Correlation between C=O Stretching Vibrational Frequency and pKa Shift of Carboxylic Acids

Identifying the pKa values of aspartic acid (Asp) and glutamic acid (Glu) in active sites is essential for understanding enzyme reaction mechanisms. In this study, we investigated the correlation between the C=O stretching vibrational frequency (νC=O) of protonated carboxylic acids and the pKa values using density functional theory calculations. In unsaturated carboxylic acids (e.g., benzoic acid analogues), νC=O decreases as the pKa increases (the negative correlation), whereas in saturated carboxylic acids (e.g., acetic acid analogues, Asp, and Glu), νC=O increases as the pKa increases (the positive correlation) as long as the structure of the H-bond network around the acid is identical. The negative/positive correlation between νC=O and pKa can be rationalized by the presence or absence of the C=C double bond. The pKa shift was estimated from the νC=O shift of Asp and Glu in proteins on the basis of the negative correlation derived from benzoic acids. The previous estimations should be revisited by using the positive correlation derived in this study, as demonstrated by quantum mechanical/molecular mechanical calculations of νC=O and electrostatic calculations of pKa on a key Asp85 in the proton-transfer pathway of bacteriorhodopsin.


■ INTRODUCTION
The carboxylic groups (COOH) of aspartic acid (Asp) and glutamic acid (Glu) in proteins play crucial roles especially in proton-transfer pathways 1−6 , as their protonation/deprotonation states can be altered due to pK a shifts caused by interactions with surrounding protein environments. 5,7 Vibrational spectroscopy using infrared light [e.g., Fourier transform infrared spectroscopy (FTIR)] can be used for identifying the protonation state of carboxylic acids. 8 The stretching vibrational frequency, ν CO , indicates the protonation state of the carboxylic group (i.e., 1690−1750 cm −1 for COOH, and1540− 1650 and ∼1300−1420 cm −1 for the asymmetric and symmetric stretching modes of COO − , respectively) ( Figure  1a). 9 ν CO of COOH in proteins can be an indicator of the pK a shifts of Asp and Glu in active sites because pK a and ν CO are affected by the surrounding (protein) environment. Infrared spectroscopy using benzoic acid analogues 8,10 showed a negative correlation between the pK a and ν CO , in which ν CO decreased as the pK a increased (Figure 1b). On the basis of this negative correlation, the observed values of ν CO have been discussed in relation to the pK a of carboxylic acids. 11,12 A light-driven proton-pumping membrane protein, bacteriorhodopsin, shows different ν CO values for the same protonated Asp. Bacteriorhodopsin displays a proton-pumping function across the membrane as a cyclic reaction that comprises a series of intermediates, designated as the J, K, L, M, N, N′, and O states (see the Results and Discussion for details). 13,14 Proton pumping involves a chromophore (the retinal Schiff base) and a key Asp residue (Asp85) located in the interior. An FTIR study showed that the ν CO value of Asp85 is 1761 cm −1 in the M intermediate state, whereas it is 1754 cm −1 in the N intermediate state, which is a decrease of 7 cm −1 from the M state. 11,15 Braiman et al. speculated that Asp85 in the N state (1754 cm −1 ) would have a higher pK a than that in the M state (1761 cm −1 ) 11 on the basis of the negative correlation between the ν CO and pK a derived from benzoic acids. 8,10 However, pK a (Asp85) must decrease during the transition from the M to N states becuase of the following reason. The retinal Schiff base is deprotonated in the M state, whereas it is protonated in the N state. Therefore, protonated Asp85 could be unstable because of a repulsive Coulombic interaction with the protonated retinal Schiff base in the N state, 11 resulting in a decrease in pK a (Asp85). A decrease in pK a (Asp85) is plausible because it facilitates proton transfer from Asp85 during the subsequent transition from the final intermediate O state to the initial state (BR) after the N state. Thus, the higher pK a (Asp85) in the N state estimated from ν CO is not consistent with the reaction mechanism of bacteriorhodopsin.
