Green Color Tuning of Visual Rhodopsins: Electrostatic Theory

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B: Biophysical Chemistry and Biomolecules

Red/Green Color Tuning of Visual Rhodopsins: Electrostatic Theory Provides a Quantitative Explanation Florimond Collette, Thomas Renger, Frank Müh, and Marcel Schmidt am Busch J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b02702 • Publication Date (Web): 13 Apr 2018 Downloaded from http://pubs.acs.org on April 19, 2018

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The Journal of Physical Chemistry

Red/Green Color Tuning of Visual Rhodopsins: Electrostatic Theory Provides a Quantitative Explanation Florimond Collette,∗ Thomas Renger, Frank Müh, and Marcel Schmidt am Busch∗ Institut für Theoretische Physik, Johannes Kepler University Linz, Altenberger Strasse 69, 4040 Linz, Austria E-mail: [email protected]; [email protected] Phone: +43 732 2468 5154. Fax: +43 732 2468 5152

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Abstract We present a structure-based theory of the long-wavelength (red/green) color tuning in visual rhodopsins and its application to the analysis of site-directed mutagenesis experiments. Using a combination of electrostatic and molecular-mechanics methods, we explain the measured mutant-minus-wild-type absorption shifts and conclude that the dominant mechanism of the color tuning in these systems is electrostatic pigment-protein coupling. An important element of our analysis is the independent determination of protonation states of titratable residues in the wild type and the mutant protein as well as the self-consistent reoptimization of hydrogen atom positions, which includes the relaxation of the hydrogen bonding network and the reorientation of water molecules. On the basis of this analysis, we propose a “dipole orientation rule” according to which both the position and the orientation of a polar group introduced in the protein environment determine the direction of the transition energy shift of the retinal chromophore.

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Introduction Cone 1,2 and rod 3 photoreceptor cell pigments are vertebrate visual opsins that initiate the signal transduction cascade in photopic (day-light) and scotopic (dim-light) vision, respectively. 4 Visual and non-visual opsins form the opsin subfamily, an integral part of the rhodopsin-like receptors family, which belongs to the G protein-coupled receptors (GPCRs) superfamily. 4–6 Opsins commonly consist of seven mostly α-helical transmembrane segments (Figure 1), and their primary function is to transduce extracellular signals into intracellular responses. 4,7,8 In visual opsins in particular, electromagnetic radiation of the ultraviolet-visible spectral region causes a light-sensitive chromophore, 11-cis retinal, to induce a conformational rearrangement of the photoreceptor. 11-cis retinal is attached to the conserved Lys296 residue of the apoprotein via a protonated Schiff base 9 whose counterion is a glutamic acid residue located at positions 113 and 181 in visual and non-visual opsins, respectively. 4 The retinal molecule can be divided into three regions: 10 the protonated Schiff base (PSB), which links the chromophore to the apoprotein, the conjugated polyene chain, which provides the extended π-system, and the β-ionone ring, the cyclic end group of the chromophore. In visual opsins, the maximum spectral sensitivity of 11-cis retinal ranges from ∼ 355 nm 13 (in short-wavelength-sensitive type 1 and 2 opsins) to ∼ 570 nm 13 (in middle-/long-wavelengthsensitive opsins), whereas in organic solvent it is located at ∼ 440 nm. 14–16 Humans normally have three types of cone pigments that are responsible for color vision, the so-called L, M, and S cones with absorption maxima at ∼ 560 nm, ∼ 530 nm, and ∼ 420 nm, respectively. 2 All of these cones use the same retinal chromophore. The remarkable change in absorption maximum between solvent and protein environment, or between different protein environments, is called opsin shift or spectral/color tuning. 17,18 It directly relates to the questions of how the genetically encoded amino acid sequence shapes the spectroscopic properties and which molecular interactions are employed. 13 The following mechanisms are discussed for the color tuning: (i) The protonation state of the chromophore. The p𝐾A value of 11-cis retinal is strongly modulated by the surrounding protein matrix. Neutralization of the Schiff base shifts the wavelength of electronic excitation 3



Figure 1: Left: Schematic diagram of bovine rhodopsin (serpentine model). Amino acid residues are shown in single-letter code. The arrow indicates Lys296 (denoted X), which is the binding site of the chromophore. The sequence starts with the lower part (N-terminus) in the extracellular domain, and ends with the upper part (C-terminus) in the cytoplasmic domain. Colored cylinders indicate the α-helical transmembrane domains (I to VII) and the cationic amphipathic helix VIII. Right: Different dielectric regions of transmembrane bovine rhodopsin in the electrostatic model of the protein and its environment (see Computational details). Figure made with TAPBS 11 and VMD. 12 by ∼ 120 nm to the blue, as observed for short-wavelength-sensitive type 1 and 2 opsins. 19–21 (ii) Chromophore distortion. The absorption maximum is sensitive to the orientation of the β-ionone ring relative to the polyene chain, which is determined by steric constraints due to the protein matrix. 22 (iii) Chromophore-residue interactions. The absorption maximum of the chromophore is tuned via interactions with dipolar or ionized amino acid residues located in proximity to the chromophore. Polarization of the electronic wave function (inductive tuning) accompanied by changes in bond-length alternation 23 (BLA) on one hand and electrostatic tuning 22 on the other are discussed. Recent theoretical quantum mechanics/molecular mechanics (QM/MM) investigations into color tuning in visual opsins have focused on the contribution of chromophore-residue interactions. 23–37 Several interesting articles have been published by Morokuma and co-workers, who studied rhodopsins and related systems using their ONIOM hybrid QM/MM tool. 23,26,27,30,31 They identified inductive tuning as the dominant color-tuning mechanism. Their results converged to the generalized “OH-site rule”. According to this rule, dipolar residues located around the PSB shift

