Absorption wavelength along chromophore low-barrier hydrogen bonds

Summary In low-barrier hydrogen bonds (H-bonds), the pKa values for the H-bond donor and acceptor moieties are nearly equal, whereas the redox potential values depend on the H+ position. Spectroscopic details of low-barrier H-bonds remain unclear. Here, we report the absorption wavelength along low-barrier H-bonds in protein environments, using a quantum mechanical/molecular mechanical approach. Low-barrier H-bonds form between Glu46 and p-coumaric acid (pCA) in the intermediate pRCW state of photoactive yellow protein and between Asp116 and the retinal Schiff base in the intermediate M-state of the sodium-pumping rhodopsin KR2. The H+ displacement of only ∼0.4 Å, which does not easily occur without low-barrier H-bonds, is responsible for the ∼50 nm-shift in the absorption wavelength. This may be a basis of how photoreceptor proteins have evolved to proceed photocycles using abundant protons.

The shape of the potential energy curve of a low-barrier H-bond is symmetric because pK a (donor) z pK a (acceptor), whereas that of a standard H-bond is asymmetric. Indeed, theoretical studies by Ikeda et al. showed that the difference in the original pK a values between the donor and acceptor groups is directly correlated with the energy difference between the two H-bond moieties (Ikeda et al., 2017). The simplest way to match the pK a values and form a low-barrier H-bond is to use identical groups as the H-bond donor and acceptor. This condition allows the easy occurrence of proton transfer via low-barrier H-bond species H 2 O.H + .OH 2 in the bulk water region. In contrast, the formations of low-barrier H-bonds between chemically different groups are often observed in protein environments. In such cases, electrostatic interactions with the protein environment equate the pK a values (proton donating abilities) of the two moieties. In contrast, salt bridges can form when the pK a difference is large. Salt bridges are strong in polar environments and play a key role in electrostatic interactions at the protein interface (Ishikita and Saito, 2014).
In the light-driven sodium-pumping rhodopsin KR2, the intermediate L-and M-states (505 and 400 nm, respectively), where the chromophore retinal Schiff base is protonated and deprotonated, reach equilibrium 26 ms after the light irradiation (Inoue et al., 2013) (Figure 1). The crystal structures of the two states It was previously proposed that in the photoactive yellow protein, a low-barrier H-bond existed between the chromophore p-coumaric acid (pCA) and Glu46 in the ground state, pG (Yamaguchi et al., 2009). However, many theoretical and experimental studies have suggested that pCA and Glu46 do not form a lowbarrier H-bond in the ground state (Graen et al., 2016;Saito and Ishikita, 2012a, 2012bThomson et al., 2019;Wang, 2019;Yoshimura et al., 2017) (Figure 1). Nearly, all of new experimental and theoretical studies have consistently shown that the H-bond is not a low-barrier H-bond, as recently reviewed in the study by Wang, 2019. (Highly unstable) deprotonated Arg52 on the protein bulk surface, which was initially proposed as ''experimental evidence'' of the presence of a low-barrier H-bond in the neutron diffraction study (Yamaguchi et al., 2009), has also been denied in the careful reinvestigation of the original diffraction data (Graen et al., 2016). Thus, a low-barrier H-bond cannot be defined by only the bond length, the H atom position, or strength of an H-bond: identification of a low-barrier H-bond can be valid only if the shape of the potential energy profile of the H-bond is symmetric (i.e., the pK a values for the two moieties are nearly equal), as suggested by Schutz and Warshel (2004).
In the ground state, Tyr42 donates an H-bond to pCA, which decreases pK a (pCA) with respect to pK a (Glu46), i.e., pK a (pCA) < pK a (Glu46) (Saito and Ishikita, 2012a). Spectroscopic studies using model systems suggested that the donation of an H-bond to pCA from Tyr42 and the low polarity of the protein environment with respect to aqueous solution contribute to pK a (pCA) < pK a (Glu46) (Koeppe et al., 2013(Koeppe et al., , 2021. However, electronic excitation results in an intermediate (pR CW ) structure (Ihee et al., 2005), forming a low-barrier H-bond between pCA and Glu46 owing to the loss of the H-bond donation from Tyr42 to pCA . The formation of a low-barrier H-bond in the pR CW structure is consistent with the observation of proton transfer from protonated Glu46 to pCA in the pR state (Xie et al., 1996). The pR state is unstable as proton transfer proceeds, leading to large structural changes in the pCA chromophore (Schotte et al., 2012) and formation of the pB state. The absorption wavelength is shortened by 110 nm during the pR (465 nm (Hoff et al., 1994)) to pB (355 nm (Hoff et al., 1994)) transition. The signaling state of the protein is the pB state, which has the shortest absorption wavelength among the photocycle intermediate states (Cusanovich and Meyer, 2003;Hellingwerf et al., 2003).
