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 pKa 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, νC=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 a).[9]

Figure 1

(a) νC=O of protonated (COOH) and deprotonated (COO–) carboxylic acids. COO– has the high-frequency asymmetric (asym) and the low-frequency symmetric (sym) stretching modes. (b) Observed correlation between νC=O and pKa in benzoic acids. (c) Relationship between νC=O and pKa in saturated acids. It was notreported.

νC=O of COOH in proteins can be an indicator of the pKa shifts of Asp and Glu in active sites because pKa and νC=O are affected by the surrounding (protein) environment. Infrared spectroscopy using benzoic acid analogues[8,10] showed a negative correlation between the pKa and νC=O, in which νC=O decreased as the pKa increased (Figure b). On the basis of this negative correlation, the observed values of νC=O have been discussed in relation to the pKa of carboxylic acids.[11,12]

A light-driven proton-pumping membrane protein, bacteriorhodopsin, shows different νC=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 νC=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 pKa than that in the M state (1761 cm–1)[11] on the basis of the negative correlation between the νC=O and pKa derived from benzoic acids.[8,10] However, pKa(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 pKa(Asp85). A decrease in pKa(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 pKa(Asp85) in the N state estimated from νC=O is not consistent with the reaction mechanism of bacteriorhodopsin.

For deprotonated saturated carboxylic acids (COO–), a correlation between the asymmetric vibrational frequency and pKa was reported; the frequency increased as pKa decreased.[9,16] For protonated saturated carboxylic acids (COOH), the relationship between νC=O and H-bond structures was reported; νC=O decreased as the number of H-bonds increased.[17−19] However, to the best of our knowledge, the correlation between νC=O and pKa remains unclear (Figure c), 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 pKa value by using an electrostatic-potential approach and the νC=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 ). 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.[20]

Figure 2

Chemical structure of (a) benzoic acid analogues and (b) acetic acid analogues with distances rC=O, rOO, and rOH. 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[100] form).

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)[21] and the N′ state (V49A mutant) at a resolution of 1.62 Å (PDB code, 1P8U).[21] 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.[22] 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[23] 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 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.[24]

pKa Calculation of Bacteriorhodopsin Asp85

The computation was based on the electrostatic continuum model by solving the linear Poisson–Boltzmann equation using the MEAD program.[25] To obtain the absolute pKa 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 pKa value (e.g., 4.0 for Asp[26]). The difference in the pKa value of the protein relative to the reference system was added to the known reference pKa value. The experimentally measured pKa values used as references were 7.2 for the Schiff base,[27,28] 12.0 for Arg, 4.0 for Asp, 9.5 for Cys, 4.4 for Glu, 10.4 for Lys, 9.6 for Tyr,[26] and 7.0 and 6.6 for the Nε and Nδ atoms of His, respectively.[29−31] 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.[32] 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 pKa 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, νC=O, were investigated for a series of protonated benzoic acid analogues (Table and Figure a) and acetic acid analogues (Table and Figure b). In benzoic acids, the calculated νC=O negatively correlates with the measured pKa value (Figure a),[10] which is consistent with the infrared spectroscopy results (Figure b).[8,10] In contrast, the calculated νC=O positively correlates with the measured pKa value[33] in acetic acids (Figure c). A similar positive correlation between the calculated νC=O and the measured pKa was also observed for hydroxycarboxylic acid analogues (Table S1, Figures S1 and S2).

Table 1

Series of Analogues of Benzoic Acida

name	structureb	R1b	R2b	pKac
3-bromobenzoic acid	1	Br	-	3.85
3-hydroxybenzoic acid	1	OH	-	4.14
3-aminobenzoic acid	1	NH2	-	4.40
3-methylbenzoic acid	1	CH3	-	4.31
4-bromobenzoic acid	2	Br	-	4.01
4-aminobenzoic acid	2	NH2	-	4.90
4-methylbenzoic acid	2	CH3	-	4.40
3-methyl-4-chloro-benzoic acid	5	CH3	Cl	4.07
3-methyl −4-bromo-benzoic acid	5	CH3	Br	4.03
3-chloro-4-methylbenzoic acid	5	Cl	CH3	4.06
3-bromo-4-methylbenzoic acid	5	Br	CH3	3.96
2-chloro-3-methylbenzoic acid	3	Cl	CH3	3.00
2-bromo-3-methylbenzoic acid	3	Br	CH3	3.90
2-methoxy-3-methylbenzoic acid	3	OCH3	CH3	3.84
2-chloro-4-methylbenzoic acid	4	Cl	CH3	3.27
2-bromo-4-methylbenzoic acid	4	Br	CH3	3.09
3-methyl-6-chlorobenzoic acid	6	Cl	CH3	3.12
3-methyl-6-bromobenzoic acid	6	Br	CH3	3.00
3-nitrobenzoic acid	1	NO2	-	3.53
4-nitrobenzoic acid	2	NO2	-	3.46
2-nitro-3-methylbenzoic acid	3	NO2	CH3	2.91
3-methyl-4-nitrobenzoic acid	5	NO2	CH3	3.65
3-nitro-4-methylbenzoic acid	5	CH3	NO2	3.62
3-methyl-6-nitrobenzoic acid	6	NO2	CH3	2.55
2-nitro-4-methylbenzoic acid	4	NO2	CH3	2.68

A previous experimental study reported that these compounds showed a negative correlation between pKa and νC=O.[8,10]

See Figure a.