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the absorption maximum to the blue, whereas a shift in the opposite direction is obtained when a similar residue is located close to the β-ionone ring. 23 An alternative view, supported by several experimental 14,38–45 and theoretical studies, 43,46–50 identifies electrostatic chromophore-residue interaction as the dominant effect in color tuning. This view has been summarized by Ernst et al. in a recent review. 22 Mathies and Stryer 51 first measured the large net displacement of positive charge from the PSB towards the β-ionone ring of retinal upon electronic excitation. The electronic reorganization is expressed by the difference in permanent dipole moment Δ𝜇 between the electronic ground state and the first excited state, which amounts to ∼ 12 D for retinal. 51,52 The large Δ𝜇 suggests a large difference in the electrostatic coupling to the protein environment between the chromophore’s ground and first excited states. Consequently, dipolar or ionized residues may modulate the absorption maximum noticeably. 14,43,53 In a perturbative treatment of the chromophore-protein interaction, electrostatic tuning of the chromophore’s transition energy is a first-order effect. 54 Inductive tuning – polarization of the chromophore by the environment and interaction of this polarization with the environment – is a second-order effect. The observed linear relationship between the absorption maximum in solution and the electrostatic interaction energy with the surrounding ions 38 is consistent with first-order perturbation theory. Similarly, the measured ∼ 60 nm red shift of the absorption maximum of retinal between the gas and the aqueous phase has been reported to be due to the electrostatic interaction between the protonated Schiff base and the counterion. 44 Experimental results are in accordance with the initial predictions of the “external pointcharge model”, 46,47,49 a simple model for estimating electrostatic interaction energies, and a coarsegrained semi-empirical computation on human cone pigments. 43 The modulation of the absorption maximum by site-directed mutagenesis in the binding site of the human cellular retinol-binding protein II (hCRBPII) has also been interpreted in terms of electrostatic tuning but are based on QM/MM computations that include inductive effects. 55 Resonance Raman spectroscopy has delivered evidence of similar electronic ground-state polarizations for the human green and red 5



cone pigments in contrast to the blue cone pigment, for which shifts in the C−C streching mode frequency indicate a change in the electronic structure. 41,43,53 Hence, there is no obvious indication that inductive effects could play a significant role in the red/green color tuning. Accordingly, it seems reasonable to explain the latter by electrostatic pigment-protein interactions. The aim of the present work is to clarify this issue by applying electrostatics at atomic detail. Such methods are well established for the computation of p𝐾A -shifts of titratable groups in the protein or redox potentials. 56–58 In the last decade, these methods have been extended to include excited states of protein-bound pigments. 54 The two major approaches are the PoissonBoltzmann/quantum chemical (PBQC) method. 59,60 and the charge density coupling (CDC) method. 61 Both are two-step quantum-chemical/electrostatic approaches that have previously been successful in explaining transition energy shifts of chromophores in photosynthetic pigment-protein complexes 59–65 and BLUF photoreceptors. 66 The quantum-chemical calculations of the ground and first excited states are performed on the isolated geometry-optimized chromophore. The resulting electrostatic potentials (ESPs) of the charge densities of the ground and excited electronic states are approximated by the ESPs of two sets of atomic partial charges. These partial charges are then used to evaluate the transition energy shifts from the electrostatic coupling with the charge density of the protein. The latter is obtained from standard molecular mechanics force fields in combination with Poisson-Boltzmann type electrostatic calculations of the most likely protonation state of the titrable amino acid residues. Our two electrostatic methods for the calculation of the transition energy shift of the chromophore differ in the way the polarizability of the protein and solvent environment are taken into account in the evaluation of the chromophore-protein charge density coupling. In PBQC, we distinguish between the polarizabilities of the protein, the membrane, and the solvent while also taking the ionic strength of the solvent into account by solving a Poisson-Boltzmann equation. In the simpler CDC method, the effect of the environmental polarization is described by one effective electric constant and the influence of the ions in the solvent is neglected. In general, the limited quality of crystal structure coordinates meets the requirements for 6


