Article pubs.acs.org/JPCB

Exciton Circular Dichroism in Channelrhodopsin Gennaro Pescitelli,*,† Hideaki E. Kato,‡,# Satomi Oishi,‡ Jumpei Ito,§ Andrés Daniel Maturana,§ Osamu Nureki,‡ and Robert W. Woody*,∥ †

Dipartimento di Chimica e Chimica Industriale, Università di Pisa, via Moruzzi 3, I-56124 Pisa, Italy Department of Biophysics and Biochemistry, Graduate School of Science, University of Tokyo, 2-11-16 Yayoi, Bunkyo-ku, Tokyo 113-0032, Japan § Department of Bioengineering Sciences, Graduate School of Bioagricultural Sciences, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan ∥ Department of Biochemistry and Molecular Biology, Colorado State University, Fort Collins, Colorado 80523, United States ‡

S Supporting Information *

ABSTRACT: Channelrhodopsins (ChRs) are of great interest currently because of their important applications in optogenetics, the photostimulation of neurons. The absorption and circular dichroism (CD) spectra of C1C2, a chimera of ChR1 and ChR2 of Chlamydomonas reinhardtii, have been studied experimentally and theoretically. The visible absorption spectrum of C1C2 shows vibronic fine structure in the 470 nm band, consistent with the relatively nonpolar binding site. The CD spectrum has a negative band at 492 nm (Δεmax = −6.17 M−1 cm−1) and a positive band at 434 nm (Δεmax = +6.65 M−1 cm−1), indicating exciton coupling within the C1C2 dimer. Time-dependent density functional theory (TDDFT) calculations are reported for three models of the C1C2 chromophore: (1) the isolated protonated retinal Schiff base (retPSB); (2) an ion pair, including the retPSB chromophore, two carboxylate side chains (Asp 292, Glu 162), modeled by acetate, and a water molecule; and (3) a hybrid quantum mechanical/molecular mechanical (QM/ MM) model depicting the binding pocket, in which the QM part consists of the same ion pair as that in (2) and the MM part consists of the protein residues surrounding the ion pair within 10 Å. For each of these models, the CD of both the monomer and the dimer was calculated with TDDFT. For the dimer, DeVoe polarizability theory and exciton calculations were also performed. The exciton calculations were supplemented by calculations of the coupling of the retinal transition with aromatic and peptide group transitions. For the dimer, all three methods and three models give a longwavelength C2-axis-polarized band, negative in CD, and a short-wavelength band polarized perpendicular to the C2 axis with positive CD, differing in wavelength by 1−5 nm. Only the retPSB model gives an exciton couplet that agrees qualitatively with experiment. The other two models give a predominantly or solely positive band. We further analyze an N-terminal truncated mutant because it was assumed that the N-terminal domain has a crucial role in the dimerization of ChRs. However, the CD spectrum of this mutant has an exciton couplet comparable to that of the wild-type, demonstrating that it is dimeric. Patch-clamp experiments suggest that the N-terminal domain is involved in protein stabilization and channel kinetics rather than dimerization or channel activity.

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INTRODUCTION Channelrhodopsins (ChRs) are being intensively studied because of their use in the photocontrol of neurons, which has given rise to the new field of optogenetics.1−3 ChRs are type-I (microbial) rhodopsins in which isomerization of a protonated all-trans retinal Schiff base to the 13-cis conformation leads to the opening of a cation channel in the protein, which conducts H+, Na+, K+, and Ca2+.4,5 Two of the most useful ChRs are ChR16 and ChR27 from the dinoflagellate Chlamydomonas reinhardtii. Kato et al.8 generated C1C2, a chimera of ChR1 and ChR2, by combining the first five transmembrane (TM) helices of ChR1 with the sixth and seventh TM helices and residues 318− 352 of ChR2. This construct expresses well in Sf9 cells and is stable and monodisperse. Crystals diffracting to 2.3 Å were obtained in the lipidic cubic phase, and the structure was © 2014 American Chemical Society

solved. C1C2 exists as a dimer in the crystal. The dimerization interface involves the N-terminal domain (residues 24−83), an extracellular loop (residues 110−119), and TM helices TM3 and TM4. The interface includes three disulfide bonds between equivalent Cys residues in the N-terminal domains of monomer A and monomer B. Although the visible−near-UV absorption spectrum of ChR has been reported,8−10 circular dichroism (CD) spectra have not been reported. The CD spectrum of the closely related protein bacteriorhodopsin (bR) has been investigated extensively, especially in its two-dimensional crystalline form, purple membrane. Purple membrane exhibits a negative CD band at Received: June 13, 2014 Revised: September 23, 2014 Published: September 23, 2014 11873

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∼600 nm and a positive band at ∼530 nm11−13 that were initially interpreted as arising from exciton coupling14−16 among the retinal chromophores in the purple membrane. The exciton interpretation was strongly questioned,17−20 but Pescitelli and Woody21 have recently shown that the exciton model accurately describes the visible CD spectrum of bR and have refuted the objections to the model. ChR, with its disulfide-stabilized dimer, presents an opportunity to test the exciton theory on a dimer, in contrast to the two-dimensional crystal of bR trimers that constitutes the purple membrane. Detergent solubilization of purple membrane has thus far led only to bR monomers. We show in this study that detergent-solubilized C1C2 gives an exciton couplet in CD. Moreover, calculations of the CD by timedependent density functional theory (TDDFT),22,23 DeVoe theory,24,25 and exciton theory,14−16 based upon the crystal structure,8 agree well with the experimental CD spectrum, demonstrating that the C1C2 dimers retain a native-like fold in detergent solution. Another objective of this study is to examine the functional role of the N-terminal domain. Because it was assumed that the N-terminal domain is a key part of the dimerization interface, we analyzed a mutant ChR, ΔN C1C2, in which residues 26− 80 of the N-terminal domain are deleted. Electrophysiological studies showed that ΔN C1C2 has faster channel kinetics, and the channel activity was comparable to that of wild-type C1C2. The CD spectrum demonstrates that ΔN C1C2 is a dimer. Given that the protonated retinal Schiff base (retPSB) is easily hydrolyzed in this mutant, it is suggested that the contacts between TM3 and TM4 suffice to maintain the dimeric state in ΔN C1C2, and the major function of the N-terminal domain is to stabilize the protein and to control the channel kinetics.