For deprotonated saturated carboxylic acids (COO − ), a correlation between the asymmetric vibrational frequency and pK a was reported; the frequency increased as pK a decreased. 9,16 For protonated saturated carboxylic acids (COOH), the relationship between ν CO and H-bond structures was reported; ν CO decreased as the number of H-bonds increased. 17−19 However, to the best of our knowledge, the correlation between ν CO and pK a remains unclear ( Figure  1c), particularly for Asp and Glu (i.e., saturated carboxylic acids). In this study, we investigated the correlation between these parameters for both unsaturated carboxylic acids (e.g., benzoic acids) and saturated carboxylic acids (e.g., acetic acids). We also calculated the pK a value by using an electrostatic-potential approach and the ν CO value of Asp85 in bacteriorhodopsin by using a quantum mechanical/ molecular mechanical (QM/MM) approach.
■ METHODS Geometry Optimization. To investigate the vibrational frequencies of the isolated carboxylic acids, the protonated carboxylic acid and two adjacent water molecules accepting the H-bond from the OH of the carboxylic group and donating the H-bond to CO were modeled ( Figure 2). These geometries were optimized by using the restricted density functional theory (DFT) method with the B3LYP functional and the 6-31g* basis set, which was performed by using the Jaguar program code. 21 The atomic coordinates of bacteriorhodopsin were taken from the X-ray structures from Halobacterium salinarum for the M state at a resolution of 1.52 Å (PDB code, 1P8H) 22 and the N′ state (V49A mutant) at a resolution of 1.62 Å (PDB code, 1P8U). 22 The N′ state was used as a model structure of the N state of the wild type Results and Discussion. The atomic partial charges of the amino acids and Schiff base were adopted from the all-atom CHARMM22 parameter set. 23 The Schiff base was considered protonated except in the M state. The electrostatic embedding QM/MM scheme was used, wherein the electrostatic and steric effects created by the protein environment were explicitly considered. To perform the QM/ MM calculation, we used the QSite 24 program code, employing the restricted DFT method with the B3LYP functional and the 6-31g* basis set. The QM region comprised the side chain of Lys216 (Schiff base), the retinal and side chain of Asp85, Tyr57, and Asp212, and the adjacent water  Chemical structure of (a) benzoic acid analogues and (b) acetic acid analogues with distances r CO , r OO , and r OH . The benzoic acid analogues are shown so that the H-bond structue is idenctial. The proton was placed at the distal oxygen atom from the substituent group at the ortho position (i.e., the higher-frequency 20 form). molecules (W603, W604, and W605 in 1IW9 and W401, W406 and W407 in 1P8U). The coordinates of the heavy atoms in the surrounding MM region were fixed at their original X-ray coordinates, whereas those of the H atoms in the MM region were optimized by using the OPLS2005 force field. All atomic coordinates in the QM region were fully relaxed (i.e., not fixed) in the QM/MM calculation.
Vibrational Frequency Calculation. Vibrational frequencies were calculated by using the same level of theory as the geometry optimizations based on the quantum-chemically optimized structures. The calculated frequencies were scaled by using a standard factor of 0.9614 for B3LYP. 25 pK a Calculation of Bacteriorhodopsin Asp85. The computation was based on the electrostatic continuum model by solving the linear Poisson−Boltzmann equation using the MEAD program. 26 To obtain the absolute pK a value of Asp85, we calculated the difference in electrostatic energy between the protonated and deprotonated states in a reference model system by using a known experimentally measured pK a value (e.g., 4.0 for Asp 27 ). The difference in the pK a value of the protein relative to the reference system was added to the known reference pK a value. The experimentally measured pK a values used as references were 7.2 for the Schiff base, 28,29 12.0 for Arg, 4.0 for Asp, 9.5 for Cys, 4.4 for Glu, 10.4 for Lys, 9.6 for Tyr, 27 and 7.0 and 6.6 for the Nε and Nδ atoms of His, respectively. 30−32 All other titratable sites were fully equilibrated to the protonation state of the target site during titration. The dielectric constants were set to 4 and 80 for the protein and water, respectively. All computations were performed at 300 K, pH 7.0, and an ionic strength of 100 mM using the QM/MM-optimized structures. The linear Poisson−Boltzmann equation was solved by using a three-step grid-focusing procedure at resolutions of 2.5, 1.0, and 0.3 Å. The ensemble of protonation patterns was sampled by using the Monte Carlo method with Karlsberg. 33 Monte Carlo sampling yielded the probabilities of the two protonation states (protonated and deprotonated) of the molecule. On the basis of the Henderson−Hasselbalch equation, the pK a value was obtained as the bias potential when the probabilities of the protonated and deprotonated states were 0.5.

