Simultaneous Analysis of Ultrafast Fluorescence Decays of FMN

Sep 18, 2008 - Ultrafast fluorescence decays of FMN binding proteins (FBP) from DesulfoVibrio Vulgaris (Miyazaki F) were analyzed with an electron tra...
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J. Phys. Chem. B 2008, 112, 13121–13127

13121

Simultaneous Analysis of Ultrafast Fluorescence Decays of FMN Binding Protein and Its Mutated Proteins by Molecular Dynamic Simulation and Electron Transfer Theory Nadtanet Nunthaboot,† Fumio Tanaka,*,† Sirirat Kokpol,‡ Haik Chosrowjan,§ Seiji Taniguchi,§ and Noboru Mataga§ Department of Chemistry, Faculty of Science, Mahasarakham UniVersity, Mahasarakham 44150, Thailand, Department of Chemistry, Faculty of Science, Chulalongkorn UniVersity, Bangkok 10330, Thailand, and Institute for Laser Technology, Utsubo-Hommachi 1-8-4, Nishiku, Osaka 550-0004, Japan ReceiVed: May 9, 2008; ReVised Manuscript ReceiVed: July 17, 2008

Ultrafast fluorescence decays of FMN binding proteins (FBP) from DesulfoVibrio Vulgaris (Miyazaki F) were analyzed with an electron transfer (ET) theory by Kakitani and Mataga (KM theory). Time-dependent distances among isoalloxazine (Iso) and Trp-32, Tyr-35, and Trp-106 in wild-type FBP (WT), among Iso and Tyr-32, Tyr-35, and Trp-106 in W32Y (Trp-32 was replaced by Tyr-32), and among Iso and Tyr-35 and Trp-106 in W32A (Trp-32 was replaced by Ala-32) were determined by molecular dynamic simulation (MD). Electrostatic energies between Iso anion and all other ionic groups, between Trp-32 cation and all other ionic groups, and between Tyr-32 cation and all other ionic groups were calculated in WT, W32Y, and W32A, from the MD coordinates. ET parameters contained in KM theory, such as frequency (ν0), a coefficient of the ET process (β), a critical distance of the ET process (R0), standard free energy related to the electron affinity of the 0 excited Iso (GIso ), and the static dielectric constant in FBP species (ε0), were determined with and without inclusion of the electrostatic energy, so as to fit the calculated fluorescence decays with the observed decays of all FBP species, by a nonlinear least-squares method according to the Marquardt algorithm. In the analyses the parameters, ν0, β, and R0 were determined separately between Trp residues and Tyr residues among all FBP species. Calculated fluorescence intensities with the inclusion of the electrostatic energy fit quite well with the observed ones of all WT, W32Y, and W32A. Introduction Intense fluorescence of free flavins is mostly markedly quenched upon the binding to proteins. In these flavoproteins, Trp and/or Tyr always exist near a isoalloxazine ring (Iso). It was demonstrated by means of picosecond-resolved1,2 and femtosecond-resolved3,4 transient absorption spectroscopy that photoinduced electron transfer (ET) from Trp and/or Tyr to the excited Iso was responsible for the remarkable quenching. Femtosecond transient absorption spectra of these flavoprotein systems revealed that the back ET reaction from the excited to the ground state takes place in tens of picoseconds.3,4 Ultrafast fluorescence dynamics of various flavoproteins have been investigated by an up-conversion technique.5-8 Donor-acceptor distance-dependent ET rates in these flavoproteins have been expressed with a center-to-center distance rather than an edgeto-edge distance.9 The distance-dependence of ET rates was analyzed with three kinds of ET theory.10 FMN binding protein from DesulfoVibrio Vulgaris (Miyazaki F) (FBP) is considered to play an important role in the electron transport process in the bacterium, but the whole picture of the electron flow and coupling of the redox proteins is not clear yet.11 Three-dimensional structures of FBP from D. Vulgaris (Miyazaki F) were determined by X-ray crystallography12 and NMR spectroscopy.13 According to these structures, tryptophan 32 (Trp-32) was closest to the isoalloxazine ring (Iso) and then tyrosine 35 (Tyr-35) and Trp-106. * Corresponding author. E-mail: [email protected]. † Mahasarakham University. ‡ Chulalongkorn University. § Institute for Laser Technology.

