www.sciencemag.org/cgi/content/full/337/6099/1225/DC1

Supplementary Materials for

The Molecular Mechanism of Thermal Noise in Rod Photoreceptors Samer Gozem, Igor Schapiro, Nicolas Ferré, Massimo Olivucci*

*To whom correspondence should be addressed. E-mail: molivuc@bgsu.edu, olivucci@unisi.it

Published 7 September 2012, Science 337, 1225 (2012)

DOI: 10.1126/science.1220461

This PDF file includes:

Materials and Methods Figs. S1 to S11 Tables S1 to S6 References (32–92)

Materials and MethodsComputational Methods and Rhodopsin Model Construction

A QM/MM method (32) with a link-atom (LA) approach (33) was used to describe the rhodopsin chromophore at the ab initio complete active space self consistent field (CASSCF) level of theory (34) while taking into account the electrostatic and steric effects imposed by the opsin which is treated at the molecular mechanics (MM) level using the AMBER force field. (35) The CASSCF method is a multiconfigurational quantum chemical (MCQC) method offering suitable flexibility for an unbiased description (i.e. with no empirically derived parameters and avoiding single-determinant wavefunctions) of the electronic and geometrical structures of the ground and excited states of a molecule. Furthermore, the CASSCF wavefunction can be used for subsequent multiconfigurational second-order perturbation theory (36) computations (CASPT2) ultimately allowing for an evaluation of energy barriers on a single electronic state and gap between different electronic states (34) in a balanced way as required by the present investigation. For the visual pigment of bovine rhodopsin, its isomers bathorhodopsin and isorhodopsin and two point mutants, (7, 37, 38) the observed λmax values were reproduced with an error of <30 nm (3 kcal/mol in excitation energy). These results have been confirmed and extended by different groups. (39-43) Similar accuracies were documented for the Archea proton pump bacteriorhodopsin (44) and the Eubacteria sensory rhodopsin from the fresh water cyanobacterium Anabaena (Nostoc) sp. PCC7120 (45) and for a number of different chromophore containing proteins (see Fig. S2). While similar studies have been carried out with different quantum chemical methods, (41, 46) the CASPT2//CASSCF remains an affordable method allowing a description of spectra, excited state reaction paths, conical intersections (CIs) and trajectories consistently. (8, 47-49) The same QM/MM method has also been used to compute classical and semiclassical trajectories that yield excited state lifetimes in qualitative agreement with the experiment. (8, 9, 50) Furthermore, different studies have shown that the chromophore gas-phase absorption can be computed in agreement with experiment, within a few kcal/mol. (51) This indicates that when excluding other factors (i.e. the accuracy of the opsin model) such a protocol can be used for simulating spectroscopic and photochemical data.

The model of wild type bovine rhodopsin was constructed on the basis of the 1U19 PDB (protein data bank) crystal structure. (52) Hydrogens were introduced and relaxed using Tinker. (53) In cases where the ionization of a residue was unknown, we made simple assumptions: the carboxylic residues located in the region near the cytoplasmic and extracellular side (far from the chromophore) were considered deprotonated if a counterion is in their vicinity. If not, these are kept protonated. For the internal Glu113, Asp83, Glu181 and Glu122 residues we used the same strategy. Glu113 is the retinal counterion and has a deprotonated state (forming a salt bridge with the protonated Schiff base). (54) The Glu122 residue near the retinal region could potentially have His211 as a counterion but Fourier Transform IR (FTIR) experiments suggest that Glu122 is protonated. (55) Accordingly, His211 and Glu122 have been taken as neutral in our model. Finally, all histidine residues have been defined as neutral with the only exception

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of His195 that is in close contact with Glu197. Asp83 was kept neutral since no counterion can be identified in its vicinity. However, the protonation state of Glu181 is still a matter of controversy, especially since evidence suggests that Glu181 becomes the counterion for the Schiff base after the transition from Lumirhodopsin to Metarhodopsin. (56) While early experimental evidence indicates a protonated state, (55) this issue is still unresolved, with recent studies unconverging. (57-59) In our model, we kept Glu181 protonated because the deprotonation of Glu181 leads to a ~60 nm blue-shift of the computed absorption in the reactant, which causes our computed absorption to be very different from the observed one. This is consistent with other QM/MM studies where deprotonation of the Glu181 leads to a large blue-shift, including Sandberg et al. (see their supporting information), (59) Frahmke et al., (58) and Tomasello et al. (60) Since we are mainly concerned with reproducing a correct description of the electrostatics around the chromophore, and the deprotonation of Glu181 seems to unbalance the environment by causing blue-shifting, we consistently use a protonated Glu181 throughout our study. Furthermore, the study by Tomasello et al. (60) have concluded that models with neutral or charged Glu181 can be safely utilized to properly study the primary photoisomerization event and its mechanism since they found the effect of deprotonating Glu181 on the photochemical reaction path to be minimal.

In our models, two crystallographic waters (from the 1u19 PDB) were included in the retinal binding cavity and treated with the TIP3P model. One of these waters (W1) stands near the Glu113 counterion, while the other (W2) is near Glu181. All other waters were considered far from the chromophore and were removed. To get a globally neutral model, a chloride ion was added near Arg147.

The QM/MM frontier is placed at the Cε-Cδ bond of Lys296, far enough from the π-conjugated backbone to avoid significant effects on the chromophore properties. . The hydrogen LA cap is placed on the QM subystem Cε atom (See Fig. S3 for Lys296 atom labels). (61) Reparameterization of the Lys296 was necessary to reflect its QM/MM status. The net charge of the MM part of lysine is set to 0 (since the positive charge is carried by the QM fragment). Therefore the charges on Lys296 were redistributed as shown in Table S1. (7)

The charge of the frontier MM carbon atom Cδ was set to 0 to ensure that the QM wavefunction is not overpolarized near the LA. The Cδ point charge originally assigned by Amber is small, and so changing it to 0 does not introduce a large imbalance. This also made possible the use of the standard MM bonded potentials (stretching, bending, etc.) for the description of the geometry at the frontier.

The van der Waals atomic parameters for retinal and the C15-N-Cε-Cδ torsion potential do not exist in AMBER. These missing parameters have been determined in such a way as to reproduce the ground state (S0) and first excited state (S1) CASSCF torsional energy profiles relative to the N-Cε-Cδ-Cγ and C15-N-Cε-Cδ dihedral angles of the model system shown in Fig. S3. (62) The resulting van der Waals parameters were (R*=1.87 Å, ε=0.0860 kcal/mol) for an sp2 carbon atom of the retinal π-system, (R*=1.87 Å, ε=0.1094 kcal/mol) for an sp3 carbon atom of retinal and (R*=0.92 Å,

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ε=0.0157 kcal/mol) for the hydrogen atom of retinal. The C15-N-Cε-Cδ torsion potential was given by: 0.750 [1 + cos(φ − 0)].

During the QM/MM optimization, all cavity side-chains were relaxed together with the two TIP3P waters, the chromophore and the connected Lys296 side-chain. The cavity side-chains are those with at least one atom less than 4Å away from any atom of the chromophore in either its 11-cis or all-trans configuration. All other residues were kept frozen at the initial 1U19 crystallographic structure. In total, 28 opsin side-chains were relaxed in all models. The optimization was performed with microiterations, such that the MM atoms were minimized by Tinker between each QM/MM optimization step. (63) The QM/MM interactions were described with electrostatic potential fitting (ESPF). (64) However, during the microiterations, Mulliken charges were used because ESPF tends to give electrostatic interactions that are too large during microiterations.

The Rh energy minima were obtained at the CASSCF/6-31G*/AMBER level. The bovine rhodopsin structure (WT) provided a starting structure for building the corresponding A2-rhodopsin model (A2-WT). In all cases the full π-system was incorporated in the active space that comprised 12-electron in 12-orbital for WT and 14-electron in 14-orbital for A2-WT. The corresponding TSCT and TSDIR models have been computed using the two-root state-average CASSCF/6-31G*/AMBER level to facilitate the description of the transition state region which is in proximity of the CI. The obtained WT, A2-WT and their TSCT and TSDIR models were used as templates to generate the corresponding mutant structures. These were generated manually using Molden (65) and relaxed using the protocol described above. In a few cases different conformers were optimized and the lowest energy conformer was chosen. For the evaluation of excitation energies and activation barriers, CASPT2 single point calculations over a three-root state-average CASSCF wavefunction were performed both with and without IPEA shift (see discussion on computations with a minimal gas model below) and with an imaginary shift of 0.2 to remove intruder states. All QM/MM calculations were performed using the protocol distributed with the MOLCAS program (66) which works in conjunction with TINKER. (53) For seven mutants it was possible to validate the models by comparing the predicted with the observed (67-71) excitation energies. We compare the computed excitation energies with the experimental ones (expressed as S1-S0 energy gap) in Fig. S4 (the exact wavelengths are also shown in Table S4). We find that we have a maximum absolute error below 5 kcal/mol and a maximum relative error of 2 kcal/mol. On average, we have a systematic blue shift of ca. 3.2 kcal/mol for the excitation energies. Again, these results are in line with those obtained for different light-sensitive proteins as shown in Fig. S2.

