Nadtanet Nunthaboot*a,
Seiji Taniguchib,
Haik Chosrowjanb and
Fumio Tanaka*b
aDepartment of Chemistry and Center of Excellence for Innovation in Chemistry, Faculty of Science, Mahasarakham University, Mahasarakham 44150, Thailand. E-mail: nadtanet.n@msu.ac.th
bDivision of Laser Biochemistry, Institute for Laser Technology, Osaka 550-0004, Japan. E-mail: fumio.tanaka@yahoo.com
First published on 26th February 2021
In the present work, we discuss about the relationship between the energy gap law and extended Dutton law in flavoproteins. The extend Dutton law is defined herein as the dependence of logarithmic rates (lnRate) of photoinduced electron transfer (ET) from aromatic amino acids to excited isoalloxazine (Iso*) on donor–acceptor distances (Rcs). Both functions of ln
Rate vs. negative values of the standard free energy gap and ln
Rate vs. Rc display a parabolic behavior, when the ET rates are ultrafast. The negative values of the standard free energy gap at peaks of ln
Rate [Xm(ES)] were obtained for FMN-binding protein, wild-type pyranose 2-oxidase, T169S (Thr169 is replaced by Ser) pyranose 2-oxidase, and medium-chain acyl-CoA dehydrogenase. The values of Rc at peaks of ln
Rate [Xm(Rc)] were also obtained for these flavoproteins. The negative values of the standard free energy gap decreased with approximate linear functions of Rc. The negative values of standard free energy gap [Xm(ESRc)] at Rc = Xm(Rc) were evaluated using the linear functions of the negative standard free energy gap with Rc. The values of Xm(ESRc) were mostly in very good agreement with the values of Xm(ES). This implies that the energy gap law and the extend Dutton law are equivalent. Xm(ES) values in ET donors displaying the linear extend Dutton law with Rc were obtained by energy gap law, and then Xm(Rc) values were evaluated with the negative standard free energy gap. Thus, the obtained Xm(Rc) values were much smaller than the Rc range obtained by the method of molecular dynamics simulation. This suggests that ET processes with linear profiles of the extend Dutton law could be parabolic when Rc becomes much shorter than the Rc range obtained by the method of molecular dynamics simulation.
Fluorescence of flavins was first found by Weber.12–14 The fluorescence of riboflavin is quenched by various biological substances.13 Fluorescence lifetimes of flavins were first studied by means of a phase-shift method.15,16 The lifetimes of FAD is 2.5 ns and that of FMN 4.7 ns. The fluorescence of flavins in the solution is quenched by Trp and Tyr.17,18 The quenching has been demonstrated to be due to ET from Trp or Tyr to Iso*, by means of a picosecond-resolved transient absorption spectroscopy19 and a femtosecond-resolved transient absorption spectroscopy.20 In many flavoproteins, the fluorescence of flavins is remarkably quenched due to ET, and their fluorescence lifetimes become extremely short, compared to those of free flavins.21–27 The ET rate from the individual donor has been evaluated with an ET theory and MDS structures, using fluorescence lifetimes or decays in these flavoproteins.24–31
Logarithmic ET rates (lnRates) linearly decrease with the donor–acceptor distances (Rc), known as the Dutton law.32 However, the ln
Rate vs. Rc relationship often displays parabolic functions with Rc in flavoproteins, when the rates are faster than ca. 1 ps−1.28–31 In these donors, the values of ln
Rate become smaller with Rc, which is called the inverted region of Rc (Rc-inverted region).28–31 In the present study, we call the ln
Rate vs. Rc relationship the extend Dutton law (EXDL). However, it is also known that the ln
Rate vs. standard free energy gap (SFEG) relationship displays parabolic functions, which is called the energy gap law (SEGL).33–36 The region of −SFEG (negative value of SFEG) greater than that at the maximum value of ln
Rate is called the inverted region of SEGL (E-inverted region). It is evident that both the parabolic relationships originated from the Marcus ET theory.1,2
The physical picture of the Rc-inverted region is not known yet. This is physically unreasonable because the ET rate becomes slower as the Rc is shorter, despite the greater interaction energy. This phenomenon was interpreted that the Marcus theory does not hold anymore in the Rc-inverted region, and the ET phenomena should be treated by molecular orbital theory.28,29,37,38 Herein, we describe the relationship between EXDL and SEGL in ET processes in flavoproteins, using the Marcus–Kakitani–Mataga (MKM) theory.1,2,39–41
Iso* + Trp → Iso− + Trp+ ΔG0 |
ΔG0 is the standard free energy gap (SFEG) between photo-products and reactants.