Various ET theories have been modeled for ET processes in bulk solution.14-22 It is not clear yet which factor is most important for ET in proteins. There should be something different in ET processes in protein from ones in bulk solution. The ET rate of FBP was much slower in crystal than in solution.23 The result suggests something about an influential factor for ET in FBP, but the reason for it is not clear yet at the present. The fluorescence lifetimes of wild type FBP (WT), W32Y (Trp-32 was replaced by Tyr-32 in FBP), and W32A (Trp-32 was replaced by Ala-32 in FBP) have been measured and a comparison among them has been made.24 Electron transfer phenomena in proteins have been precisely described in review articles by Marcus and Sutin15 and Gray and Winkler.25 Fluorescence lifetimes of Trp were analyzed by means of MD26-28 and QM/MM29-31 methods. In these works, a resonance energy transfer or ET from Trp was explicitly taken into account for the analyses. Time-resolved fluorescence of FAD32 and oxidized and reduced flavodoxin33 was analyzed by MD. ET from Tyr in flavin reductase and flavodoxin reductase was investigated by the QM/MM method.29 Ultrafast ET of DNA photolyase was also worked by MD.34 In these works, however, not every ET parameter in ET theory had been obtained through the analyses of the fluorescence decays. In the present work, ultrafast fluorescence dynamics of WT, W32Y, and W32A has been analyzed simultaneously with common ET parameters contained in the ET theory of Kakitani and Mataga20-22 (KM theory), by means of a nonlinear leastsquares method.

10.1021/jp804130j CCC: $40.75  2008 American Chemical Society Published on Web 09/18/2008

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Methods MD Simulation. The starting structure of the wild-type (WT) FBP was taken from one of 20 NMR structures (pdb code 1AXJ).13 The initial structures of W32A and W32Y were obtained by modifying the WT. Tryptophan at position 32 was replaced by tyrosine and alanine, for W32Y and W32A, respectively. The replacements of amino acids were carried out by using Swiss PDB Viewer.35 All missing hydrogen atoms of the protein were added using the LeaP module of the AMBER software package.36 The parm99 force field37 was used to describe the protein, while force field parameters for the Iso were obtained from Schneider and Suhnel.38 The WT, W32Y, and W32A, were solvated by 6344, 6345, and 6347 TIP3P water molecules, respectively. For each protein, to release bad contacts and relax the systems, the added water molecules were minimized followed with energy minimization of the entire system. Afterward, the whole system was heated from 10 to 298 K over 50 ps and was further equilibrated under periodic boundary conditions at 298 K. The simulations were performed over 2200 ps for WT and 3000 ps for the two mutated systems. Data were collected during the last 1000 ps (1200-2200 ps) for WT and during the 2000 ps (1000-3000 ps) for W32Y and W32A. All MD calculations were carried out using the AMBER8 software package.36 The system was set up under the isobaricisothermal ensemble (NPT) with a constant pressure of 1 atm and constant temperature of 298 K. Electrostatic interaction was corrected by the Particle Mesh Ewald method.39 The SHAKE algorithm40 was employed to constrain all bonds involving hydrogen atoms. A cutoff distance of 10 Å was employed for a nonbonded pair interaction. MD calculations were performed with the time steps of 2 fs. ET Theory. The ET rate by KM theory20-22 is expressed by eq 1:

ν0 kET ) 1 + exp{β(R - R0)}

[



exp -

(

∆G0 ) EIP - G0Iso

8

ES(Iso) )

4

C C

4λSkBT

]

)(

1 1 1 1 1 + 2a1 2a2 R ε∞ ε0

)

C C

Glu Iso Asp +∑ + ∑ ε0RIsoIso(Glu-i) ε0RIso(Asp-i) i)1

i)1

5

9

2 CIsoCLys CIsoCArg CIsoCP + + (4) ε R (Lys-i) i)1 ε0RIso(Arg-i) i)1 ε0RIso(P-i) i)1 0 Iso

∑

∑

8

ES(Trp-32) )

∑

4

C C

C C

Glu 32 Asp +∑ + ∑ ε0R3232(Glu-i) ε0R32(Asp-i) i)1

5

{∆G0 - e2/ε0R + λS + ES}2

(3)