Transition states were optimized using the restricted-step rational-function-optimization method. (72) Since QM/MM frequency analysis has not yet been implemented in MOLCAS, initial attempts to optimize a transition state had to rely on a guess Hessian computed at a suitable guess structure. The quality of the Hessian is evaluated by looking at the reaction vector, thus making sure that it describes the expected isomerization motion connecting the reactant (Rh) and the product (bathoRh). The selected guess Hessian was saved and read by the program in all subsequent

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transition state optimizations. The optimizations were considered completed after convergence to a stationary point (i.e. when the analytical gradients are below the standard thresholds) and the corresponding final updated transition vector represents the correct bicycle-pedal motion. The resulting single transition states are considered acceptable representations of the average transition state operating in the protein environment. The protocol we use is generally accepted for the optimization of transition states in conformationally not flexible protein environments (e.g. in enzyme catalysis (see refs (73-75)) and where the x-ray crystallographic structure already provides an acceptable representation of the protein backbone. On the other hand, our work is not concerned with reproducing the absolute value of the potential energy barriers (which, according to the adopted protocol, may be upper limits), but rather with the barrier differences (e.g. TSCT-TSDIR) and the barrier changes. These are less sensitive to the details of the methodology used.

Since we cannot verify the transition states by frequency calculations, we use instead classical trajectory calculations to verify that TSCT and TSDIR correspond to saddle points driving the isomerization. For each stationary point, two trajectories were launched in the positive and negative direction of the reaction vector obtained during the transition state search. The trajectory program (50) is part of the Molcas software package, and uses the Verlet algorithm to propagate the Newton equations of motion. (76) The trajectories were run with a timestep of 1 fs, and with infinitesimal initial velocities parallel to the reaction vector. In Fig. S5, we show a few trajectory points in the vicinity of the optimized TSCT and TSDIR structures and following the minimum energy path dominated by the isomerization coordinate. As expected, the descent to Rh is energetically steeper than for bathoRh. These trajectories, as well as the energy profile along the BLA coordinate (see definition below), support the general shape of the S0 potential energy surface presented at the bottom of Fig. 2A in the manuscript.

In order to demonstrate that TSCT and TSDIR lie on opposite sides of the CI, we computed the excited and ground state energies along series of structures produced by a linear interpolation/extrapolation of the coordinates of TSDIR and TSCT (see energy profile along the interpolation shown in the top of Fig. 2A in the main manuscript). As documented in Fig. S6 the coordinate defined by this interpolation is largely dominated by a bond length alternation (BLA) change in which the double bond and single bond of the protonated Schiff base region exchange length. Such a coordinate is referred as the BLA coordinate. The interpolated structures reveal a CI point between the two transition states with an intermediate bond alternation, as expected. Its structure is displayed in Fig. 2B in the report text. In Fig. S7, we show the energies of the two crossing states at the 2-root state averaged CASSCF and 3-root CASPT2 levels. The shape of the energy profiles does not change along the scan when the method is changed, and the positions of TSCT and TSDIR remain substantially the same. This is a good indication that the transition states optimized at the CASSCF level are not very different than those that would be obtained with CASPT2 (see a further discussion below). The energies only change in relative stability as the Φion charge transfer configuration is stabilized upon CASPT2 correction, a fact which is not unexpected in the context of previous studies (77). This

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causes the CI to shift towards the TSDIR. Finally, in order to show that the transition states in all the mutants lie on opposite sides of the CI, in Table S2 we present the degree of charge transfer at each transition state to demonstrate the different electronic characters of TSCT and TSDIR.

Out of the 24 transition states, only one could not be successfully optimized. This is the TSCT for A292S of A2-rhodopsin (the most blue-shifted and high energy of all considered A2-WT mutant). We speculate that this transition state could not be optimized because it ceases to exist at the CASSCF level due to a change in the shape of the CI from peaked to sloped where only one transition state exists. (28) As a result, the point corresponding to TSCT is left out of Fig. 2C in the manuscript.

We mention in the manuscript an estimate for the wavelengths where maximum visual sensitivity would be expected for A1 and A2 pigments. Those values were obtained by linear regression of the TSCT and TSDIR points plotted in Fig. 2C in the main manuscript. The point of intersection of the two regression lines signifies the wavelength where TSDIR would begin to control the thermal isomerization and an anti-Barlow correlation should be observed. The predicted values of 470 nm in A1 pigments and 475 nm in A2 pigments are reported after accounting for a 3.2 kcal/mol systematic blue-shift error in our computed excitation energies.

The mutants that we model in this study have been studied by other computational groups before. For instance, the E113D, A292S, T118A, and A269T mutants have all been studied by Rajamani et al (78) and Altun at al (79) (but with different computational methods). Even the A2 system has been investigated before in WT Rh. (80) However, for our purposes, these mutants allow us to investigate the effect of mutations (substantially, a change in the electrostatic environment) on the thermal activation barrier through both TSDIR and TSCT, and to allow the simulation of a Barlow correlation (as well as an unexpected anti-Barlow correlation). Moreover, the purpose of the A2 models is to explain the observed increase in thermal noise due to the A1→A2 chromophore replacement as documented by Ala-Laurila et al. (15)

MRCISD+Q energies, expanded basis set and CASPT2 optimization

Computations on a minimal gas-phase PSB11 model:

Due to the size of the PSB11 chromophore and length of its π-conjugated chain (e.g. for the A2 chromophore) the structure optimization of Rh, TSDIR and TSCT are consistently carried out at the CASSCF level using the modest 6-31G* basis set. As a consequence, the evaluation of the potential energy is carried out via single point CASPT2//CASSCF/6-31G* computations (the cost of CASPT2 numerical gradients makes the optimization impossible for Rh). In order to establish the reliability of these computations and, in turn, of the presented results and theory, here we discuss a set of benchmark calculations on a minimal PSB11 model, the penta-2,4-dieniminium cation (PSB3). This model displays the same potential energy features of Rh but it is small

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enough to allow for MRCISD+Q/6-31++G** computations (81) and CASPT2/6-31G* optimization.

TSCT-TSDIR energy difference:

PSB3 features a CASPT2 energy profile along the BLA coordinate remarkably similar to the one of Fig. 2A of the manuscript and Fig. S7. Invariably the profiles incorporate the two critical TSCT and TSDIR structures (confirmed via analytical frequencies computations). We have tested the effect of the MRCISD+Q//CASSCF/6-31G* correction (see Fig. S8A) with respect to the CASPT2//CASSCF/6-31G* level. We find that MRCISD+Q leads to further stabilization of TSCT with respect to TSDIR and to a consequent displacement of the CI towards TSDIR (actually the CI changes from peaked to sloped, and TSDIR in becomes an excited state minimum rather than a transition state). (28) We have also looked at the effect of CASPT2(IPEA=0.25) energy corrections, where the IPEA shift is a recommended modification to the zeroth order wavefunction for CASPT2. (82) We found that the results upon introducing the IPEA shift are consistent with the MRCISD+Q results yielding a stabilized TSCT. Along the same BLA coordinate, we also looked at the effect of the 6-31++G** basis (see Fig. S8B). We found that while this effect is more limited, it also increases the relative stability of TSCT. In conclusion, the improvement of both the method and basis set leads to a stabilized TSCT.

TSCT and TSDIR, as well as cis-PSB3, were re-optimized at the CASPT2 and CASPT2(IPEA=0.25) levels and new BLA coordinates were generated. The resulting geometries and energy profiles are similar to the ones found via CASSCF optimization (see Fig. S8C). The most prominent difference is in TSDIR, where the C-N bond is 1.29 Å when optimized at the CASSCF level and 1.32 Å when optimized at the CASPT2 level (the IPEA shift leads to a limited difference). However, the TSCT and TSDIR relative energies remain almost unchanged, and the conclusions regarding the shape of the potential energy surface remain the same for both the CASSCF or CASPT2 optimized structures.

Excitation energy and barrier computations:

At cis-PSB3 the CASPT2(IPEA=0.25) energy is blue-shifting with respect to the CASPT2 energy. However, the effect of expanding the basis set is red-shifting. These effects counterbalance each other. This can be explained by the fact that the IPEA increases the energy of states with open-shell character. (82) At cis-PSB3 the ground state is closed-shell, but the excited state, which has a dominant charge transfer character, has some diradical character. As shown in Table S3, if we account for the effect of optimizing at the CASPT2 level, the red-shifting effect of improving the basis set and the CASPT2 optimization is nearly exactly equal to the blue-shifting effect of the IPEA shift. Therefore, at cis-PSB3 the excitation energies computed at the CASPT2//CASSCF/6-31G* turns out to be a good approximation for CASPT2(IPEA=0.25)//CASPT2/ANO-

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VTZP, which may explain the success of such a modest level for getting excitation energies comparable to experimental ones. At the level of the transition states the situation is different. In fact, TSDIR (which has a charge distribution similar to ground state cis-PSB3) is now purely open-shell while TSCT is purely closed-shell. This has the effect of increasing the TSCT and TSDIR gap. However, the basis set expansion better stabilizes the charge transfer character and further increases the energy gap instead of compensating the change, and so the effect of the IPEA shift and the basis set expansion becomes additive for the transition states. Therefore the evaluation of energy barriers and relative stabilities is more accurately carried out at the CASPT2(IPEA=0.25)//CASSCF/6-31G* level as clearly displayed in Table S3.