The ET rate by MKM theory is typically expressed by eqn (1):1,2,30–32
![]() | (1) |
In eqn (1), t is the MDS time. The value of k(t) is expressed in ps−1.
![]() | (2) |
The mean value of ΔG0(t) over the MDS time, t, is ΔG0. Here ΔGe is the electronic energy gap, obtained as follows:
ΔGe = EIP − EEA | (3) |
The second term of eqn (2) is electrostatic (ES) energy between donor cations and acceptor anions (ESDA). εDA0 is the static dielectric constant near donor and acceptor molecules. The third term is the ES energy between the ion-pair and ionic groups in the protein, which is described elsewhere.28–31
ΔG0(t) is dependent on the environment near a donor and an acceptor molecule as in anoxygenic photosynthetic bacteria.42 Tyr residues (termed YZ and YD) in Photosystem II of the bacteria display the difference in redox potential despite that they are also symmetrically arranged in the vicinity of the same electron donor (P680). The rates of electron transfer from these Tyr residues to P680 differ by at least 3 orders of magnitude. In our model, the difference in ΔG0(t) is taken into account in the following ways.
(a) EEA is dependent on the environment surrounding Iso*. The hydrogen bonds between Iso and nearby amino acids should be the main factors to influence upon EEA. This quantity is determined so as to reproduce experimental fluorescence decay. The decay depends on the environment surrounding Iso and donor.
(b) εDA0 depends on the polarity between Iso and donor molecules inside the protein.
(c) Enet(t) is dependent on the positions of the donor and acceptor molecules.
Even though Ip values of an isolated donor molecule are used in our model, all other quantities in ΔG0(t) depend on the environment surrounding donor and acceptor molecules.
In eqn (1), λ(t) is the solvent reorganization energy described elsewhere,28–31 given by Marcus.1,2
The logarithmic ET rate is given by eqn (4).
![]() | (4) |
![]() | (5) |
![]() | (6) |
In the present work, abbreviations, lnRate = ln{k(t)}, SFEG = ΔG0(t), and Rc = Rc(t) are used.
EXDL is expressed as the lnRate vs. Rc relationship and SEGL as the ln
Rate vs. −SFEG relationship. A relationship −SFEG vs. Rc is called here the ESRC.
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Fig. 1 MDS structure of FBP.29 FMN A and FMN B denote FMN in Sub A and in Sub B. Trp32A and Trp32B denote Trp32 in Sub A and in Sub B, and so in Trp106A and Trp106B. |
Fig. 2 shows the SEGL in FBP. In any ET donor, lnRates also depended on −SFEG with parabolic functions, as y = A2x2+B2x + C2, where y = ln
Rate, x = −SFEG. The coefficients, A2, B2, and C2 are listed in Table 1. The values of A2, B2, and C2 (Trp32 in Sub A) were −26.1, 40.3 and −13.4 in Trp32A and −27.1, 40.0 and −12.7 in Trp32B. The values of A2, B2, and C2 were −28.0, 47.7 and −18.0 in Trp106A and −114, 194 and −80.0 in Trp106B.