0 GIso is the standard Gibbs energy related to electron affinity of the excited Iso. The EIP values of Trp and Tyr used for the analysis were 7.2 and 8.0 eV, respectively.41 Electrostatic Energy in the Proteins. Protein systems contain many ionic groups, a situation that is different from systems in bulk solution. The ES values between Iso- and all ionic amino acid residues including phosphate anions of FMN [ES(Iso)], between Trp-32+ and all ionic amino acid residues including phosphate anions of FMN [ES(Trp-32)], between Tyr35+ and all ionic amino acid residues including phosphate anions of FMN [ES(Tyr-35)], and between Trp-106+ and all ionic amino acid residues including phosphate anions of FMN [ES(Trp-106)] are expressed as eqs 4, 5, 6, and 7, respectively

i)1

kBT × 4πλS

2 C32CLys C32CArg C32CP + + (5) ε R (Lys-i) i)1 ε0R32(Arg-i) i)1 ε0R32(P-i) i)1 0 32

9

∑ (1)

Here ν0 is an adiabatic frequency and β a coefficient related to the ET process. R and R0 are the donor-acceptor distance and a critical donor-acceptor distance for the ET process, respectively. R was expressed as a center-to-center distance rather than an edge-to-edge distance9,10,43 between a donor and an acceptor, which was obtained as an average distance of all pairs between atoms in Iso and aromatic atoms in Trp or Tyr. The ET process is adiabatic when R < R0 and nonadiabatic when R > R0. kB, T, and e are the Boltzmann constant, temperature, and electron charge, respectively. In the present work, we introduced an electrostatic energy, ES, in the proteins into KM theory, which is described later. λs is known as the solvent reorganization energy14 and is expressed as eq 2

λs ) e2

for Trp, and p-methylphenol for Tyr were obtained by semiempirical molecular orbital method (PM3). (2) The volumes of these molecules were determined as asymmetric rotors. (3) Radii of the spheres having the same volumes as the asymmetric rotors were obtained. The value of a1 of Iso was 0.224 nm, and a2 values for Trp and Tyr were 0.196 and 0.173 nm, respectively. The standard free energy change was expressed with an ionization potential of the ET donor, EIP, as eq 3.

(2)

where a1 and a2 are the radii of the acceptor and donor when these reactants are assumed to be spherical, and ε∞ and ε0 are the optical and static dielectric constants. The optical dielectric constant used was 2.0, which was common in all systems. The radii of Iso, Trp, and Tyr were determined in the following way: (1) Three dimensional sizes of lumiflavin for Iso, 3-methylindole

∑

8

ES(Tyr-35) ) 5

∑

4 C35CGlu C35CAsp + + ε R (Glu-i) i)1 ε0R35(Asp-i) i)1 0 35

∑

∑

9

C C

2

C C

C C

Lys 35 Arg 35 P +∑ + (6) ∑ ε0R3535(Lys-i) ε0R35(Arg-i) ∑ ε0R35(P-i) i)1

i)1

8

ES(Trp-106) )

C

C

C

C

106 Glu 106 Asp + + ∑ ε0R106 (Glu-i) ∑ ε0R106(Asp-i) i)1

i)1

5

i)1

4

2 C106CLys C106CArg C106CP + + (7) ε R (Lys-i) i)1 ε0R106(Arg-i) i)1 ε0R106(P-i) i)1 0 106

∑

9

∑

∑

In eqs 4-7, CIso is the charge of Iso anion and is equal to -e. C32, C35, and C106 are the charges of Trp-32 cation, Tyr-35 cation, and Trp-106 cation, respectively, and all equal to +e. CGlu and CAsp are the charges of Glu and Asp in FBP, respectively, and are equal to -e. CLys and CArg are the charges of Lys and Arg, respectively, and are equal to +e. CP is the charge of phosphate of FMN and equal to -e. FBP contains eight Glu’s, four Asp’s, five Lys’s, nine Arg’s, and two negative charges at FMN phosphate. Distances between Iso and the ith Glu (i ) 1-8) are denoted as RIso(Glu-i). Distances between Trp-32 and the ith Glu (i ) 1-8) are denoted as R32(Glu-i), and so on. The ES in eq 1 was expressed as follows

Analysis of Ultrafast Fluorescence Decays of FBP

J. Phys. Chem. B, Vol. 112, No. 41, 2008 13123

Trp For kET (t′), ES ) ES(Iso) + ES(Trp)

(8)

Tyr (t′), ES ) ES(Iso) + ES(Tyr) For kET Typ kTrp ET (t′) and kET (t′) denote ET rates from Trp

