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Abstract

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

The time-dependent characteristics of firefly bioluminescence initiated by manual injection of adenosine triphosphate (ATP) into buffer solution containing luciferin (Ln), luciferase (Luc) and Mg2+ were measured with a resolution of 10 ms, and compared with those obtained by photolysis of caged ATP. The time course depends on pH; both rise and decay rates decrease when pH is lowered from 7.8 to 6.8. In contrast, the parameter λ in the kinetic formula related to diffusion of ATP is almost independent of pH. The pH dependence of the time course of bioluminescence can be explained by the same pH tendency as the rate of ATP binding at the active site of Luc. The time-resolved spectra can be decomposed into two Gaussian components with maxima at 2.2 and 2.0 eV. At pH 7.8, the band at 2.2 eV is more intense than that at 2.0 eV for all three concentration conditions. At lower pH, the band at 2.2 eV becomes weaker than that at 2.0 eV. The intensity ratio of the 2.0 and 2.2 eV bands is constant for duration time of 600 s for both injection and photolysis experiments, and the above conclusions are unaffected by the concentration ratio [Ln]/[Luc].


Introduction

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

Firefly bioluminescence is generated by the enzymatic reaction of the substrate D-luciferin (Ln) with luciferase (Luc) in the presence of oxygen and Mg2+ to reach the electronically excited state of oxyluciferin (Oxyln), and has drawn the curiosity of researchers for many years. In 1959, the quantum yield of bioluminescence for the fireflies Photinus pyralis was reported to be 88% ± 25% at pH 7.6 [1]. In a recent reverification experiment, however, the quantum yield was 41.0% ± 0.7% and spectral analysis gave three components with maxima at 2.2, 2.0 and 1.85 eV [2]. In addition, the color change from yellow-green to red with a decrease in pH was assigned to a decrease in the intensity of the band at 2.2 eV [2]. Although the color of firefly bioluminescence can be modulated by the addition of metal ions other than Mg2+, or mutation of some Luc amino acid residues, this mechanism is still not fully understood [3]. White et al. assigned red and yellow-green bioluminescence to the keto and enol forms of the excited state of Oxyln respectively [4, 5]. However, Branchini et al. observed both red and yellow-green bioluminescence from the keto form of 5,5-dimethyloxyluciferin [6]. In contrast, McCapra proposed that the color variation was a result of different geometrical structures of Oxyln in its electronically excited state based on quantum chemical calculations [7]: the yellow-green bioluminescence is from the planar structure of Oxyln in its excited state, whereas the red arises from the orthogonal conformation of the excited state in which the benzothiazole and thiazoline rings of Oxyln are twisted around the C2–C2′ bond. Nakatsu et al. clarified the crystal structure of Luc from Luciola cruciata (Genji botaru) with Oxyln binding at its active site by X-ray diffraction [8]. They assigned the yellow-green bioluminescence to Oxyln rigidly constrained by the hydrophobic isoleucine in the active site of Luc, and the red bioluminescence to relaxation of the constraint induced by a change in the hydrogen-bonding network of the amino acid residues around the active site of Luc. Despite the several models given above, the mechanism of the color change has not yet been unambiguously clarified [9, 10].

We have already identified several reaction characteristics through kinetic analysis in the millisecond time range of in vitro firefly bioluminescence using photolytic reactions of caged adenosine triphosphate (cATP) [11]. However, for the ordinary method of in vitro firefly bioluminescence initiated by manually injecting an ATP solution into a solution of Luc and Ln containing Mg2+, there is very little data on bioluminescence intensity changes in the millisecond range. Accordingly, we developed a time course measurement system that accurately records the origin of the time scale at the instant of ATP injection. We also measured time-resolved bioluminescence spectra using a multichannel photomultiplier system to obtain information about the aforementioned color change. This kind of measurement is not possible using conventional multichannel photodiode arrays because of their low sensitivity. Here, we report real-time progression of the total light intensity and spectrum of in vitro firefly bioluminescence together with their dependence on pH and reactant concentrations. The variation and characteristics of the bioluminescence mechanism are clarified by comparison with results obtained from photolysis of cATP.