■ RESULTS AND DISCUSSION
Benzoic and Acetic Acids. The vibrational frequencies of the CO stretching bond, ν CO , were investigated for a series of protonated benzoic acid analogues (Table 1 and Figure 2a) and acetic acid analogues (Table 2 and Figure 2b). In benzoic acids, the calculated ν CO negatively correlates with the measured pK a value (Figure 3a), 10 which is consistent with the infrared spectroscopy results ( Figure 3b). 8,10 In contrast, the calculated ν CO positively correlates with the measured pK a value 34 in acetic acids (Figure 3c). A similar positive correlation between the calculated ν CO and the measured pK a was also observed for hydroxycarboxylic acid analogues (Table S1, Figures S1 and S2).
As pK a increases, the CO bond distance (r CO ; Figure  2a) increases in benzoic acids (Figure 4a). On the other hand, it decreases in acetic acids as pK a increases (Figure 4c). In benzoic acids, the distance of the C−C bond (r C−C ; Figure 2a) connecting the benzene ring to the carboxylic group also correlates with the measured pK a value (Figure 4b). The calculations for various H-bond structures show that ν CO decreases as the number of H-bonds increases ( Figure S3), as previously reported. 17−19 In both benzoic acids and acetic acids, the O−H distance of the protonated carboxylic group (r OH ; Figure 2) increases as pK a decreases ( Figure S4c,d). The same trend has been reported in a DFT study of chlorophenols. 35 This is because as pK a decreases, the deprotonation is facilitated and the proton departs from the donor O atom; thus, r OH increases. In addition, the H-bond distance between the oxygen atoms of the carboxylic acid and the water molecule, r O...O (Figure 2), decreases as pK a decreases in both cases ( Figure S4a,b). This is because the H-bond distance tends to shorten as the pK a difference between the donor (carboxylic group) and acceptor (water molecule) moieties approaches zero, 36 forming a lowbarrier hydrogen bond (LBHB).
The correlation between r CO and pK a in acetic acids (Figure 3c) is opposite to that observed for benzoic acids (Figure 3a) because of the opposite correlations between r OH and r CO [positive for acetic acids (Figures 4c and S4d) and negative for benzoic acids (Figures 4a and S4c)]. Because ν CO is determined by the CO bond strength, ν CO increases as r CO decreases (being a stronger CO bond),  The positive and negative correlations between r OH and r CO in acetic acids and benzoic acids can be explained by the    (Figures 5 and 6). Acetic acids have no CC bonds conjugated with the carboxylic group ( Figure 6). In this case, as the proton leaves the donor O atom, the resonance effect between the CO and C−O bonds in the carboxylic group becomes more pronounced, which weakens the double-bond nature of the CO bond. Thereafter, the CO bond strength is weakened, resulting in a longer r CO than the typical CO bond distance (Figure 6b). In contrast, benzoic acids have a CC bond on the phenyl group conjugated with the carboxylic group ( Figure 5). When benzoic acids have an electrondonating substituent (e.g., NH 2 ), the excess electrons are localized on the benzene ring ( Figure 5a). As the deprotonated carboxylic group is destabilized by repulsive interactions with these excess electrons, pK a increases. Simultaneously, the C−C bond connecting the carboxylic group to the benzene ring has a partial double-bond structure. The bond alternation effect between the C−C and CO bonds becomes less pronounced, thereby weakening the CO bond strength, resulting in a long CO distance (r CO ). When benzoic acid has an electronaccepting substituent (e.g., NO 2 ), the substituent extracts an electron, yielding a positive partial charge on the benzene ring ( Figure 5b). As the deprotonated carboxylic group is stabilized by attractive interactions with the positive partial charge, pK a decreases. Simultaneously, the C−C bond connecting the carboxylic group to the benzene ring has a single-bond nature exclusively, resulting in a longer r C−C (Figure 5b). The bond alternation effect becomes more pronounced and strengthens the CO bond, resulting in a short CO distance (r CO ). Thus, aspartic acids and benzoic acids show positive and negative correlations, respectively, between r OH and r CO and between pK a and ν CO . Bacteriorhodopsin. We investigated the correlation between ν CO and pK a in proteins using bacteriorhodopsin for the following reasons: (i) the protonation and deprotonation of Asp are essential in the proton pump function of bacteriorhodopsin, (ii) considerable knowledge of its vibrational spectra from FTIR studies has been accumulated, (iii) the protein structures of the intermediate states have been repoted, and (iv) the pK a values of key residues have been reported.
