Keywords

1 Introduction

Quinones are redox-active cofactors in many photosynthetic reaction centers. Ubiquinone serves as an electron acceptor at the QA and QB binding sites in photosynthetic reaction centers of purple bacteria (PbRC) from Rhodobacter sphaeroides and as an electron donor in cytochrome bc1. Menaquinone (vitamin K2) is the acceptor at the QA site in PbRC from Blastochloris viridis, whereas phylloquinone (vitamin K1) is the active center at the A1A and A1B sites in photosystem I (PSI). Plastoquinone serves as an electron acceptor at the QA and QB sites in photosystem II (PSII) (Fig. 1) (Robinson and Crofts 1984; Rutherford et al. 1984; Okamura et al. 2000; Brettel and Leibl 2001; Wraight 2004) and as an electron donor in cytochrome b6f.

Fig. 1
figure 1

Molecular structures of (a) ubiquinone (n = 10), (b) menaquinone and phylloquinone (n = 3 to 9), and (c) plastoquinone (n = 6 to 9), where n is the number of isoprene units

Full size image

Prince et al. measured the redox potential for one-electron reduction, Em(Q/Q●−), of 1,4-quinones, including ubiquinone, menaquinone (phylloquinone), and plastoquinone, in dimethylformamide (DMF) versus saturated calomel electrode (SCE) (Prince et al. 1983). Swallow also measured Em(Q/Q●−) for small 1,4-quinones in water versus normal hydrogen electrode (NHE) (Swallow 1982). As mentioned (Kishi et al. 2017), experimentally measured Em(Q/Q●−) in DMF versus SCE can be practically converted to Em(Q/Q●−) in water versus NHE by adding 480 mV.

2 Em for Quinones in Water and in Protein Environments

Kishi et al. reported the Em(Q/Q●−) values in water versus NHE as −163 mV for ubiquinone, −260 mV for menaquinone (phylloquinone), and −154 mV for plastoquinone (Table 1) by quantum chemical calculation of the free energy difference between the neutral state Q and the reduced state Q●− in the aqueous phase (Kishi et al. 2017). Before that study, it was a matter of debate whether Em(Q/Q●−) for quinone in DMF could be relevant to calculate the Em values in photosynthetic reaction centers when using theoretical approaches, namely, electrostatic calculations. Notably, in electrostatic calculations, only the difference between the Em of quinone in bulk water and quinone in the protein environment can be computed. Thus, to obtain, for example, Em(A1) in PSI, it is necessary to determine the Em(Q/Q●−) for phylloquinone in a reference system (preferentially in water) and add the calculated Em difference.

Table 1 Experimentally measured Em(Q/Q●−) (exp.) versus SCE (Prince et al. 1983; Swallow 1982) and calculated Em(Q/Q●−) (calc.) versus NHE (Kishi et al. 2017)
Full size table

Previously, to calculate Em(A1) in PSI, Ptushenko et al. used Em(Q/Q●−) = −800 mV for phylloquinone in DMF versus NHE, by assuming a liquid junction potential between SCE in DMF and NHE in water (Ptushenko et al. 2008). However, it should be noted that Em(Q/Q●−) for quinones in the two systems differs by 600 mV even in the absence of the liquid junction potential, i.e., the discrepancy between the Em(Q/Q●−) values in the two systems cannot be explained by the liquid junction potential, as previously demonstrated (Kishi et al. 2017).