UV CD spectrum of C1C2 was analyzed by CDPro29 to estimate the secondary structure content in solution. For comparison, the α-helix and β-strand contents in the crystal were calculated from the comments in the PDB file 3UG98 and with the program DSSP.30,31 For patch-clamp, HEK293 cells were cultured on polylysinecoated, glass-bottom culture dishes (Matsunami) and were transfected with 0.1 mg of a plasmid construct containing the GFP-tagged C1C2 or the GFP-tagged ΔN C1C2 mutant. At 24−30 h after transfection, the cells were placed in a bath medium containing 140 mM NaCl, 1 mM CaCl2, 2 mM MgCl2, 5 mM glucose, and 10 mM HEPES (pH 7.4), under an inverted microscope (Olympus IX71). A borosilicate patch pipet (Harvard Apparatus), with a resistance of about 5−8 MΩ, was filled with 140 mM KCl, 5 mM EGTA, 2 mM MgCl2, and 10 mM HEPES (pH 7.2). C1C2 currents were recorded in the voltage-clamp mode of the whole-cell configuration. The cells were held at a membrane potential of −80 mV and were depolarized by 10 mV voltage steps of 1.8 s up to 70 mV. The light-dependent currents were activated 200 ms after the depolarization step with 465 nm light (1.5 mWmm−2) for 1000 ms, elicited by a high-power LED illumination system (LEX2-B, Brainvision) connected to an A/D converter (Digidata 1440, Axon CNS, Molecular Devices), controlled by the pClamp10 software (Axon CNS). Currents were measured using an Axopatch 200B amplifier (Axon CNS, Molecular Devices), filtered at 2 kHz, and sampled at 5 kHz using a Digidata 1440A digitizer (Axon CNS) controlled by the pClamp10 software (Axon CNS). Theoretical Methods. The calculations generally followed the methods used for bR.21 Details are described in the Supporting Information. Equations contained in the Supporting Information are referenced in the text using the prefix “S”, for example, eq S1. Geometry. The starting geometry for the calculations was obtained from the 2.3 Å X-ray structure of the C1C2 chimera between ChR1 and ChR2 of Chlamydomonas reinhardtii8 (PDB32 code 3UG9). The input geometries for TDDFT calculations were generated by cutting the retPSB and surrounding residues (see below) at specific bonds, which were then “capped” by hydrogen atoms; all hydrogen atoms were then optimized with DFT at the B3LYP/6-31G(d) level while all heavy atoms were kept frozen. The retPSB moiety was cut at the N−Cε bond of the Lys296 residue to produce a −CHNH2+ terminal (Chart 1). The two acidic residues (Glu162 and Asp292) were cut at the Cβ−Cγ and Cα−Cβ bonds, respectively, to produce two acetate groups. The same

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METHODS Experimental Methods. The gene encoding C1C2 and its ΔN mutant (Δ26−80) were cloned into the modified pFastBac1 vector for expression in Sf9 insect cells, and these proteins were expressed and purified as previously described.8 The samples were dissolved in a buffer containing 150 mM NaCl, 50 mM Tris-HCl (pH 8.0), 5% glycerol, 0.05% ndodecyl-β-D-maltoside (DDM), and 0.5% cholesterylhemisuccinate (CHS). The total protein concentration was 0.73 mg/ mL (19 μM, for a MW of 37411, estimated with ExPASy26) for C1C2 and 0.13 mg/mL (4.2 μM, MW 31312) for ΔN mutant. The samples were stored at 5 °C and handled exclusively in the dark. Absorption and CD spectra were measured on darkadapted samples after conditioning at room temperature. Different quartz cells were used (conditions are reported in the figure legends) to maximize the signal-to-noise ratio. Distilled water was used as a blank to measure the baselines. Absorption spectra were measured with a Jasco V-650 spectrophotometer. The absorption spectrum was fit to a Gaussian and to a log-normal distribution as described in the Supporting Information.27,28 CD spectra were measured with a Jasco J-715 spectropolarimeter under the following conditions: scanning speed, 100−200 nm/min; bandwidth, 2 nm; response, 1 s; 32 accumulations. CD spectra were minimally smoothed using the fast Fourier transform (FFT) algorithm in Jasco Spectra Manager software, v. 1.53, Jasco corporation, 2002. Peaks in absorption and CD spectra were assigned using the second-derivative algorithm (Savitzky−Golay procedure, thirdorder polynomial, 15−25 data points) and the deconvolution algorithm (fwhm 40−50) in Jasco Spectra Manager. The far-

Chart 1

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system used in the TDDFT calculations. These origins are shown for each model in Tables S2−S7 in the Supporting Information. Extrinsic Coupling Calculations. First-order perturbation theory49 was used to evaluate the coupling between retPSB transitions and aromatic and peptide groups using eqs S43−S45 (Supporting Information). All coupling contributions were evaluated in the monopole approximation (eq S39, Supporting Information) using scaled Mulliken50 charges (see Table S8, Supporting Information) from CAM-B3LYP/TZVP calculations for the 470 nm transition in the retinal and transition monopoles for the peptide and aromatic transitions from Woody and Sreerama.51 Other transition parameters for the retinal are given in Table 2. The calculations included both chains of the dimer.

treatment was applied to bR (here reconsidered for comparison), starting from the 1.55 Å X-ray structure (PDB code 1C3W).33 In this case, the Lys residue was Lys216, and the two acidic residues were Asp85 and Asp212. The “ion pair” model (Chart 1) was built in both cases by including N-methyl retPSB (i.e., cutting the Cε− Cδ bond of the Lys296 (C1C2) or Lys216 (bR) residue to produce a −CHNH + −CH 3 terminal), the two acetate ions, and a water molecule involved in a hydrogen bond with the ion pair, namely Wat619 (C1C2) or Wat402 (bR). In the “ion pair/active site” (QM/MM) model, a two-layer ONIOM procedure was employed.34,35 The high (QM) layer comprised the groups included in the ion pair model described above. In the low (MM) layer, all residues with at least one atom within a distance of 10 Å from any of the atoms of the ion pair were considered, cutting the respective peptide bonds with the residues outside of the threshold. All dangling peptide bonds were then capped by hydrogen atoms, and all hydrogen atoms in the MM layer were optimized with a molecular mechanics force field (MMFF).36 In the QM/MM model, the partial charges from the MM layer (generated with QEq formalism)37 were incorporated in the QM Hamiltonian (electronic embedding). In monomer calculations, one of the two equivalent subunits of C1C2 was considered. In dimer calculations, the two subunits were considered with a relative arrangement derived from the X-ray structure.8 MMFF and DFT geometry optimizations were run with Gaussian 09.38 TDDFT Calculations. TDDFT calculations22,23 were run with Gaussian 09.38 A screening of DFT functionals and basis sets was run for the retPSB model, both as a monomer and as a dimer. In the screening, the hybrid B3LYP,39 BH&HLYP,40,41 and PBE042 functionals and the long-range corrected CAMB3LYP43 functional were used. In the same screening, the two Ahlrich basis sets SVP and TZVP44,45 were employed, in addition to a version of TZVP (aug-TZVP) augmented with a set of (1s1p1d/1s1p) functions taken from the most diffuse functions of aug-cc-pVDZ.46 On the basis of the screening results, the CAM-B3LYP/TZVP combination was selected as the calculation method of choice. DeVoe Calculations. The classical DeVoe polarizability theory24,25 (see the Supporting Information) was applied to the 470 nm transition in ChR for comparison with the TDDFT and exciton calculations. The imaginary part of the complex polarizability was generated from the Gaussian fit to the absorption spectrum of ChR, and the real part was then calculated by a Kronig-Kramers transform (eq S6, Supporting Information).47,48 The electric dipole transition moments were obtained from the TDDFT calculations, and scaled to reproduce the observed dipole strength (Table 2). The transitions were centered at the origin used in the TDDFT calculations. The point-dipole approximation was used to calculate the interchromophoric coupling. Exciton Calculations. Exciton calculations were run using the equations reported in the Supporting Information (eqs S32−S35), employing the spectroscopic and geometric parameters for the 470 nm transition summarized in Table 2. The direction of the electric dipole transition moment and the magnitude and direction of the magnetic dipole transition moment were derived from the TDDFT calculations. TDDFT overestimates the magnitude of the electric dipole transition moments relative to that derived from experiment by 23−31%. The electric dipole transition moments were therefore scaled to the experimental value (9.64 D). The electric dipole transition moment was centered at the origin of the retPSB coordinate