Protein | Donorb | Coefficient of parabolic function | Xm(ES)c (eV) | Range of −SFEG (eV) | ||
---|---|---|---|---|---|---|
A2 | B2 | C2 | ||||
a The values of ln![]() |
||||||
FBP WT | Trp32A | −26.1 | 40.3 | −13.4 | 0.77 | 0.87–1.15 |
Trp32B | −27.1 | 40 | −12.7 | 0.82 | 0.78–1.15 | |
Trp106A | −28 | 47.7 | −18 | 0.90 | 0.72–1.10 | |
Trp106B | −114 | 193 | −80 | 0.94 | 0.5–0.95 | |
P2OWT | Trp168B | −15.3 | 56.8 | −50 | 1.86 | 1.81–1.92 |
Trp168C | −13.4 | 50 | −43.8 | 1.87 | 1.79–1.91 | |
Trp168D | −18.3 | 68.2 | −60.5 | 1.86 | 1.79–1.89 | |
P2OT169S | Trp168A | −13.4 | 56.4 | −57 | 2.10 | 1.62–1.71 |
Trp168B | −24.4 | 103 | −1.7 | 2.11 | 1.62–1.71 | |
Trp168D | −22.4 | 95.4 | −98.8 | 2.13 | 1.61–1.71 | |
MCAD | Trp166A | −19.3 | 92.5 | −110 | 2.40 | 2.33–2.54 |
Trp166B | −9.28 | 43.9 | −50.4 | 2.37 | 2.3–2.58 | |
Trp166C | −9.65 | 44.3 | −49.1 | 2.30 | 2.25–2.41 | |
Trp166D | −9.5 | 45 | −51.9 | 2.37 | 2.33–2.54 |
The values of −SFEG at peak in lnRate were obtained as Xm(ES) = −B2/(2A2). These values are listed in Table 1, and were 0.77 eV in Trp32A, 0.82 eV in Trp32B, 0.90 eV in Trp106A and 0.94 eV in Trp106B. The variation ranges of −SFEG are also listed in Table 1. The values of Xm(ES) were all within the range of −SFEG variation. The values of −SFEG greater than Xm(ES) are called the inverted region of SEGL (E-inverted region) and those smaller than Xm(ES) the E-normal region.
![]() | ||
Fig. 3 MDS structures of tetrameric WT P2O.30 Panel (A) shows the entire tetrameric WT P2O. The ribbons represent the protein backbones, Sub A in blue, Sub B in yellow, Sub C in pink, and Sub D in green. FAD molecules are indicated with blue stick models. Panel (B) shows the local structure at the FAD binding site in Sub A. Trp168 and nearby ionic amino acids, Glu358, Asp452, Lys91 and Arg472, are also shown in Panel (B). |
Fig. 4 shows the SEGL plots of Trp168 at 480 nm in WT P2O. The profiles of Sub B, Sub C and Sub D were well described with parabolic functions. The coefficients are listed in Table 1. The values of A2, B2, and C2 were −15.8, 56.8 and −50.0 in Sub B, −13.4, 50.0 and −43.8 in Sub C, and −18.3, 68.2 and −60.5 in Sub D. The values of Xm(ES) were 1.86 eV in Sub B, 1.87 eV in Sub C and 1.86 eV in Sub D. The range of variations in −SFEG was 1.81–1.92 eV in Sub B, 1.79–1.91 eV in Sub C and 1.79–1.89 eV in Sub D. Thus, the values of lnRate were partly in the E-inverted region and partly in the E-normal region.
![]() | ||
Fig. 4 SEGL in WT P2O. Trp168B, Trp168C and Trp168D denote Trp168 in Sub B, Sub C and Sub D, respectively. These donors are fast components and emission-wavelength-dependent.25 The emission wavelength monitored is 480 nm. Insets show the approximate parabola functions. R2 denotes the determination coefficient. |
![]() | ||
Fig. 5 Comparison of the MDS structures at the Iso binding site between T169S P2O and WT P2O.31,44 The structures of T169S P2O are shown in gray and WT P2O in blue. W168 and H167 denote Trp168 and His 167, respectively, and S169 and T169 denote Ser169 and Thr169. (A), (B), (C) and (D) denote subunits. |
The EXDL plots of 480 nm in T169S P2O are shown in Fig. S3 in ESI.† The EXDL profiles in Sub A, Sub B and Sub D display a parabolic behavior, but linear in Sub C.31 The coefficients of the parabolic functions are listed in Table S1 (ESI†). The values of Xm(Rc) in T169S P2O are 0.71 in Sub A, 0.73 in Sub B and 0.72 nm in Sub D. The range of Rc variation is 0.68–0.79 in Sub A, 0.66–0.79 in Sub C and 0.68–0.84 nm in Sub D. Thus, the values of lnRate are partly in the Rc-inverted region and partly in the Rc-normal region.