(9)

where and Tyr, respectively. Observed and Calculated Fluorescence Decays. Observed fluorescence decay functions were expressed by eq 10 for WT,23 by eq 11 for W32Y,24 and by eq 12 for W32A.24

FWT obs (t) ) 0.96 exp(-t/0.169) + 0.04 exp(-t/1.5) (10) FW32Y obs (t) ) exp(-t/9.5)

(11)

FW32A obs (t) ) exp(-t/30.1)

(12)

Lifetimes are expressed in ps unit. The calculated decays42 were expressed as eqs 13, 14, and 15 for WT, W32Y, and W32A, respectively, Trp-32 Tyr-35 Trp-106 FWT (t′) + kET (t′) + kET (t′)}t〉AV calc(t) ) 〈exp - {kET

(13) FW32Y calc (t) ) 〈exp

-{

}t〉AV

Tyr-32 Tyr-35 Trp-106 kET (t′) + kET (t′) + kET (t′)

(14) Tyr-35 Trp-106 FW32A (t′) + kET (t′)}t〉AV calc (t) ) 〈exp - {kET

kTrp-32 (t′), kTyr-35 (t′), ET ET

kTrp-106 (t′) ET

(15)

where and are ET rates from Trp32, Tyr-35, and Trp-106, respectively, to the excited Iso, which are given by eq 1. 〈...〉AV means averaging of the exponential

Figure 3. MD structure of W32A near Iso in water.

function in eq 13 over t′ up to 1 ns at 2 ps time intervals, over t′ up to 2 ns with 0.1 ps time intervals in eq 14, and over t′ up to 2 ns with 0.1 ps time intervals in eq 15. In eqs 13-15, we assumed that the decay functions during MD time ranges can be always expressed by exponential functions at every instant of time, t′. Determination of ET Parameters. The unknown ET parameters contained in KM theory were determined to obtain the minimum value of Dev2, defined by eq 16, by means of a nonlinear least-squares method, according to Marquadt algorithm.

Dev2 )

NWT WT 2 {FWT calc(ti) - Fobs (ti)} 1 + NWT i)1 FWT(t )

∑

obs

1 NW32Y

NW32Y

∑ i)1

i

{

}

W32Y 2 FW32Y calc (ti) - Fobs (ti) FW32Y obs (ti)

1 NW32A

+

NW32A

W32Y 2 {FW32A calc (ti) - Fobs (ti)}

i)1

FW32A obs (ti)

∑

(16)

NWT, NW32Y, and NW32A denote numbers of time intervals of WT, W32Y, and W32A, respectively. NWT was 300, NW32Y 200, and NW32A 300. Deviations between the observed and calculated intensities in WT, W32Y, and W32A were expressed by eqs 17, 18, and 19, respectively. Figure 1. MD structure of WT near Iso in water.

Deviation(WT;ti) )

Deviation(W32Y;ti) )

Deviation(W32A;ti) )

WT {FWT calc(ti) - Fobs (ti)}

√FWT obs (ti) W32Y {FW32Y calc (ti) - Fobs (ti)}

√FW32Y obs (ti) W32A {FW32A calc (ti) - Fobs (ti)}

√FW32A obs (ti)

(17)

(18)

(19)

Results

Figure 2. MD structure of W32Y near Iso in water.

Comparison of Molecular Structure among WT, W32Y, and W32A Obtained by MD. Molecular structures around Iso of WT, W32Y, and W32A are illustrated by Figures 1-3. In W32Y, Trp-32 was replaced by Tyr-32 (Figure 2). In W32A, Trp-32 is replaced by Ala-32, which is not shown in Figures 4

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Figure 4. Distance between Iso and nearby aromatic amino acids in W32Y. R32, R35, and R106 indicate average distances between Iso and Tyr-32, between Iso and Tyr-35, and between Iso and Trp-106, respectively.

Figure 7. Interplaner angles between Iso and nearby aromatic amino acids in W32Y. Tyr32, Tyr35, and Trp106 indicate the angles between Iso and Tyr-32, between Iso and Tyr-35, and between Iso and Trp106, respectively.

Figure 5. Distance between Iso and nearby aromatic amino acids in W32A. R35 and R106 indicate average distances between Iso and Tyr35, and between Iso and Trp-106, respectively.

Figure 8. Interplaner angles between Iso and nearby aromatic amino acids in W32A. Tyr35 and Trp106 indicate the angles between Iso and Tyr-35 and between Iso and Trp-106, respectively.