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estimating the Coulomb coupling at the molecular force-field level by CDC. High-level quantummechanical computations, however, are more sensitive to coordinate distortions. Therefore, optimization of crystal structure coordinates at the quantum-chemical or QM/MM-theoretical level is needed to correct these distortions. In a QM/MM treatment, a large part of the protein is included by classical mechanics/electrostatics, whereas the chromophore – and often also part of its environment – is described quantum-mechanically. 26,27,30,31 The interface between the QM and the MM part must be chosen carefully in order to avoid artifacts. 67 The present electrostatic methods avoid such artifacts by performing the QC calculations on the isolated chromophore. However, it is thereby limited to address mainly first-order transition energy shifts but also includes those second-order effects that are related to the polarization of the environment, described in a different way in PBQC and CDC, as discussed above. Other second-order transition energy shifts, e.g., due to dispersive chromophore-protein interactions or due to the electronic polarization of the chromophore by the protein are neglected in our treatment. Our study presents structure-based simulations of electrochromic shifts in site-specific mutants of bovine rhodopsin. Since our methods are static, i.e., require specified heavy-atom positions, and crystal structures of mutants are not available, we restrict the present study to mutants, where the modeling of heavy-atom positions is straightforward. The selected mutants sample the space around the entire chromophore and thus allow electrostatic tuning to be evaluated in different regions and, since most involve changes in hydroxy groups, challenge the “OH-site rule”. The remainder of this work is organized as follows: First, the electrostatic methods are described, including their parametrization and how they can be used to calculate mutant-minuswild-type absorption shifts. This is followed by an analysis of how steric constraints imposed by the protein matrix on the conformation of 11-cis retinal modulate the difference in the permanent dipole moment between the excited and the electronic ground states. Finally, we present the results of applying the electrostatic methods to a variety of absorption shifts in single-site mutants of bovine rhodopsin and evaluate the amount of electrostatic tuning.

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Computational methods The mutant-minus-wild type shift in transition energy of the chromophore Δ𝐸mut−wt is obtained from the difference in electrostatic transition free energy between the mutant (mut) and the wild type (wt) as (mut) (wt) Δ𝐸mut−wt = Δ𝐺e−g − Δ𝐺e−g ,

(1)

(mut/wt) where the electrostatic transition free energy Δ𝐺e−g is defined as

(mut/wt) Δ𝐺e−g = ∑ 𝑞𝑗(mut/wt) (𝜙 (e) (⃗𝑟𝑗 ) − 𝜙 (g) (⃗𝑟𝑗 )) .

(2)

𝑗

Here, the charge density of the protein in the mutant and in the wild type is represented by atomic partial charges (APCs) 𝑞𝑗(mut) and 𝑞𝑗(wt) , respectively, at position 𝑟⃗𝑗 of the respective atom of the protein. The position of heavy atoms in the wild type are taken from the crystal structure. The positions of hydrogen atoms and those of the heavy atoms of the mutant that are not present in the wild type are modeled as described below. The term 𝜙 (e) (⃗𝑟) − 𝜙 (g) (⃗𝑟) in eq 2 denotes the difference in electrostatic potential between the excited (e) and the ground (g) state of the chromophore at the position of protein atom 𝑗. In PBQC, these potentials are obtained from the solution of a linearized Poisson-Boltzmann equation (LPBE) ∇ · (𝜀r (⃗𝑟)∇𝜙 (g/e) (⃗𝑟)) = − (g/e)

where 𝑄𝐼

1 (g/e) ∑ 𝑄𝐼 𝛿(⃗𝑟 − 𝑅⃗𝐼 ) + 𝜅 2 (⃗𝑟)𝜀r (⃗𝑟)𝜙 (g/e) (⃗𝑟) , 𝜀0 𝐼

(3)

denote APCs of the 𝐼 th atom of the chromophore at position 𝑅⃗𝐼 in the ground (g) and

excited (e) state, obtained from a fit of the electrostatic potential of the respective charge densities. The latter are obtained from quantum-chemical calculations on the isolated chromophore, as described below. In this type of electrostatic computation, we assign different values for relative permittivity 𝜀r (⃗𝑟) to the protein interior (𝜀p ), the membrane interior (𝜀memb ; also approximating the detergent belt in the case of solubilized rhodopsin), and the surrounding aqueous solvent (𝜀solv ). This is the reason, why the relative permittivity 𝜀r (⃗𝑟) in eq 3 is position-dependent (see Figure 1, 8


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right). Similarly, the inverse Debye length 𝜅(⃗𝑟) depends on the position, because the ions in the solution are allowed to enter neither the protein nor the membrane. Details of the assignment of 𝜀r (⃗𝑟) and 𝜅(⃗𝑟) are given below. In CDC, the electrostatic potential 𝜙 (g/e) (⃗𝑟) is obtained analytically by neglecting the ionic strength of the solvent and by assigning the same effective relative permittivity 𝜀eff to the whole system. In this case the potential becomes 𝜙 (g/e) (⃗𝑟) =

(g/e)