Materials and Methods

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

Materials

Measurements were carried out for three different concentration conditions at each of three pH values (6.8, 7.0 and 7.8), as presented in Table 1. Ln (Sigma, St. Louis, MO), Luc (Sigma), MgSO4 (Wako, Osaka, Japan), ATP (Calbiochem, La Jolla, CA) and cATP (Dojindo laboratory, Kumamoto, Japan) were each diluted with pH-adjusted 4-(2-hydroxyethyl)-1-piperazineethane sulfonic acid (HEPES). A quantity of 0.25 mL of each Ln, Luc, MgSO4, HEPES buffer solution and ATP or cATP were prepared to give a total of 1.00 mL excluding ATP for measurements by ATP injections or 1.25 mL mixing all the reagent solutions for measurements by cATP photolysis, which was placed in a 10 mm × 10 mm × 50 mm quartz cell. As shown in Table 1, concentration conditions 1 and 2 are for measurements by ATP injections and concentration condition 3 is for the measurement by cATP photolysis. To verify the effect of concentration conditions on the bioluminescence spectra and their time evolution, concentration conditions 1 and 2 were set with [Ln] > [Luc] and with [Ln] < [Luc] respectively. For concentration condition 3, cATP was photolyzed with the third harmonic of a Nd:YAG laser (355 nm), and the amount of generated ATP is estimated as 0.016 mm [11]. The chemical reaction of bioluminescence was carried out at room temperature (20–25°C).

Table 1. Concentration conditions for measurements (mm). The pH of HEPES buffer was adjusted to 6.8, 7.0 or 7.8 for each concentration condition
 Concentration 1Concentration 2Concentration 3
D-luciferin0.0451.1 × 10−40.045
Luciferase1.6 × 10−39.9 × 10−30.80
MgSO40.501000.50
ATP0.660.99(0.016)
cATP0.80

Time course measurement

To observe the time course of bioluminescence by ATP injection in the millisecond range, we developed a measurement system in which the time origin is determined as the instant when ATP is injected into the quartz cell. The quartz cell was irradiated by the third harmonic of a Nd:YAG pulsed laser (355 nm) electrically synchronized with ATP injection by a micropipette, and the signal caused by Ln fluorescence (~520 nm) was regarded as the time origin of measurements. The diameter of the laser beam was 6 mm. The bioluminescence from each sample was narrowed with a 6 mm aperture, focused by a convex lens, passed through a band-pass filter (530–610 nm), detected by a photomultiplier tube (R585, Hamamatsu Photonics, Hamamatsu, Japan) and counted by a photon counter (photon counting unit C9744, counting board M8784, both from Hamamatsu Photonics). Counting was carried out with a gate time of 10 ms for 600 s. A schematic diagram of the apparatus used for time course measurements of bioluminescence intensity is shown in Fig. 1.

image

Figure 1. Apparatus used for time course measurements of bioluminescence intensity.

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Spectral measurement

Bioluminescence spectra were measured using the same system as the time course measurement except that a 32-channel fast photosensor module (H8353-02F, Hamamatsu Photonics) was used as a spectrometer and a detector. The system was operated with a photomultiplier voltage of 900 V, and a sampling period of 100 ms for 630 s. The spectral sensitivity of the 32-channel fast photosensor module was calibrated with the spectrum of a tungsten lamp as an approximation of black body radiation, and bioluminescence spectra were corrected by this sensitivity. A schematic diagram of the apparatus used for time-resolved measurements of bioluminescence spectra is depicted in Fig. 2.

image

Figure 2. Apparatus used to measure time-resolved bioluminescence spectra.

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Emission spectra were decomposed into two Gaussian functions as shown in Eq. (1), where I0 is background intensity, σ is standard deviation and xc is emission peak energy.