Figure 6. Interplaner angles between Iso and nearby aromatic amino acids in WT. Tr32, Tyr35, and Trp106 indicate the angles between Iso and Trp-32, between Iso and Tyr-35, and between Iso and Trp-106, respectively.

Figure 9. Electrostatic energy in W32Y, here denoted as Eiso, indicates the electrostatic energy between Iso anion and other ionic amino acids including two phosphate anions (given by eq 4). E32, E35, and E106 indicate electrostatic energies between Trp cation and other ionic amino acids including two phosphate anions (given by eq 5), between Tyr-35 cation and other ionic amino acids including phosphate anions (given by eq 6), and between Trp-106 cation and other ionic amino acids including phosphate anions (given by eq 7), respectively.

and 5. In WT, the mean distances over MD time ranges obtained by MD was 0.64 nm between Iso and Trp-32, 1.05 nm between Iso and Tyr-35, and 0.99 nm between Iso and Trp-106. These distances were compared with NMR distances13 of 0.84 nm between Iso and Trp-32, 0.74 nm between Iso and Tyr-35, and 0.82 nm between Iso and Trp-106. In crystal,12 these distances were 0.71 nm between Iso and Trp-32, 0.77 nm between Iso and Tyr-35, and 0.85 nm between Iso and Trp-106. The MD distance between Iso and Trp-32 was quite shorter than those obtained by NMR and crystal structures, while MD distances between Iso and Tyr-35 and also between Iso and Trp-106 were quite longer than those obtained by NMR and crystal structures. Interplaner angles between aromatic planes of Iso and Trp or Tyr are illustrated in Figures 6-8. Two rings of Iso and Trp32 were almost parallel (about 10°) in the time range of 0-0.6 ns, while it increased a little afterward. The interplaner angles between Iso and Tyr-35 and between Iso and Trp-106 were almost constant and perpendicular (about 90°). In W32Y and W32A, the fluctuation of the interplaner angles was much

greater than that in WT. The angles between Iso and Tyr in W32Y and between Iso and Tyr-35 in W32A increased markedly with MD time, from 20° to 50° in W32Y and to 70° in W32A. In the mutated FBP species, the molecular sizes of replaced amino acids of Tyr-32 and Ala-32 are much smaller than Trp in WT, which may cause the great fluctuation of the structure near the Iso binding site in these proteins. Fluctuation of Electrostatic Energy in the Proteins. Electrostatic energies, ES(Iso) in eq 4, ES(Trp-32) in eq 5, ES(Tyr35) in eq 6, and ES(Trp-106) in eq 7, are illustrated in Figure S1 (Supporting Information) for WT, in Figure 9 for W32Y, and in Figure 10 for W32A. In Figure 10 for W32A, ES(Trp32) is not present. In these figures, the value of ε0 used was 9.86, which was obtained by the best-fit procedure described in the Methods section (see also Table 1). Mean electrostatic energies over MD time ranges in WT were 0.071 eV for ES(Iso),

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J. Phys. Chem. B, Vol. 112, No. 41, 2008 13125

Figure 10. Electrostatic energy in W32A, here denoted as Eiso, indicates the electrostatic energy between Iso anion and other ionic amino acids including two phosphate anions (given by eq 4). E35 and E106 indicate electrostatic energies between Tyr-35 cation and other ionic amino acids including phosphate anions (given by eq 6), and between Trp-106 cation and other ionic amino acids including phosphate anions (given by eq 7), respectively. Figure 11. Fluorescence decays of FMN in WT. Fobs and Fcalc indicate the observed and calculated fluorescence decays of WT. The upper panel shows the deviation between the observed and calculated intensities, expressed by eq 17.