Fig. 6 shows the SEGL plots of Trp168 at 480 nm in T169S P2O. The profiles of Sub A, Sub B and Sub D were well described with parabolic functions as in WT P2O. The coefficients are listed in Table 1. The values of A2, B2, and C2 were −13.4, 56.4 and −57.0 in Sub A, −24.4, 103 and −1.7 in Sub B, and −22.4, 95.4 and −98.8 in Sub D. The values of Xm(ES) were 2.10 eV in Sub A, 2.11 eV in Sub B and 2.13 eV in Sub D. The range of variations in −SFEG was 1.62–1.71 eV in Sub A, 1.62–1.71 eV in Sub B and 1.61–1.71 eV in Sub D. Thus, the values of lnRate were partly in the E-inverted region, and partly in the E-normal region.
![]() | ||
Fig. 6 SEGL in T169S P2O. Trp168A, Trp168B and Trp168D denote Trp168 in Sub A, Sub B and Sub D, respectively. These donors are fast components and emission-wavelength-dependent for the decay measurements.26 The emission wavelength monitored is 480 nm. Insets show the approximate parabola functions. R2 denotes the determination coefficient. |
![]() | ||
Fig. 7 MDS structures of MCAD45,46 Panel (a) shows the entire structure of the tetramer, and panel (b) shows the local structure near the FAD-binding site. MCAD contains four Trps as potential donors. Trp166 is shown in green, Trp175 in red, Trp57 in blue and Trp317 in yellow. The structures of lower panel are prepared with RasWin Molecular Graphics (http://www:Rasmol.org). |
The EXDL plots are shown in Fig. S4 in ESI.† 45 The EXDL profiles all in Sub A, Sub B, Sub C and Sub D display a parabolic behavior. The coefficients of the parabolic functions are listed in Table S1 (ESI†). The values of Xm(Rc) in Trp166 are 0.76 in Sub A, 0.81 in Sub B, 0.74 in Sub C and 0.80 nm in Sub D. The range of Rc variation is 0.77–1.0 in Sub A, 0.72–0.97 in Sub B, 0.75–0.95 in Sub C, and 0.75–1.0 nm in Sub D.45 The values of lnRate are partly in the Rc-inverted region and partly in the Rc-normal region.
Fig. 8 shows the SEGL plots of Trp166 in MCAD. The values of lnRate are taken from the work reported.46 The profiles in all subunits were well described with parabolic functions. The coefficients were listed in Table 1. The values of A2, B2, and C2 were obtained as −19.3, 92.5 and −110 in Sub A, −9.28, 49.3 in Sub C and −50.4 in Sub B, and −9.65, 44.3 and −49.1 in Sub C, and −9.5, 45.0 in Sub C and −51.9 in Sub D. The values of Xm(ES) were 2.40 eV in Sub A, 2.37 eV in Sub B, 2.30 eV in Sub C and 2.37 eV in Sub D. The range of variations in −SFEG was 2.33–2.54 eV in Sub A, 2.3–2.58 eV in Sub B, 2.25–2.41 eV in Sub C, and 2.33–2.54 eV in Sub D. Thus, the values of ln
Rate were partly in the E-inverted region and partly in the E-normal region, in all subunits.
