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Abstract

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and Methods
  5. Results and Discussion
  6. Conclusion
  7. Acknowledgements
  8. References
  9. Supporting Information

Ground-state vibrational analyses of firefly luciferin and its conjugate acids and bases are performed. The Gibbs free energies obtained from these analyses are used to estimate pKa values for phenolic hydroxy and carboxy groups and the N–H+ bond in the N-protonated thiazoline or benzothiazole ring of firefly luciferin. The theoretical pKa values are corrected using the experimental values. The concentrations of these chemical species in solutions with different pH values are estimated from their corrected pKa values, and the pH dependence of their relative absorption intensities is elucidated. With the results obtained we assign the experimental spectra unequivocally. Especially, the small peak near 400 nm at pH 1–2 in experimental absorption spectra is clarified to be due to the excitation of carboxylate anion with N-protonated thiazoline ring of firefly luciferin. Our results show that the pKa values of chemical species, which are contained in the aqueous solutions, are effective to assign experimental absorption spectra.


Introduction

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and Methods
  5. Results and Discussion
  6. Conclusion
  7. Acknowledgements
  8. References
  9. Supporting Information

The absorption and fluorescence spectra of firefly luciferin called as luciferin in this article, which is a substrate of bioluminescence reaction, have been studied to understand the mechanism of firefly bioluminescence [1-13]. In particular, the detailed experimental investigations for the absorption and emission of luciferin in aqueous solutions at different pH values have been reported by some groups [3, 6, 7].

It is relatively easy to theoretically predict the absorption process of molecules of modest size. The developments of high-performance computing machinery and ab initio program codes make it possible to optimize ground-state structures and to estimate the relative energies between the ground and excited states and the oscillator strengths of electron excitation for molecules as large as luciferin. Because the intensity of the absorption is proportional to the square of the oscillator strength, the absorption spectra can be assigned by carrying out such calculations.

However, because the luciferin molecule in solutions can take various forms of conjugate bases and conjugate acids as well as the neutral form, we have to identify which form exists depending on the pH values. The chemical structural formula of luciferin and its conjugate acids and bases is shown in Fig. 1. In our previous study [11], we reported the results of density functional theory (DFT) calculations for the electronically excited states of a part of these chemical species, which are luciferin (LH2), Phenolate-LH, Phenol-LH, L2−, LH2-3H+, LH2-3′H+, Phenolate-LH-3H+, Phenolate-LH-3′H+, Phenol-LH-3H+ and Phenol-LH-3′H+ in Fig. 1. We obtained the theoretical results that support the part of the experimental assignment of the spectra and, in addition, we newly suggested the likelihood of containing the excitation of LH2-3H+ at around 400 nm in aqueous solution at pH 1. In this previous study, we noticed that, with the relative magnitude of the absorption intensity in aqueous solution for species in Fig. 1 that depends on their concentrations in solutions as well as oscillator strength for absorption we could understand the absorption processes more satisfactorily.

image

Figure 1. Molecular structures of luciferin and its conjugate acids and bases. The notations used in the previous study [11] were (6′OH, 4COOH) for Luciferin, LH2, (6′O, 4COOH) for Phenolate-LH, (6′OH, 4COO) for Phenol-LH (6′OH, 4COO), (6′O, 4COO) for L2–, (6′OH, 3H+, 4COOH) for LH2-3H+, (6′O, 3H+, 4COOH) for Phenolate-LH-3H+, (6′OH, 3H+, 4COO) for Phenol-LH-3H+, (6′O, 3H+, 4COO) for L2–-3H+, (3′H+, 6′OH, 4COOH) for LH2-3′H+, (3′H+, 6′O, 4COOH) for Phenolate-LH-3′H+, (3′H+, 6′OH, 4COO) for Phenol-LH-3′H+ and (3′H+, 6′O, 4COO) for L2–-3′H+.

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When the pH value of the solution is tuned well experimentally [7], the concentration of species in the S0 state can be predicted using the pKa values for all possible species in the S0 state. The pKa values for some of the species can be measured experimentally. For example, the pKa value for the hydroxy group of Phenol-LH is experimentally known to be 8.7 [3]. However, theoretical evaluation of pKa values for other species is required because the pKa values for them have not been determined.