  • display math(1)

Results and Discussion

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

Time course measurement

The results of the time course measurements of firefly bioluminescence intensity are shown in Figs. 3 and 4. For the measurements by ATP injection, bioluminescence arose within 1 s at pH 7.8, and lasted until 100 s (Fig. 3a,d). The rise and decay of bioluminescence occurred later as pH decreased (Fig. 3b,c,e and f). Moreover, the bioluminescence intensity weakened as pH lowered; at pH 6.8, it was reduced to 1/20 that at pH 7.8 for concentration condition 1. In contrast, the onset of bioluminescence did not depend on pH for the measurements with cATP [11]. In this case, it is thought that cATP and Ln are bound at the active site of Luc before initiation of the photolytic reaction, so the reaction rate is independent of pH. Consequently, the pH dependence of the time course of bioluminescence intensity by ATP injection indicates that ATP diffusion or the rate of ATP binding by Luc depends on pH.

image

Figure 3. Time course of firefly bioluminescence intensity for concentration conditions 1 (a, b, and c) and 2 (d, e and f). Solid lines represent the smoothed experimental curve and dashed lines represent the curves fitted using Eq. (10).

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image

Figure 4. Time course of firefly bioluminescence intensity initiated by the photolysis of cATP (pH 7.8). Concentration condition is described in the text.

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The time evolution of bioluminescence intensity for the measurements by cATP photolysis can be expressed as Eq. (5) on the basis of chemical Eqs. (2)-(4) [11]. In these equations, the parameters in parentheses (k1, k2 and k3) represent the rate constants for reactions (2), (3) and (4) respectively.

  • display math(2)
  • display math(3)
  • display math(4)
  • display math(5)

The bioluminescence time course for the photolysis of cATP in Fig. 4 was well fitted by Eq. (5). For measurements by ATP injection, Eq. (2) should be replaced with

  • display math(6)

Here, it should be noted that this chemical equation implies that two elementary steps are involved: one is Luc taking ATP inside its active site, which is followed by production of Ln-AMP. In this case, it takes a finite time for injected ATP to reach the proximity of Luc in the solution. It is difficult to quantitatively analyze the time courses of bioluminescence intensity during the homogenization of ATP because the solution was violently stirred by the injection and detected bioluminescence intensity was integrated over the quartz cell.

As a simplified case, the one-dimensional diffusion model (see Supplementary Materials) is helpful to estimate the effect of ATP diffusion. According to this model, we approximated the time dependence of [ATP] by inline image. Here, λ = π2D/4a2 is evaluated by the diffusion coefficient D and the width of the quartz cell a. The rate equations for [Ln·Luc] and [Ln-AMP·Luc] are described by Eqs. (7) and (8) respectively.

  • display math(7)
  • display math(8)

In Eq. (8), the reaction shown in Eq. (3) is regarded as a first-order reaction because the concentration of oxygen is much higher than that of Ln or Luc as estimated below. At a pressure of O2 of 1 atm and 273 K, 0.031 mL O2 is absorbed by 1 mL water. The partial pressure of O2 in the air is 0.21, so the concentration of oxygen dissolved in the sample solution is estimated to be 2.9 × 10−4 m. This value is much higher than the concentration of Ln or Luc of 10−6−10−7 m, which control the reaction under concentration condition 1 or 2. Bioluminescence intensity is proportional to [Ln-AMP·Luc] [11], whose time evolution is determined by Eqs. (7) and (8). Taking inline image into account, one obtains

  • display math(9)

where K1′ is the rate constant when the reaction shown in Eq. (3) is regarded as a quasi-first-order reaction. This is plausible after the homogenization of ATP because [ATP] is much higher than [Ln·Luc]. Substituting Eq. (9) into Eq. (8), one obtains an equation that determines the time evolution of [Ln-AMP·Luc]; however, an analytical solution of this equation cannot be derived. It is therefore necessary to fit the observed time course to a phenomenological function to decompose the time evolution of bioluminescence into three components; diffusion of ATP molecules, increase in [Ln-AMP·Luc] by the reaction shown in Eq. (6) and decrease in [Ln-AMP·Luc] by the reaction shown in Eq. (3). Accordingly, we used Eq. (10) for the fitting.

  • display math(10)

When the diffusion is fast enough, the numerator of Eq. (10) becomes inline image, similar to that of Eq. (5). This term is interpreted as a sum of inline image and inline image, which represents the increase in [Ln-AMP·Luc] by the reaction shown in Eq. (6) and the decrease in [Ln-AMP·Luc] by the reaction shown in Eq. (3) respectively. Equation (10) takes into account the delayed increase in [Ln-AMP·Luc] caused by the diffusion of ATP as inline image. This approximation is not ideal, but it allows us to decompose the observed time course into three components and qualitatively discuss the underlying mechanism.