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RESULTS

Experimental Results. Geometry of the System. As in other microbial-type rhodopsins, the retPSB moiety in C1C2 adopts an all-trans retinal conformation and is covalently bound as a Schiff base to Lys296 on the seventh TM domain (Figure 1A).8 The retPSB moieties bound to the two dimer subunits lie at a distance of about 23 Å (measured between the middle points of the two polyene systems, Figure 1B). The average planes of the polyene systems are almost parallel to each other (Figure 1B), while the main axes of the polyenes define an angle of ∼155° (Figure 1C). Considering that the 470 nm transition is polarized along the main axis of each polyene (see below), the two polyenes define an overall negative exciton chirality.16 The conjugated polyene from C1C2 is almost planar (Figure 1D), with a root-mean-square (RMS) deviation from the average plane of 0.085 Å. The two carboxylate groups involved in the Schiff base counterion (residues Glu162 and Asp292) lie on the opposite sides of the polyene plane (Figure 1E). The shortest distances from the retPSB nitrogen to the oxygen atoms of Glu162 and Asp292 and the water molecule are 3.4, 3.0, and 4.4 Å, respectively.8 Experimental Absorption and CD Spectra of C1C2. The absorption and CD spectra of C1C2 in the visible and near-UV are shown in Figure 2a,b. The absorption spectrum shows evidence of vibronic fine structure, with the absorption maximum at 472 nm, a distinct shoulder near 450 nm, and less distinct shoulders near 415 and 390 nm. The maximum extinction coefficient is 4.64 × 104 M−1 cm−1 at 472 nm. The CD spectrum of C1C2 in the visible (Figure 2b) consists of an approximately symmetrical couplet with a negative maximum at 492 nm (Δεmax = −6.17 M−1 cm−1) and a positive maximum at 434 nm (Δεmax = +6.65 M−1 cm−1). It is not possible to accurately determine the rotational strengths for two closely overlapping CD bands of opposite sign because the rotational strengths of the two bands are tightly coupled to their separation in wavelength.52 Bayley therefore defined a couplet strength, S, which is the peak-topeak amplitude of the couplet. The couplet strength is S = −12.82 M−1 cm−1. Numerical integration of the CD spectrum gives the apparent rotational strengths R+app = −0.138 DBM (Debye−Bohr magneton, 1 DBM = 0.9273 × 10−38 cgs) for the long-wavelength negative lobe and R−app = +0.298 DBM for the short-wavelength positive lobe, for a net rotational strength of +0.160 DBM. (Note that the +/− in the subscripts refer to the long- and short-wavelength bands, respectively, not to the sign of the bands themselves. In addition, these apparent rotational 11875

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methods used in CDPro (SELCON3,29,54 CONTINLL,29,55 and CDSStr56) give consistent results, with an average α-helix content of 64% and a β-strand content of 5%. The α-helix content is higher than that reported in the PDB file (60%) or by DSSP (55%). Moreover, the DSSP analysis gives a larger unordered content than the CDPro analysis (27 versus 18%). These discrepancies may be attributable to the substantial extent of missing electron density in the crystal, amounting to 16% of the protein. This has been counted as unordered in the DSSP analysis, but it may contain short helices, β-strands, and turns. Experimental Absorption and CD Spectra of C1C2 ΔN Mutant. For the C1C2 ΔN mutant, the absorption spectrum (Figure 2c) shows a diminished 470 nm band and a maximum at ∼350 nm that is absent in the wild-type spectrum. The 350 nm absorption is attributable to free all-trans retinal (λmax = 380 nm in methanol),57 the concentration of which is estimated to be 1.8 μM from the reported extinction coefficient (εmax = 4.7 × 104 M−1 cm−1 in methanol).57 This concentration of free retinal indicates that the mutant dimer has lost ∼50% of its retinal. The visible CD spectrum of C1C2 ΔN (Figure 2d) shows a negative couplet of diminished magnitude relative to that of the wild-type. The long-wavelength negative band is shifted to 488 nm with Δεmax = −4.1 M−1 cm−1, and the positive band is at 434 nm with Δεmax = 3.3 M−1 cm−1. Thus, the couplet strength is S = −7.4 M−1 cm−1. Much, if not all, of the diminished intensity is attributable to the loss of retinal. In the near-UV, the CD of C1C2 ΔN shows no band near 340 nm, a negative band at 308 nm (Δεmax = −5.0 M−1 cm−1), a negative band at 285 nm (Δεmax = −9.0 M−1 cm−1), and a positive band at 260 nm (Δεmax = +9.2 M−1 cm−1). The band at 285 nm is comparable in intensity to the corresponding band of the wild-type, consistent with the assignment to aromatic side chains. The diminished intensity of the 260 nm band supports its assignment to the retinal chromophore. Channel Activities and Kinetics of C1C2 Wild-Type and Its ΔN Mutant. In patch-clamp experiments, the photocurrent amplitude and the reversal potential of C1C2 ΔN are similar to those of the wild-type (Figure 3a−c). However, the offset time constant (τOFF) of the ΔN mutant is smaller than that of wildtype (Figure 3d), suggesting that the N-terminal domain is involved in controlling the channel kinetics in the P3520 or later intermediate. Theoretical Results. TDDFT Calculations for the Monomer and Dimer. Because of its paramount importance in living processes, the retinal chromophore and its models have been extensively investigated by quantum mechanical calculations.58,59 The use of DFT with the long-range corrected CAM-B3LYP functional has emerged as one of the methods with the best cost/accuracy compromise in predicting geometries, vertical excitation energies, transition moments, and photophysical processes of retinoids.60−64 After a preliminary screening where several DFT functionals and basis sets were tested (see the Methods section), which led to similar results to those found before for bR,21 the CAM-B3LYP/TZVP combination was selected for TDDFT calculations. The results are summarized in Table 1. When only the retPSB chromophore from C1C2 (see the Methods section) was considered in the calculations (Table 1), the calculated transition energy for the first (S0 → S1) transition was 2.31 eV (536.4 nm). While the absolute match with the experimental transition energy is not an issue, we were

Figure 1. (A) Crystal structure of the C1C2 dimer, viewed parallel to the membrane. (B,C) Relative arrangement of the two retPSB moieties, viewed from the extracellular side (B) and parallel to the membrane (C), that is, perpendicular and along the interchromophoric direction, respectively. (D,E) The retPSB and its counterion viewed perpendicular (D) and parallel (E) to the average polyene plane. In all drawings, the retPSB (A) or the conjugated polyene (B− D) are colored yellow.

strengths are much smaller than the true rotational strengths of the two exciton bands because of extensive cancellation.) At shorter wavelengths, the CD spectrum exhibits a positive band at 342 nm (Δεmax = +2.43 M−1 cm−1), a negative band (Δεmax = −3.46 M−1 cm−1) at 305 nm, a stronger negative band (Δεmax = −9.10 M−1 cm−1) at 285 nm, and a positive band (Δεmax = +20.52 M−1 cm−1) at 259 nm. The 342 and 259 nm bands are attributed to the retinal chromophore (as a PSB), and the 285 nm band is attributed to aromatic side chains. In the far-UV, the CD spectrum of C1C2 (Figure S3, Supporting Information) has negative bands at 220 nm (Δεmax = −4.70 M−1 cm−1 per residue) and 209 nm (Δεmax = −5.42 M−1 cm−1 per residue) and a positive band (Δεmax = 10.87 M−1 cm−1 per residue) at 193 nm. These CD bands are characteristic of the α-helix,53 consistent with the high helix content of C1C2.8 The results of the CDPro29 analysis are shown in Table S1, Supporting Information. The three 11876

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Figure 2. Experimental UV−vis absorption (a,c) and CD spectra (b,d) of C1C2 ChR (a,b) and C1C2 ΔN mutant (c,d). Cell path lengths of 0.5 and 2 cm, respectively; other conditions are reported in the Experimental Methods section. Numbers represent apparent peak wavelengths; italic numbers in parentheses were obtained by second-derivative and deconvolution analysis (see the Experimental Methods section). The arrow indicates the absorption band assigned to free retinal.