The purpose of this study is to investigate the absorption process of luciferin in aqueous solution at different pH values based on theoretically estimated pKa values. To obtain the pKa values in the S0 state, we need to optimize the structures of luciferin and its conjugate acids and bases (shown in Fig. 1) and then perform vibrational analyses. The Gibbs free energies calculated in these analyses are used to estimate the pKa values. The details of the calculations are explained in the materials and methods section, and the results are presented in the results and discussion section. The main results are summarized in the conclusions section.

Materials and Methods

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and Methods
  5. Results and Discussion
  6. Conclusion
  7. Acknowledgements
  8. References
  9. Supporting Information

Geometry determination and vibrational analyses in the S0 state and vertical excitation energies

The equilibrium structures of luciferin and its conjugate acids and bases in the S0 state (Fig. 1) were reported previously [11], except for L2−-3H+ and L2−-3′H+; the structures of these two species are determined in this study. In these calculations, hybrid density functional theory (DFT) B3LYP method was used with the aug-cc-pVTZ basis set [14-16]. According to previous theoretical studies [5, 11], the S1 state of luciferin is described by a single-electron excitation from the highest occupied Kohn-Sham orbitals (designated as HOMOs) to the lowest unoccupied Kohn-Sham orbital (designated as LUMOs), wherein the HOMO and LUMO are of π character. This S1 state is a valence excited state in nature as we will discuss later. Because the time-dependent density functional theory (TDDFT) using the B3LYP functional is known to be useful for describing such excited states [17], our theoretical predictions of excitation energies in the absorption spectra were based on the TDDFT calculations performed with the same basis set and functional.

The solvation effect in aqueous solution was taken into account by the polarizable continuum model (PCM) in all the calculations [18]. Because the excitation process is much faster than the movement of solvent molecules, we performed linear-response calculations with nonequilibrium solvation to obtain the excitation energies of the S0 structures.

The vibrational analyses for the S0 equilibrium structures were performed at the same level of calculations as the geometry optimizations. The geometry optimizations and vibrational analyses of H2O and H3O+ in the S0 state were also performed by the B3LYP/aug-cc-pVTZ method with solvent effects. The Gibbs free energies were calculated at 298.15 K and 1.00 atm using unscaled vibrational frequencies. All calculations were performed using the GAUSSIAN09 [19] program.

Estimation of pKa

The acid dissociation reaction of relevant molecules, denoted by AH, in an aqueous solution is assumed to be:

  • display math(1)

Then, the Gibbs free energy of this reaction was used to estimate the pKa values by the following equation:

  • display math(2)

where ∆G (J mol−1), R (JK−1 mol−1) and T (K) correspond to the Gibbs free energy of reaction in Eq. (1), the gas constant and the temperature respectively.

In the case of organic molecules, correction using reference molecules with known pKa values gives reasonable pKa results [20]. In this study, we use the following Eq. (3) to obtain the pKa values for luciferin and its conjugate acids and bases. In Eq. (3), BH is a reference compound which is the same as or similar to the molecules under investigation, and inline image, inline image and inline image are the pKa values calculated, experimentally known and corrected respectively.

  • display math(3)

This is derived from the correction to the free energy of reaction as shown below in which inline image are the calculated, experimental and corrected free energies of reaction respectively. The calculated free energy of reaction was calibrated by the error estimated in the acid dissociation reaction of a reference compound.

  • display math(4)

We can point out that in Eq. (4) the errors caused by approximations in various aspects of the free energy calculations such as the DFT calculations, the treatment of solvation effect and the calculations of the enthalpy and entropy terms using the DFT results are corrected with the experimental values as references. In energy extrapolation methods such as ONIOM and G4 in the field of computational chemistry, additivity is often assumed to give valuable results. Eq. (4) can be regarded as one of such extrapolation methods and is expected to give reliable results [21, 22].