Computations on Rh:

We recompute the energy profiles along the BLA coordinate of Fig. 2A in order to show the effect of the IPEA value and basis set expansion. As apparent from Fig. S9, the effects seen in PSB3 are confirmed for Rh. Both the change from IPEA=0 to IPEA=0.25 and the expansion of the basis from 6-31G* to 6-31++G**stabilize TSCT with respect to TSDIR. As a result, the difference in energy between TSCT and TSDIR, which we found to be 4.8 kcal/mol at the CASPT2//CASSCF/6-31G*/AMBER level becomes 12.1 kcal/mol at the CASPT2(IPEA=0.25)//CASSCF/6-31++G**/AMBER level. This is a strong indication that our main conclusions are reinforced when improving the computational accuracy. In Table S5, we report, for all mutants, the CASPT2 excitation energies and activation barriers using IPEA=0.25 and the 6-31G* basis. By comparing Table S4 and S5 we find, as expected, that the energy barrier of TSDIR in every mutant increases while the TSCT energy barrier remains relatively unchanged. Notice that the excitation energies with the IPEA become very different from the experimental ones due to a large blue shift. However, the PSB3 results (see above) indicate that the expansion of the modest 6-31G* basis set to the ANO-VTZP at the CASPT2 optimized geometry reduces the discrepancy. These computations are presently unpractical in Rh.

The main conclusions from the PSB3 benchmark computations are:

i) As shown in Fig. S8A CASPT2//CASSCF/6-31G* computations with an IPEA of 0.25 yield a TSCT and TSDIR relative stability (and an energy profile along the BLA coordinate) very close to the energy difference obtained via MRCISD+Q//CASSCF/6-31G*. Therefore it is concluded that CASPT2 with an IPEA of 0.25 may be used to reproduce activation energies consistent with MRCISD+Q, which is our (variational)reference method for accuracy.

ii) As shown in Fig. S8B the effect of the 6-31G* to 6-31++G** basis set expansion further stabilizes TSCT with respect to TSDIR at both the MRCISD+Q and CASPT2(IPEA=0.25) levels.

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iii) As shown in Fig. S8C the TSCT and TSDIR geometry optimization at the CASPT2(IPEA=0.25)/6-31G* and CASPT2/6-31G* levels does not significantly affect the geometries nor the relative stabilities of TSCT and TSDIR.

iv) In Table S3 we show that the CASPT2//CASSCF/6-31G* produces excitation energies comparable to CASPT2(IPEA=0.25)//CASPT2/ANO-L-VTZP due to error cancellation (the IPEA shift is blue-shifting while the basis set is red-shifting the excitation energy). This indicates that the CASPT2//CASSCF/6-31G* produces a better agreement with higher level of theories with respect to CASPT2(IPEA=0.25)//CASSCF/6-31G*.

v) In Table S3 and Fig S8A we show that the TSCT and TSDIR reaction barriers are better evaluated at the CASPT2(IPEA=0.25)//CASSCF/6-31G* level rather than the CASPT2//CASSCF/6-31G* level.

vi) For Rh the excitation energy may be computed at the CASPT2//CASSCF/6-31G*, however, the TSCT and TSDIR relative stability and reaction barriers must be computed at the CASPT2(IPEA=0.25)//CASSCF/6-31G* level.

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1114 (2010).90. P. Altoe et al., J. Phys. Chem. B 113, 15067(2009).91. A. A. Granovsky, J. Chem. Phys. 134, 214113 (2011).92. A. J. Varandas, J. Chem. Phys. 131, 124128 (2009).

11

12

Fig. S1Reinterpretation of the λmax/λc relationship. A. Experimentally, λc is measured by looking at the temperature dependence of the normalized sensitivity. (16) Therefore, from a spectroscopic viewpoint, λc could be interpreted as the longest wavelength capable of bringing the system to its electronically excited state. From the Franck-Condon principle and consistently with the analysis in ref. (22), it follows that this wavelength corresponds to the 0-0 excitation energy rather than to the vertical excitation energy. In this figure we also show the CASPT2//CASSCF/6-31G* (8) computed difference between the the vertical excitation energy and the 0-0 excitation energy in bovine Rh, which is of the order of ca. 10 kcal/mol. B. Top: The energy profile of a CASPT2//CASSCF/6-31G* excited state trajectory computation of bovine Rh (from ref. (8)). The CI is reached in about 100 fs. Bottom: The change in the C11=C12 bond length along the same trajectory, demonstrating that the initial relaxation is dominated by a stretching mode (double bond expansion and single bond contraction... See center left figure) that is orthogonal to the reaction coordinate, as previously reported. (77, 83) When considering the vertical excitation energy provided by the model of ca. 60 kcal/mol and the relaxation along the stretching mode of 10 kcal/mol (shown in part A of the figure), we obtain a λmax/λc ratio of 477/572 = 0.83. The close vicinity of this value to the 0.84 ratio mentioned above provides a spectroscopic reinterpretation of this coefficient reflecting and pointing to an initial excited state relaxation coordinate dominated by a stretching mode. C. A scheme portraying the relationship between the vertical excitation energy ΔE(S1-S0) (λmax), EaP (λc) and EaT, and the photoactivation (solid arrows) and thermal activation (dashed arrows) paths. In spite of the large structural difference between the FC region on the excited state and the TSCT region on the ground state these regions have similar charge distributions. Notice that after the initial stretching relaxation described in and occurring along the FC region (see dotted harmonic well), the excited state evolution becomes dominated by the isomerization motion (twisting about the C11-C12 bond) indicated by the curly arrow. This two-mode excited state relaxation dynamics out of the Franck-Condon point has been assessed both experimentally and theoretically. (77, 83) The observed limited variations of the λmax/λc value in different pigments (16) finds an explanation when considering that it reflects the “depth” of the excited state “well” representing the stretching mode (i.e. the difference between the vertical and 0-0 excitation energies) and it is a property of the chromophore itself. On the other hand, one has to conclude that the λc (and therefore EaP) is associated to the 0-0 excitation energy rather than to the isomerization barrier located, structurally, very far from the Franck-Condon region. Furthermore spontaneous fluorescence studies (84) show that, for bovine rhodopsin, EaP has the same energy of the photoexcited pigment and it must therefore be significantly larger than the thermal activation energy EaT of a canonical ground state transition state.

13

Fig. S2Accuracy of the CASPT2/CASSCF//MM QM/MM protocol for modeling photoreceptors. Comparison between observed and computed absorption (S0→S1, S0→S2) and emission (S1→S0) λmax values of a set of protein pigments (rhombuses indicate data from the author labs. Triangles indicate data from other groups). These include bovine rhodopsin (Rh), bathorhodopsin (bathoRh), isorhodopsin (iso-Rh) the Rh mutants E113D and G121L, (29, 60) bacteriorhodopsin (bR), (44) Anabaena sensory rhodopsin (ASR), (45) the green fluorescent protein (GFP), (85) the photoactive yellow protein (PYP), (86) the tryptophan containing proteins parvalbumin (Parv) and Monellin (Mone), (87) luciferase, (88) the GFP-like mutant Dronpa (89) and phytochrome. (90)

14

Fig. S3A schematic representation of the Schiff base between Lysine and a retinal model. The link atoms was introduced between Cδ and Cε. The labeled dihedrals were parameterized in our QM/MM model.

1. The QM/MM Scheme The QM/MM force-field is defined by the following Hamiltonian:

Q Qn Nj i i

QM MM vdW bondedi=1 j 1 i=1 j=1ij ij

Z qqH H H E E

r r

where QMH describes the QM segment in the vacuum, represents the MM segment and the remaining terms describe the interactions between the QM and MM segments. These include:

MMH

(i) the electrostatic interaction of QM electrons and nuclei with the MM point

charges (qj), (ii) the short-range van der Waals interactions (EvdW) and (iii) additional parametrized potentials (Ebonded) required to correctly describe

the QM/MM frontier geometry (see Scheme 2).

Scheme 2. Notice that the QM wavefunction is polarized by the MM point charges. In contrast, the MM point charges remain constant during the calculation. On the other hand, the charges of the chosen Amber96 force-field (1) take into account the polarization effect in a mean-field way.

Scheme 3.

15

Fig. S4Correlation between computed and observed excitation energies for bovine Rh (WT), 5 of its mutants and one derivative featuring the A2-chromophore (WT-A2). The energies have been computed at the CASPT2//CASSCF/6-31G*/AMBER level. The experimental data are from refs. (67-71)

16

Fig. S5CASSCF/6-31G*/AMBER classical trajectories starting from TSCT and TSDIR and representing the relaxation towards Rh (negative time) and BathoRh (positive time). The energies are shown relative to Rh. The points corresponding to the optimized TSs are indicated with filled circles. Each trajectory point corresponds to a time-step of 1 fs.

20

25

30

35

40

-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11

TSCT TSDIR

To Rh

To bathoRh

Trajectory point

ΔE (

kcal

/mol

)

17

Fig. S6The bond lengths along the π-backbone of PSB11 in bovine Rh at the 2-root state average CASSCF/6-31G* optimized transition states and CI structure obtained via interpolation.

Bond

Len

gth

(Å)

Bond

1.25

1.30

1.35

1.40

1.45

1.50

C(5-6) C(6-7) C(7-8) C(8-9) C(9-10) C(10-11) C(11-12) C(12-13) C(13-14) C(14-15) C15-N

TSCT TSDIR CI

56

7

8

9

10

1112

1314

15

1

23

4

5

PSB3

Friday, February 10, 2012

18

Fig. S7Ground state and first excited state energy values along the BLA coordinate (see supplementary text) connecting TSDIR and TSCT for bovine Rh. The graph shows both the CASSCF/6-31G*/AMBER and CASPT2//CASSCF/6-31G*/AMBER energy profiles along the scan. While the conical intersection (indicated with a full circle for each method) moves towards TSDIR upon CASPT2 energy correction, the transition states maintain substantially the same position. The energies are relative to the corresponding Rh energy. The dashed arrows indicate the change in energy of TSDIR and TSCT upon CASPT2 correction. The ΨCT and ΨDIR symbols indicate the configuration dominating the electronic wavefunction of the corresponding profiles.