The obtained time courses are reproduced well by this equation, as shown in Fig. 3. The optimum adjustment parameters for each concentration condition are shown in Table 2.

Table 2. Optimal adjustment parameters in Eq. (10)
pHConcentration 1Concentration 2
K1′ [s−1]k2 [s−1]λ [s−1]K1′ [s−1]k2 [s−1]λ [s−1]
7.84.00.0402.53.70.0303.8
7.00.520.0182.00.470.0122.0
6.80.360.0172.00.355.0 × 10−32.0

The λ value is larger by five orders of magnitude than that estimated by λ = π2D/4a2 using the diffusion coefficient of ATP, = (1.6–3.3) × 10−11 m2 s−1 [12], and the width of the quartz cell, = 0.01 m. The diffusion coefficient is defined under a concentration gradient in steady state, but in this case, bioluminescence was triggered by rapidly injecting ATP into the solution in one shot. It is therefore reasonable that the time taken to reach equilibrium is much shorter than that in a static environment. In Table 2, K1′ and k2 reduce with decreasing pH. This means that both the rise and decay of bioluminescence occur later as pH decreases. In contrast, λ is almost independent of pH and concentration conditions. Consequently, the pH dependence of the rise of bioluminescence is not caused by the diffusion of ATP, but instead by the rate of ATP binding in the proximity of the active site of Luc.

The optimal pH for the bioluminescence reaction of Photinus pyralis is around 8, and the isoelectric point of Luc estimated from its charged amino acid residues is 6.4 [13]. Then, leaving the optimal pH of 7.8 and approaching the isoelectric point at 6.4, the ionized and local conformational changes of some amino acid residues around the active site of Luc could reduce the rate of ATP binding at the active site of Luc. In other words, as pH is lowered from 7.8, the rise and decay times of bioluminescence are delayed and the change in Luc interacting with Oxyln* induced a redshift of emission from yellow-green to red with a simultaneous decrease in quantum yield. Furthermore, the delay of the rise of bioluminescence caused by an increase in the concentration of H+ ([H+]) is not observed for bioluminescence using cATP, and the rate constant k1 in Eq. (2) does not depend on pH [11]. The delayed rise time of the bioluminescence induced by the ATP injection with increasing [H+] is related to the reduction in the rate of ATP binding at the active site of Luc.

In this respect, the Michaelis constants (Km) of Ln/Luc for ATP under concentration conditions 1 and 2 were evaluated according to the data obtained by Moss et al. concerning the dependence of Km for ATP on the concentration of Ln (hereafter called the ATP-Ln/Luc curve) [14]. The experimental conditions of Moss et al. (buffer solution of n-glycylglycine at pH 7.8, with a final Luc concentration of 1–10 nm) and this study (buffer solution of HEPES, Luc concentration conditions as listed in Table 1) are not identical. However, Km could be estimated from the ATP-Ln/Luc curve assuming that the magnitude relation with Km showed qualitatively the same tendency. As a result, the Km for concentration conditions 1 and 2 were estimated to be Km1 ~ 300 μm and Km2 ~ 700 μm respectively, showing that the affinity of Ln/Luc for ATP is smaller for concentration condition 2 than 1. Thus, the rate constant K1′ given in Table 2 and the corresponding Km have a positive correlation. Although Moss et al. only obtained ATP-Ln/Luc curves at pH 7.8, the magnitude relation with Km in the cases of pH 7.0 and 6.8 are expected to show the same tendency as the case of pH 7.8 because K1′ for concentration condition 1 is always larger than that for 2 at the same pH. This implies that Km increases as K1′ decreases with pH, which explains the experimental evidence that the light intensity of in vitro firefly bioluminescence reduces as pH is lowered.