Spectroscopic studies showed that changes in the absorption wavelength were observed in response to the H + migration toward the H-bond partner using the model systems (Koeppe et al., 2011). Hereby, the influence iScience Article of the H + position on UV/vis spectra was investigated by replacing the acceptor group. In the H-bonds between phenol derivatives (Ph) and anions (X À ), dual UV-vis absorption peaks derived from [Ph-H.X À ] and [Ph À .H-X] were observed (Koeppe et al., 2011), which indicates that H + localizes at the proton donor and acceptor moieties (Koeppe et al., 2011(Koeppe et al., , 2017Pylaeva et al., 2015). In practice, the proton vibrational functions are delocalized, solvent fluctuations are present, and only average O-H distances and UV-vis spectra can be measured experimentally (e.g., Koeppe et al., 2011Koeppe et al., , 2017Pylaeva et al., 2015). Thus, it might be a great challenge to simulate the experimental spectra computationally. On the other hand, the maximum absorption wavelengths in the chromophores of the proteins can be calculated appropriately, as demonstrated for microbial rhodopsins (Tsujimura andIshikita, 2020, 2021;Tsujimura et al., 2021aTsujimura et al., , 2021b. Here we look for chromophore H-bonds and investigate how the electronic structure and the absorption wavelength of the chromophore change owing to the H + migration using a quantum mechanical/molecular mechanical (QM/MM) approach.

RESULTS AND DISCUSSION
Using the time-dependent density functional theory (TD-DFT) method, we calculated the excitation energies for the photocycle intermediate states (pG [295 K], pG [110 K], I T , pR 0 , pR CW , and pB 0 ) and the Y42F mutant of photoactive yellow protein. The calculated excitation energy, E TD-DFT (eV), has a high correlation with the experimentally determined energy, E abs (eV) ( Figure 2, R 2 = 0.977), and is best described by the following equation: The shape of the potential energy profile for the H-bond (i.e., the H-bond donor and acceptor distance remains unchanged in response to the H + movement, Figures 3, 4A, and S2A and Table S1) is symmetric, which indicates that a low-barrier H-bond forms between Glu46 and pCA in the intermediate pR CW structure, as suggested in the QM/MM calculations . The low-barrier H-bond formation suggests that the release of the H + from Glu46 to pCA occurs easily. The shape of the potential energy profile for proton transfer (i.e., the H-bond donor and acceptor distance changes in response to the H + movement) is also symmetric, which conforms that a low-barrier H-bond forms in the pR CW structure (Figures 4A  and S2B and Table S1). In contrast, the shape of the potential energy profile for the corresponding H-bond is asymmetric in the ground pG state ( Figure 4B), which suggests that the H-bond is not a low-barrier H-bond in the pG state Ishikita, 2012a, 2013).
The excitation from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO) is the main characteristic of the excited state of pCA. When H + is located at the Glu46 moiety (i.e., before the proton transfer), the calculated absorption wavelength is $470 nm ( Figure 5A, using the the second-order perturbation theory (CASPT2) method) or $460 nm ( Figure 5B, using the TD-DFT method), which is consistent with the experimentally determined absorption wavelength of 465 nm for the pR state (Hoff et al., 1994). Correlation between the excitation energy calculated using the TD-DFT method (E TD-DFT ) and the experimentally measured absorption energy (E abs ); coefficient of determination R 2 = 0.977 (0.956 when excluding the pB 0 structure) The experimentally measured absorption energies correspond to 446 nm (Meyer, 1985) for pG, 510 nm (Ujj et al., 1998) for I T and pR 0 (both corresponding to the I 0 state), 465 nm (Hoff et al., 1994) for pR CW , 355 nm (Hoff et al., 1994) for pB 0 , and 458 nm for Y42F (Brudler et al., 2000). iScience Article Intriguingly, as the H + approaches the pCA moiety along the low-barrier H-bond, the absorption wavelength decreases from 460-470 nm to 410-420 nm ( Figure 5). The absorption wavelength decreases continuously when calculated using the CASPT2 method ( Figure 5A) and discontinuously when calculated using the TD-DFT method ( Figure 5B). The observed decrease of $50 nm in the absorption wavelength is comparable to the decrease of 51 nm observed upon the protonation of isolated pCA in water (Putschö gl et al., 2008).