30

40

50

60

70

80

-1 0 1 2 3 4 5 6 7 8 9 10 11

BLA coordinate

ΔE (

kcal

/mol

)

CASPT2//CASSCF/6-31G* - ΨCT

CASPT2//CASSCF/6-31G* - ΨDIR

CASSCF/6-31G* - ΨDIR

CASSCF/6-31G* - ΨCT

TSCT TSDIR

19

45

50

55

60

65

-2 -1 0 1 2 3 4 5 6 7 8 9 10 11

ΔE (

kcal

/mol

)

BLA coordinate

MRCISD+Q/6-31G* - ΨDIR

CASPT2/6-31G* - ΨCT

MRCISD+Q/6-31G* - ΨCT

CASPT2(IPEA=0.25)/6-31G* - ΨCT

CASPT2(IPEA=0.25)/6-31G* - ΨDIR

CASPT2/6-31G* - ΨDIR

TSCT TSDIR

45

50

55

60

65

-2 -1 0 1 2 3 4 5 6 7 8 9 10 11

MRCISD/6-31G* - ΨDIR

MRCISD/6-31++G* - ΨDIR

MRCISD/6-31G* - ΨCT

MRCISD/6-31++G* - ΨCT

CASPT2(IPEA=0.25)/6-31G* - ΨDIR

CASPT2(IPEA=0.25)/6-31++G* - ΨDIR

CASPT2(IPEA=0.25)/6-31G* - ΨCT

CASPT2(IPEA=0.25)/6-31++G* - ΨCT

BLA coordinate

ΔE (

kcal

/mol

)

TSCT TSDIR

45

50

55

60

65

-2 -1 0 1 2 3 4 5 6 7 8 9 10 11

ΔE (

kcal

/mol

)

BLA coordinate

CASPT2(IPEA=0.25)//CASSCF - ΨDIR

CASPT2(IPEA=0.25)//CASPT2(IPEA=0.25) - ΨDIR

CASPT2(IPEA=0.25)//CASSCF - ΨCT

TSCT TSDIR

-92.5°

-92.9°

Bond Lengths (Å)1.3861.3891.390

1.3961.3961.395

1.4581.4581.459

1.4101.4081.417

1.3211.3251.293

-92.4°

Bond Lengths (Å)

-93.2°

-92.7°

1.3781.3791.370

1.4011.4011.398

1.4551.4551.457

1.3611.3601.353

1.3561.3561.349

-93.1°

CASPT2(IPEA=0.25)//CASPT2 - ΨDIR

CASPT2(IPEA=0.25)//CASPT2(IPEA=0.25) - ΨCT

CASPT2(IPEA=0.25)//CASPT2 - ΨCT

A

B

C

Saturday, February 11, 2012

20

Fig. S8Energy profiles along the BLA coordinate computed for the gas-phase chromophore model PSB3. The positions of the CI at each level is marked with a full circle color-coded for each method. The ΨCT and ΨDIR symbols indicate the configuration dominating the electronic wavefunction of the corresponding profiles. Energies are reported relative to cis-PSB3 optimized and computed at the same level of theory. A. 2-root CASPT2/6-31G*, CASPT2(IPEA=0.25)/6-31G* and MRCISD+Q/6-31G* (where Q is the original Davidson correction). (81) The BLA coordinate is computed by interpolation on the basis of CASSCF/6-31G* optimized TSDIR and TSCT. B. 2-root CASPT2 (IPEA=0.25) and MRCISD+Q with both 6-31G* and 6-31++G** basis sets. The BLA coordinate is based on CASSCF/6-31G* optimized TSDIR and TSCT. C. Comparison of the CASPT2(IPEA=0.25) energies along the BLA coordinate computed on the basis of optimized CASSCF, CASPT2 and CASPT2(IPEA=0.25) TSDIR and TSCT. The bond lengths and central torsional deformation values are shown for the optimized CASPT2(IPEA=0.25) structure (in blue), CASPT2 structure (in green) and CASSCF structure (in red) . Notice that in the case of CASPT2 (IPEA=0.25) TSDIR is no longer a transition state due to the CI being sloped and was optimized as an S1 minimum. The energy spikes along the scan (point 4) are documented artifacts arising from the presence of a degeneracy in the CASSCF reference wavefunction (91) or, in the case of MRCISD+Q (point 8) due to a degeneracy in the uncorrected MRCISD). (92)

21

Fig. S9The 3-root state average CASPT2/6-31G*/AMBER, CASPT2(IPEA=0.25)/6-31G*/AMBER and CASPT2(IPEA=0.25)/6-31++G**/AMBER energies along the BLA coordinate of bovine Rh. This is the same BLA coordinate presented at the top of Fig. 2A in the manuscript and also in Fig. S7. The energies are relative to the corresponding Rh energy. The dashed arrows indicate the change in energy of TSDIR and TSCT upon introduction of the IPEA and expansion of the basis set. At the CASPT2(IPEA=0.25)/6-31G*/AMBER level of theory, we find that TSCT lies ca. 11 kcal/mol lower in energy than TSDIR. The positions of the CI at each level is marked with a full circle. The ΨCT and ΨDIR symbols indicate the configuration dominating the electronic wavefunction of the corresponding profiles.

30

40

50

60

-1 TSCT 1 2 3 4 5 6 7 8 9 TSDIR 11

CASPT2/6-31G* - ΨCT

CASPT2/6-31G* - ΨDIR

CASPT2(IPEA=0.25)/6-31G* - ΨDIR

CASPT2(IPEA=0.25)/6-31G* - ΨCT

CASPT2(IPEA=0.25)/6-31++G** - ΨDIR

CASPT2(IPEA=0.25)/6-31++G** - ΨCT

BLA coordinate

ΔE (

kcal

/mol

)

TSCT TSDIR

22

18

20

22

24

26

28

30

1.7 1.8 1.9 2.1 2.2 2.3

1/λmax (10-3 nm-1)

-log[

k(se

c-1)]

Larval Tiger Salamander rod A2

Bullfrog porphyropsin rod A2

Hybrid Stugeon rod A2

Sturgeon rod A2

Bullfrog rodHuman rod

CommonToad red rod

Monkey (Macaque) rodSpotted Dogfish rod

Cane Toad red rod

Clawed Frog rod A2

E113D A2F261Y A2

A269T A2WT A2

T118A A2

E113DF261Y

A269TWT

A292S

T118A

1 10 20 30 40

45

50

!

60

-ln k

1/λmax

Fig. S10Simulation of the -logk vs. 1/λmax relationship. By using the set of our computed TSCT EaT values and the same Hinshelwood pre-exponential factor used in Luo et al. (with m=45) (16) it is possible to successfully simulate the Barlow relation for 11 rod pigments using the logk=logA(EaT,T)-EaT/RT expression (open circles). Note that by “pre-exponential factor” A(EAT, T) we meant the full set of terms preceding the “exponential factor” e^(-EAT/RT) in the expression of the rate constant k. In the case of the Hinshelwood model this factor depends on EAT, T, and m. The computed relation is compared with experimental data (crosses), which are collected in ref. (15). The positive slope of the -logk vs. 1/λmax relation computed with a constant pre-exponential factor (m=1, dashed line) clearly shows that the Hinshelwood pre-exponential factor modulates (decreases) the slope of the relation. Indeed, as shown in the inset (bottom right corner) the slope decreases as a function of the number of modes m but this will never result into a change of the slope from positive to negative. We find that any m value between 40 and 50 reproduces the experimental slope satisfactorily. It is also shown that the empirically derived EaT=0.84hc/λmax relationship, where the EaT values are not computed but obtained via the assumption EaT=EaP reproduces the experimental slope with m=45 (open squares) and it is substantially parallel to our computed -logk vs. 1/λmax relation. This is promptly explained by the fact that the excited state region near the FC point (determining the value of EaP) has the same electronic structure of TSCT (as pointed out in Fig. S1).

23

Fig. S11Changes in the Schiff Base - Glu113 Hydrogen Bonding at Rh, TSCT and TSDIR. Liu et al. measured a kinetic isotope effect for thermal isomerization in Rh and found it to be ~1.6. (14) This deuterium effect can potentially be explained by our model. We show in this figure a superposition of the chromophore structure (with Lys296, Glu113 and the two waters) showing the difference in geometry of Rh, TSCT and TSDIR. The table shows the difference in hydrogen bonding at the two transition states. The bubble diagram shows the Mulliken charges distribution on the N-H bond for Rh and TSCT. The AMBER point charge on the oxygen atom of the Glu113 counterion is also given. Note that the H-bond distance increases considerably in TSCT, while it decreases for TSDIR. Therefore, in TSCT there is a weakening of the very strong hydrogen bond between the Schiff base and

Rh TSDIR TSCT

N-H (Å)

H---O1 (Å)

N-H----O1

1.025 1.023 1.001

1.686 1.653 1.799

175.8º 171.4º 174.7º

W2

W1

W2W2Rh TSCT-0.8-0.8

-0.6

+0.5+0.6-0.3

24

counterion (i.e. a weakening of the H---O bond between the Schiff base hydrogen and the oxygen of the counter-ion). Meanwhile the N-H bond becomes stronger (as indicated by its shortening) at TSCT. Due to the difference in the zero point vibrational energy between deuterium and hydrogen at the level of the reactant, this makes the transition state for deuterium higher in energy. In fact, this observed isotope effect further confirms our finding that TSCT controls the thermal isomerization. If TSDIR were to control thermal isomerization, we would expect to find an inverse kinetic effect due to a slight strengthening of the hydrogen bond at the transition state.