Figure 3. Electrophysiological characterization of C1C2 ΔN mutant. (a) Photocurrent traces of the wild-type (left) and ΔN mutant (right). (b) The peak amplitudes of the photocurrents, normalized by the cell’s input capacitance. Values are means and the s.e.m. of 6−21 experiments. (c) The current−voltage (I−V) relationships of the wild-type (left) and ΔN mutant (right) between −70 and +80 mV. (d) Photocurrent kinetics of wildtype and ΔN mutants. Opening rates (τon) (left) and closing rates (τoff) (right) are listed, and values are means and the s.e.m. of 6−21 experiments (*).

concerned that the calculated transition energy E0→1 for C1C2 retPSB was slightly lower than that calculated for bR retPSB under the same conditions (2.40 eV, 516.8 nm, Table 1). Thus,

a red shift of 19.6 nm was predicted by CAM-B3LYP/TZVP for C1C2 with respect to bR, contrasting with the experimental observation of a blue shift of ∼90 nm.21 It must be stressed that 11877

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Table 1. TDDFT Calculations for ChR (C1C2) and bR Monomer and ChR Dimera Monomer Calculations C1C2 modelb

λ (nm)

retPSB ion pair QM/MM

536.4 383.4 427.6

modelb retPSB ion pair QM/MM

E (eV) 2.311 3.234 2.899 Dimer

diff.c

bR fd

λ (nm)

E (eV)

1.40 516.8 2.399 1.66 398.9 3.108 1.55 510.7 2.428 Calculations (C1C2)

f

Δλ (nm)

1.55 1.82 1.55

−19.6 15.5 83.1

λ (nm)

fd

ΔE (cm−1)

R (DBM)e

536.5 533.8 401.9 400.5 436.8 430.0

0.16 2.51 0.02 3.21 1.14 1.91

90.33

−54.0 +53.3 −20.4 +19.3 −7.39 +6.54

87.91 356.5

a

All calculations run with CAM-B3LYP/TZVP. bSee the Methods section for the description of the three models. cCalculated transition wavelength difference (in nm) between C1C2 and bR. dOscillator strength. eRotational strength (in DBM, 1 DBM = 0.9273 × 10−38 cgs).

the retPSB geometries extracted from C1C2 and bR are very similar to each other, with a RMS deviation for C and N atoms amounting to 0.246 Å; if only the conjugated polyene (from C6 to N) is considered, the RMS deviation is further reduced to 0.175 Å. As observed above, the RMS deviation from the average plane of the conjugated polyene from C1C2 is 0.085 Å, to be compared with 0.174 Å for bR. This latter finding may explain the small red shift predicted for C1C2 with respect to bR. The discrepancy of the calculated relative transition energies for C1C2 and bR with experiment can therefore be attributed to the different environment of the chromophore in the two proteins. Analysis of the hydropathic character65 of the binding pockets highlights a great difference between the two proteins (Figure 4). In C1C2 ChR, only the protonated Schiff base experiences a hydrophilic environment, while the polyene chain and especially the ionone ring are in a hydrophobic environment. In bR, by contrast, the entire chromophore is in a moderately to strongly hydrophilic environment. The impact of the chromophore−opsin interaction on the photoexcitation of rhodopsin and related proteins is still the object of many investigations.60,66,67 As summed up in a recent contribution by Valsson et al.,60 full consensus on the role played by the protein environment in tuning the excitation energy of the chromophore has not been reached yet. In the case of rhodopsin, it is known that the addition of a counterion induces a large blue shift on the retPSB transitions, but this effect seems to be largely counterbalanced by the remaining protein matrix.60,68,69 Here, we modeled the counterion and the protein matrix by considering an ion pair and a QM/MM model, respectively, as discussed in the Methods section. In keeping with the known trends,60 adding the counterions (at the QM level) induced a very strong blue shift on the S0 → S1 transition energy of both C1C2 and bR, but the further inclusion of the protein pocket (at the MM level) shifted the transition back to the red (Table 1). Apart from the absolute values of transition energies, it is apparent that when the QM/ MM model is used, the E0→1 is higher for ChR (2.90 eV) than that for bR (2.43 eV). The predicted wavelength difference is

Figure 4. Hydrophobicity plots of the two binding pockects of C1C2 and bR according to the hydropathic character65 analysis. Structures taken the from PDB database, codes 3UG98 and 1C3W,33 respectively. The plots were obtained with Discovery Studio v3.5 (Accelrys Software Inc., 2012).

83 nm, which is in very good agreement with the experimental value of ∼90 nm.21 This result is especially noteworthy in consideration of the relatively simple QM/MM model employed here, in contrast with a model including a larger QM portion, which is considered crucial for a more accurate simulation.60 For the C1C2 retPSB model, the S0 → S1 transition is practically a HOMO → LUMO ππ* excitation. This is associated with a substantial electron displacement from the β-ionone side toward the iminium side of retPSB, in a very similar manner to bR.21 When the counterion is included in the QM layer (both in the ion pair and in the QM/MM models), the transition acquires contributions from three different excitations. While the one with the largest CI coefficient is similar to the ππ* excitation of retPSB, the minor ones involve π- and π*-type orbitals partially localized on the acetate ion from Glu162. Among other things, this is responsible for slight differences in the orientation of the electric dipole transition moments, which however affects the exciton coupling in the dimer substantially (see below). In Table 1 and Figure 5, the results of CAM-B3LYP/TZVP calculations for the three models (retPSB, ion pair, and QM/ MM) of C1C2 dimers are summarized. In all cases, the calculations predict a couple of transitions with similar energies and opposite rotational strengths in the visible range, that is, an exciton couplet. Also, in all cases, the predicted exciton couplet is negative, in keeping with the experimental CD spectrum of 11878

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DeVoe Calculations. The DeVoe polarizability theory24,25 provides a description of the interaction of a set of coupled oscillators, which is a classical representation of coupled quantum mechanical transition dipole moments. The theory has proven useful for predicting the absorption and CD spectra of systems ranging from small molecules71 to proteins72 and nucleic acids.73 Pescitelli and Woody21 applied DeVoe theory to bR. Advantages of the DeVoe method include the following: (1) it considers all orders of interaction; (2) it explicitly considers the band shape of the transition(s); (3) it is applicable to weak coupling,74 that is, when the coupling energy of the oscillators is small compared to the vibronic bandwidth, which is certainly the case for ChR and bR. CD spectra calculated by the DeVoe theory for the three models under consideration are shown in Figure 6. The retPSB Figure 5. CD spectra and rotational strengths (vertical bars) calculated by TDDFT for the dimers of the three models of C1C2 ChR: RetPSB (blue), ion pair (dotted red), and QM/MM (green). For plotting the CD spectra, transition moments are scaled to the experimental transition moment magnitude. A Gaussian band shape was assumed with the transition energy and bandwidth from a fit to the absorption spectrum.