Reference (10).

Table 2

Series of Analogues of Acetic Acid

name	structurea	Xa	pKab
bromoacetic acid	7	Br	2.86
iodoacetic acid	7	I	3.12
chloroacetic acid	7	Cl	2.86
fluoroacetic acid	7	F	2.66
acetic acid	7	H	4.76

See Figure b.

Reference (33).

Figure 3

Correlation between the measured pKa and νC=O. (a) Calculated νC=O of benzoic acids shown in Table and Figure a. The determination coefficient R2 is 0.91. (b) Measured νC=O of benzoic acids.[10]R2 is 0.94. (c) Calculated νC=O of acetic acids shown in Table and Figure b. R2 is 0.84. The solid line indicates the fitting line for F, Br, Cl, and I (R2 = 0.92). The dotted line indicates the fitting line for F, Br, Cl, I, and H for comparison (R2 = 0.85).

Table 3

Calculated pKa, Distances of the O–H (rOH) and C=O Bonds (rC=O), the H-Bond Distance of OAsp85-H···OH (rO···O), and the Calculated and Observed νC=O Values for Asp85 in Bacteriorhodopsin

		calculation			experimenta
state	Schiff baseb	pKa	rOH (Å)	rO···O (Å)	rC=O (Å)	νC=O (cm–1)	νC=O (cm–1)
M	deprotonated	13.2	0.998	2.642	1.208	1827	1761
N′c	protonated	7.0	1.000	2.544	1.216	1785	1756

Reference (15).

Protonation state of the retinal Schiff base.

The observed νC=O values of Asp85 in the N and N′ states were the same.[36]

As pKa increases, the C=O bond distance (rC=O; Figure a) increases in benzoic acids (Figure a). On the other hand, it decreases in acetic acids as pKa increases (Figure c). In benzoic acids, the distance of the C–C bond (rC–C; Figure a) connecting the benzene ring to the carboxylic group also correlates with the measured pKa value (Figure b). The calculations for various H-bond structures show that νC=O decreases as the number of H-bonds increases (Figure S3), as previously reported.[17−19]

Figure 4

Correlation between the measured pKa and the calculated distances. (a) C=O bond distance (rC=O) of benzoic acids. R2 is 0.93. (b) C–C bond distance (rC–C) of benzoic acids. R2 is 0.84. (c) C=O bond distances (rC=O) of acetic acids. The solid line indicates the fitting line for F, Br, Cl, and I for comparison (R2 = 0.86). The dotted line indicates the fitting line for F, Br, Cl, I, and H for comparison (R2 = 0.54).

In both benzoic acids and acetic acids, the O–H distance of the protonated carboxylic group (rOH; Figure ) increases as pKa decreases (Figure S4c,d). The same trend has been reported in a DFT study of chlorophenols.[34] This is because as pKa decreases, the deprotonation is facilitated and the proton departs from the donor O atom; thus, rOH increases. In addition, the H-bond distance between the oxygen atoms of the carboxylic acid and the water molecule, rO...O (Figure ), decreases as pKa decreases in both cases (Figure S4a,b). This is because the H-bond distance tends to shorten as the pKa difference between the donor (carboxylic group) and acceptor (water molecule) moieties approaches zero,[35] forming a low-barrier hydrogen bond (LBHB).

The correlation between rC=O and pKa in acetic acids (Figure c) is opposite to that observed for benzoic acids (Figure a) because of the opposite correlations between rOH and rC=O [positive for acetic acids (Figures c and S4d) and negative for benzoic acids (Figures a and S4c)]. Because νC=O is determined by the C=O bond strength, νC=O increases as rC=O decreases (being a stronger C=O bond), thus corroborating the results of a previous DFT study on carboxylic acids.[18]

The positive and negative correlations between rOH and rC=O in acetic acids and benzoic acids can be explained by the presence or absence of a C=C double bond (Figures and 6). Acetic acids have no C=C bonds conjugated with the carboxylic group (Figure ). 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 rC=O than the typical C=O bond distance (Figure b). In contrast, benzoic acids have a C=C bond on the phenyl group conjugated with the carboxylic group (Figure ). When benzoic acids have an electron-donating substituent (e.g., NH2), the excess electrons are localized on the benzene ring (Figure a). As the deprotonated carboxylic group is destabilized by repulsive interactions with these excess electrons, pKa 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 (rC=O). When benzoic acid has an electron-accepting substituent (e.g., NO2), the substituent extracts an electron, yielding a positive partial charge on the benzene ring (Figure b). As the deprotonated carboxylic group is stabilized by attractive interactions with the positive partial charge, pKa decreases. Simultaneously, the C–C bond connecting the carboxylic group to the benzene ring has a single-bond nature exclusively, resulting in a longer rC–C (Figure b). The bond alternation effect becomes more pronounced and strengthens the C=O bond, resulting in a short C=O distance (rC=O). Thus, aspartic acids and benzoic acids show positive and negative correlations, respectively, between rOH and rC=O and between pKa and νC=O.