To correct the inline image value for the phenolic OH groups of luciferin and its conjugate bases, the inline image value for the hydroxy group of Phenol-LH, known to be 8.7 experimentally [3], was used. When the pKa values are experimentally unknown, we choose alternate reference compounds keeping in mind that the pKa value is controlled by the stability of the anion, which depends on its electronic nature. In our case, the reference compounds for the O–H bond in carboxy group, N3–H and N3′–H bonds are needed (The N3–H and N3′–H bonds are the N–H+ bonds in the N-protonated thiazoline and benzothiazole rings, respectively, as shown in Fig. 1). We chose the reference compounds as follows: Acetic acid was used as a reference compound to correct the inline image values for carboxy groups. The inline image value for acetic acid is 4.8 [23]. In the cases of the N3–H and N3′–H bonds, the inline image values for protonated benzothiazole [24] and N-methylpropan-2-imine (S. A. Hardinger, private communication, http://www.chem.ucla.edu/harding/lecsups/pKatable30.pdf) were used. The N3 atom in the thiazoline ring of luciferin has a π bond only with C2. Accordingly, the N–H+ bond of protonated N-methylpropan-2-imine is assumed to be similar to that of N3-protonated luciferin. The experimental pKa values for protonated benzothiazole and N-methylpropan-2-imine are 1.2 and 5.5 ([24], Hardinger, private communication) respectively. The structures of protonated benzothiazole and N-methylpropan-2-imine are presented in the Supporting Material for convenience.

Results and Discussion

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and Methods
  5. Results and Discussion
  6. Conclusion
  7. Acknowledgements
  8. References
  9. Supporting Information

pKa values

Table 1 lists the corrected pKa values, inline image, of luciferin and its conjugate bases in the S0 state: the corresponding calculated values, inline image, are shown in Table S1 (see Supplementary Materials). The inline image values for the hydroxy group of both LH2 and Phenol-LH are close to 8, and those for the carboxy group of LH2 and Phenolate-LH are close to 3. The inline image values listed in Table 1 are as expected because these values can be considered as reasonable in light of standard organic chemistry data for pKa values: 8 for phenolic hydroxy groups and 3 for carboxy groups [23]. The inline image value of the hydroxy group (entries 1 and 4) is higher than that of the carboxy group (entries 2 and 3).

Table 1. pKacorr of luciferin and its conjugate bases
Acid dissociation reactionpKacorr
ReactantProduct
  1. a

    Experimental value from ref. [3].

  2. b

    Experimental value from ref. [21].

LH2 + H2OPhenolate-LH + H3O+7.7
LH2 +  H2OPhenol-LH + H3O+2.8
Phenolate-LH + H2OL2– + H3O+3.8
Phenol-LH + H2OL2– + H3O+8.7a
CH3COOH + H2OCH3COO + H3O+4.8b

Table 2 shows the inline image values of luciferin conjugate acids in the S0 state with the N–H+ bond; the corresponding inline image values are shown in Table S2 (Supplementary Materials). Because the pKa values for iminium ions are known to be positive and less than 10 (Hardinger, private communication), we can say that the pKa values for the N–H+ bonds in the N-protonated thiazoline and benzothiazole rings shown in Table 2 are reasonable.

Table 2. pKacorr of luciferin conjugate acid
Acid dissociation reactionpKacorr
ReactantProduct
  1. a

    Experimental value from ref. [22].

  2. b

    Experimental value from ref. [23].

C7H5SNH+ + H2OC7H5SN + H3O+1.2a
NH+(CH3)C(CH3)2 + H2ON(CH3)C(CH3)2 + H3O+5.5b
LH2-3′H+ + H2OLH2 + H3O+−2.8
LH2-3H+ + H2OLH2 + H3O+−5.9
Phenolate-LH-3′H+ + H2OPhenolate-LH + H3O+3.1
Phenolate-LH-3H+ + H2OPhenolate-LH + H3O+1.4
Phenol-LH-3′H+ + H2OPhenol-LH + H3O+−0.4
Phenol-LH-3H+ + H2OPhenol-LH + H3O+1.0
L2–-3′H+ + H2OL2– + H3O+5.0
L2–-3H+ + H2OL2–  + H3O+7.2

As shown in Table 2, deprotonation of the phenolic hydroxy group increases the inline image value for N3–H bond drastically; the values for N3–H bond in Phenol-LH-3H+ and L2−-3H+ are 1.0 and 7.2, respectively, and those in LH2-3H+ and Phenolate-LH-3H+ are −5.9 and 1.4 respectively. The phenolate anion derived upon deprotonation of the phenolic hydroxyl group on the benzothiazole ring results in a resonance structure with a p-benzoquinone imine moiety as shown in Fig. 2, in which there is a negative charge at N3 in the thiazoline ring. Therefore, the pKa values for the N3–H bond in the molecules having a phenolate anion moiety are higher than those in the molecules having a phenolic OH group.

image

Figure 2. Resonance structure with a p-benzoquinone imine moiety for Phenolate-LH and L2–.