𝑄 1 ∑| 𝐼 | 4𝜋𝜀0 𝜀eff 𝐼 |𝑅⃗𝐼 − 𝑟⃗| | |

(4)

and the mutant-minus-wild type transition energy shift is given as

Δ𝐸mut−wt =

1 4𝜋𝜀0 𝜀eff

(g) ⎛ 𝑄 (e) − 𝑄 (g) 𝑄𝐼(e) − 𝑄𝐼 (wt) ⎞⎟ (mut) 𝐼 ⎜∑ 𝐼 𝑞 − ∑ |⃗ | 𝑞𝑘 ⎟ . ⎜ 𝐼 ,𝑗 ||𝑅⃗𝐼 − 𝑟⃗𝑗 || 𝑗 𝐼 ,𝑘 |𝑅 𝐼 − 𝑟⃗𝑘 | ⎝ ⎠ | | | |

(5)

It should be noted that in both methods, CDC and PBQC, the set of protein APCs 𝑞𝑗(mut) and 𝑞𝑘(wt) take into account non-standard protonation states of ionizable groups in the protein, as determined by the electrostatic and Monte Carlo methods described below. These protonation states may in principle differ between mutant and wild type.

Quantum-chemical calculations The APCs of the wild-type and mutant proteins were taken from the CHARMM22 molecular mechanics force field. 68,69 The APCs of the 11-cis retinal Schiff base in the ground and excited states were obtained from a fit of the electrostatic potentials of the respective charge densities with CHELP-BOW 70 based on quantum-chemical computations employing density functional theory (DFT) and time-dependent DFT (TDDFT) in the Tamm-Dancoff approximation 71 with different exchange-correlation (XC) energy functionals and a 6-31G* basis set 72,73 (Table S1, Supplementary Material). The electronic structure method to compute APCs of the retinal chromophore was chosen by virtue of a comparison of the computed difference Δ𝜇 between excited and ground state 9



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permanent dipole moment with experimental data. 51,74–77 Since the latter are not available for the protonated 11-cis retinal Schiff base and else have significant error margins due to approximations in the analysis of spectroscopic data, we tried to just get the right order of magnitude of Δ𝜇. Without the Schiff base, Δ𝜇 is between 10 and 15 D for all-trans, 9-cis, 11-cis, and 13-cis retinal. 51,75–77 Formation of the Schiff base linkage does not affect this range of dipole values strongly, while protonation of the Schiff base seems to increase Δ𝜇 slightly by about 2 D within the experimental error margins. 51 In general, the APCs are obtained from fully geometry-optimized chromophore coordinates in vacuo. In visual opsins, 11-cis retinal adopts a conformation inside the binding pocket of the photoreceptor that deviates significantly from the fully optimized conformation in vacuo. The most pronounced differences between the two conformations concern the distortion of the β-ionone ring relative to the polyene chain. In order to see how this conformational change influences Δ𝜇, we performed (i) restrained geometry optimizations, where the β-ionone ring with respect to the polyene chain was constrained in its original orientation (a dihedral angle of 148° between the atoms C9, C10, C11, and C17), and (ii) (fully) unrestrained optimizations of 11-cis retinal. Initial geometries of 11-cis retinal were taken from the crystal structure of bovine rhodopsin at 2.2 Å resolution (PDB code: 1U19). 78 Table 1: Difference in the Permanent Dipole Moment Between Electronic Ground State and First Excited State Calculated for 11-cis Retinal After Applying an Unrestrained Geometry Optimization or One Where the Dihedral Angle That Determines the Orientation of the β-ionone Ring Was Fixed to Its Value in the Crystal Structure of Bovine Rhodopsin at 2.2 Å Resolution (PDB Code: 1U19; Ref 78) QC method TDDFT/B3LYP TDDFT/BHHLYP HF-CIS

restrained unrestrained 28.4 17.8 3.6

23.4 11.0 3.5

All values are given in units of Debye. APCs for TDDFT/BHHLYP (restrained) can be found in Table S1, Supplementary Material.

Geometry optimizations were carried out applying DFT with the B3LYP XC energy functional 10


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and a 6-31G* basis set using the quantum chemistry package Jaguar. 79 Based on these restrained and (fully) unrestrained optimized coordinates of 11-cis retinal, Δ𝜇 was calculated using two hybrid XC functionals, B3LYP and BHHLYP, 73 and the HF-CIS method. Please note that the dependence of the dipole moment of excited and the ground state on the origin of the coordinate systems cancels in the difference Δ𝜇, since the charge of the retinal chromophore is the same in the excited and the ground state. As can be seen from the data with unconstrained geometry optimization in Table 1, only the BHHLYP XC functional yields Δ𝜇 values in the range expected for the relaxed chromophore based on the experimental data. Therefore, we preferred TDDFT/BHHLYP. This electronic structure method predicts an increase of Δ𝜇 by 7 D due to the distortion of the β-ionone ring. Accordingly, we based the determination of APCs on the computations with restrained geometry optimization corresponding to Δ𝜇 = 17.8 D.