0.011 eV for ES(Trp-32), 0.11 eV for ES(Tyr-35), and 0.075 eV for ES(Trp-106). It was most in ES(Tyr-35) and least in ES(Trp-32). In W32Y, the mean electrostatic energies were 0.044 eV for ES(Iso), 0.075 eV for ES(Trp-32), 0.154 eV for ES(Tyr-35), and 0.086 eV for ES(Trp-106). It was again most in ES(Tyr-35) and least in ES(Iso). In W32A, the mean electrostatic energies were 0.051 eV for ES(Iso), 0.156 eV for ES(Tyr-35), and 0.148 eV for ES(Trp-106). It was also most in ES(Tyr-35) and least in ES(Iso). In all cases, the electrostatic energies were always positive. Fluorescence Decays. Fluorescence decays of WT, W32Y, and W32A were calculated with the best-fit ET parameters, which were determined by the method described above. Among ET parameters contained in KM theory, ν0, β, and R0 were assumed to be different between Trp and Tyr. These parameters for Trp were used commonly among Trp-32, Trp-106 in WT, Trp-106 in W32Y, and Trp-106 in W32A. The parameters for Tyr were used commonly among Tyr-35 in WT, Tyr-32 and Tyr-35 in W32Y, and Tyr-35 in W32A. Figure 11 shows the fluorescence decays of WT. The observed two-exponential decay function was quite well reproduced by the calculated decay with these ET parameters. The upper panel of Figure 11 shows a deviation between the observed and calculated decay functions given by eq 17. Figure 12 shows the fluorescence decays of W32Y. The observed decay function was a single exponential with lifetime of 9.5 ps. The coincidence of the calculated decay function with the observed one was quite good, though the calculated decay was a little nonexponential. Figure 13 shows the fluorescence decay functions of W32A. The observed decay was a single exponential with lifetime of 30.1 ps, while the calculated one was nonexponential. Time ranges in Figures 12 and 13 were chosen to be similar with the observed ones.24 Intensity ranges of the decays of W32Y and W32A with long lifetimes were rather narrow, because of the method used (the up-conversion method may not be very accurate for the measurements of decays with long

Figure 12. Fluorescence decays of FMN in W32Y. Fobs and Fcalc indicate the observed and calculated fluorescence decays of W32Y. The upper panel shows the deviation between the observed and calculated intensities, expressed by eq 18.

lifetime). It is not clear whether the both observed decays of W32Y and W32A are really single exponential or not. ET Parameters in KM Theory. The best-fit ET parameters are listed in Table 1. Agreement between the observed and calculated decay functions was much better with the inclusion of ES into the ET rate than without the ES. The values of Dev2 was 2.50 × 10-3 without ES and 5.24 × 10-4 with ES. The values of ν0, β, and R0 for Trp were 1010 ps-1, 20.4 nm-1, and 0.563 nm, respectively, without ES, and 1016 ps-1, 21.0 nm-1, and 0.570 nm, respectively, with ES. The values of ν0, β, and R0 for Tyr were 234 ps-1, 6.60 nm-1, and 1.14 × 10-7 nm,

TABLE 1: ET Parameters Obtained by the Best-Fit Procedurea ET parameters for Trp -1

-1

ET parameters for Tyr

ES energy

ν0 (ps )

β (nm )

R0 (nm )

ν0 (ps )

β (nm-1)

R0 (nm-1)

0 c GIso (eV)

ε0

Dev2d

neglected included

1010 1016

20.4 21.0

0.563 0.570

234 197

6.64 6.25

0.00 0.00

8.97 8.97

10.0 9.86

2.59 × 10-3 5.24 × 10-4

b

-1

-1

a Kakitani and Mataga (KM) theory20-22 was used to determine the ET rate. b Electrostatic energies between Iso anion and other ionic 0 groups, and between Trp or Tyr cation and other ionic groups in FBP were defined by eqs 4-7 in the text. c ∆GIso was -1.77 eV for Trp and d 2 -0.97 eV for Tyr. Dev was defined by eq 16 in the text.

13126 J. Phys. Chem. B, Vol. 112, No. 41, 2008

Figure 13. Fluorescence decays of FMN in W32A. Fobs and Fcalc indicate the observed and calculated fluorescence decays of W32A. The upper panel shows the deviation between the observed and calculated intensities, expressed by eq 19.