C1C2 in the visible region. However, the values of the oscillator and rotational strengths for the two exciton components, as well as the coupling energy, vary substantially for the three models. Thus, the exciton rotational strengths differ by 1 order of magnitude between retPSB (−54.0 and +53.3 DBM) and the QM/MM model (−7.39 and +6.54 DBM), with the ion pair model showing intermediate values (−20.4 and +19.3 DBM). The energy difference between the two components (twice the coupling energy) is similar for retPSB and ion pair models (around 90 cm−1 in both cases), but it is four times larger for the QM/MM model (∼350 cm−1). Thus, the presence of the static point charges of the MM layer leads to an enhancement of the dipolar coupling energy.70 In Figure 5, the CD spectra obtained from TDDFT calculations on the dimers for the three models are shown. The spectra were obtained by associating to each computed rotational strength a Gaussian band with a 55.7 nm exponential width (from the best-fit of the experimental absorption spectrum; see above). The couplet strength S value calculated directly from TDDFT calculations on the dimer is −49.82 M−1 cm−1 for retPSB and is much larger than the observed value. However, to be compared with experiment and other calculations, this value needs to be scaled to correct for the overestimation of the electric dipole transition moment. The scaling factor for this correction is 0.7618, and it appears to the fourth power in the couplet strength; therefore, scaling reduces S by a factor of 0.3367, to −16.77 M−1 cm−1, much closer to the experimental value. After application of a Gaussian band shape, only a negative band is observed for the ion pair model because the imbalance between the two exciton components is too large relative to their mean value (8%). The difference in rotational strengths of the two exciton components is even larger in the QM/MM model (13%), but because of the larger exciton splitting, a strongly asymmetric couplet is obtained with a ∼5fold difference in band amplitudes. The CD spectra plotted in Figure 5 were scaled with factors of 0.3367, 0.4318, and 0.4244 for retPSB, ion pair, and QM/MM, respectively, to take into account the discussed electric dipole transition moment overestimation.

Figure 6. CD spectra calculated by DeVoe theory for three models of C1C2 ChR: RetPSB (blue), ion pair (dotted red), and QM/MM (green). Transition moments are scaled to the experimental transition moment magnitude. The point-dipole approximation was used to calculate the interchromophore coupling. A Gaussian band shape was assumed with the transition energy and bandwidth from a fit to the absorption spectrum.

model gives the strongest couplet, with a negative maximum of −12.26 M−1 cm−1 at 488 nm and a positive maximum of +10.71 M−1 cm−1 at 426 nm. The couplet strength is S = −22.97 M−1 cm−1. The ion pair model gives a couplet with about 1/3 of this amplitude, S = −7.95 M−1 cm−1, and the couplet from the QM/ MM model is about 1/2 that of the retPSB model, S = −12.03 M−1 cm−1. Exciton Coupling. The exciton coupling energies (Table 2) calculated for the three models are very similar, ranging from −27.5 cm−1 for retPSB to −29.0 cm−1 for the ion pair. The negative sign of the coupling energy corresponds to the C2polarized A band occurring at lower energy than the B band, as is also the case with bR.21 The exciton splittings on the wavelength scale fall within the narrow range of 1.22 (retPSB) to 1.28 nm (ion pair). The exciton rotational strengths, however, differ strongly for the three models. The μ−μ coupling (Table 3) varies by more than 3-fold between retPSB (±18.65 DBM) and ion pair (±5.89 DBM), with QM/MM at an intermediate value (±9.03 DBM). This variation stems from the dependence of the μ−μ coupling on the orientation of the two transition dipole moments. Rμμ is proportional to sin 2θ cos ϕ (eqs S32 and S33, Supporting Information), where θ and ϕ describe the orientation of the transition moment in a spherical polar coordinate system (Figure S2, Supporting 11879

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Table 2. Spectroscopic and Structural Parameters for the ChR 470-Banda μtheor (D) μemp (D)b λtheor (nm) λemp (nm)b Δemp (nm)b r (Å)c θ (deg)d ϕ (deg)e Im m (BM)f θm (deg)g ϕm (deg)h V (cm−1)i ΔE (cm−1)j δλ (nm)k R+ (DBM)l S (M−1 cm−1)m

retPSB

ion pair

QM/MM

12.6545 9.64 536.43 458 55.67 11.7240 104.2258 175.6541 1.0215 81.6774 −95.7003 −27.5075 −55.0150 1.2153 −16.8346 −13.12,n −16.13o

11.8922 9.64 399.26 458 55.67 11.7744 94.3115 185.0349 3.2375 89.3035 −84.0261 −29.0397 −58.0793 1.2830 −4.5194

11.9432 9.64 434.31 458 55.67 11.7744 96.6504 185.5056 2.6593 69.9819 −85.9928 −28.6653 −57.3305 1.2664 −8.2230

Table 3. Coupling Contributions to Exciton Bands A exciton μ−μ exciton m−μ + μ−m aromatic μ−μ aromatic m−μ aromatic μ−m peptide μ−μ peptide m−μ and μ−m total exciton μ−μ exciton m−μ + μ−m aromatic μ−μ aromatic m−μ aromatic μ−m peptide μ−μ peptide m−μ and μ−m total

a

Theoretically derived data are extracted from TDDFT calculations at the CAM-B3LYP/TZVP level. bThe observed absorption spectrum (this work) has a maximum at 472 nm. Upon integration, the longwavelength band gives a dipole strength of 92.9 D2, corresponding to a transition moment magnitude of 9.64 D. Fitting the spectrum to a Gaussian band shape gives a bandwidth of 55.67 nm and λmax = 458 nm. cr is the distance of the center of the retPSB chromophore from the two-fold axis of the dimer. From the crystal structure (PDB code 3UG9). dThe angle between the electric dipole transition moment and the two-fold z-axis, from TDDFT calculations. eThe angle between the projection of the electric dipole transition moment in the xy-plane and the +x-axis, from TDDFT calculations. fThe magnitude of the magnetic dipole transition moment in Bohr magnetons. The magnitude and direction of m are obtained from TDDFT calculations. g The angle between the magnetic dipole transition moment and the two-fold z-axis, from TDDFT calculations. hThe angle between the projection of the magnetic dipole transition moment in the xy-plane and the +x-axis, from TDDFT calculations. iExciton coupling energy between transition moments in the dimer. jExciton splitting energy in the dimer. The energy of the A component minus that of the B component. kExciton splitting on the wavelength scale. lMean exciton rotational strength with the sign of the long-wavelength component. Note that these values include contributions of coupling with aromatic and peptide groups. mCouplet strength: ΔεmaxA − ΔεmaxB. The difference in intensity of the A and B bands is too large in the ion pair and QM/MM models to give a couplet for the total rotational strength. nGaussian band shape. oLog-normal band shape.