Electrostatic computations Crystal structures of bovine 78 rhodopsin provided the heavy-atom coordinates of the wild type. Hydrogen atom positions were generated and energetically optimized by molecular mechanics using CHARMM 68 with the CHARMM22 force field. 69 Besides parts of the amino-acid residue that has been mutated, all remaining heavy-atom coordinates of the mutant proteins were kept in conformance with the corresponding wild-type crystal structure. For the mutated residue, only the part of the respective wild-type residue similar to the mutated one was retained. The atoms of the mutated side chain not present in the wild type were modelled and energetically optimized by means of molecular mechanics geometry optimization based on the CHARMM22 force field. Protonation states of titratable amino-acid residues were determined by a combination of solvation free-energy calculations based on the linearized Poisson-Boltzmann equation using the TAPBS front-end 11 connected to the Adaptive Poisson-Boltzmann Solver APBS 80 and MonteCarlo titration based on the Metropolis approach 81 as implemented in Karlsberg2. 82 Whereas in the simplest standard techniques the carboxyl groups are treated with implicit protons, in this study explicit protons are considered in all mutated residues and for those carboxyl groups 11



in the vincinity of the retinal. This treatment further allows us to determine which of the two carboxyl oxygen atoms binds the proton in the protonated case. The following set of relative permittivity values is used in the computation of protonation probabilities: 𝜀p = 4.0, 𝜀memb = 2.0, and 𝜀solv = 80.0. The inverse Debye length 𝜅(⃗𝑟) in the LPBE (eq 3) corresponds to a 0.1 M NaCl solution. After determination of the protonation probability ⟨𝑥⟩ of each titratable group in the protein, such a group is fixed in its protonated state, if ⟨𝑥⟩ > 0.5, and its deprotonated state, if ⟨𝑥⟩ ≤ 0.5 at pH 7. The APCs 𝑞𝑗(mut) and 𝑞𝑘(wt) used in the electrostatic computations of transition energies described above represent these protonation states. In a next step, all hydrogen atom positions are reoptimized (and the protonation states confirmed). Overviews of the protonation probabilities in the wild-type and every mutant protein are given in Table S2–S7 and Figure S5, Supplementary Material; the resulting protonation pattern is largely compatible with a previous Poison-Boltzmann-type study. 83 In a nutshell, for the wild type and every mutant protein (if applicable): His195 and His278 are positively charged, all others histidines are neutral (His65 having its proton on Nδ1 , the others on Nε2 ); Asp83, Glu122, Glu181, and Glu201 are protonated; all other titratable residues are in their standard protonation state. Independent evidence for the protonation of Asp83 and Glu122 was obtained with Fourier-transform infrared spectroscopy (FTIR) on the D83N and E122Q mutants. 84 The LPBE for the electrostatic potential of the chromophore’s ground and excited states (eq 3) are solved by using TAPBS 11 employing the same relative permittivity values as above except that 𝜀p = 2.0. Details of this implementation of the PBQC method can be found in refs 54 and 60. To a certain extend the 𝜀p used in the calculation of transition energy shifts is an adjustable parameter, which compensates for uncertainties in the quantum chemical calculations of atomic partial charges. The present value 𝜀p = 2.0, however, is in a very typical range also found for other chromophores. 60

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Results Calculations of transition energy shifts (mutant-minus-wild type) are presented for five mutants of bovine rhodopsin and compared with experimental data. An important question that needs to be considered before the difference spectra can be calculated is how well the structure of the mutants can be defined. If the size and the structure of the amino acid changed in the mutant is close to that of the wild type, we expect that conformational changes that go beyond the mutated residues are unlikely and that the structure of the mutated residue can be well predicted by the molecular mechanics applied here. On this basis we have divided mutants found in the literature into two groups. The first group involves those mutants for which the number of heavy atoms differs from that of the wild type at most by Δ𝑁HA = 1. For the second group, in which Δ𝑁HA > 1, we consider structures of the mutants as less certain. Only mutants of the first group are modeled in the present study. Hydrogen atom positions and protonation probabilities are optimized for each mutant. For a qualitative evaluation of the transition energy shifts, it is instructive to consider the two-dimensional projection of the ESP difference between the excited and the ground states of 11-cis retinal Δ𝜙 = 𝜙 (e) − 𝜙 (g) in Figure 2. The potential difference is strongly negative at the PSB and the polyene chain, and strongly positive at the β-ionone ring. The general rule for deriving the direction of the absorption shift (mutant-minus-wild type) according to eq 2 is that introducing a negative charge to the negative region (red in Figure 2) or a positive charge to the positive region (blue in Figure 2) of the potential difference shifts the electronic transition of the chromophore to the blue. A red shift in the absorption maximum of the chromophore results from the introduction of a negative charge to the positive region or a positive charge to the negative region of the Δ𝜙. In the D83N mutant, aspartic acid is replaced by asparagine. Evaluation of the protonation probabilities of titratable residues in the wild type reveals a protonated aspartic acid (see Figure S2, Supplementary Material, and above). The carboxyl group in the wild type is exchanged with an amine group in the mutant. From the two possible orientations of the amine group, the one with the lower energy (obtained from the molecular force field) is chosen. It should be noted that in the 13



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Figure 2: Projection of the positions of the mutated amino acid residues into the chromophore plane and schematic electrostatic potential (ESP) difference between ground and excited states of 11-cis retinal Δ𝜙 = 𝜙 (e) − 𝜙 (g) obtained with (TD)DFT and the BHHLYP XC functional. The positive and the negative regions of the potential difference (excited-minus-ground-state) are colored in shades of blue and red, respectively. APCs in Table S1, Supplementary Material.