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It is needed to demonstrate the validity of reference compounds. We examined this by estimating the inline image value for the N3–H bond of luciferin using other reference compounds. The inline image values for protonated benzylidene benzylamine [25], 2-methyl-2-oxazoline and 2-phenyl-2-oxazoline [26] shown in Fig. S1 were used in the preliminary calculations. In the case of luciferin, the thiazoline ring including the N3 atom is connected with the aromatic benzothiazole ring. Taking into account electronic effects by this aromatic substituent, protonated benzylidene benzylamine was expected to be a good reference compound for estimating the inline image value for the N3–H bond of N3-protonated luciferin. Also, 2-methyl-2-oxazoline or 2-phenyl-2-oxazoline has the potential to be reasonable reference compounds because the oxazoline ring in these compounds is yielded by simply replacing the S atom in the thiazoline ring by its congener O atom.

In contrast with these anticipations, whereas the relative absorption intensities obtained using these reference compounds were completely different from the experimental spectra, the relative absorption intensities using the pKacorr values that were obtained using N-methylpropan-2-imine as the reference compound reproduce the experimental spectra well as will be discussed later. These results show that protonated N-methylpropan-2-imine is a better reference compound for N3-protonated luciferin. Moreover, we can say that the N3 atom in luciferin has received few influence from the other atoms in the five-membered ring.

Concentrations of chemical species

The energies for excitation from the S0 state to some low-lying singlet excited states in the seven conjugated acids are shown with the oscillator strengths in Fig. 3. The S1 state of these molecules corresponds to the excitation from the HOMO to the LUMO, wherein HOMO and LUMO are of π character. These orbitals at the S0 equilibrium structures are shown in Fig. S2. Figure S3 shows the relationship between excitation energy and the HOMO–LUMO gap at the S0 structure. The corresponding results for luciferin and its conjugated bases were reported in ref. [11]. According toin ref. [11] and Fig. 3, the excitation energies of the 12 species are in the experimentally scanned range of absorption spectra. Whether or not their absorption spectra appear in the experiments depends on their concentrations in the S0 state.

image

Figure 3. Oscillator strength for (a)LH2 -3′H+, (b) Phenol-LH-3H+, (c) Phenol-LH-3′H+, (d) Phenolate-LH-3H+, (e) Phenolate-LH-3′H+, (f) L2–-3H+ and (g) L2–-3′H+.

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To estimate the concentrations, first let us consider the following acid dissociation reactions in a cation, AH3+, a neutral species, AH2, and an anion, AH, for which the acid dissociation constants are inline image respectively.

  • display math(5)
  • display math(6)
  • display math(7)

Then, the concentrations of the cation, the anion and the dianion relative to that of the neutral species can be presented as a function of the solution pH and Ka values as shown in Eq. (8).

  • display math(8)

Then, we can determine the relative concentrations of the species. For instance, because the pKa value for the hydroxy group of Phenol-LH is 8.7, the relationship between the concentrations of Phenol-LH and L2− in an aqueous solution at pH 10 is given by following equation:

  • display math(9)

Using the relative concentrations, we can estimate the molar fraction of luciferin and its conjugate acids and bases.

Figure 4 and Table 3 show the molar fraction of each species as a function of pH. The concentrations of some of L2−, Phenol-LH, L2−-3H+, LH2 and Phenol-LH-3H+ in solution at every pH value are high, and the contributions from the other species in the absorption spectra are low.

Table 3. Molar fraction of luciferin and its conjugate acids and bases in the S0 state. Eabsexp is the experimental absorption energy in nanometers [ref. [7]]. Eabscal is the theoretical absorption energy in nanometers
 Eabscal (Eabsexp)pH
1086421
  1. a

    These calculated energies were reported in ref. [11].