25

Table S1.A table showing the re-parameterized MM charges for Lysine 296, which is covalently bound to retinal. Since the positive charge is carried by the QM moiety, the total charge for the MM moiety is 0.

Atom N Cα Ccarbonyl HN Ocarbonyl Hα

Charge -0.3981 -0.2400 0.6840 0.2246 -0.6396 0.1426

Atom Cβ Hβ Cγ Hγ Cδ Hδ

Charge -0.0094 0.0362 0.0187 0.0103 0.0000 0.0621

26

Table S2.The total Mulliken charges that reside on the β-ionone moiety for the reactant ground state, reactant excited state, TSDIR, and TSCT for each mutant. These values represent the degree of charge transfer for each model, and are computed by summing the charges on all the atoms which are on the β-ionone side of the isomerizing bond.

Charge on β-ionone moietyCharge on β-ionone moietyCharge on β-ionone moietyCharge on β-ionone moiety

Rh-S0 Rh-S1 TSDIR TSCT

A2-E113DA2-F261YA2-A269T

A2-WTA2-T118AA2-A292S

E113DF261YA269T

WTA292ST118A

0.1714 0.5648 0.0404 0.91490.1481 0.5090 0.0306 0.93700.1488 0.5052 0.0308 0.92120.1448 0.4917 0.0311 0.91100.1266 0.4322 0.0263 0.93040.1351 0.4459 0.0347 -0.1620 0.5145 0.0467 0.91930.1441 0.4547 0.0334 0.90200.1433 0.4489 0.0252 0.90300.1416 0.4416 0.0233 0.90060.1295 0.3918 0.0220 0.90250.1189 0.3614 0.0115 0.8970

27

Table S3.A table investigating the effect of using CASPT2(IPEA=0.25), expanding the basis set, and optimizing the structures at the CASPT2 level on the excitation energies of cis-PSB3, the activation barriers via TSCT and TSDIR, and on the relative energies of ground state cis- and trans-PSB3.

Single point calculation

method

Optimization method

CASPT2(6-31G*)

CASPT2(IPEA=0.25)

(6-31G*)

CASPT2(IPEA=0.25) (6-31++G**)

CASPT2(IPEA=0.25)

(ANO-L-VDZP)

CASPT2(IPEA=0.25)

(ANO-L-VTZP)

CASPT2(IPEA=0.25)

(ANO-L-VDZP)

CASPT2(IPEA=0.25)

(ANO-L-VTZP)

CASSCF (6-31G*)

CASSCF (6-31G*)

CASSCF (6-31G*)

CASSCF (6-31G*)

CASSCF (6-31G*)

CASPT2(6-31G*)

CASPT2 (6-31G*)

cis-PSB3 FC excitation

energy (kcal/mol)

TSCT S0 energy relative to cis-

PSB3 (kcal/mol)

TSDIR S0 energy relative to cis-PSB3(kcal/mol)

92.0 98.2 95.8 95.1 94.1 93.2 92.3

49.3 48.9 47.3 47.6 48.0 47.6 48.0

50.6 55.2 54.4 54.6 56.3 54.4 56.2

28

Tabl

e S4

: A ta

ble

givi

ng t

he a

bsol

ute

and

rela

tive

3-ro

ot s

tate

ave

rage

CA

SPT2

ene

rgie

s fo

r the

rea

ctan

t and

the

two

trans

ition

st

ates

TS C

T an

d TS

DIR

for e

ach

of th

e A1

and

A2

mut

ants

gen

erat

ed in

this

stud

y. T

he C

ASP

T2 re

fere

nce

wei

ghts

are

als

o sh

own.

ener

gy

of

11-

cis

stru

ctur

e (H

artr

ee)

Ref

eren

ce

Wei

ght

Ene

rgy

of

TS

CT (H

artr

ee)

Ref

eren

ce

Wei

ght

Ene

rgy

of

TS

DIR

(H

artr

ee)

Ref

eren

ce

Wei

ght

calc

ulat

ed

λ max

(nm

)ex

per

imen

tal

λ max

(nm

)S

0-S

1 E

nerg

y g

ap f

or

TS

CT

S0-

S1

Ene

rgy

gap

fo

r T

SD

IR

TS

CT E

nerg

y re

lati

ve t

o 1

1-ci

s (k

cal/

mo

l)

TS

Dir E

nerg

y re

lati

ve t

o 1

1-ci

s (k

cal/

mo

l)

A2_

E11

3D

S0A

2_E

113D

S1A

2_E

113D

S2

A2_

F261

Y

S0A

2_F2

61Y

S1A

2_F2

61Y

S2

A2_

A26

9T

S0A

2_A

269T

S1A

2_A

269T

S2

A2_

WT

S0A

2_W

TS1

A2_

WT

S2

A2_

T11

8A

S0A

2_T

118A

S1A

2_T

118A

S2

A2_

A29

2S

S0A

2_A

292S

S1A

2_A

292S

S2

E11

3DS0

E11

3DS1

E11

3DS2

F261

Y

S0F2

61Y

S1F2

61Y

S2

A26

9TS0

A26

9TS1

A26

9TS2

WT

S0W

TS1

WT

S2

A29

2SS0

A29

2SS1

A29

2SS2

T11

8AS0

T11

8AS1

T11

8AS2

-870.179032

0.5269

-870.136813

0.5232

-870.124246

0.5236

529

-19

826

34-870.092940

0.5157

-870.106169

0.5171

-870.111694

0.5170

529

-19

826

34-870.043826

0.5178

-870.056989

0.5154

-870.052863

0.5188

529

-19

826

34

-870.201804

0.5270

-870.158521

0.5223

-870.145551

0.5236

521

-15

1127

35-870.114298

0.5156

-870.134894

0.5176

-870.128755

0.5169

521

-15

1127

35-870.068835

0.5176

-870.072441

0.5189

-870.075445

0.5188

521

-15

1127

35

-870.201953

0.5270

-870.157570

0.5221

-870.147714

0.5236

512

-13

1128

34-870.113044

0.5157

-870.137116

0.5178

-870.130584

0.5170

512

-13

1128

34-870.068617

0.5176

-870.072833

0.5189

-870.077371

0.5190

512

-13

1128

34

-870.199929

0.5271

-870.152742

0.5230

-870.144666

0.5237

506

520

1112

3035

-870.109829

0.5156

-870.135844

0.5171

-870.125407

0.5171

506

520

1112

3035

-870.066357

0.5174

-870.073414

0.5149

-870.073597

0.5188

506

520

1112

3035

-870.194239

0.5273

-870.146212

0.5225

-870.142385

0.5235

494

-10

1730

33-870.102038

0.5159

-870.130120

0.5174

-870.115667

0.5165

494

-10

1730

33-870.063668

0.5173

-870.068129

0.5190

-870.073826

0.5177

494

-10

1730

33

-870.202922

0.5272

--

-870.149222

0.5237

492

--

16-

34-870.110269

0.5159

--

-870.124094

0.5169

492

--

16-

34-870.072326

0.5172

--

-870.079913

0.5182

492

--

16-

34

-871.378120

0.5239

-871.325059

0.5204

-871.308866

0.5203

500

510

246

3343

-871.286923

0.5130

-871.287174

0.5129

-871.299933

0.5147

500

510

246

3343

-871.242067

0.5148

-871.238562

0.5117

-871.222597

0.5169

500

510

246

3343

-871.400907

0.5240

-871.347462

0.5200

-871.342539

0.5206

481

510

1513

3437

-871.306086

0.5130

-871.323676

0.5128

-871.322396

0.5144

481

510

1513

3437

-871.266676

0.5145

-871.262772

0.5114

-871.258507

0.5169

481

510

1513

3437

-871.401323

0.5241

-871.348131

0.5203

-871.339327

0.5208

478

514

1012

3339

-871.306004

0.5131

-871.331983

0.5143

-871.320517

0.5146

478

514

1012

3339

-871.267459

0.5131

-871.259921

0.5107

-871.254039

0.5174

478

514

1012

3339

-871.400441

0.5241

-871.345057

0.5203

-871.337794

0.5208

475

498

713

3539

-871.304548

0.5131

-871.333162

0.5144

-871.317395

0.5145

475

498

713

3539

-871.266799

0.5144

-871.255584

0.5106

-871.252545

0.5174

475

498

713

3539

-871.403579

0.5243

-871.343653

0.5201

-871.343375

0.5208

454

491

1416

3838

-871.303180

0.5133

-871.320839

0.5128

-871.318225

0.5146

454

491

1416

3838

-871.270757

0.5140

-871.258475

0.5114

-871.259041

0.5173

454

491

1416

3838

-871.394131

0.5243

-871.328486

0.5190

-871.339931

0.5208

452

484

618

4134

-871.293401

0.5135

-871.319105

0.5146

-871.311043

0.5145

452

484

618

4134

-871.263164

0.5138

-871.239450

0.5158

-871.255128

0.5174

452

484

618

4134

29

Tabl

e S5

: A ta

ble

givi

ng th

e ab

solu

te a

nd re

lativ

e 3-

root

stat

e av

erag

e C

ASP

T2(I

PEA

=0.2

5) e

nerg

ies f

or th

e re

acta

nt a

nd th

e tw

o tra

nsiti

on s

tate

s TS

CT

and

TSD

IR fo

r eac

h of

the

A1

and

A2

mut

ants

gene

rate

d in

this

stu

dy. T

he C

ASP

T2 re

fere

nce

wei

ghts

are

al

so sh

own.