Although not clearly stated by Ptushenko et al. (2008), it seems likely that in their computational model, the electrostatic interaction between the PSI protein environment and the A1 phylloquinone molecule was originally underestimated and that they needed the unusually low Em value of −800 mV for phylloquinone as a reference, mainly to reproduce the reported low Em(A1) in PSI (e.g., −810 mV (Vos and van Gorkom 1990), −754 mV (Iwaki and Itoh 1994), and −700 mV (Brettel and Leibl 2001)). Using the unusually low Em value of −800 mV for phylloquinone in DMF versus NHE allowed them to conveniently match their calculated value to the reported low Em(A1) value. However, using the unusually low Em value would simultaneously cause a problem in reproducing the Em(QA) of −150 mV for the same quinone species (menaquinone) in PbRC (Brettel and Leibl 2001). That is, they must explain how the PbRC protein environment is able to increase Em(Q/Q●−) = −800 mV in DMF versus NHE for phylloquinone to −150 mV at the QA site in the PbRC protein environment. Obviously, this is impossible in the PbRC protein electrostatic environment, as demonstrated in numerous electrostatic calculations (Rabenstein et al. 1998; Ishikita and Knapp 2004; Zhu and Gunner 2005). It seems plausible that the Em values measured in water versus NHE (−260 mV for menaquinone (phylloquinone)) (Kishi et al. 2017) are more relevant to the Em values in proteins than the Em values measured in DMF versus SCE (unless the proteins are solvated in DMF).

This fact would be more understandable when considering Em of QB near the protein bulk surface in PbRC and PSII. Em(Q/Q●−) is −154 mV for plastoquinone in water versus NHE, which is more consistent with Em(QB) = +90 mV versus NHE in PSII determined using spectroelectrochemistry (Kato et al. 2016) than Em(QB) ≈ −750 mV in DMF versus NHE (Kishi et al. 2017). Again, these results confirm that Em(Q/Q●−) in water versus NHE is more relevant to Em(Q/Q●−) in protein environments than Em(Q/Q●−) in DMF versus SCE.

3 Alternative Approach for Calculating Em of Quinones and Other Cofactors

There are other approaches for calculating Em of redox-active groups isolated in a solvent, including quinone molecules. As the basis of quantum chemistry, the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energy levels are associated with Em for one-electron oxidation and for one-electron reduction, respectively (Watanabe and Kobayashi 1991). Indeed, the experimentally measured Em for ten 1,4-quinones in dimethylformamide (DMF) versus SCE (Prince et al. 1983) is strongly correlated with the LUMO level of quinone in the neutral state in the aqueous phase (coefficient of determination R2 = 0.97, Fig. 2).

Fig. 2
figure 2

Correlation between experimentally measured Em for ten 1,4-quinones in dimethylformamide (DMF) versus saturated calomel electrode (SCE) (Prince et al. 1983) and calculated LUMO energy level (ELUMO) for neutral quinones (coefficient of determination R2 = 0.97). The 1,4-quinones shown are 1,4-benzoquinone, methyl-1,4-benzoquinone, 2,3-dimethyl-1,4-benzoquinone, 2,5-dimethyl-1,4-benzoquinone, 2,6-dimethyl-1,4-benzoquinone, trimethyl-1,4-benzoquinone, tetramethyl-1,4-benzoquinone, 1,4-naphthoquinone, 2-methyl-1,4-naphthoquinone, and 2,3-dimethyl-1,4-naphthoquinone. ELUMO can be calculated using a quantum chemical approach. We employed the restricted density functional theory (DFT) method with the B3LYP functional and 6-31g++∗∗ basis sets for Q (S = 0), using the Gaussian (Frisch et al. 2004) program code with the PCM method for DMF. Solvent molecules were considered implicitly, using the SCRF = water option and the SCRF = dimethylformamide option with dielectric constants of 78.355 for water and 37.219 for DMF (i.e., default values). (For further details, including the atomic coordinates, see ref. Kishi et al. 2017)

Full size image

The MO-based approach presented herein requires quantum chemical calculation of the neutral state only, whereas the previous approach reported by Kishi et al. (2017) requires quantum chemical calculation of both the neutral and reduced states. The strong correlation between the calculated Em values and the LUMO energy levels indicates that the Em values are in fact determined by the molecular structures in the neutral states (prior to reduction of the quinones) and that structural changes that may be induced in response to reduction of the quinones are negligibly small in terms of Em. This approach can also be applied to other redox-active cofactors, e.g., chlorophylls (Watanabe and Kobayashi 1991).