L2–430a(390)0.950.161.9 × 10−31.8 × 10−52.7 × 10−83.0 × 10−10
Phenol-LH352a(310)0.0480.810.970.910.130.015
Phenol-LH-3H+4155.3 × 10−119.0 × 10−81.1 × 10−51.0 × 10−30.0150.017
Phenol-LH-3′H+4771.7 × 10−123.0 × 10−93.5 × 10−73.3 × 10−54.8 × 10−45.5 × 10−4
Phenolate-LH4465.6 × 10−79.6 × 10−61.1 × 10−51.1 × 10−51.5 × 10−61.8 × 10−7
Phenolate-LH-3H+4891.5 × 10−152.5 × 10−123.0 × 10−102.8 × 10−84.2 × 10−74.7 × 10−7
Phenolate-LH-3′H+5277.6 × 10−141.3 × 10−101.5 × 10−81.4 × 10−62.1 × 10−52.4 × 10−5
LH2342a3.0 × 10−95.2 × 10−66.1 × 10−40.0580.850.97
LH2-3H+426a4.2 × 10−257.2 × 10−208.6 × 10−168.1 × 10−121.2 × 10−81.3 × 10−7
LH2-3′H+409a4.8 × 10−228.1 × 10−179.7 × 10−139.2 × 10−91.3 × 10−51.5 × 10−4
L2−-3H+4861.6 × 10−30.0270.0320.0304.4 × 10−35.0 × 10−4
L2−-3′H+5179.9 × 10−61.7 × 10−42.0 × 10−41.9 × 10−42.8 × 10−53.1 × 10−6
image

Figure 4. Molar fraction of luciferin and its conjugate acids and bases. Black line with open circle: Phenol-LH; red line with open circle: L2–; green line with open circle: LH2; blue line with open circle: Phenolate-LH; black line with full box: Phenol-LH-3H+; black line with open box: Phenol-LH-3′H+; red line with full box: L2–-3H+; red line with open box: L2–-3′H+; green line with full box: LH2-3H+; green line with open box: LH2-3′H+; blue line with full box: Phenolate-LH-3H+; blue line with open box: Phenolate-LH-3′H+.

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As shown in Fig. 4, in aqueous solution at pH 10, the concentration of L2− is the highest. The number of Phenol-LH molecules is 5% of that of L2− molecules. Compared with the pH 10 results, in aqueous solution at pH 8, the relative ratio of the concentration of Phenol-LH to that of L2− is reversed. As shown in Table 3, 81% of the solute molecules in this aqueous solution are Phenol-LH and the concentration of L2− falls to 16%.

In aqueous solution at pH 6, 97% of the solute molecules take the form Phenol-LH. As shown in Fig. 4, the concentration of the second most abundant species, L2−-3H+, is 3.3% of that of Phenol-LH, and the concentration of the third most abundant component, L2−, is only 0.2% of that of Phenol-LH. At pH 4, 91% of the solute molecules remain as Phenol-LH. As shown in Fig. 4, the concentration of the second most abundant form in this solution, LH2, is much higher than that in the pH 6 solution, and its concentration is 6.4% of that of Phenol-LH.

Compared with the pH 4 results, in aqueous solution at pH 2, the relative ratio of the concentration of Phenol-LH to that of LH2 is reversed. The form Phenol-LH-3H+ is the second most abundant, its concentration being 15% of that of the most abundant species, LH2. At pH 1, 97% of the molecules are LH2. The concentrations of the second and third most abundant forms, Phenol-LH-3H+ and Phenol-LH, are 1.8% and 1.5% of that of LH2 respectively.

Relative absorption intensities for chemical species at various pH values

The relative intensities of absorption of the species in solution were evaluated as a product of the molar fraction of the species at the various pH values and the oscillator strength for the excitation. The theoretical absorption intensities thus obtained are shown against the excitation energies calculated by the TDDFT method in Fig. 5. According to the experimental spectra [7], the width of the absorption peak at pH 10 can be estimated as 0.2 eV. This peak is due only to the excitation of a single species, the S0–S1 excitation of L2− molecules. Thus, in Fig. 5, the width of the Gaussian line shape for the peaks of the other species is assumed to be 0.2 eV.

image

Figure 5. Theoretical Excitation Energy and Relative Absorption Intensity at pH 1, 2, 4, 6, 8 and 10.

