acids on the excitation energies (electrostatic or electronic polarization) cancels to each other. Although electronic polarization significantly affects BLA pattern in geometry, it does not have a notable effect on the first excitation energy of native Rh. The effect of BLA change resulting from electronic polarization on the excitation energy (redshift of 25 nm at the TD-B3LYP level going from ME geometry to EE geometry) is counterbalanced by the change in H-bond strength between PSBR and Glu113 (A. Altun, S. Yokoyama and K. Morokuma, unpublished data). Hence, the complete protein effect on excitation energies happens to be equal to the electrostatic effect of Glu113 in the TD-B3LYP/AMBER study (A. Altun, S. Yokoyama and K. Morokuma, unpublished data). In SACCI/MM (39) and aug-MCQDPT2/MM (40) calculations, Glu113 and the remaining protein environments contribute to the first excitation energy more than ±100 nm separately. However, their contributions are much smaller (30 nm or less) in the CASPT2/MM (44) and B3LYP/MM (39; A. Altun, S. Yokoyama and K. Morokuma, unpublished data) studies (see footnotes of Table 1).

Spectral shifts resulting from mutations

Glu113 is conserved in virtually all visual pigments. As mentioned above, the effects of all the residues other than Glu113 on the first excitation energy of the wild-type (WT) bovine Rh cancel out in one of the TD-B3LYP/AMBER studies (A. Altun, S. Yokoyama and K. Morokuma, unpublished data). However, mutagenesis analyses show that various amino acid changes can cause λ_max-shifts (1,2). Indeed, TD-B3LYP/AMBER (A. Altun, S. Yokoyama and K. Morokuma, unpublished data) and CASPT2/AMBER (53) calculations can predict λ_max-shifts resulting from mutations within 10 and 20 nm (except E113Q, see below), respectively. In order to calculate the effects of mutations on absorption spectra accurately, some care must be taken.

1. Both electrostatic and electronic polarization contributions (Table 2) must be incorporated (A. Altun, S. Yokoyama and K. Morokuma, unpublished data). For example, the mutagenesis of E122Q decreases the λ_max by 20 nm and the TD-B3LYP/AMBER calculation predicts a spectral shift of −11 nm (Table 2). The calculated shift is fully attributable to electronic polarization (A. Altun, S. Yokoyama and K. Morokuma, unpublished data), which can be rationalized in terms of BLA change—carboxylic OH moiety of E122 (AMBER charge: −0.19) is replaced by an NH₂ moiety (AMBER charge: −0.09) in the E122Q mutant. These moieties are oriented toward the H atoms of one of the methyl groups attached to the C1 atom of PSBR. Electron transfer from this methyl to the nitrogen atom of PSBR is decreased as negative charge around it is halved with the mutation. In this case, the polyene chain possesses more positive charge, resulting in increased BLA that blueshifts the first vertical excitation energy (see above). The λ_max of E122D (475 nm) is more blueshifted than E122Q (480 nm) as the side chain terminal of deprotonated Asp (D) possesses more negative charge than Gln (Q) (A. Altun, S. Yokoyama and K. Morokuma, unpublished data).

2. The protonation state of mutated residues must be properly defined. For example, the λ_max-shift does not occur for the G90D mutant when protonated Asp90 is used (Table 2). However, when Asp90 is deprotonated, the first excitation energy is 475 nm (A. Altun, S. Yokoyama and K. Morokuma, unpublished data), which is close to the experimental λ_max of 483 nm (Table 2).

3. Conformation of the mutated residues must be properly modeled. For example, there are many possible side chain conformations of Ser292, Thr269 and Gln122 in A292S, A269T and E122Q mutants (Table 2). Some of them increase the λ_max whereas some others decrease it. Solvent water molecules can help keep the side chains in the preferred conformations (A. Altun, S. Yokoyama and K. Morokuma, unpublished data).

It has been detected that the λ_max of intermediates in the photoactivation of bovine Rh with E113Q depends strongly on pH (54). The λ_max of this mutant in the dark state changes from 384 nm at pH of 8.2 to 496 nm at pH of 5.5, while the corresponding values of its photoproduct assigned to bathorhodopsin are 408 and 530 nm, respectively (54). The retinal structures in the E113Q photocycle were assigned by comparing their absorption spectra with those in the WT Rh. TD-B3LYP/AMBER excitation energies (A. Altun, S. Yokoyama and K. Morokuma, unpublished data) of the 11-cis-retinal (409 nm for SBR and 530 nm for PSBR, Table 2) agree perfectly with the experimental values of the photoproduct assigned to bathorhodopsin rather than those of 11-cis-retinal. Hence, retinal in the dark state of E113Q might be different from that of the WT rhodopsin. If so, the assignment of photoproducts in the phototransduction cycle of E113Q requires revisions.