ener

gy

of

11-

cis

stru

ctur

e (H

artr

ee)

Ref

eren

ce

Wei

ght

Ene

rgy

of

TS

CT (H

artr

ee)

Ref

eren

ce

Wei

ght

Ene

rgy

of

TS

DIR

(H

artr

ee)

Ref

eren

ce

Wei

ght

calc

ulat

ed

λ max

(nm

)ex

per

imen

tal

λ max

(nm

)S

0-S

1 E

nerg

y g

ap f

or

TS

CT

S0-

S1

Ene

rgy

gap

fo

r T

SD

IR

TS

CT E

nerg

y re

lati

ve t

o 1

1-ci

s (k

cal/

mo

l)

TS

Dir E

nerg

y re

lati

ve t

o 1

1-ci

s (k

cal/

mo

l)

ener

gy

of

11-

cis

stru

ctur

e (H

artr

ee)

Ref

eren

ce

Wei

ght

Ene

rgy

of

TS

CT (H

artr

ee)

Ref

eren

ce

Wei

ght

Ene

rgy

of

TS

DIR

(H

artr

ee)

Ref

eren

ce

Wei

ght

calc

ulat

ed

λ max

(nm

)ex

per

imen

tal

λ max

(nm

)S

0-S

1 E

nerg

y g

ap f

or

TS

CT

S0-

S1

Ene

rgy

gap

fo

r T

SD

IR

TS

CT E

nerg

y re

lati

ve t

o 1

1-ci

s (k

cal/

mo

l)

TS

Dir E

nerg

y re

lati

ve t

o 1

1-ci

s (k

cal/

mo

l)

ener

gy

of

11-

cis

stru

ctur

e (H

artr

ee)

Ref

eren

ce

Wei

ght

Ene

rgy

of

TS

CT (H

artr

ee)

Ref

eren

ce

Wei

ght

Ene

rgy

of

TS

DIR

(H

artr

ee)

Ref

eren

ce

Wei

ght

calc

ulat

ed

λ max

(nm

)ex

per

imen

tal

λ max

(nm

)S

0-S

1 E

nerg

y g

ap f

or

TS

CT

S0-

S1

Ene

rgy

gap

fo

r T

SD

IR

TS

CT E

nerg

y re

lati

ve t

o 1

1-ci

s (k

cal/

mo

l)

TS

Dir E

nerg

y re

lati

ve t

o 1

1-ci

s (k

cal/

mo

l)

A2_

E11

3D

S0A

2_E

113D

S1A

2_E

113D

S2

A2_

F261

Y

S0A

2_F2

61Y

S1A

2_F2

61Y

S2

A2_

A26

9T

S0A

2_A

269T

S1A

2_A

269T

S2

A2_

WT

S0A

2_W

TS1

A2_

WT

S2

A2_

T11

8A

S0A

2_T

118A

S1A

2_T

118A

S2

A2_

A29

2S

S0A

2_A

292S

S1A

2_A

292S

S2

E11

3DS0

E11

3DS1

E11

3DS2

F261

Y

S0F2

61Y

S1F2

61Y

S2

A26

9TS0

A26

9TS1

A26

9TS2

WT

S0W

TS1

WT

S2

A29

2SS0

A29

2SS1

A29

2SS2

T11

8AS0

T11

8AS1

T11

8AS2

-870.169890

0.5292

-870.127773

0.5255

-870.105457

0.5286

457

-27

226

40-870.070130

0.5217

-870.085484

0.5227

-870.101781

0.5195

457

-27

226

40-870.019107

0.5241

-870.035951

0.5212

-870.025763

0.5261

457

-27

226

40

-870.192597

0.5293

-870.148854

0.5201

-870.126742

0.5287

449

-21

527

41-870.091026

0.5217

-870.114752

0.5277

-870.118788

0.5194

449

-21

527

41-870.044996

0.5237

-870.045343

0.5262

-870.048349

0.5262

449

-21

527

41

-870.192764

0.5293

-870.147765

0.5203

-870.128908

0.5287

443

-19

528

40-870.089811

0.5217

-870.116843

0.5276

-870.120851

0.5194

443

-19

528

40-870.044707

0.5237

-870.045722

0.5262

-870.050357

0.5263

443

-19

528

40

-870.190750

0.5293

-870.143616

0.5252

-870.125934

0.5287

437

520

187

3041

-870.086425

0.5217

-870.115275

0.5227

-870.115408

0.5195

437

520

187

3041

-870.042564

0.5236

-870.051642

0.5208

-870.046305

0.5262

437

520

187

3041

-870.185014

0.5296

-870.136645

0.5199

-870.123647

0.5284

426

-17

1330

39-870.077979

0.5222

-870.110086

0.5278

-870.103566

0.5195

426

-17

1330

39-870.040563

0.5233

-870.041239

0.5263

-870.045764

0.5254

426

-17

1330

39

-870.193720

0.5295

--

-870.130553

0.5286

424

--

11-

40-870.086345

0.5221

--

-870.112650

0.5197

424

--

11-

40-870.048926

0.5232

--

-870.052065

0.5258

424

--

11-

40

-871.370234

0.5259

-871.317796

0.5223

-871.291614

0.5250

434

510

300

3349

-871.265314

0.5186

-871.269739

0.5177

-871.291327

0.5168

434

510

300

3349

-871.219676

0.5205

-871.219882

0.5172

-871.197852

0.5236

434

510

300

3349

-871.392994

0.5260

-871.340183

0.5218

-871.325123

0.5252

417

510

217

3343

-871.283843

0.5188

-871.306212

0.5176

-871.313858

0.5165

417

510

217

3343

-871.244840

0.5201

-871.244266

0.5168

-871.233700

0.5237

417

510

217

3343

-871.393403

0.5260

-871.340847

0.5221

-871.322007

0.5254

416

514

176

3345

-871.283773

0.5189

-871.313295

0.5193

-871.312477

0.5167

416

514

176

3345

-871.245697

0.5201

-871.239874

0.5163

-871.229610

0.5240

416

514

176

3345

-871.392522

0.5260

-871.337826

0.5221

-871.320476

0.5254

413

498

157

3445

-871.282227

0.5190

-871.314451

0.5194

-871.309341

0.5166

413

498

157

3445

-871.245080

0.5200

-871.235724

0.5161

-871.228140

0.5240

413

498

157

3445

-871.395701

0.5262

-871.336410

0.5219

-871.326112

0.5254

395

491

2110

3744

-871.280398

0.5192

-871.303348

0.5176

-871.310067

0.5166

395

491

2110

3744

-871.249205

0.5196

-871.239928

0.5168

-871.234562

0.5239

395

491

2110

3744

-871.386219

0.5262

-871.319941

0.5167

-871.322667

0.5254

394

484

1212

4240

-871.270553

0.5195

-871.300365

0.5239

-871.302939

0.5165

394

484

1212

4240

-871.241757

0.5194

-871.213722

0.5228

-871.230793

0.5240

394

484

1212

4240

30

Table S6.Cartesian coordinates Tables for wild type bovine Rh with A1 and A2 chromophores for Rh, TSCT and TSDIR