Figure 5

Correlation between rOH and rC=O in benzoic acids. (a) 4-Aminobenzoic acid with pKa = 4.9.[10] (b) 2-Methyl-6-nitrobenzoic acid with pKa = 2.6.[10] The calculated values of νC=O, rOH, rC=O, and rC–C are shown.

Figure 6

Correlation between rOH and rC=O in acetic acids. (a) Acetic acid with pKa = 4.8.[33] (b) Fluoroacetic acid with pKa = 2.7.[33] The calculated values of νC=O, rOH, and rC=O are shown.

Bacteriorhodopsin

We investigated the correlation between νC=O and pKa 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 pKa 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 a). In the initial BR state, Asp85 is deprotonated[13,14,37] and Asp96 is protonated;[13−15,21] the Glu194/Glu204 pair shares one proton;[38] 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.[39,40] Subsequently, it changes to a standard 13-cis form during the transition from the K to L state, removing the twist.[14,39,41] 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[42,43]) 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.[13−15,36] The N state transitions to the N′ state with proton intake from the cytoplasmic side to Asp96.[14,21,36] 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.[13−15,42] Here, we focus on the M and N′ intermediate states (Figure a).

Figure 7

Structure of bacteriorhodopsin. (a) Intermediate states in the cyclic reaction and titratable sites involving the proton pump function in bacteriorhodopsin. The light enegy induces the first transiton from the initial BR state to the J intermediate state. The proton transfer from Asp96 to the retinal Schiff base bonded to Lys216 (red arrow) occurs during the transition from the M to N states. The proton transfer from the cytoplasmic side to Asp96 (blue arrow) occurs during the transition from the N to N′ states. QM/MM-optimized structures of the (a) M and (b) N′ states with calculated νC=O(Asp85). The black arrows indicate the C=O bond of Asp85. The blue label indicates the O...O distance between Asp85 and the adjacent water molecule (W603).

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 νC=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.[36] 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 νC=O and pKa of the wild type are similar to the N′ state of the V49A mutant.

By use of the electrostatic method, pKa(Asp85) was calculated to be 13.2 (Table ), which is consistent with the value of >11 estimated by FTIR analysis.[43] 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 [νC=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 and Table ), 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 νC=O and pKa (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.[38] A quantitative investigation of the relationship between νC=O and pKa using an identical structure will be needed in the future.

The QM/MM-optimized geometry shows that the O–H bond distance, rOH, in the N′ state is longer than that in the M state, whereas the C=O bond distance, rC=O, in the N′ state is shorter than that in the M state (Table ). The O–O distance, rO···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 pKa(Asp85) decreases. These tendencies are the same as those in acetic acids and can be explained by a similar scheme (Figure ): 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 rC=O than the typical C=O bond distance (Figure a–c).

Figure 8

Correlation between rOH and rC=O of Asp85 in bacteriorhodopsin: (a) M state and (b) N′ state. The calculated values of νC=O, rOH, and rC=O are shown. (c) Extreme case wherein Asp85 is deprotonated, i.e., pKa(Asp85) ≪ 7.

The lower pKa(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 pKa(Asp85) value should not be less than 7, and (ii) as the Schiff base is also protonated in the N′ state, the pKa(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 c). Thus, a decrease in the νC=O of Asp85 observed in bacteriorhodopsin during the transition from the M to N′ (N) state is attributable to a decrease in the pKa 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[21] compared with that of the M state[44] (Figure S5). The downshift of νC=O observed in bacteriorhodopsin during the transition from the M to N′ (N) state can be explained by the decrease in pKa(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 pKa and νC=O (Figure b). In contrast, when carboxylic acid has no conjugated C=C bond (i.e., saturated carboxylic acids), a positive correlation exists (Figure a). Note that these correlations cannot be used when the H-bond structures are not identical. Indeed, the slope and intercept of the fitting line depend on the number of water molecules H-bonded with the carboxylic group (Figure S3), although this tendency does not depend on it.

Figure 9

Schematic image of the correlation between pKa and νC=O: (a) saturated carboxylic acids (e.g., Asp); (b) unsaturated carboxylic acids (e.g., benzoic acids).

The pKa 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 νC=O value of acetic acids increases as pKa decreases (Figure a), whereas in benzoic acids, νC=O decreases as pKa decreases (Figure c). The correlation between pKa and νC=O depends on the presence or absence of the C=C double bond conjugated with the carboxylic group (Figures and 6). These findings can be extended to general saturated or unsaturated carboxylic acids: the pKa and νC=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 ). 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 and Figure ). 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.[8,10]