exciton μ−μ exciton m−μ + μ−m aromatic μ−μ aromatic m−μ aromatic μ−m peptide μ−μ peptide m−μ and μ−m total

retPSB Model −18.6516 −0.3503 2.6415 0.0308 −0.0180 −0.3167 −0.0032 −16.6675 Ion Pair Model −5.8894 −0.0285 2.0975 0.0079 −0.0094 −0.3086 −0.0011 −4.1316 QM/MM Model −9.0299 −1.0163 2.3152 0.1869 −0.0128 −0.3028 −0.0341 −7.8938

B

net

18.6516 0.2245 −2.5287 0.1541 0.0083 0.3961 0.0957 17.0016

0 −0.1258 0.1128 0.1849 −0.0097 0.0794 0.0925 0.3341

5.8894 −0.5100 −1.7138 0.4985 0.0179 0.4440 0.2812 4.9072

0 −0.5385 0.3837 0.5064 0.0085 0.1354 0.2801 0.7756

9.0299 0.6256 −1.9936 0.3176 0.0165 0.4123 0.1979 8.6062

0 −0.3907 0.3215 0.5046 0.0036 0.1095 0.1639 0.7124

chromophore calculated by TDDFT. The ion pair gives negative values for the Rμm of both A and B bands and a larger net rotational strength, Rμm = −0.54 DBM. Finally, QM/ MM gives a negative rotational strength for the A band and a positive value for the B band, with a net Rμm = −0.39 DBM, intermediate between the other two models. The net negative rotational strength from the exciton effect in all three models contrasts with the net positive rotational strength observed experimentally. The small absolute intensity obtained for the intrinsic rotational strength Rμm is attributable to a substantially planar chromophore, as observed above. This is in sharp contrast with, for example, the case of rhodopsin, the CD spectrum of which is dominated by the intrinsic chirality of the chromophore.75 The coupling of the retinal transitions with transitions in the aromatic side chains and peptide backbone gives rise to additional rotational strength, summarized in Table 3. The coupling contributions are similar for all three models; therefore, we will only describe those for the retPSB model in detail. The largest of these contributions is from aromatic μ−μ coupling, that is, coupling of the electric dipole transition moment of the retinal with electric dipole transition moments in the aromatic side chains. These contributions to the individual exciton components are opposite in sign to those from the retinal chromophores, thus diminishing the couplet strength. For retPSB, the contributions to the A and B bands are +2.64 and −2.53 DBM, respectively, with a net value of +0.11 DBM. Aromatic m−μ coupling, that is, coupling of the retinal magnetic dipole transition moment with electric dipole transition moments in the aromatic side chains, is weaker but makes positive contributions to both exciton components and leads to a larger net value of +0.18 DBM. The converse

Information). The factor of cos ϕ is essentially −1 for all three models, but sin 2θ is −0.48, −0.15, and −0.23 for retPSB, ion pair, and QM/MM, respectively. This factor, thus, is responsible for the 3-fold difference between the retPSB and ion pair models. A more physical explanation of the difference between retPSB and ion pair or QM/MM models is that, for the latter models, the transition moments are within 5−6° of the equatorial plane of the dimer. Thus, they are approximately coplanar, and the scalar triple product R12 · μ2 × μ1 is small. By contrast, the transition moment in retPSB is about 15° out of the equatorial plane, and the scalar triple product is substantially larger. The μ−m contribution to the exciton coupling in retPSB is shown in Table 3. For the A band, Rμm = −0.35 DBM, and for the B band, Rμm = 0.22 DBM. Thus, the net μ−m coupling is −0.13 DBM, the intrinsic rotational strength of the retinal 11880

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aromatic μ−m coupling is still weaker and contributes only −0.01 DBM to the net rotational strength. Coupling with peptide group transitions makes contributions that are about an order of magnitude smaller than those of the aromatic side chains. The peptide μ−μ contributions are −0.32 DBM to the A band and +0.40 DBM to the B band, for a net value of +0.08 DBM. Thus, the peptide μ−μ contributions reinforce the intrinsic exciton couplet strength, in contrast to the aromatic contributions. The combined m−μ and μ−m coupling with the peptide groups makes a net contribution of +0.09 DBM. For retPSB, the resultant rotational strengths for the A and B bands are −16.67 and +17.00 DBM, with a resultant of +0.33 DBM. Keeping in mind that the A band is lower in energy, our calculations predict a negative exciton couplet for retPSB and a modest net positive rotational strength, in qualitative agreement with experiment. The ion pair model gives similar results for the coupling effects, but the net rotational strengths from each contribution are generally larger than those for retPSB model. The total rotational strengths for the A and B bands are −4.13 and +4.91 DBM, respectively, with a net value of +0.78 DBM. Coupling with protein chromophores in the QM/MM model gives results generally intermediate between the retPSB and ion pair models. The A and B bands have total predicted rotational strengths of −7.89 and +8.61 DBM, respectively, and the net rotational strength is +0.71 DBM. CD spectra were calculated using the predicted rotational strengths and assuming Gaussian band shapes with the predicted splittings and the empirical bandwidth given in Table 2. These simulated spectra are shown in Figure 7, and the

Table 4. Couplet Strength of the 470 nm Band scaled exciton expt.a retPSB ion pair QM/MM

TDDFTb

DeVoec

−49.82f noneg −14.87j

−22.97 −7.95 −12.03

Gaussiand −12.82 −13.12 noneh noneh

log-normale −16.06 nonei nonei

a This work. Units of M−1 cm−1. bCalculated from the rotational strengths and wavelengths of the exciton bands predicted by TDDFT for the ChR dimer and a Gaussian band shape with the empirical bandwidth (55.67 nm). Note that these results differ from the others in this table in that they are not subjected to a scaling factor to bring the electric dipole transition moment into agreement with experiment. c Calculated by the DeVoe method using scaled transition dipole moments, a Gaussian band shape, and the point-dipole approximation for interchromophore coupling. This calculation considers only μ−μ coupling between the retinal chromophores and does not include μ− m coupling or interactions with the aromatic and peptide groups. d Electric dipole transition moment scaled to an empirical value of 9.64 D. A Gaussian band shape was assumed for the A and B exciton bands, with the transition wavelength and bandwidth obtained by fitting the absorption spectrum. Dipole coupling energy calculated in the monopole approximation. The rotational strengths include the coupling with aromatic and peptide transitions, which diminishes the magnitude of the couplet. eThe experimental absorption spectrum was fit to a log-normal band shape. This band shape was used with the theoretical rotational strengths (Table 2) and exciton splitting to calculate the CD spectra of the A and B exciton bands. These bands were then added to give the predicted CD spectrum of the dimer. Dipole coupling energy calculated in the monopole approximation. The rotational strengths include the coupling with aromatic and peptide transitions, which diminishes the magnitude of the couplet. f For retPSB, the scaling factor for the transition moment magnitude is 0.7618, and this reduces the couplet strength by 0.76184 = 0.3367, to −16.77 M−1 cm−1. gBecause the two exciton components are predicted to differ significantly in magnitude (8%), the larger negative band (A) is dominant. A very weak positive band is predicted at 297 nm, with a magnitude of 0.5% that of the negative band. hBecause the two exciton components are predicted to differ significantly in magnitude (17% for the ion pair and 9% for QM/MM versus 2% for retPSB), a single positive band is predicted for the visible region in the case of the ion pair model, and a strongly dominant positive band is predicted for the QM/MM model, with a weak negative band at 574 nm. iThe predicted spectra for these models are not couplets in the usual sense because of the large discrepancy in magnitude (8-fold for QM/MM and 34-fold for ion pair). jThe couplet is distinctly asymmetric with a ∼5-fold difference in band amplitudes. The scaling factor for transition moment magnitudes is 0.8072, and this reduces the couplet strength by 0.80724 = 0.4244, to −6.31 M−1 cm−1.