The LUMO energy level of pCA is not significantly affected by the H + position ( Figure 6A). On the other hand, the HOMO energy level decreases more significantly than the LUMO energy level as the H + approaches the pCA moiety. This behavior is due to the localization of LUMO at the Cys69 moiety and the localization of HOMO at the protonation site (hydroxyl group moiety) ( Figure 6B). Thus, the absorption wavelength (HOMO to LUMO) decreases as the H + approaches the pCA moiety along the low-barrier H-bond ( Figure 6).
Notably, there are several limitations of TD-DFT (e.g., Barbatti and Crespo-Otero, 2014). The discontinuous decrease in the absorption wavelength observed in the TD-DFT calculation ( Figure 5B) is likely an artifact of the methodology. The excited state can include double excitations that are not properly described by single-excitation TD-DFT. The question about adequate description of charge-transfer is still open even with the CAM-B3LYP functional (Yanai et al., 2004).
The presence of the discontinuous decrease in the absorption wavelength observed in the TD-DFT calculation is not due to structural changes induced by the H + displacement since the planarity of the double bond and the thioester region in pCA remains unchanged ( Figure S3). The discontinuous decrease in the absorption wavelength is also observed even when the functional/basis set is replaced (e.g., the CAM-B3LYP functional, Yanai et al., 2004, Figure S4), or the H-bond donor and acceptor distance can iScience Article change in response to the H + movement (the potential energy profile for proton transfer, Figure S5), as far as TD-DFT is employed.
In the time-resolved XFEL structure of KR2 (Skopintsev et al., 2020) obtained 30 ms or 150 ms after the light irradiation, a low-barrier H-bond forms between the retinal Schiff base and Asp116 when Ser70 does not donate an H-bond to Asp116 (Figures 7, S6, and S7 and Table S2), as suggested in recent theoretical studies (Tsujimura and Ishikita, 2021). This is consistent with the fact that the intermediate L-state (with protonated Schiff base) and M-state (with deprotonated Schiff base) reach equilibrium 26 ms after the light irradiation (Inoue et al., 2013) (Figure 1).
In both CASPT2 and TD-DFT calculations of KR2, the absorption wavelength decreases continuously as the H + approaches the Asp116 moiety along the low-barrier H-bond (Figure 8). In the low-pH structure (crystalized at pH 4 and soaked at pH 8) of KR2 (Kato et al., 2015), the retinal Schiff base and Asp116 form a low-barrier H-bond (Tsujimura and Ishikita, 2021). The continuous decrease in the absorption wavelength is also observed along the low-barrier H-bond in the low-pH structure when calculated using the TD-DFT method ( Figure S8). The similarity in the H-bond energy and absorption wavelength profiles between the time-resolved XFEL structure ( Figure 8) and the low-pH structure ( Figure S8) confirms that the low-pH structure has the characteristic of the M-state, as suggested in recent theoretical studies (Tsujimura and Ishikita, 2021).
The excitation from the HOMO to the LUMO is the main characteristic of the excited state of retinal Schiff base. The HOMO energy level of the retinal Schiff base remains essentially constant ( Figure 9A). On the A B Figure 4. Potential energy profile for H-bonds and proton transfer in photoactive yellow protein (A) pR CW (Ihee et al., 2005)  iScience Article other hand, the LUMO energy level increases more significantly than the HOMO energy level as the H + approaches the Asp116 moiety ( Figure 9A). This behavior is attributed to the localization of LUMO at the protonation site (Schiff base moiety) and the localization of HOMO at the b-ionone ring moiety ( Figure 9B). As a result, the absorption wavelength (HOMO to LUMO) continuously decreases as the H + approaches the Asp116 moiety along the low-barrier H-bond (Figure 8).
The absorption wavelength of $500 nm for the protonated Schiff base calculated using the TD-DFT method is close to the experimentally measured value of 505 nm for the L-state (Inoue et al., 2013). The calculated absorption wavelength of $430 nm for the deprotonated Schiff base is also comparable to the experimentally measured value of 400 nm for the M-state (Inoue et al., 2013) ( Figure 8B).