There are two different experimental results for the E181Q mutant of bovine Rh, one of which shows almost no spectral shift (49) and the other finds redshift of 10 nm (55). TD-B3LYP/AMBER results (Table 2) are more consistent with the first (A. Altun, S. Yokoyama and K. Morokuma, unpublished data).

HALOBACTERIAL RHODOPSINS

Halobacterial Rh, e.g. bR, hR, sRI and sRII (ppR), all belong to the seven-transmembrane receptor family like vertebrate Rh (3). The chromophore is the retinal in both halobacterial (all-trans form) and vertebrate (11-cis form) Rh (Fig. 1). As halobacterial and vertebrate Rh share the same backbone structure and chromophore, the spectral tuning mechanism in bovine Rh with regard to BLA change also applies to halobacterial Rh (12). Further, structural changes induced by the protein electrostatics cause less than 10 nm of λ_max-shift in halobacterial Rh at TD-B3LYP, SORCI and OM2 levels (12,56). In the following, we will focus on the calculation of excitation energies and the protein parts that shift the excitation energies.

Calculation of excitation energies

The all-trans-retinal in the protein environment of bR (in vacuo) absorbs light at 568 (610) nm (3,51). Many QM/MM studies have been conducted in calculating excitation energies for bR (for a review, see Ref. [23]). The bR protein environment decreases the excitation energy in experimental (~40 nm) and theoretical studies (23). In the theoretical analyses, both QM/MM excitation energies and the amount of spectral shifts differ significantly depending on the choice of QM method and QM/MM settings (23), analogous to bovine Rh. For example, the retinal in the protein environment of bR absorbs light at around 490 nm at TD-B3LYP/AMBER (39,56), OM2-MRCI/CHARMM (12,23) and OM2-CIS/CHARMM (23) levels. However, gas-phase values calculated at TD-B3LYP (55), OM2-MRCI (12,23) and OM2-CIS (23) levels for the bare chromophore at QM/MM geometries are 512, 582 and 530 nm, respectively. The vertical excitation energy calculated at the SORCI/CHARMM level (530 nm) is closer to the experimental result than the results of the QM/MM studies at the above levels (490 nm), but it still differs from the experimental value by ~40 nm (12,23). The SORCI calculation in the gas phase (667 nm) gives a larger difference of 57 nm (12,23). The gas-phase CASPT2 excitation energy (606 nm) reproduces λ_max of all-trans retinal (610 nm) in the gas phase (3,51). The difference in the high-level CASPT2 (606 nm) and SORCI (667 nm) values may not be caused by the quality of the methods, but it may depend on the selection of the basis set (ANO vs SV[P]), active space and threshold values for configuration selections, and some other factors.

At a semiempirical level, environmental polarization increases the first excitation energy of bR by ~80 nm (57). When this semiempirical estimation is applied to the TD-B3LYP/AMBER value of 491 nm (56), TD-B3LYP/AMBER calculations reproduce experimental results. To reproduce the spectral shift of bR relative to the gas phase or solution at CIS/CHARMM and CIS levels with the 3-21G basis set, the inclusion of the effect of environmental polarization is also necessary (58). However, SACCI/AMBER calculations (basis set: D95[d]) that include Asp85(75) and a crystallographic water (W402) in the QM region (Fig. 4) reproduce the absorption maximum of bR (SRII) without such an environmental polarization effect within 10 nm (556 [490] nm) (39).

Figure 4.

H-bond network of bacteriorhodopsin (pdb code: 1C3W, left) and sensory rhodopsin II (pdb code: 1H68, right) around all-trans-retinal.

Calculation of excitation energies and spectral shifts of retinals is a challenging problem and, at this point, the errors introduced in the calculated excitation energies are larger for the gas phase than for the protein case.

The source of spectral shifts

Compared with those of the other bacterial Rh, the λ_max of sRII (497 nm) is blueshifted by ~70 nm (3). Many experimental (3) and theoretical (12,59,60) studies were performed to understand the source of this blueshift. Experiments show that each amino acid change has only a small contribution to the total shift (3). MNDO-PSDCI (59) or CASSCF/AMBER (60) calculations suggested that the differences in the coordinates of Arg82(72) or Asp212(201) of bR (sRII) were the main reason for the spectral shift, but this claim was challenged by experiments (3) and a recent extensive QM/MM analysis (12). In a recent QM/MM study, it was shown that semiempirical OM2-MRCI/CHARMM calculations reproduce high-level SORCI/CHARMM results for the spectral shifts (12). In the following, therefore, we shall consider the results at the OM2-MRCI and OM2-MRCI/CHARMM levels.