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The difference between the theoretical excitation energies at the TD-B3LYP/aug-cc-pVTZ level and the experimental ones is nearly 30 nm. This difference is nonessential in our study because the relative values of the theoretical excitation energies agree well with those of the experimental ones.

Next, the contributions of chemical species in Fig. 1 in the experimental absorption spectra are discussed using the relative absorption intensities in Fig. 5. As shown in Fig. 5(a), the absorption intensity for the excitation of L2− is the largest in the pH 10 aqueous solution. The absorption intensity due to Phenol-LH is quite small. On the other hand, the excitation in Phenol-LH gives the largest absorption intensity in solution at pH 8, as shown in Fig. 5(b). There are two peaks due to the excitation of L2−. One of the peaks is hidden, and the intensity of another peak near 420 nm is 25% of that of the main peak of Phenol-LH. It is found that there is also a small peak for the excitation of L2−-3H+ at higher than 500 nm. It could not be measured because it is hidden by the peak of L2−.

In aqueous solution at pH 6, the excitation of Phenol-LH has the largest absorption intensity. As shown in Fig. 5(c), the second largest intensity is possessed by the excitation of L2−-3H+, and not L2−. Compared with the relative absorption intensities in solution at pH 6 in Fig. 5(c), those at pH 4 in Fig. 5(d) include the excitation of LH2. Because the excitation energy of LH2 is close to that of Phenol-LH, their absorption peaks overlap.

As shown in Fig. 5(e), it is clear that the relative intensity for the excitation of LH2 is the largest in solution at pH 2. The peak corresponding to the excitation of Phenol-LH is obscured because its excitation energy is close to that of LH2. The relative intensity for the excitation of Phenol-LH-3H+ is ca 20% of that of LH2.

The absorption intensity for the excitation of LH2 is the largest in solution at pH 1, as shown in Fig. 5(f). The second largest relative intensity corresponds to the excitation of Phenol-LH-3H+. The relative intensity for the excitation of Phenol-LH is very small. Comparison between the absorption intensities in Fig. 5(f) and the experimental spectra [7] strongly suggests that the peaks corresponding to the S1–S3 excited states of Phenol-LH-3H+ (Fig. 3[b]) appear near 400 nm in the absorption spectra.

The results in Fig. 5 can clearly account for the experimental absorption spectra, to suggest that the pKa values are needed to obtain the correct relative intensities among chemical species. The comparison between the experimental absorption spectra and the relative absorption intensities reveals the hidden peaks due to the minor chemical species. These results would be useful to understand the detail of emission processes of luciferin.

According to the above results and the results of the previous study [11], we finally obtained the following assignment for the absorption spectra of luciferin in aqueous solution: at pH 10 the absorption peak of only L2− appears; at pH 8, main absorption peak due to Phenol-LH and a weak absorption peak due to L2− are observed; the absorption peak due to Phenol-LH appears at pH 4–6 and the main absorption peak due to LH2 and a weak absorption peak due to Phenol-LH-3H+ appear at pH 1–2. The comparison of the assignment in this study with that of the previous one [11] is shown in Table 4, which clearly indicates the achievements obtained here. These results also show that not only the absorption energies but also pKa values are useful to assign experimental absorption spectra in aqueous solutions.

Table 4. Assignment for peaks at around 330 and 400 nm of the experimental absorption spectra in the previousa and this study. That in italics is for the peak hidden by the main peak
 330 nm400 nm
Previous studyaThis studyPrevious studyaThis study
  1. a

    Ref. [11].

pH 10S2–S3 of L2−S2–S3 of L2−S1 of L2−S1 of L2−
pH 8S1–S3 of Phenol-LHS1–S3 of Phenol-LHS1 of L2−