In bacteriorhodopsin, the proton pump function involves four protonatable sites: aspartic acid Asp96 on the cytoplasmic side, Asp85 and the retinal Schiff base in the middle region of the transmembrane helices, and pairing of Glu194 and Glu204 on the extracellular side (Figure 7a). In the initial BR state, Asp85 is deprotonated 13,14,38 and Asp96 is protonated; [13][14][15]22 the Glu194/Glu204 pair shares one proton; 39 the retinal Schiff base has an all-trans form. During the transition from the J to K state, the retinal Schiff base is transformed into a twisted 13-cis form by photoisomerization. 40,41 Subsequently, it changes to a standard 13-cis form during the transition from the K to L Figure 5. Correlation between r OH and r CO in benzoic acids. (a) 4-Aminobenzoic acid with pK a = 4.9. 10 (b) 2-Methyl-6-nitrobenzoic acid with pK a = 2.6. 10 The calculated values of ν CO , r OH , r CO , and r C−C are shown. Figure 6. Correlation between r OH and r CO in acetic acids. (a) Acetic acid with pK a = 4.8. 34 (b) Fluoroacetic acid with pK a = 2.7. 34 The calculated values of ν CO , r OH , and r CO are shown. state, removing the twist. 14,40,42 During the transition from the L to M state, two proton transfers (from the retinal Schiff base to Asp85 13−15 and from the Glu194/Glu204 pair to the extracellular side of the membrane 43,44 ) occur. The proton transfers are followed by the next proton transfer from Asp96 to the retinal Schiff base during the transition from the M to N state. [13][14][15]37 The N state transitions to the N′ state with proton intake from the cytoplasmic side to Asp96. 14,22,37 During the transition from the N′ to the O state, the retinal Schiff base returns to the all-trans form from the 13-cis form. Finally, the O state moves to the initial BR state, accompanied by proton transfer from Asp85 to the Glu194/Glu204 pair. [13][14][15]43 Here, we focus on the M and N′ intermediate states (Figure 7a).
The V49A mutant has been used as a model system for the N state in bacteriorhodopsin because it has a longer lifetime in the N and N′ states than the wild type. An FTIR study showed that the ν CO values of Asp85 in both the N and N′ states of the V49A mutant were the same as that in the N state of the wild type. 37 In this study, the N′ state structure of the V49A mutant was used as a model structure of the N state of the wild type by assuming that ν CO and pK a of the wild type are similar to the N′ state of the V49A mutant.
By use of the electrostatic method, pK a (Asp85) was calculated to be 13.2 (Table 3), which is consistent with the value of >11 estimated by FTIR analysis. 44 In contrast, it was calculated to be 7.0 in the N′ state. The calculated vibrational frequency of the CO stretching bond of protonated Asp85 [ν CO (Asp85)] thus shows a downshift of 42 cm −1 in the transition from the M (1827 cm −1 ) to the N′ (1785 cm −1 ) states ( Figure 7 and Table 3), which is qualitatively consistent with the observed downshift of 7 cm −1 from the M (1761 cm −1 ) to the N (1756 cm −1 ) states. 15 These results indicate that the tendency of the correlation between ν CO and pK a (i.e., the positive correlation) is the same as that observed in acetic acids. The calculated downshift of 42 cm −1 is quantitatively overestimated with respect to the experimental downshift of 7 cm −1 . This might be because of (1) the uncertainty of X-ray crystal structures and (2) a difference in the H-bond structure between the M and N′ structures. Note that the calculated frequency in the protein environment is highly sensitive to the H-bond structure as demonstrated in the calculation of the O−D stretching frequency of water molecules in bacteriorhodopsin. 39 A quantitative investigation of the relationship between ν CO and pK a using an identical structure will be needed in the future.