A1 Wild Type Rh C 10.78545996 4.60725533 -3.37360289 C 10.91253524 4.32799279 -1.86690434 C 12.16467430 4.98604238 -1.25947560 C 12.56609589 4.38302030 0.10096841 N 11.54608448 4.54633455 1.14658296 H 10.89185309 5.67747271 -3.53583922 H 11.60197215 4.12318434 -3.90744823 H 10.97152595 3.25215152 -1.72228376 H 10.02693526 4.70394138 -1.35246799 H 12.00282516 6.06355316 -1.16169044 H 12.99915570 4.82717416 -1.94455745 H 13.46550829 4.87700469 0.43545572 H 12.75431476 3.32953897 -0.04321363 H 11.57391806 5.41468639 1.68981275 C 0.38173483 -1.01602107 2.72982298 C -0.18671105 -1.82912782 1.55114238 C -0.95007219 -0.96862127 0.55378576 C -0.01920027 0.08053500 -0.04200870 C 0.84726582 0.78316456 0.98677136 C 1.06646139 0.27439208 2.22503700 C 1.99961658 0.92145137 3.19434815 C 3.26662013 1.29373980 2.90742502 C 4.21856329 1.92471884 3.83825191 C 5.40890136 2.36487944 3.34238866 C 6.40839421 3.12052163 4.09212372 C 7.68429947 3.48091349 3.77801569 C 8.53532974 3.13288552 2.63087928 C 9.69327768 3.85231147 2.49479204 C 10.61824448 3.68895650 1.39656085 C -0.75833960 -0.65472549 3.70533935 C 1.39316458 -1.91329240 3.46864376 C 1.41963443 2.09600204 0.48963903 C 3.81104977 2.04523722 5.28627716 C 8.14223355 2.01612512 1.68586559 H 1.75846895 2.74163163 1.28849464 H 2.26204764 1.93601353 -0.17736150 H 0.66549772 2.62752435 -0.08675249 H 0.63272849 -0.37136684 -0.78888765 H -0.60129807 0.82162285 -0.58239515 H -1.35312088 -1.58807022 -0.24423989 H -1.79474772 -0.48778051 1.03789262 H -0.82422929 -2.61443833 1.94675811 H 0.63259943 -2.32698568 1.03328753 H -0.38834438 -0.08149948 4.55115945 H -1.55421715 -0.09137465 3.23198332 H -1.20549151 -1.56108382 4.10365382 H 1.74624811 -1.46664132 4.39168604 H 0.92547104 -2.86048776 3.72293126 H 2.25943476 -2.12598147 2.84732288 H 1.63235563 1.04306294 4.19840661 H 3.62420886 1.14347794 1.90292170 H 5.58805305 2.19652258 2.29796405 H 6.06034657 3.54199137 5.01661331 H 8.15178029 4.16223912 4.47010768 H 9.91311659 4.66603896 3.17171810 H 10.58784783 2.82508971 0.75628083 H 4.62735758 2.34863371 5.92470320 H 3.01119466 2.76618151 5.41388790 H 3.45328220 1.09237365 5.66020570 H 8.97502195 1.62464312 1.11660256 H 7.69804802 1.19362810 2.23131179 H 7.40637047 2.36926849 0.97204027 O 10.51978743 1.86548232 4.84634899 O 9.91427639 8.70804953 1.90710475 H 9.42115243 8.49223603 2.72073762 H 10.64617679 8.05839946 2.00887492 H 10.01048640 1.94145342 4.02144966 H 10.28133829 2.73891536 5.21952274

A1 Wild Type TSDIR C 10.75916063 4.62359981 -3.32208687 C 10.81306512 4.40268334 -1.79722647 C 12.05134765 5.06404988 -1.16143183 C 12.41611561 4.46492939 0.21064371 N 11.41962198 4.72495161 1.25790587 H 10.88753671 5.68486654 -3.52063020 H 11.59371215 4.11143319 -3.79783240 H 10.84074493 3.33239178 -1.60350958 H 9.91426858 4.81406977 -1.33460351 H 11.89205779 6.14363699 -1.07867291 H 12.90473413 4.89990343 -1.82196547 H 13.34744567 4.90630700 0.52945672 H 12.52601262 3.39791343 0.09069202 H 11.48896539 5.62318198 1.74281881 C 0.40178442 -0.98884597 2.60074851 C -0.27243363 -1.51386672 1.31882772 C -1.25008608 -0.51401760 0.72193378 C -0.51001191 0.75957305 0.33178881 C 0.46054196 1.24738573 1.39058690 C 0.89549466 0.46477045 2.41087061 C 1.88114073 0.91216454 3.42565121 C 3.03746143 1.62126903 3.18271802 C 4.06581705 1.89135973 4.13203504 C 5.21258746 2.63731339 3.70128613 C 6.43816084 2.69150970 4.30780835 C 7.55033084 3.55547476 3.86418307 C 8.55325545 3.19121244 2.97678261 C 9.57159584 4.12494507 2.66816523 C 10.50079177 3.89030164 1.61161599 C -0.59190647 -1.07666716 3.77675842 C 1.59233702 -1.91955300 2.90221482 C 0.90151283 2.67781747 1.17483013 C 3.96019409 1.33800137 5.52974795 C 8.53739151 1.82207285 2.31099859 H 1.27340181 3.14501855 2.07602610 H 1.67841727 2.73925669 0.41620832 H 0.06016075 3.26667275 0.82025477 H 0.04571548 0.60253779 -0.59394674 H -1.22677614 1.54602266 0.11662781 H -1.74478536 -0.94251613 -0.14703178 H -2.03599062 -0.28161382 1.43229421 H -0.77130971 -2.45345732 1.54191372 H 0.49470048 -1.73828476 0.57873131 H -0.18399614 -0.65114915 4.68725997 H -1.52222147 -0.56459732 3.56248779 H -0.83260002 -2.11642324 3.98245242 H 2.03967418 -1.72152855 3.86921957 H 1.26074515 -2.95432780 2.90137339 H 2.36508208 -1.81449185 2.14541342 H 1.70899270 0.55898269 4.42636984 H 3.21823635 1.95623054 2.17700486 H 5.08438140 3.20904800 2.79677993 H 6.63231010 2.08185310 5.17425027 H 7.60694319 4.53991163 4.29996699 H 9.66148108 5.04694251 3.22184942 H 10.46490171 2.97532662 1.05107188 H 4.78361365 1.65383568 6.15693286 H 3.05064958 1.68172236 6.01045335 H 3.93829365 0.25304306 5.52936715 H 9.49031496 1.30601834 2.41848764 H 7.77189655 1.19597426 2.74363261 H 8.33477719 1.89306045 1.24804941 O 10.62056996 1.81882453 4.89532232 O 10.01486368 8.70192582 1.93442308 H 9.52231830 8.46315019 2.74184609 H 10.81377092 8.14312790 2.08410093 H 9.88317743 1.92175378 4.26676796 H 10.61256834 2.73121664 5.24376077

A1 Wild Type TSCT C 10.77490993 4.60075286 -3.30937008 C 10.84579773 4.29519319 -1.79906517 C 12.06955665 4.92823042 -1.11092003 C 12.46511347 4.22512297 0.20325156 N 11.52624618 4.42218143 1.27777486 H 10.88291991 5.67344608 -3.45013016 H 11.61234758 4.12583649 -3.81830871 H 10.89800665 3.21744361 -1.67934871 H 9.94055649 4.65545629 -1.30804821 H 11.88140249 5.98879711 -0.92524213 H 12.92167158 4.84897945 -1.78704855 H 13.42430541 4.62325355 0.50490880 H 12.58246813 3.16749753 -0.00283301 H 11.55644017 5.30816692 1.76109138 C -0.00356704 -0.88351005 2.85798486 C -0.64718330 -1.65958747 1.69609532 C -1.52250236 -0.77857344 0.82129118 C -0.69026394 0.33853771 0.20296409 C 0.33630033 0.96582319 1.12001733 C 0.67134996 0.40979086 2.32366794 C 1.67197306 0.98698599 3.21710799 C 2.82347955 1.66546580 2.88662645 C 3.81729254 2.01965992 3.82945649 C 5.00714302 2.63396857 3.32414343 C 6.20642079 2.61619082 3.97019225 C 7.41851553 3.33308209 3.53426955 C 8.42131582 2.88568890 2.73701037 C 9.60326648 3.72978948 2.55086633 C 10.49706844 3.58206315 1.53273285 C -1.07465747 -0.55118284 3.91410652 C 1.04662447 -1.81141641 3.49929229 C 0.91176183 2.24619603 0.55665645 C 3.63595848 1.79221599 5.30551080 C 8.36903122 1.52942096 2.06500796 H 1.19616244 2.96095381 1.31707267 H 1.78180135 2.04018315 -0.06291087 H 0.16833764 2.71920050 -0.07306390 H -0.14233260 -0.03244096 -0.66399714 H -1.34255791 1.12358222 -0.16475643 H -1.97116410 -1.37083816 0.02934481 H -2.34832734 -0.36713353 1.39099543 H -1.22523053 -2.47947071 2.10905880 H 0.13867898 -2.10525505 1.08935116 H -0.68854164 0.08685310 4.70578319 H -1.95616057 -0.07880436 3.49185579 H -1.42585077 -1.46116527 4.38791760 H 1.43788795 -1.42584477 4.43504187 H 0.59096040 -2.77010065 3.72182467 H 1.87996572 -1.98644680 2.82417470 H 1.51640506 0.78220712 4.25955681 H 3.05382785 1.85001435 1.85636113 H 4.94646560 3.09054843 2.35252767 H 6.28191737 2.06289291 4.89152072 H 7.51694226 4.30293309 3.99770258 H 9.69495948 4.60667148 3.17509852 H 10.42570828 2.74583473 0.85678432 H 3.46609104 0.74908957 5.54272341 H 2.77991305 2.36410190 5.64819696 H 4.48474782 2.15231747 5.86078697 H 9.25552697 0.94959544 2.30596359 H 7.50488788 0.95095811 2.36791313 H 8.34515800 1.62977809 0.98629110 O 10.50511018 1.98963098 4.77684142 O 9.93114972 8.70419367 1.92476705 H 9.45544769 8.44454457 2.73561230 H 10.66502034 8.04446353 1.98593898 H 10.43768883 2.34254361 3.86065252 H 10.10994129 2.78561332 5.19464366