Table 2: Absorption Shifts Mutant Minus Wild Type in Units of Inverse Centimeter and Nanometer for the Site-Directed Mutants of Bovine Rhodopsin Calculated With Different Methods Compared to Experimental Values D83N cm−1

nm

E122Q cm−1

exp. +200a,b −5b +800a,c PBQC +90 −2.5 +900 CDC +130 −3.5 +720 CDC (std. prot.)f +80 −2.0 +3820

A164S

nm

cm−1

−20c −22.5 −18.0 −95.5

nm

F261Y cm−1

−75d +2d −400d −40 +1.0 −310 −30 +0.5 −300 −0 +0.0 −200

nm

A292S cm−1

nm

+10d +370a,e/ +380a −9e/ −9.5e +7.5 +320 −8.0 +7.5 +320 −8.0 +5.0 +310 −7.5

The shifts are relative to the 20000 cm−1 / 500 nm absorption maximum in the wild type of bovine rhodopsin. 85 a Estimated value based on the published shift in units of nanometer. b See ref 84. c See refs 84–86. d See ref 87. e See refs 14,88,89. f Standard protonation pattern as defined in the Results section.

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determination of this energy a reorientation of nearby water molecules is taken into account by the reoptimization of the hydrogen atom positions (see Computational methods). The calculated absorption shift of 3.5 nm and 2.5 nm to the blue with CDC and PBQC, respectively, explains the experimental 5 nm blue shift reasonably well. A major part (≈ 2 nm) of this shift is due to reorientation of the neighboring water molecules (see Figure S2, Supplementary Material, and above). In the E122Q mutant, 84–86 a glutamic acid – which was calculated to be protonated (neutral; see above), with the unprotonated oxygen in immediate proximity of the β-ionone ring – is exchanged by a glutamine. The orientation of the amine group was determined as described for Asn83 above. One side-chain amide proton of Gln protrudes towards the β-ionone ring (see Figure S3, Supplementary Material). Hence, electrostatically, this mutation corresponds mainly to the introduction of a positive partial charge in the strongly positive region of the potential difference of the chromophore. According to eq 2, this exchange should shift the absorption maximum of the mutated photoreceptor to the blue. The quantitative evaluation of the absorption shift indeed reveals a blue shift by 22.5 nm and 18.0 nm with PBQC and CDC, respectively, which explains the experimental blue shift of 20 nm. 84–86 Three site-directed mutants, namely A164S, F261Y, and A292S introduce a hydroxy group to the protein matrix of the photoreceptor near the retinal 87 (see Figure S4, Supplementary Material, and Figure 3a–d, respectively). A correlation between the magnitude of the observed shift and the distance of the hydroxy dipole to the β-ionone ring, which forms the positive region of the electrostatic potential difference (Figure 2), is expected. Residues 261 and 292 are located in immediate proximity to the retinal, whereas residue 164 is located further away. Therefore, the absorption shift observed for A164S is small (+2 nm), 87 whereas the F261Y and A292S mutants show pronounced changes in transition energy by 10 nm to the red 87 and 9/9.5 nm to the blue, 14,88,89 respectively. The orientation of the hydroxy group introduced in the A292S mutant is determined by a hydrogen bond to a nearby water molecule. This water molecule has itself a different orientation 15



Figure 3: Visualisation of mutated residues 261 and 292 close to the retinal chromophore (green) and parts of their environment in the wild type (a and c), in the F261Y mutant (b), and in the A292S mutant (d). The orientation of the hydroxyl group of Tyr261 is determined by a hydrogen bond to Gly121, while that of Ser292 is determined by the interaction with a nearby water molecule. Figure made with VMD. 12

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in the mutant as in the wild type (see Figure 3c–d). The partially negatively charged oxygen then approaches the chromophore in the negative region of the difference potential. The introduced hydroxy group and the reorientation of the water molecule contribute 2.5 nm and 3.5 nm, respectively, to the computed blue shift of 8 nm, which is in reasonable agreement with the experimental values. In case of the A164S (see Figure S4, Supplementary Material) and F261Y (see Figure 3a–b) mutants, the introduced hydroxy groups point away from the positive region of the difference potential, of the β-ionone ring, and the computed red shifts are conform to the experimental data (Table 2). +15 +10 calculated shift (nm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


PBQC CDC

+5 0 −5 −10 −15 −20 −25 −25 −20 −15 −10 −5 0 +5 +10 +15 measured shift (nm)