The QM/MM-optimized geometry shows that the O−H bond distance, r OH , in the N′ state is longer than that in the M state, whereas the CO bond distance, r CO , in the N′ state is shorter than that in the M state ( Table 3). The O−O distance, r O···O , of the H-bond between Asp85 and the adjacent water molecule (W603) is shortened during the transition from the M to N′ states because pK a (Asp85) decreases. These tendencies are the same as those in acetic acids and can be explained by a similar scheme (Figure 8): Asp has no CC bonds conjugated with the carboxylic group. As the proton leaves the donor O atom, the resonance effect between the CO and C−O bonds in the carboxylic group becomes more pronounced, which weakens the double-bond nature of the CO bond. Thereafter, the CO bond strength is weakened, resulting in a longer r CO than the typical CO bond distance (Figure 8a−c).
The lower pK a (Asp85) value (=7.0) in the N′ state than that in the M state (=13.2) is rationalized by the following: (i) because Asp85 is protonated in the N′ state, the pK a (Asp85) value should not be less than 7, and (ii) as the Schiff base is also protonated in the N′ state, the pK a (Asp85) value should decrease from that in the M state because of the repulsive interaction with the positive charge of the protonated Schiff base (Figure 7c). Thus, a decrease in the ν CO of Asp85 observed in bacteriorhodopsin during the transition from the M to N′ (N) state is attributable to a decrease in the pK a of Asp85. Braiman et al. tried to explain the downshift as being caused by a local structural alteration of the C helix, which affects the environment of Asp85 in the transition from the M to N′ (N) states. 11 However, no significant structural change was observed in the C helix in the crystal structure of the N′ state reported later 22 compared with that of the M state 45 ( Figure S5). The downshift of ν CO observed in bacteriorhodopsin during the transition from the M to N′ (N) state can be explained by the decrease in pK a (Asp85) without invoking the structural change effect of the C helix.
Carboxylic Acids. The findings of this study can be extended to general saturated or unsaturated carboxylic acids. When the carboxylic acid has a CC bond with the carboxylic group (i.e., unsaturated carboxylic acids), a negative correlation exists between pK a and ν CO (Figure 9b). In contrast, when carboxylic acid has no conjugated CC bond (i.e., saturated carboxylic acids), a positive correlation exists (Figure 9a). Note  The pK a shift of Asp and Glu in proteins was estimated from the negative correlation derived from benzoic acids 8,10 (e.g., in discussions on Asp85 11 and Asp96 12 in bacteriorhodopsin). These estimations should be revisited by using the positive correlation derived in this study, which may lead to completely opposite conclusions, as demonstrated here for bacteriorhodopsin.

■ CONCLUSIONS
The ν CO value of acetic acids increases as pK a decreases (Figure 3a), whereas in benzoic acids, ν CO decreases as pK a decreases (Figure 3c). The correlation between pK a and ν CO depends on the presence or absence of the CC double bond conjugated with the carboxylic group ( Figures 5 and 6). These findings can be extended to general saturated or unsaturated carboxylic acids: the pK a and ν CO values of saturated carboxylic acids (e.g., acetic acids) shows a positive correlation, whereas these two parameters shows a negative correlation in unsaturated carboxylic acids (e.g., benzoic acids) ( Figure 9). This relationship can be applied to Asp or Glu in proteins as long as the structure of the H-bond network around the acid is identical, as shown by using the QM/MM calculations for bacteriorhodopsin (Table 3 and Figure 7). The previous discussions about Asp and Glu in proteins should therefore be revisited by using the positive correlation derived in this study instead of the well-established negative correlation derived from benzoic acids. 8