31

A2 Wild Type Rh C 10.78208971 4.60975305 -3.36911032 C 10.90755196 4.33172523 -1.86148978 C 12.14801597 5.01135694 -1.25415045 C 12.57460074 4.40805781 0.09779184 N 11.56366509 4.54361029 1.15561426 H 10.88637423 5.67999001 -3.53219865 H 11.60106263 4.12761749 -3.90101225 H 10.98409248 3.25684047 -1.71752615 H 10.01543112 4.69305361 -1.34779434 H 11.96445794 6.08452933 -1.14791750 H 12.98104036 4.87583815 -1.94592557 H 13.46551328 4.91957625 0.42723091 H 12.78492955 3.35987287 -0.05361918 H 11.55760707 5.42441594 1.67913674 C 0.47823587 -1.15706258 2.81412285 C 0.00994388 -1.92531220 1.56113362 C -0.73898159 -1.05656132 0.58819524 C -0.43089656 0.24371090 0.48169172 C 0.60880813 0.86922434 1.32411702 C 1.08888442 0.20249237 2.40546092 C 2.08712579 0.79098758 3.33613933 C 3.29606214 1.27472858 2.97641238 C 4.27714471 1.89797035 3.88074462 C 5.44318049 2.36605095 3.35601177 C 6.43546567 3.14686396 4.09242202 C 7.71140920 3.50454743 3.77889428 C 8.57653719 3.11567081 2.65706325 C 9.74724313 3.81520175 2.52892402 C 10.67277541 3.65516653 1.43008831 C -0.71998360 -0.91292751 3.75165717 C 1.50416168 -2.04315093 3.54247808 C 1.03782222 2.25199800 0.88723412 C 3.92437504 1.99302017 5.34498293 C 8.18292439 1.98484912 1.72926988 H 1.52436995 2.80910211 1.67479865 H 1.71971054 2.19180176 0.04290931 H 0.16918402 2.81972657 0.56191459 H -0.93581377 0.87125252 -0.23233295 H -1.48001094 -1.50421126 -0.05098935 H -0.60272449 -2.76788758 1.86959212 H 0.87772854 -2.34599808 1.05087291 H -0.42890269 -0.34244193 4.62731552 H -1.51084312 -0.36970943 3.24951658 H -1.13132401 -1.85768475 4.09721162 H 1.79494549 -1.63384883 4.50318880 H 1.07639635 -3.02495362 3.72642691 H 2.40414401 -2.17741374 2.94782141 H 1.79916884 0.80675834 4.37337940 H 3.57216843 1.23089047 1.93635933 H 5.59363109 2.21954250 2.30296189 H 6.07367381 3.59827160 4.99740027 H 8.16491332 4.21559512 4.44972894 H 9.96130725 4.64090134 3.19289705 H 10.66929866 2.77871447 0.80637788 H 4.76513297 2.29161268 5.95395817 H 3.12671035 2.70950089 5.50841559 H 3.58914707 1.03272335 5.71987530 H 9.01996027 1.57429468 1.17976689 H 7.72657064 1.17735323 2.28701872 H 7.45719293 2.33051610 1.00124231 O 10.51665730 1.85694367 4.87362790 O 9.89517775 8.71989907 1.90293008 H 9.40990424 8.49736503 2.71923664 H 10.63398795 8.07692522 1.99658281 H 10.09154369 1.95754338 4.00444034 H 10.21511214 2.70811306 5.25352432

A2 Wild Type TSDIR C 10.76242281 4.62255317 -3.33230472 C 10.81780099 4.39279851 -1.81076508 C 12.05237461 5.05246149 -1.16969111 C 12.41489729 4.44047259 0.19590419 N 11.41240235 4.69091572 1.23720179 H 10.88630137 5.68493852 -3.52766069 H 11.59577246 4.11340803 -3.81368262 H 10.85285748 3.32179002 -1.62435268 H 9.91577638 4.79493929 -1.34634632 H 11.89169364 6.13039086 -1.07450103 H 12.90645383 4.89318873 -1.83011580 H 13.34276490 4.88098126 0.52520414 H 12.52839107 3.37536154 0.06476036 H 11.46536087 5.59001459 1.72427924 C 0.43233131 -1.03343699 2.60905258 C -0.20893047 -1.61225064 1.32962542 C -1.05205872 -0.62532300 0.57389155 C -0.69851919 0.66893280 0.55886178 C 0.40529871 1.18336880 1.39113203 C 0.93094874 0.41134072 2.38360160 C 1.92168871 0.88140668 3.37079835 C 3.05997275 1.62582430 3.14298375 C 4.07482638 1.88760245 4.10719037 C 5.23096954 2.61818417 3.67847401 C 6.43771348 2.71082158 4.31376107 C 7.55974671 3.54945545 3.85284975 C 8.53356499 3.17864796 2.93743216 C 9.56455768 4.09599948 2.63071111 C 10.49912590 3.84801288 1.58540821 C -0.58725340 -1.06637830 3.76134699 C 1.61289989 -1.95910961 2.95665370 C 0.82315857 2.60932924 1.12423091 C 3.94604136 1.34271390 5.50888218 C 8.51313279 1.80349695 2.28551964 H 1.19023179 3.10074148 2.01518667 H 1.60346298 2.65437334 0.36834570 H -0.02163253 3.18039640 0.75274685 H -1.24306895 1.37560841 -0.04352838 H -1.86379357 -0.98303412 -0.03442713 H -0.77820988 -2.49892672 1.59471981 H 0.57929521 -1.94825587 0.65636472 H -0.18247234 -0.62886328 4.66738152 H -1.49529607 -0.53233930 3.50674233 H -0.85762277 -2.09439748 3.98719090 H 2.04506268 -1.74052867 3.92534159 H 1.27644697 -2.99189642 2.97170763 H 2.39834232 -1.87270507 2.21054748 H 1.76080647 0.52228797 4.36985077 H 3.24840379 1.97482916 2.14338804 H 5.11475975 3.16271394 2.75563180 H 6.60606035 2.16851861 5.22880882 H 7.66752160 4.51349105 4.32421809 H 9.66719536 5.01893183 3.18027498 H 10.47592816 2.92949660 1.02921643 H 4.77090195 1.64248759 6.14229329 H 3.03974199 1.70263231 5.98520050 H 3.90473914 0.25826601 5.51230202 H 9.46380638 1.28635453 2.41228030 H 7.74323385 1.18683663 2.72300020 H 8.32599200 1.86112330 1.21958405 O 10.60275628 1.84749520 4.91407852 O 9.92823231 8.74020754 1.91300069 H 9.44589516 8.52063070 2.73163343 H 10.70636417 8.15027244 2.04709729 H 9.87634973 1.92984324 4.27026337 H 10.57269078 2.76858410 5.24215676

A2 Wild Type TSCT C 10.77961213 4.59294825 -3.31300740 C 10.86407394 4.27208343 -1.80619361 C 12.08759601 4.90973046 -1.12191046 C 12.49939841 4.21740849 0.19176512 N 11.56464356 4.39770749 1.27199644 H 10.88990091 5.66645458 -3.44594337 H 11.61156454 4.12051001 -3.83310366 H 10.92970025 3.19419212 -1.69827330 H 9.95834055 4.61801297 -1.30608405 H 11.89686399 5.97009504 -0.93992701 H 12.93718405 4.83172022 -1.80123162 H 13.45093985 4.63857564 0.48819075 H 12.64100590 3.16053696 -0.00611784 H 11.56540769 5.29234533 1.74047955 C 0.02956045 -0.90718623 2.82328749 C -0.57993465 -1.68917821 1.64011443 C -1.27561202 -0.80535783 0.64987693 C -0.82288986 0.43722973 0.41359093 C 0.30692335 0.99613575 1.14869474 C 0.73317140 0.37531190 2.30684857 C 1.73072985 0.93488851 3.16768508 C 2.82806219 1.72388951 2.85271000 C 3.80473916 2.06392712 3.79765933 C 4.99545938 2.71186278 3.31448483 C 6.20652409 2.63322464 3.92818687 C 7.42648205 3.33626200 3.48362924 C 8.43162181 2.87155257 2.69685753 C 9.60557608 3.72237689 2.49355555 C 10.51979393 3.56138425 1.49692851 C -1.07465088 -0.54003007 3.82703860 C 1.03485787 -1.85197660 3.51125780 C 0.87456125 2.26668532 0.56373554 C 3.62870928 1.78440941 5.26889583 C 8.38986685 1.50848497 2.03828235 H 1.15984190 2.99292884 1.31313733 H 1.74547497 2.04454194 -0.04788897 H 0.13429475 2.72356650 -0.08005953 H -1.31741883 1.08156908 -0.28820147 H -2.11231872 -1.18896253 0.09534525 H -1.26595434 -2.43196971 2.03123797 H 0.20331529 -2.23788099 1.11894464 H -0.69581100 0.07369990 4.63807703 H -1.88194824 -0.00276262 3.34487362 H -1.49806836 -1.43590745 4.26738362 H 1.37918427 -1.47844784 4.46925167 H 0.55873214 -2.80756008 3.70311385 H 1.90249327 -2.03220929 2.88231637 H 1.64824758 0.63632768 4.19492237 H 3.03495957 1.96954844 1.83076618 H 4.92475395 3.21104709 2.36459812 H 6.28808643 2.03799561 4.82267599 H 7.53008787 4.32115174 3.91067350 H 9.68513019 4.60840224 3.10463973 H 10.46492874 2.72080813 0.82466924 H 3.55955978 0.72327218 5.47853627 H 2.72052069 2.26065656 5.62007808 H 4.43667297 2.20380447 5.84398068 H 9.28753038 0.94586158 2.27985403 H 7.53332134 0.92401765 2.35140189 H 8.36151549 1.59436101 0.95749870 O 10.51648766 1.96145732 4.76010711 O 9.90841391 8.69270711 1.91770427 H 9.44087624 8.43399268 2.73409085 H 10.64178406 8.03179178 1.97469738 H 10.43334457 2.28994050 3.83713281 H 10.14234961 2.77165547 5.16863215

32

1

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