Figure 7. Calculated CD spectra for three models of C1C2 ChR: retPSB (blue), ion pair (dotted red), and QM/MM (green). Rotational strengths include both intrinsic and coupling contributions. Transition moments and charges are scaled to the experimental transition moment magnitude. A Gaussian band shape was assumed for each exciton component. Transition energies and bandwidths are from a Gaussian fit to the absorption spectrum.

resultant rotational strength and the mean rotational strengths of the two exciton components. If the two exciton components have rotational strengths of equal magnitude, a symmetrical couplet results. With increasing disparity between the components, the larger component becomes increasingly dominant, and ultimately, the smaller component is completely obscured. The cancellation of the weaker band is especially significant when the exciton coupling energy is small and the bandwidth is large, as in the current case. It is useful to examine the ratio of the net rotational strength to the mean rotational strength of the components. For an ideal couplet, this ratio is zero. The values for the retPSB, ion pair, and QM/MM models are 0.02, 0.17, and 0.09, respectively. Thus, the retPSB approaches an ideal couplet, whereas the ion pair shows no evidence of a couplet, and the QM/MM model is a borderline

results are summarized in Table 4. Only the retPSB model gives a predicted CD spectrum showing the characteristic couplet observed in the experimental CD spectrum of C1C2 (Figure 2b). The other two models give spectra with what appears to be a single positive band, although the QM/MM model has a very weak negative lobe above 550 nm that is barely detectable on the scale shown. The qualitative differences in the spectra are the result of differences in the relative magnitudes of the 11881

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The DeVoe method uses scaled transition moments and a Gaussian fit to the observed absorption spectrum; therefore, it requires no further scaling. However, it only considers the exciton μ−μ coupling; therefore, it should be compared with exciton CD spectra calculated with this coupling alone (Table 3). Such calculations give S values of −13.52, −5.51, and −6.82 M−1 cm−1, respectively, for retPSB, ion pair, and QM/MM. Thus, the relative values are in agreement between DeVoe and exciton calculations. The scaled exciton calculations include both intrinsic and coupling contributions. For the retPSB model, the Gaussian band shape gives the best agreement with experiment for the observed couplet strength, but as noted above, the log-normal band shape reproduces the relative magnitudes of the positive and negative lobes more accurately. The ion pair and QM/MM models fail to give a couplet that even qualitatively reproduces the observed spectrum.

case. The net rotational strength must be an order of magnitude smaller than the mean rotational strengths of the components for an exciton couplet to be detectable for the bandwidth used here. While the retPSB model reproduces the observed couplet, it will be noted that the relative magnitudes of the positive and negative lobes are not in agreement with experiment. The ratio |Δε−/Δε+| (where the subscript +/− refer to the long- and short-wavelength maxima, not to their signs) is 3.0 in the predicted spectrum and 1.08 experimentally. The failure to reproduce this qualitative feature is due in part to the overestimate of the net rotational strength; experimentally, Rnet = 0.16, whereas the theoretical value for retPSB is 0.33 DBM, and for the other models, it is more than 2-fold larger. In addition, the relative magnitudes of the two lobes may be influenced by the band shape, which is closer to a log-normal distribution than to a Gaussian. CD spectra have therefore been calculated for the three models using the log-normal distribution, obtained as described in the Supporting Information, for each of the two exciton bands, and the results are shown in Figure 8 and Table 4. All three models give a

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DISCUSSION The vibronic fine structure observed in the 470 nm band of ChR contrasts with the absence of such a structure in bR. Polar environments lead to broadening of vibronic bands and thus obscure vibronic fine structure.76−78 The presence of fine structure in the 470 nm band of ChR implies that the retPSB is in a relatively nonpolar environment compared to that in bR, consistent with the plots shown in Figure 4. For bR, the exciton Rμμ is ∼±40 DBM,21 more than twice as large as that for the retPSB model of ChR and an order of magnitude larger than that for the ion pair. Rμμ for bR and for ChR show the same angular dependence, differing only by the coefficient, which is 3/2 for bR and 1 for ChR. This ratio reflects the presence of three chromophores in bR and two in ChR. In bR, the chromophore is tilted more strongly from the equatorial plane (θ = 111°) compared with ChR (θ = 104° for retPSB model, 94° for ion pair, 97° for QM/MM). This gives a factor of sin 2θ = −0.67 for bR, which is ∼1.5-fold larger than that for the retPSB model of ChR. Together with the factor of 1.5 in the coefficients, this accounts for the factor of 2 ratio of Rμμ for bR and the retPSB model of ChR. There have been few direct comparisons of the results of DeVoe theory24,25 and exciton theory, but in those cases, the similar results obtained by the two methods demonstrate that the exciton splittings in weak and strong coupling are similar. Cech et al.73 found that for the dinucleoside monophosphate ApA, “remarkably good agreement with the polarizability [DeVoe] theory is obtained by using Gaussians of bandwidth 1.5 kK for each polymer band.” (The low-energy band in the monomer ApA spectrum has a bandwidth of 1.6 kK, 1 kK= 1000 cm−1.) Pescitelli et al.79 compared the matrix method and DeVoe results for bis-porphyrin steroids and found very good agreement for cases in which only one transition in each porphyrin was considered. In our previous study of bR21 and in the present work, the results from DeVoe theory agree reasonably well with those from exciton theory. As a result, we conclude that exciton theory is applicable to weakly coupled systems such as the multimeric rhodopsins. It should be noted that the vast majority of applications of exciton theory to organic and biochemical systems involve weak coupling and that the strong-coupling expression for the exciton splitting has been used successfully in treating these systems.16,80,81 The N-terminal deletion mutant ΔN C1C2 is of interest because the N-terminal domain is part of the dimerization domain. Deletion of this domain might provide a monomeric

Figure 8. Calculated CD spectra for three models of C1C2 ChR: retPSB (blue), ion pair (dotted red), and QM/MM (green). Rotational strengths include both intrinsic and coupling contributions. Transition moments and charges are scaled to the experimental transition moment magnitude. A log-normal band shape was assumed for each exciton component. Transition energies and bandwidths are from a fit of the log-normal distribution to the absorption spectrum.

biphasic CD spectrum, but the ion pair and QM/MM models have weak negative bands at long wavelengths, whereas the retPSB model gives a couplet that is in satisfactory qualitative agreement with experiment. The ratio |Δε−/Δε+|, is 1.11 for the log-normal distribution, which agrees well with the experimental value of 1.08. Table 4 compares the couplet strengths calculated by several methods with the observed couplet strength, S = −12.82 M−1 cm−1. As discussed above, the S values calculated directly from TDDFT calculations must be scaled to correct for the overestimation of the electric dipole transition moment. After applying the correction, the scaled TDDFT value for retPSB is −16.77 M−1 cm−1, comparable to the experimental value and to the results from exciton calculations. TDDFT does not give a true couplet for the ion pair or QM/MM models because the imbalance between the two exciton components is too large relative to their mean value. 11882