Figure 4: Correlation between the computed and measured absorption shifts given in Table 2. Blue dots represent values computed with the PBQC method, orange circles the ones obtained with the CDC method. Figure 4 shows the correlation between calculated and measured mutant-minus-wild-type shifts for PBQC and CDC. Theory and experiment are in excellent agreement with an RMS deviation of 2.3 nm for PBQC and 2.1 nm for CDC. Interestingly, the simple CDC method already describes the experimental values quantitatively. In order to see how far we can simplify our procedure, we have calculated transition energy shifts with the CDC method, assuming a standard protonation pattern in the protein, that is, glutamate and aspartate residues are negatively charged, arginine and lysine residues are positively charged, and histidine, cysteine, and tyrosine residues are neutral. The resulting shifts are 17



shown in the last row of Table 2. The most striking difference compared to the non-standard protonation pattern is the additional 77.5 nm blue shift of the E122Q mutant, where the change of the protonation state of Glu122 causes a 81.5 nm blue shift. Since Glu122 is located in the positive region of the difference potential of the chromophore (see Figure 2), the negative charge on this residue in the standard protonation state shifts the wild type spectrum to the red and, hence, the mutant-minus-wild-type difference in absorption maximum to the blue. At first glance, we would have expected a significant difference also for the D83N mutant, since Asn83 was calculated to be also in its non-standard (neutral) protonation state. But the reorientation of a nearby water molecule compensates for the charge gain and leads to a rather moderate shift difference between the two protonation patterns. The remaining mutants also show moderate differences in the shifts calculated for the standard with respect to the non-standard protonation pattern. It is worth noting that in almost all cases the agreement with the experimental transition energy shifts becomes worse in the standard protonation pattern. The RMS deviation of the calculated shifts with respect to the experimental values increases from 2.1 nm for the non-standard protonation pattern to 37.9 nm. If the major contributor to this large difference – the E122Q mutant – is excluded, the RMS deviation still increases from 1.8 nm to 3.2 nm.

Discussion Electrostatic tuning has long been discussed as an important color-tuning mechanism, 22 but a theoretical study providing a comprehensive quantitative analysis of the phenomenon has hitherto been missing – a gap that is filled by our study. It provides a structure-based analysis of electrochromic shifts in bovine rhodopsin that evaluates electrostatic tuning corresponding to first-order and partly second-order perturbation theory in the pigment-protein coupling. The excellent correlation between calculated and measured mutant-minus-wild type absorption shifts demonstrates that red/green color tuning via chromophore-residue interactions is dominated by

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electrostatics. This finding suggests that additional shifts that are due to, e.g., changes in dispersive chromophore-protein interactions between wild type and mutant, are of minor importance to the observed absorption shifts. The electrostatic potential difference Δ𝜙 = 𝜙 (e) − 𝜙 (g) between the first excited and the ground states of retinal identifies the PSB as the negative and the β-ionone ring as the positive region. Hence, upon electronic excitation of retinal, electron density shifts from the β-ionone ring towards the PSB (Figure 2). The protein environment can electrostatically stabilize the excited state relative to the ground state either (i) by placing a positive charge in the negative potential difference of retinal (i.e., in the neighborhood of the PSB) or (ii) by placing an opposite charge in the vicinity of the β-ionone ring. Such a stabilization would lead to a red shift of the transition energy, whereas an opposite charge would induce a blue shift. Hence, for polar side groups of amino acid residues, such as hydroxy group dipoles, color tuning depends critically on the orientation of this polar group with respect to the retinal chromophore. In the case of the F261Y mutant, the hydroxy dipole in the mutant is introduced such that the negative end (the oxygen) approaches the positive potential difference of the β-ionone ring (see Figure 3b), thereby causing a red shift in the transition energy of retinal. A similar orientation but in the negative region of the difference potential, near the PSB, is obtained for the hydroxy group in the A292S mutant (see Figure 3d), which explains the blue shift caused by the dipole. However, to understand the experimentally observed blue shift, one also has to consider the reorientation of a water dipole (see Figure 3c–d). The latter results are formally in agreement with a recent QM/MM study 23 in which the “OH-site rule” was inferred: it suggests that the hydroxy dipole shifts the absorption maximum of the photoreceptor to the red, independently of its orientation relative to the β-ionone ring, whereas a hydroxy dipole in the neighborhood of the PSB will always lead to a blue shift. Based on our results, we have to conclude that this rule only applies to situations where the OH-dipole points away from the retinal chromophore. If the orientation of the OH-dipole was opposite, e.g., because of the hydrogen bonding network, an opposite shift would result. We, 19