Spectral measurement

Figures 5-7 show time-resolved spectra of firefly bioluminescence. Each spectrum can be resolved into two Gaussian functions with maxima at about 2.2 and 2.0 eV. As shown in Fig. 8, the integrated intensity ratio of the two peaks is approximately constant up to 600 s for both ATP injection and cATP photolysis experiments, so Figs. 5-7 show the bioluminescence spectra accumulated in the time range from 2.1 to 4.9 s after ATP injection or cATP photolysis. In the measurements for ATP injection, at pH 7.8, the band at 2.2 eV is more intense than that at 2.0 eV for both concentration conditions. With lowering pH, the intensity of the band at 2.2 eV weakens relative to that at 2.0 eV and the maxima of the bioluminescence spectra shift to the low energy side. However, this trend depends on the concentration conditions, and the decrease in intensity of the band at 2.2 eV is comparatively small in the case of concentration condition 2. For the measurements with cATP photolysis, the observed pH dependence of the relative intensity of the band at 2.2 eV is similar to the case of the ATP injection measurements: the intensity of the band at 2.2 eV is relatively strong at pH 7.8, but weakens to lower intensity than that of the band at 2.0 eV as the pH decreases. The spectral shape changes with lowering pH, similar to the case of concentration condition 1 for ATP injection.

image

Figure 5. Firefly bioluminescence spectra accumulated in the time range from 2.1 to 4.9 s after ATP injection for concentration condition 1. (a) pH 7.8, (b) pH 7.0 and (c) pH 6.8. Observed spectra were decomposed into two bands with maxima at 2.0 and 2.2 eV (dashed lines). Solid lines correspond to the sum of these bands.

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image

Figure 6. Firefly bioluminescence spectra accumulated in the time range from 2.1 to 4.9 s after ATP injection for concentration condition 2. (a) pH 7.8, (b) pH 7.0 and (c) pH 6.8. Observed spectra were decomposed into two bands with maxima at 2.0 and 2.2 eV (dashed lines). Solid lines correspond to the sum of these bands.

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image

Figure 7. Firefly bioluminescence spectra accumulated in the time range from 2.1 to 4.9 s after cATP photolysis. (a) pH 7.8, (b) pH 7.0 and (c) pH 6.8. Observed spectra were decomposed into two bands with maxima at 2.0 and 2.2 eV (dashed lines). Solid lines correspond to the sum of these bands.

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image

Figure 8. Time variation of the integrated intensity ratio of the bands at 2.2 and 2.0 eV at pH 7.8. For the measurements of ATP injection, (a) and (b) correspond to concentration conditions 1 and 2 respectively. (c) is the case of cATP photolysis.

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From our experimental results shown in Figs. 5-7, the in vitro bioluminescence spectra depend mainly on pH and partially on concentration conditions. Because our developed apparatus cannot measure the absolute quantum yield of bioluminescence, we could not examine the conclusion by Ando et al. that the intensity of the band at 2.2 eV decreases with lowering pH, whereas that of the band at 2.0 eV is almost independent of pH [2].

Interestingly, we quantitatively observed the time courses and time-resolved spectra of firefly bioluminescence in the time range of milliseconds for the first time by the manual ATP injection technique. We identified some characteristics of this reaction, such as pH-dependent rise and decay of the time course and pH-dependent color change of bioluminescence spectra. Furthermore, we found that the integrated intensity ratio of red to yellow-green emission is almost constant within a data acquisition time of 0.1 s. This fact implies that concentration equilibrium can be attained between excited molecules with emission peaks at 2.0 and 2.2 eV. Solntsev et al. clarified the photoinduced dynamics of Oxyln and two of its chemically modified analogues by pico/nanosecond time-resolved spectroscopy, and supposed that Oxyln could undergo keto–enol tautomerization and proton transfer in its excited state but not in its ground state [15]. Accordingly, the concentration equilibrium can be caused by some primary factors like the structural and electronic changes of Oxyln in its excited state, and the specific interactions between the active site of Luc and the functional groups of Oxyln*. To elucidate the pH-dependent color-tuning mechanism of firefly bioluminescence, it is necessary to determine the energy profile along the reaction path by time-resolved spectroscopy rather than steady-state spectroscopy. In particular, it is important to develop equipment with a time resolution of under milliseconds to measure photoexcitation initiated by a chemical reaction.

Acknowledgements

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

This work was partially supported by a Grant-in-Aid for Scientific Research (21651067).