In contrast, the absorption wavelengths calculated using the CASPT2 method ( Figure 8A, $380 nm for the protonated Schiff base and $330 nm for the deprotonated Schiff base) are significantly short with respect to the measured values (Inoue et al., 2013). The same tendency was also observed in previous studies by Pedraza-Gonzá lez et al., as the absorption wavelength of KR2 calculated using the CASPT2 method was $120 nm shorter than the measured value (Nakajima et al., 2021;Pedraza-Gonzá lez et al., 2019). Only when they intentionally protonated Asp251, they were able to obtain the experimentally measured absorption wavelength. However, protonation of Asp251 is energetically unlikely because it exists near iScience Article the positively charged Schiff base (3.8 Å , Skopintsev et al., 2020) and Arg109 (2.7 Å , Skopintsev et al., 2020). In the present study, the calculated pK a value for Asp251 is À1.3. In addition, no bands are observed in the protonated carboxylate region (1700-1750 cm À1 ) in Fourier-transform infrared spectroscopy (Ono et al., 2014). Furthermore, the time-resolved XFEL structures of KR2 show that Asp251 binds a positive charged sodium ion in the intermediate state (Skopintsev et al., 2020). These results suggest that Asp251 is deprotonated. Consistently, the absorption wavelength of KR2 calculated using the TD-DFT method is comparable with the measured value when Asp251 is deprotonated ( Figure 8B) (Tsujimura and Ishikita, 2020).

Conclusions
The following two characteristics have already been reported for low-barrier H-bonds: (1) pK a . pK a (donor) and pK a (acceptor) are nearly equal along a low-barrier H-bond, facilitating proton transfer to the acceptor moiety (Perrin and Nielson, 1997;Warshel et al., 1995) ( Figure 10A).
(2) Redox potential (E m ). As the H + transfers along a low-barrier H-bond, E m (donor) decreases and E m (acceptor) increases continuously, facilitating electron transfer to the acceptor moiety ) ( Figure 10B). Based on the findings A B iScience Article presented here, we are able to report another characteristic of low-barrier H-bonds, i.e., (3) absorption wavelength ( Figure 10C). If the HOMO is localized at the protonation site of the chromophore (e.g., pCA), the absorption wavelength shortens as H + reaches the unprotonated chromophore moiety (Figure 10C, top panel). If the HOMO is located away, but the LUMO is located at the protonation site of the chromophore (e.g., retinal Schiff base), the absorption wavelength lengthens as H + reaches the A B C Figure 10. Properties of low-barrier H-bonds between chemically different groups in protein environments (A) pK a difference (DpK a ) between the H-bond donor (D) and acceptor (A) moieties (Perrin and Nielson, 1997;Warshel et al., 1995). (B) E m for the H-bond donor (E m (D)) and acceptor (E m (A)) moities . (Top) H-bond donor as an electron donor (e.g., TyrZ in photosystem II (Kawashima et al., 2018;Saito et al., 2011Saito et al., , 2020   iScience Article unprotonated chromophore moiety ( Figure 10C, bottom panel). Changes in the absorption wavelength along the H-bond should also occur in standard H-bonds in response to the H + movement, although H + is predominantly localized at the H-bond donor moiety.
The mechanism of the absorption wavelength shifts during the photocycle is often oversimplified and is explained as ''structural change'' or ''conformational change'' especially when the molecular mechanism is unclear. Hence, the definition of ''structural (conformational) change'' is ambiguous. The present result shows that the H + displacement of only $0.4 Å , which does not easily occur without low-barrier H-bonds, is responsible for the $50-nm shift in the absorption wavelength (Figures 5 and  8). That is, ''the H + displacement of only $0.4 Å '' mainly corresponds to ''structural (conformational) change.'' These findings may provide insights to help understand how photoactive proteins have evolved to control chromophore energetics using abundant protons and design the photocycle by tuning the chromophore electronic states.

Limitations of the study
The results depend on the original atomic coordinates of the crystal structures. The original side-chain orientations may affect the results, although the geometries of the chromophore moieties are quantumchemically optimized.

STAR+METHODS
Detailed methods are provided in the online version of this paper and include the following: where f 1n is the oscillator strength, E n is the excitation energy of the n-th excited state, and c is a standard deviation (0.2 eV). When f(E) takes the maximum value, E is considered as the maximum value for the excitation energy, i.e., E TD-DFT . In KR2, the absorption energy (E abs in eV) was empirically corrected from the following equation (obtained for 13 microbial rhodopsins; coefficient of determination R 2 = 0.920) (Tsujimura and Ishikita, 2021