The H-bond network of bR (SRII) around the retinal (Fig. 4), which is composed of retinal Asp85(75), Asp212(201), Arg82(72) and three water molecules, is responsible for 30–40% of the spectral shift at the OM2-MRCI level (12). Neither of these amino acids is responsible individually for the spectral shift at the OM2 level, in agreement with the experimental result. However, the most significant contributions to the calculated excitation energies (or to the opsin shift) come from Asp85(75) and Asp212(201) at the OM2-MRCI (12) and TD-B3LYP (61) levels. Although the effect of Asp85(75) at the SORCI/CHARMM and OM2-MRCI/CHARMM levels is ~100 nm and mainly electrostatic (12), SACCI/AMBER calculations predict the same amount of effect to be quantum mechanical (39). The inclusion of Asp85(75) in the QM region may improve the agreement of the calculated excitation energies at the SORCI/CHARMM and OM2-MRCI/-CHARMM levels with the experiments. Arg82(72) side chain orients differently in bR and sRII (Fig. 4). The effects of Arg82(72) orientation and the water molecules in the H-bond network on the calculated excitation energies and spectral shifts are very small (12,61).

Only 10 amino acids of bR and sRII differ around 5 Å vicinity of the retinal. When all these amino acids in sRII are mutated with those in bR (bR/sRII mutant), 44% of the shift was detected by experiments (3). SORCI/CHARMM (OM2-MRCI/CHARMM) calculations predict that 50% (60%) of the spectral shift is caused by bR/sRII mutation, agreeing with the experimental results (12).

The QM/MM calculations (12) show that the effects of counterion residues on the excitation energies and spectral shifts are not additive, but aromatic Tyr and Trp and polar Thr, Ala, Ser and Gly residues in the binding pocket have additive effects (12). T204A, G130S, V108M and A131T sites in the binding pocket have a significant impact on the spectral tuning in agreement with the experimental result (12). Glu194(Pro183), Glu204(Asp193), Ser141(Gly130), Thr142(Ala131) and Ala215(Thr204) of bR (sRII) have sizable influences (12). Theory also suggests that A11T and S44P, outside the binding pocket, have small but distinct influences (12), but this has not been studied experimentally. In conclusion, the differences in the λ_max of sRII and other bacterial Rh are caused by amino acids within and outside the binding pocket.

PHOTOACTIVE YELLOW PROTEIN

Photoactive yellow protein is a small (125 amino acids, Fig. 5) water-soluble light-sensitive receptor found in halophilic bacteria and is responsible for the negative phototaxic response to blue light (7,8). Its chromophore, p-coumaric acid (pCA), is covalently bound to Cys69. PYP has a λ_max of 446 nm, while the bare chromophore (pCA) absorbs light at 460 nm in the gas phase (7,8). PYP is a very flexible protein and the hole-burning experiment of PYP at 10 Kindicates an inhomogeneous ground state (62). In agreement with this experimental result (62), CASPT2/AMBER excitation energy calculations (QM region: pCA and carboxyl group of Glu46) on 10 snapshots of a short MDtrajectory find λ_max of 455 (4 snapshots), 415 (one snapshot) and 390 (5 snapshots) nm (63,64). The average value of the excitation energies of 10 snapshots (429 nm) agrees with the experimental value within 15 nm.

Figure 5.

Photoactive yellow protein (pdb code: 2PHY) with some highlighted amino acids that are important for the opsin shift.

CASPT2/AMBER calculations (63,64) show that electron transfer occurs from phenolate oxygen of the pCA to its carbonyl oxygen upon electronic excitation, consistent with the result of a spark spectroscopy experiment (65). In particular, electrostatics of hydroxyl groups of Glu46, Tyr42 and Thr50 with phenolate oxygen of the pCA account for 37%, 27% and 9% of the protein effect on the first excitation energy, respectively. It appears on 12 mutants of PYP that contributions of some amino acids of the WT PYP to the first excitation energy correlate well with the experimental λ_max of the mutants of these amino acids (63,64).

CONCLUSIONS

QM/MM calculations provide significant contributions to the understanding of spectral tuning mechanism of Rh and PYP. Excitation energies calculated in the gas phase are variable. However, with appropriate selection of QM and MM methods and of QM/MM interaction schemes, the QM/MM calculations predict both experimental absorption maxima and spectral contributions of each amino acid on the λ_max-shift reasonably well. QM/MM calculations thus improve our understanding of how visual pigments tune their absorption maxima from 350 to 650 nm. These theoretical analyses have already shown to be useful in calculating excitation energies and spectral shifts not only of Rh and PYP but also of red, green and blue human visual pigments (66,67).