respectively, without ES, and 197 ps-1, 6.25 nm-1, and 2.21 × 0 10-8 nm, respectively, with ES. The values of GIso were 8.97 eV without and with ES, and ε0 was 10.0 without ES and 9.86 with ES. Comparing ET parameters with ES between Trp and Tyr, the values of ν0 were 1016 ps-1 for Trp and 197 ps-1 for Tyr. The frequency factor was more than 5 times higher in Trp than in Tyr. The values of β were 21.0 nm-1 in Trp and 6.25 nm-1 in Tyr. β was more than 3 times higher in Trp than in Tyr. The value of R0 was 0.57 nm in Trp but practically zero in Tyr. Free energy of the excited Iso associated with its electron 0 affinity, GIso was 8.97 eV, and ε0 was 9.86 with ES, as stated above. ET Rates in WT, W32Y, and W32A. Time-dependent ET rates from Trp-32, Tyr-35, and Trp-106 to the excited Iso in WT are shown in Figure S2 (Supporting Information). Mean ET rates over the MD time range were 5.82 ps-1 for Trp-32, 1.1 × 10-6 ps-1 for Tyr-35, and 2.3 × 10-3 ps-1 for Trp-106 in WT. Figure S3 (Supporting Information) shows the timedependent ET rates from Tyr-32, Tyr-35, and Trp-106 in W32Y. Mean ET rates over the MD time range were 0.0884 ps-1 for Tyr-32, 0.004 13 ps-1 for Tyr-35, and 0.023 ps-1 for Trp-106. The ET rate from Tyr-32 in W32Y was 1.5% of that from Trp32 in WT. Figure S4 (Supporting Information) shows the ET rates from Tyr-32 and Trp-106 in W32A. Mean ET rates over the MD time range were 5.84 × 10-4 ps-1 for Tyr-35 and 0.0471 ps-1 for Trp-106. Discussion The observed three decays of WT, W32Y, and W32A in the femtosecond to picosecond time domain were simultaneously analyzed with common ET parameters by KM theory and MD. The agreement between the observed decays of WT, W32Y, and W32A with the corresponding calculated decays was quite good, but not complete. The calculated decay functions were always nonexponential, while the observed ones in W32Y and W32A were exponential. The observed decay curves were always nonexponential, which were deconvoluted with two- or three-exponential functions.23,24 It was assumed that a decay function with the lifetime longer than ca. 50 ps was ascribed to be from free FMN with a lifetime of 5 ns dissociated from the protein, because the measurement system used is not accurate enough for decays with lifetime over ca. 50 ps. In some

Nunthaboot et al. flavoproteins there may really exist a lifetime component of several tenths of a picosecond, which could bring about a nonexponential decay function, but this component was assumed to be from free FMN. From a theoretical point of view, it is not clear whether we can use the expressions of KM theory20-22 and other theory14-19 for the analyses of the transient fluorescence in such a short time domain of femtoseconds to picoseconds. Further, the theories are based on continuum model for solvents, but the environment surrounding the donor and acceptor is not uniform in the protein. In the present analysis, KM theory was used for ET rate, since it could reproduce well the observed ET rates in 10 flavoprotein systems9 and also the fluorescence decay43 of WT among ET theories.14-22 In the previous work on WT,43 the same parameters of ν0, β, and R0 were used both for Trp and for Tyr. These parameters were here defined separately between Trp and Tyr, because we could not reproduce the observed all fluorescence decays of WT, W32Y, and W32A good enough if we assume these ET parameters are same between Trp and Tyr. In the present work the electrostatic energies (ES) between Iso anion and other ionic groups and also between Trp or Tyr cation and other ionic groups were introduced into the ET theory. The inclusion of ES drastically improved the fitting between the observed and calculated decays, which suggests that ES plays an important role in ET in the proteins. The importance of ES on ET from Tyr to the excited Iso was also recognized in the work of flavin reductase and flavodoxin reductase according to QM/MM by Callis et al.30 In this work, however, the fluorescence dynamics of these flavoproteins had not been analyzed. The nonexponential decay of WT with very short lifetimes was evident, but those of W32Y and W32A were not very clear. The calculated decays of W32Y and W32A were slightly nonexponential. When a gate time for fluorescence sampling is very narrow, as in WT, distributions of the values of ET rate must be very heterogeneous in the averaging time range (1 ns for WT), which may induce the nonexponential fluorescence decay. When the gate time is quite long, ET rate may be averaged out during the lifetimes, which may reduce a deviation of the fluorescence decay from the exponential function as in W32Y or W32A. ES may enhance the heterogeneity in the ET rate. The values of ν0 were 1016 ps-1 in Trp and 197 ps-1 in Tyr. The values of β were 21.0 nm-1 in Trp and 6.25 nm-1 in Tyr. The values of R0 were 0.57 nm in Trp and almost zero in Tyr. The result of Tyr suggests that an electronic interaction energy between the excited Iso and Tyr is very weak, so ET processes in FBP are nonadiabatic.22 The reliability of these values is not clear at the present, though the method of the analysis in the present work is considered to be the most precise compared to those in the previous works9,43 and other works. The values of ν0, β, and R0 obtained on the basis of the experimental data in bulk solution by Rehm and Weller44 and Nishikawa et al.45 were 5 ps-1, 12 nm-1, and 1.2 nm, respectively.22 The value of ν0 in FBP was much higher than that in the bulk solutions, which may be characteristics for the ultrafast ET in flavoproteins. The value of β in the bulk solution was about twice that of Trp, and about half that of Tyr in bulk solution. The values of R0 for Trp and Tyr in FBP were much shorter than that in the 0 bulk solution. GIso was 8.97 eV, which was common among 0 WT, W32Y, and W32A. The free energy changes, ∆GIso ) 0 EIP - GIso, were -1.77 eV for Trp and -0.97 eV for Tyr. The value of ε0 obtained in the present work was 9.86, which was quite higher than those obtained in the previous works.9,43