![]() | ||
Fig. 8 SEGL in MCAD. Trp166A, Trp166B, Trp166C and Trp166D denote Trp166 in Sub A, Sub B, Sub C and Sub D, respectively. The values of ln![]() |
![]() | ||
Fig. 9 ESRC profiles in FBP. Trp106 in Sub B has two conformations with Rc shorter than 1.15 nm and longer than 1.15 nm.29 ESRC profile of Trp106B is shown with Rc shorter than 1.15 nm. |
Protein | Donorb | Coefficients of linear function | Xm(Rc)c (nm) | Xm(ES)d (eV) | Xm(ESRc)e (eV) | |
---|---|---|---|---|---|---|
B3 | C3 | |||||
a Relationship, Rc vs. −SFEG. The values of −SFEG were approximated as y = B3x + C3, where y = −SFEG, and x = Rc.b A, B, C, D denote subunits.c Xm(Rc) = −B1/(2A1). The values Xm(Rc) are also listed in Table S1 in ESI.d Xm(ES) = −B2/(2A2). The values of Xm(ES) are also listed in Table 1.e Xm(ESRc) = B3![]() |
||||||
FBP WT | Trp32A | −1 | 1.73 | 0.82 | 0.77 | 0.91 |
Trp32B | −1.66 | 2.16 | 0.82 | 0.82 | 0.80 | |
Trp106A | −0.66 | 1.52 | 0.90 | 0.90 | 0.92 | |
Trp106B | −0.82 | 1.64 | 0.94 | 0.94 | 0.87 | |
P2OWT | Trp168B | −0.58 | 2.3 | 0.74 | 1.86 | 1.87 |
Trp168C | −0.6 | 2.3 | 0.73 | 1.87 | 1.86 | |
Trp168D | −0.44 | 2.17 | 0.73 | 1.86 | 1.85 | |
P2OT169S | Trp168A | −0.48 | 2.44 | 0.71 | 2.10 | 2.10 |
Trp168B | −0.51 | 2.48 | 0.73 | 2.11 | 2.11 | |
Trp168D | −0.39 | 2.4 | 0.72 | 2.13 | 2.12 | |
MCAD | Trp166A | −0.32 | 2.71 | 0.76 | 2.40 | 2.47 |
Trp166B | −0.45 | 2.83 | 0.81 | 2.37 | 2.46 | |
Trp166C | −0.34 | 2.62 | 0.74 | 2.30 | 2.37 | |
Trp166D | −0.38 | 2.75 | 0.80 | 2.37 | 2.45 |
Fig. S5 (SI†) shows the ESRC in WT P2O. The values of −SFEG also decreased with Rc in WT P2O. The values of B3 and C3 were −0.581 and2.3 in Sub B, −0.60 and 2.30 in Sub C, and −0.44 and 2.17 in Sub D. Fig. 10 shows the ESRC in T169S P2O. The values of B3 and C3 were −0.48 and 2.44 in Sub A, −0.51 and 2.48 in Sub B, and −0.39 and 2.40 in Sub D. Fig. S6 (ESI†) shows the ESRC in MCAD. The values of B3 and C3 were −0.32 and 2.71 in Sub A, −0.45 and 2.83 in Sub B, −0.34 and 2.62 in Sub C, and −0.38 and 2.75 in Sub D. Sometimes, the linearity between −SFEG and Rc was not good.
![]() | ||
Fig. 10 ESRC profiles in T169S P2O. Trp168A, Trp168B, and Trp168D are fast components and dependent on the emission wavelength for the decay measurements. The emission wavelength is 480 nm.26 Insets show the approximate linear functions. R2 denotes the determination coefficient. The values of SFEG and Rc are taken from ref. 31. |
Thus, the values of Xm(ES) agreed well with those of Xm(ESRc) in donors, lnRates of which display a parabolic behavior in EXDL.
Protein | Donorb | Wave-length (nm) | SEGLc | Xm(ES)f (eV) | EXDLd | Xm(Rc)g (nm) | ESRCe | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
A4 | B4 | C4 | B5 | C5 | B6 | C6 | |||||
a In these ET systems the ln![]() ![]() |
|||||||||||
WT P2O | Trp168B | 580 | −21.4 | 72.2 | −58.2 | 1.69 | −4.61 | 5.87 | 0.54 | −0.581 | 2.00 |
Trp168C | 580 | −16.9 | 57.6 | −46.3 | 1.70 | −5.11 | 6.22 | 0.51 | −0.6 | 2.01 | |
Trp168D | 580 | −22.5 | 75.5 | −50.7 | 1.68 | −4.61 | 5.81 | 0.46 | −0.441 | 1.88 | |
T169S P2O | Trp168A | 580 | −10.8 | 42.3 | −39.1 | 1.96 | −6.78 | 6.34 | 0.07 | −0.476 | 1.99 |
Trp168B | 580 | −15.7 | 61.3 | −57 | 1.95 | −6.61 | 6.3 | 0.15 | −0.508 | 2.03 | |
Trp168D | 580 | −25.8 | 94.9 | −85.1 | 1.84 | −6.15 | 5.98 | 0.29 | −0.388 | 1.95 |
![]() | ||
Fig. 11 SEGL in WT P2O in the normal region. The emission wavelength monitored for the decay measurements is 580 nm.25 The values of SFEG and ET rates are taken from ref. 30. |
Fig. S8 in ESI† shows the EXDL profiles of the donors of fast components at 580 nm of emission wavelength, and of slow component of Sub C in T169S P2O.31 The EXDL profiles display approximate linear functions. The coefficients of the linear functions of EXDL, y = B5x + C5, are listed in Table 3. The values of coefficients, B5 and C5, are −6.78 and 6.34 in Sub A, −6.61 and 6.3 in Sub B, and −6.15 and 5.98 in Sub D. The coefficients in the slow component of Sub C were −17.3 and 10.2.31 The SEGL profiles in T169S P2O are shown in Fig. 12. The SEGL profiles displayed all approximate parabolic functions, y = A4x2+B4x + C. The values of coefficients in T169S P2O, A4, B4 and C4, were −10.8, 42.3 and −39.1 in Trp168A, −15.7, 63.1, and −57 in Trp168B, and −25.8, 94.9, and −85.1 in Trp168D. The values of Xm(ES) were 1.96 eV in Trp168A, 1.95 eV in Trp168B and 1.84 eV in Trp168D.