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protein. The mutant has channel activity comparable to that of the wild-type when expressed in HEK293 cells (Figure 3), but the absorption spectrum (Figure 2c) indicates a significant loss of retinal in vitro. Thus, the holoprotein appears to be less stable in detergent micelles than in vivo. The CD spectrum of the ΔN mutant retains the exciton couplet of the wild-type, albeit at reduced amplitude. The diminished amplitude is largely attributable to the loss of retinal, and the persistence of the exciton couplet indicates that the mutant remains, largely or completely, in dimeric form. Thus, the N-terminal extracellular residues are not necessary for dimerization of ChR. In view of the destabilization of the retinal linkage in the mutant, the N-terminal domain may function in the stabilization of this linkage. The intrinsic CD of the retinal chromophore in ChR is negative, whereas the CD arising from coupling with protein groups is positive. Thus, it is necessary to include the coupling contribution to account for the observed net positive rotational strength of ChR, just as it is for bR.21 In principle, the QM/MM model should provide the best account of the spectra of ChR. Indeed, this model reproduces the transition energy for ChR better than either of the other models. It should be noted, however, that the retPSB model provides the best agreement with the transition energy in bR (Table 1). Moreover, the ChR transition energies for retPSB and QM/MM models bracket the observed transition energy. However, the above observations are likely to be related to a systematic error in predicted transition energies typical of TDDFT calculations.82 It must be stressed that the QM/MM model employed here is relatively simple. In particular, it is likely that the QM layer should be much larger than our ion pair to get accurate CD calculation results.60 The retPSB model is the only model that reproduces the exciton couplet. The key feature that distinguishes the three models is the electric dipole transition moment direction. The retPSB transition moment differs from those for QM/MM and the ion pair by 13.6 and 12.3°, respectively. These relatively small differences have a profound effect on the magnitudes of the exciton couplet, leading to a 3-fold difference in its magnitude. Thus, the retPSB model provides a better value for the transition moment direction than the QM/MM model.

Article

ASSOCIATED CONTENT

S Supporting Information *

Detailed methods, including fitting the absorption spectrum, DeVoe calculations, exciton calculations, and coupling with aromatic and peptide groups; Tables S1−S8, showing the secondary structural analysis of C1C2, coordinates for the retPSB monomer and dimer, coordinates for the ion pair monomer and dimer, coordinates for the QM /MM monomer and dimer, and monopole charges for the three models; Figures S1−S3, showing a fit of the absorption spectrum to a lognormal distribution, the coordinate system for a ChR dimer, and the experimental far-UV CD spectrum of C1C2; and references for the Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (G.P.). *E-mail: [email protected] (R.W.W.). Present Address #

H.E.K.: Department of Molecular and Cellular Physiology, Stanford University School of Medicine, Stanford, CA 94305, U.S.A. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Deisseroth, K.; Feng, G.; Majeska, A. K.; Miesenbock, G.; Ting, A.; Schnitzer, M. J. Next-Generation Optical Technologies for Illuminating Genetically Targeted Brain Circuits. J. Neurosci. 2006, 26, 10380−10386. (2) Deisseroth, K. Optogenetics. Nat. Methods 2011, 8, 26−29. (3) Fenno, L.; Yizhar, O.; Deisseroth, K. The Development and Application of Optogenetics. Annu. Rev. Neurosci. 2011, 34, 389−412. (4) Zhang, F.; Vierock, J.; Yizhar, O.; Fenno, L. E.; Tsunoda, S.; Kianianmomeni, A.; Prigge, M.; Berndt, A.; Cushman, J.; Polle, J.; et al. The Microbial Opsin Family of Optogenetic Tools. Cell 2011, 147, 1446−1457. (5) Ernst, O. P.; Lodowski, D. T.; Elstner, M.; Hegemann, P.; Brown, L. S.; Kandori, H. Microbial and Animal Rhodopsins: Structures, Functions, and Molecular Mechanisms. Chem. Rev. 2014, 114, 126− 163. (6) Nagel, G.; Ollig, D.; Fuhrmann, M.; Kateriya, S.; Musti, A. M.; Bamberg, E.; Hegemann, P. Channelrhodopsin-1: A Light-Gated Proton Channel in Green Algae. Science 2002, 296, 2395−2398. (7) Nagel, G.; Szellas, T.; Huhn, W.; Kateriya, S.; Adeishvili, N.; Berthold, P.; Ollig, D.; Hegemann, P.; Bamberg, E. Channelrhodopsin2, a Directly Light-Gated Cation-Selective Membrane Channel. Proc. Natl. Acad. Sci. U.S.A. 2003, 100, 13940−13945. (8) Kato, H. E.; Zhang, F.; Yizhar, O.; Ramakrishnan, C.; Nishizawa, T.; Hirat, K.; Ito, J.; Aita, Y.; Tsukazaki, T.; Hayashi, S.; et al. Crystal Structure of the Channelrhodopsin Light-Gated Cation Channel. Nature 2012, 482, 369−374. (9) Ernst, O. P.; Murcia, P. A. S.; Daldrop, P.; Tsunoda, S. P.; Kateriya, S.; Hegemann, P. Photoactivation of Channelrhodopsin. J. Biol. Chem. 2008, 283, 1637−1643. (10) Ritter, E.; Stehfest, K.; Berndt, A.; Hegemann, P.; Bartl, F. J. Monitoring Light-Induced Structural Changes of Channelrhodopsin-2 by UV−Visible and Fourier Transform Infrared Spectroscopy. J. Biol. Chem. 2008, 283, 35033−35041. (11) Becher, B. M.; Cassim, J. Y. Effects of Light Perturbation on Circular-Dichroism of Purple Membrane from Halobacteria-halobium. Biophys. J. 1975, 15, 66a. (12) Heyn, M. P.; Bauer, P. J.; Dencher, N. A. Natural CD Label to Probe Structure of Purple Membrane from Halobacterium halobium

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CONCLUSIONS The CD spectrum of ChR in the visible region is dominated by the exciton coupling between the retinal PSB chromophores in the two subunits. The low polarity of the retinal-binding pocket in ChR is reflected in the relatively blue-shifted absorption band of ChR and in its vibronic fine structure, which is absent in bR. Although the QM/MM model gives the best description of the transition energy for ChR, the retPSB model gives the best description of the transition moment direction and is the only model that reproduces the observed exciton couplet. As with bR, it is necessary to consider the coupling of the retinal chromophore with aromatic and peptide chromophores in the protein to explain the net positive rotational strength of the visible band. The CD spectrum of the ΔN C1C2 mutant, with an N-terminal deletion, has an exciton couplet, demonstrating that the mutant remains dimeric. The integration of the CD spectrum and electrophysiological analyses suggests that the hydrophobic interactions between TM3 and TM4 suffice to maintain the C1C2 dimer, and the major function of the Nterminal domain is to stabilize the protein and to control the channel kinetics. 11883

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