therefore, conclude that the “OH-site rule” has to be extended to the “dipole-orientation rule” that takes into account both the location and the orientation of hydroxy and other polar groups including water molecules. In the context of site-directed mutagenesis experiments, the critical question arises of whether the mutation introduces only local changes at the position of the mutated residue or whether neighbouring residues also significantly change their conformation. For all the mutants, only the conformation of those atoms that differ between mutant and wild-type residue and the protonation pattern of the protein are optimized. From the strong correlation between the electrostatic calculations of site energy shifts and the experimental values we conclude that it is indeed mainly the mutated residue and the protonation pattern of the protein that vary and that other conformational changes can be ignored, at least for the mutants discussed so far. For the mutants with larger changes in the number of heavy atoms (Δ𝑁HA > 1), our preliminary calculations give significantly less agreement with measured color shifts, indicating that the mutation indeed involves larger structural changes, as expected. Finally, we note that the present study is related in spirit to the recent work by Stenrup at al., 90 who introduced a simple electrostatic model in combination with empirical p𝐾A predictions to explain the pH-dependency of the absorption spectrum of Anabaena sensory rhodopsin. Besides our electrostatic/Monte Carlo approach for the calculation of protonation probabilities, there are two important differences between the present and the earlier 90 electrostatic transition energy shift calculations: (i) the charged state of titratable groups in the protein was described by a single integer charge earlier, whereas in the present case atomic partial charges are used for both the charged and the uncharged state; in the neighborhood of the retinal chromophore, we find it important to even model the protons of the titratable residue explicitly; (ii) the non-titratable part of the protein was treated as a rigid background earlier, whereas here all hydrogen positions were allowed to change in response to the change of the protonation pattern or a mutation. In particular, the relaxation of the hydrogen-bonding pattern and the reorientation of water molecules, described in this way, was found to be important for the explanation of the color tuning. The latter result 20


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is in agreement with QM/MM calculations on color variants of hCRBPII, 55 which are capable to describe also more global structural changes occurring for the class of mutants with a larger change in number of heavy atoms not considered in the present study. In our computations we inferred an increase of the difference in the dipole moment between electronic ground state and first excited state Δ𝜇 of 11-cis retinal in the protein environment which is due to the inclination of the β-ionone ring relative to the polyene chain. Indeed an increase of Δ𝜇 was suggested for bacteriorhodopsin. 52 However, the crystal structure of the all-trans retinal in bacteriorhodopsin revealed a rather planar orientation of the β-ionone ring. Obviously, also other effects can lead to an increase in Δ𝜇, for example polarization effects of the retinal wave function by the protein environment. Of course, we cannot exclude the possibility that the excellent agreement between calculated and measured color shifts, obtained here, relies to some extent on error compensation effects. For example, the choice of the XC-functional could compensate for the lack of polarization. Irrespectively, it is important to note that our electrostatic calculations suggest that there is no significant change in the polarization between the wild type and the mutants studied here. Therefore, we conclude that electrostatic effects are responsible for the red/green color tuning.

Conclusion Two electrostatic methods, known as the Poisson-Boltzmann/quantum chemical (PBQC) and charge density coupling (CDC) methods, in combination with molecular-mechanics modeling of the side-chain conformation of single amino-acid residues, were used to explain the red/green color tuning of the retinal chromophore in visual rhodopsins. The excellent correlation between calculated mutant-minus-wild-type electrochromic shifts and experimental data provides evidence for the dominant contribution of electrostatic interactions to this color tuning of visual rhodopsins. Although the importance of these interactions was recognized 40 years ago by Honig et al. 46,47 , to the best of our knowledge, the present study represents the first structure-based verification of this

21



idea in atomic detail. Important details in the calculations have been the choice of the XC functional used in the quantum-chemical calculation of the atomic partial charges of retinal and further taking into account the tilt in relative orientation between the β-ionone ring and the polyene chain in this calculation. With the BHHLYP XC functional, it was possible to obtain an order of magnitude of the difference dipole moment between the first excited state and the ground state of retinal that is in agreement with experimental data. Another important point is the independent determination of the protonation states of titratable residues by Poisson-Boltzmann/Monte-Carlo calculations. In one case (the E122Q mutant) a dramatic improvement of the calculated shift occurred, while in the other cases a systematically better compliance with the experimental transition energy was still obtained. According to the “OH-site rule” introduced by Sekharan et al., 23 introduction of a hydroxy group in the vicinity of the β-ionone ring of the retinal always causes a red shift of the absorption maximum, whereas introduction of a hydroxy group in the vicinity of the PSB always causes a blue shift. On the basis of the present analysis, we propose a modified version of this rule called “dipole orientation rule”. According to this new rule, depending on its orientation, introduction of a dipolar group in either region around the retinal can cause both types of shifts and eventually water dipole orientations have to be considered as well.

Supporting Information Available Schematic skeletal structure of 11-cis retinal with the used numbering scheme for heavy atoms, CHARMM atom types and computed atomic partial charges of the retinal chromophore and Lys269 in the ground and excited states, visualization of mutated residues 83, 122, and 164, Monte Carlo protonation probabilities of titratable residues at pH 7 in the wild type, Monte Carlo titration curves of selected residues in the wild type, Monte Carlo protonation probabilities of titratable residues at pH 7 in all the mutants.

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Graphical TOC Entry

calculated shift

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measured shift

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Green Color Tuning of Visual Rhodopsins: Electrostatic Theory

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