![]() | ||
Fig. 12 SEGL in T169S P2O in the normal region of −SFEG. The emission wavelength monitored for the decay measurements is 580 nm.25 The values of ET rates and SFEG are taken from ref. 31. |
The values of −SFEG were approximated to be linear functions of Rc, as mentioned above: y = B6x + C6, where x = Rc and y = −SFEG. The values of the coefficients, B6 and C6, are listed in Table 3. In WT P2O, the values of B6 and C6 were −0.581 and 2.00 in Trp168B, −0.60 and 2.01 in Trp168C, and −0.441 and 1.88 in Trp168D. In T169S P2O, the values of B6 and C6 were −0.476 and 1.99 in Trp168A, −0.508 and 2.03 in Trp168B, and −0.388 and 1.95 in Trp168D. The values of Xm(Rc) were evaluated with the linear relationship of y = B6x + C6, where y = Xm(ES) and x = Xm(Rc). The values of Xm(Rc) are listed in Table 3. The values of Xm(Rc) were 0.54 in Trp168B, 0.51 in Trp168C, and 0.46 nm in Trp168D in WT P2O. The values of Xm(Rc) were 0.07 in Trp168A, 0.15 in Trp168B, and 0.29 nm in Trp168D in T169S P2O. These values of Xm(Rc) were much smaller than the range of Rc variation listed in Table S1† in ESI. Thus, the parabolic behavior in EXDL could be obtained when Rc becomes shorter around Xm(Rc) in ET donors, the logarithmic ET rates of which display linear functions with Rc in the range of Rc obtained by MDS structures.
The origin of the parabolic behavior of SEGL is rather simple, because −SFEG contains only in {ΔG0(t)+λ(t)}2 term in eqn (4). The dependence of lnRate on Rc, however, is not so simple, because many terms in eqn (1) or (4) depend on Rc, as shown in the time-dependent terms. The behavior of EXDL with Rc may be classified into three groups from the point of view of the approximate functions, (a) parabolic function, (b) linear function, and (c) no clear functional relation. Linear profiles of EXDL along Rc are found in WT P2O30 and T169S P2O31 at emission wavelengths other than 480 nm, and slow components of Sub A in WT P2O30 and of Sub C in T169 P2O,31 as described above, and in D-amino acid oxidase.47 Sometimes EXDL profiles do not display any clear relationship between ln
Rate and Rc.48
The Tyr cation radical plays a very important role in photosystem II to produce molecular oxygens.49,50 ET from Tyr in flavin photoreceptors is also essential for biological functions of AppA51 and TePixD.52 Tyr residues in flavodoxins from Desulfovibrio vulgaris53 and Helicobacter pylori48 are donors which display ultrafast ET to Iso*. Normally, the ET rates from Tyrs are rather slow as in D-amino acid oxidase,37 because EIP is higher by 0.8 eV than that of Trp.54 The biological significance of Tyr cation radicals produced as a consequence of ET to Iso* is not known in the flavoproteins described here.
Footnote |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/d0ra09716k |
This journal is © The Royal Society of Chemistry 2021 |