Analysis of Ultrafast Fluorescence Decays of FBP According to an atom radial distribution function obtained by the MD structure of WT, several water molecules exist surrounding FMN (manuscript in preparation). One of them locates near O4 of Iso between Iso and Trp32. These water molecules may contribute to the quite high ε0. ET in WT was fastest from Trp-32 and slowest from Tyr-35. ET from Tyr-35 was slower than that from Trp-106 in W32A. The value of ν0 in Tyr was only 20% of that in Trp. This may be the main reason why the ET rate of Tyr-32 in W32Y was much lower compared to that of Trp-32 in WT24 (see also Figure S3 of the Supporting Information). Quantitative analyses of ultrafast ET rates in proteins have been rarely reported in the previous works.26-34 Transient fluorescence (or absorbance) is the only observed data for ultrafast ET phenomena. Accordingly, it is very important to analyze the ET rate so as to reproduce the observed transient fluorescence. In the present work, we have determined every ET parameter of KM theory by the nonlinear least-squares method. The present method may be applicable for other ET processes in proteins, including flavoproteins. Acknowledgment. We would like to acknowledge the Computational Chemistry Unit Cell, Chulalongkorn University, for use of the computing facilities. This work was financially supported by the annual government statement of expenditure of Mahasarakham University (fiscal year 2009). Supporting Information Available: Figures S1-S3. This information is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Karen, A.; Ikeda, N.; Mataga, N.; Tanaka, F. Photochem. Photobiol. 1983, 45, 495–502. (2) Karen, A.; Sawada, M. T.; Tanaka, F.; Mataga, N. Photochem. Photobiol. 1987, 45, 49–54. (3) Zhong, D.; Zwail, A. Proc. Natl. Acad. Sci. U.S.A. 2001, 98, 11867– 11872. (4) Pan, J.; Byrdin, M.; Aubert, C.; Eker, A. P. M.; Brettel, K.; Vos, M. H. J. Phys. Chem. B 2004, 108, 10160–10167. (5) Mataga, N.; Chosrowjan, H.; Shibata, Y.; Tanaka, F. J. Phys. Chem. B 1998, 102, 7081–7084. (6) Mataga, N.; Chosrowjan, H.; Shibata, Y.; Tanaka, F.; Nishina, Y.; Shiga, K. J. Phys. Chem. B 2000, 104, 10667–10677. (7) Mataga, N.; Chosrowjan, H.; Taniguchi, S.; Tanaka, F.; Kido, N.; Kitamura, M. J. Phys. Chem. B 2002, 106, 8917–8920. (8) Tanaka, F.; Mataga, N. Trends Chem. Phys. 2004, 11, 59–74. (9) Tanaka, F.; Chosrowjan, H.; Taniguchi, S.; Mataga, N.; Sato, K.; Nishina, Y.; Shiga, K. J. Phys. Chem. B 2007, 111, 5694–5699. (10) Tanaka, F.; Rujkorakarn, R.; Chosrowjan, H.; Taniguchi, S.; Mataga, N. Chem. Phys. 2008, 348, 237–241. (11) Kitamura, M.; Kojima, S.; Ogasawara, K.; Nakaya, T.; Sagara, T.; Niki Miura, K.; Akutsu, H.; Kumagai, I. J. Biol. Chem. 1994, 269, 5566– 5573. (12) Suto, K.; Kawagoe, K.; Shibata, N.; Morimoto, K.; Higuchi, Y.; Kitamura, M.; Nakaya, T.; Yasuoka, N. Acta Crystallogr., Sect.D 2000, 56, 368–371.

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