References

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and Methods
  5. Results and Discussion
  6. Acknowledgements
  7. References
  8. Supporting Information
  • 1
    Seliger, H. H. and W. D. McElroy (1959) Quantum yield in the oxidation of firefly luciferin. Biochem. Biophys. Res. Commun. 1, 2124.
  • 2
    Ando, Y., K. Niwa, N. Yamada, T. Enomoto, T. Irie, H. Kubota, Y. Ohmiya and H. Akiyama (2008) Firefly bioluminescence quantum yield and color change by pH-sensitive green emission. Nat. Photonics 2, 4447.
  • 3
    Wang, Y., H. Kubota, N. Yamada, T. Irie and H. Akiyama (2011) Quantum yields and quantitative spectra of firefly bioluminescence with various bivalent metal ions. Photochem. Photobiol. 87, 846852.
  • 4
    White, E. H., E. Rapaport, T. A. Hopkins and H. H. Seliger (1969) Chemi- and bioluminescence of fireflyluciferin. J. Am. Chem. Soc. 91, 21782180.
  • 5
    White, E. H., M. G. Steinmetz, J. D. Miano, P. D. Wildes and R. Morland (1980) Chemi- and bioluminescence of firefly luciferin. J. Am. Chem. Soc. 102, 31993208.
  • 6
    Branchini, B. R., M. H. Murtiashaw, R. A. Magyar, N. C. Portier, M. C. Ruggiero and J. G. Stroh (2002) Yellowgreen and red firefly bioluminescence from 5,5-dimethoxyluciferin. J. Am. Chem. Soc. 124, 21122113.
  • 7
    McCapra, F. (1996) Mechanisms in chemiluminescence and bioluminescence unfinished business. In Bioluminescence and Chemiluminescence (Edited by J. W. Hastings, L. J. Kricka and P. E. Stanley), pp. 715. Jhon Wiley & Sons, Chichester, U.K.
  • 8
    Nakatsu, T., S. Ichiyama, J. Hiratake, A. Saldanha, N. Kobashi, K. Sakata and H. Kato (2006) Strauctural basis for the spectral difference in luciferase bioluminescence. Nature 440, 372376.
  • 9
    Naumov, P., Y. Ozawa, K. Ohkubo and S. Fukuzimi (2009) Spectroscopy of oxyluciferin, the light emitter of firefly bioluminescence. J. Am. Chem. Soc. 131, 1159011605.
  • 10
    Naumov, P. and M. Kochunnoonny (2010) Spectral-structural effects of the keto-enol-enolate and phenol-phenolate equilibria of oxyluciferin. J. Am. Chem. Soc. 132, 1156611579.
  • 11
    Kageyama, T., M. Tanaka, T. Sekiya, S. Ohno and N. Wada (2011) The reaction process of firefly bioluminescence triggered by photolysis of caged-ATP. Photochem. Photobiol. 87, 653658.
  • 12
    Rostovtseva, T. K. and S. M. Bezrukov (1998) ATP transport through a single mitochondrial channel, VDAC, studied by current fluctuation analysis. Biophys. J . 74, 23652373.
  • 13
    Viviani, V. R., T. L. Oehlmeyer, F. G. C. Arnoldi and M. R. Brochetto-Braba (2005) A new firefly luciferase with bimodal spectrum: Identification of structural determinants of spectral pH-sensitivity in firefly luciferases. Photochem. Photobiol. 81, 843848.
  • 14
    Moss, G. W. J., N. P. Franks and W. R. Lieb (1991) Modulation of the general anesthetic sensitivity of a protein: A transition between two forms of firefly luciferase. Proc. Natl Acad. Sci. USA 88, 134138.
  • 15
    Solntsev, K. M., S. P. Laptenok and P. Naumov (2012) Photoinduced dynamics of oxyluciferin analogues: Unusual enol “super”photoacidity and evidence for keto-enol isomerization. J. Am. Chem. Soc. 134, 1645216455.

Supporting Information

  1. Top of page
  2. Abstract
  3. Introduction
  4. Materials and Methods
  5. Results and Discussion
  6. Acknowledgements
  7. References
  8. Supporting Information
FilenameFormatSizeDescription
php12146-sup-0001-DataS1.docxWord document30KData S1. Effect of ATP diffusion estimated from a one-dimensional diffusion model.

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