S1 of L2−

S1 of L2-3H+

pH 6S1–S3 of Phenol-LHS1–S3 of Phenol-LH
pH 4S1–S3 of Phenol-LH

S1–S3 of Phenol-LH

S1–S3 of LH2

pH 2S1 of LH2

S1–S3 of LH2

S1–S3 of Phenol-LH

Phenol-LH

-3H +
S1 of LH2–3H+S1–S3 of Phenol–LH–3H+
pH 1

S2 of LH2–3H+

S1 of LH2

S1–S3 of LH2

S4, S5 of Phenol–LH–3H+

S1 of LH2–3H+S1–S3 of Phenol–LH–3H+

Let us examine more closely the difference in assignment between the present and previous studies [11] shown in Table 4. According to the studies over the last few decades, the structure of luciferin is considered to be L2− in basic solution and Phenol-LH in acidic solution [1-10]. The oscillator strength and excitation energy for L2− and Phenol-LH by the semi empirical calculations supported these results [5, 9]. The oscillator strengths obtained by ab initio quantum chemical calculations are nowadays commonly used to assign absorption spectra [27], and this conventional method was used to understand the absorption spectra of luciferin [8]. Following these results, in ref. [11] we used ab initio calculations of the oscillator strengths and excitation energies for luciferin and its conjugate acids and bases to assign absorption spectra for luciferin over a wider range of pH values [7]. The characteristic of experimental absorption spectra in ref. [7] is the peak near 400 nm in the strongly acidic solution. To assign this peak, we had paid attention in our previous study to the N3-protonated chemical species of LH2. We had found that the calculated excitation energy to the S1 state of LH2-3H+ is near 426 and ca 400 nm before and after calibration of the difference between the theoretical and experimental excitation energies. We had also found that the corresponding oscillator strength of this species is large. Then, in ref. [11], it had been concluded that LH2-3H+ was an origin of the peak near 400 nm in the strongly acidic solution, as shown in Table 4. From the present study, it is concluded that Phenol-LH-3H+ is an origin of the peak near 400 nm in the strongly acidic solution. It means that in the case in which absorption peaks are overlapped, the conventional method is not enough to assign spectra.

According to this study, the relative absorption intensities obtained by both oscillator strengths and concentrations given by the pKa values for chemical species in aqueous solutions are useful to assign the absorption spectra depending on the pH values. The pKa values for luciferin and its conjugate acids and bases shown in Tables 1, 2 will be used to assign its fluorescence spectra which will be reported elsewhere.

Conclusion

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and Methods
  5. Results and Discussion
  6. Conclusion
  7. Acknowledgements
  8. References
  9. Supporting Information

Vibrational analyses in the ground state for firefly luciferin and its conjugate acids and bases were performed. The Gibbs free energies obtained from these analyses were used to estimate the pKa values. Instead of performing large-scale calculations, which included a large number of solvent molecules, the theoretical pKa values were corrected using the experimental ones for the 6′OH and 4COOH groups and the N3H and N3′H bonds of luciferin. These corrected pKa values are reasonable in light of the known pKa values of organic molecules.

The concentrations of luciferin and its conjugated acids and bases were estimated from their corrected pKa values. The relative absorption intensity for each excitation at different pH values was obtained. From these data, it is found that the small peak near 400 nm at pH 1–2 in the experimental absorption spectra [7] is due to the excitation of Phenol-LH-3H+. The pKa values of chemical species, which are contained in the aqueous solutions, are effective to assign the experimental absorption spectra.

A similar analysis is possible for oxyluciferin because its structure involves a simple substitution of the carboxy group in luciferin by a hydroxy group. Information on pKa values for oxyluciferin could be used to understand the assignment of fluorescence processes of oxyluciferin in the spent luminescence solution.

Acknowledgements

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and Methods
  5. Results and Discussion
  6. Conclusion
  7. Acknowledgements
  8. References
  9. Supporting Information

Calculations were carried out at the computer center of Nagoya University. Helpful conversations with Dr Yu Wang of the University of Tokyo and Dr Masaki Tsukamoto of Nagoya University are gratefully acknowledged.

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  5. Results and Discussion
  6. Conclusion
  7. Acknowledgements
  8. References
  9. Supporting Information
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Supporting Information

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and Methods
  5. Results and Discussion
  6. Conclusion
  7. Acknowledgements
  8. References
  9. Supporting Information
FilenameFormatSizeDescription
php12052-sup-0001-TableS1-S2-FigS1-S3.docxWord document8606K

Table S1. inline image of luciferin and its conjugate bases.

Table S2. inline image of luciferin conjugate acids.

Figure S1. Molecular structure for reference molecules.

Figure S2. HOMO and LUMO at the S0 structure of the chemical species in Fig. 3.

Figure S3. Relationship between excitation energy and the HOMO–LUMO gap at the S0 structure.

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