3226
J. Phys. Chem. B 2002, 106, 3226-3236
Pigment-Protein Interactions in Bacterial Reaction Centers and Their Influence on Oxidation Potential and Spin Density Distribution of the Primary Donor Frank Mu1 h,†,§ Friedhelm Lendzian,† Mason Roy,‡ JoAnn C. Williams,‡ James P. Allen,‡ and Wolfgang Lubitz*,†,| Max-Volmer-Laboratorium fu¨ r Biophysikalische Chemie, Technische UniVersita¨ t Berlin, Strasse des 17. Juni 135, D-10623 Berlin, Germany, Institut fu¨ r Experimentalphysik, Freie UniVersita¨ t Berlin, Arnimallee 14, D-14195 Berlin, Germany, Department of Chemistry and Biochemistry and Center for the Study of Early EVents in Photosynthesis, Arizona State UniVersity, Tempe, Arizona 85287-1604, and Max-Planck-Institut fu¨ r Strahlenchemie, Stiftstr. 34-36, D-45470 Mu¨ lheim an der Ruhr, Germany ReceiVed: August 10, 2001; In Final Form: December 11, 2001
To study the specific influence of the protein environment in bacterial photosynthetic reaction centers on the oxidation potential and the spin density distribution of the primary electron donor (P), a dimer of the two bacteriochlorophyll (BChl) a molecules PL and PM, site-directed mutants at positions L131 and M160 near the 131-keto groups of the BChls were constructed, in which the native Leu residue was exchanged to either Ser, Asn, Asp, Gln, Glu, or His. In addition, each mutation at one position was combined with the change of Leu to His at the respective other position. For each series of mutants the P/P•+ oxidation potential Vox was determined by electrochemical methods and related to the spin density distribution FL/FM of the unpaired electron of P•+ between PL and PM as determined by ENDOR/TRIPLE resonance spectroscopy. The model by Artz et al. (Proc. Natl. Acad. Sci. U.S.A. 1997, 94, 13582-13587) was revised, extended, and applied to the four series of mutants. Despite its simple nature, the model is able to reproduce the observed related changes of Vox and FL/FM as a result of hydrogen bonding to the 131-keto group of one dimer half and allows for reasonable estimates of orbital energy shifts due to pigment-protein interactions when long-range effects and electron-phonon coupling are considered. On the basis of this model, a hydrogen bond from His to the 131-keto group stabilizes the HOMO of BChl a by approximately 100 meV, which is in reasonable agreement with other experimental data. The electronic coupling between the dimer halves is on the order of 120 to 160 meV, and the reorganization energy associated with a complete charge transfer from PL to PM is between 100 and 200 meV in keeping with earlier estimates.
I. Introduction In the photosynthesis of bacteria, algae, and higher plants, solar energy is absorbed by protein-bound pigments, e.g., bacteriochlorophylls (Figure 1), and funneled to specialized pigments that constitute the so-called reaction center (RC),1 in which the charge separation takes place.2 In all RCs there exists a specific pigment, the primary donor (P), which donates an electron to a series of electron acceptors when it is excited either by direct absorption of a photon or via energy transfer from light-harvesting pigments. The RC can be classified into two types based upon the nature of the electron acceptors.3 The X-ray structure is known for both types of RC4-9 and shows (as a common feature) the presence of an approximate 2-fold symmetry axis relating both the cofactors and the protein subunits. However, at least in RCs of purple bacteria, only one of the two branches of cofactors appears to be photochemically active.10 If we denote the electron acceptors collectively with A, we can * Corresponding author. E-mail:
[email protected]; fax.: +49 208 306 3955. † Technische Universita ¨ t Berlin. ‡ Arizona State University. § Freie Universita ¨ t Berlin. | Max-Planck-Institut Mu ¨ lheim/Ruhr.
Figure 1. Molecular structure of BChl a with IUPAC numbering scheme.
write the primary processes in photosynthesis as follows: hν
kPA
kAP
P0A 98 P*A {\ } P•+A•- 98 P0A * kAP
(1)
Here P0 is the ground state of the primary donor, P* its first excited singlet state, and P•+ and A•- are the radical cation of
10.1021/jp0131119 CCC: $22.00 © 2002 American Chemical Society Published on Web 02/28/2002
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J. Phys. Chem. B, Vol. 106, No. 12, 2002 3227
Figure 2. X-ray crystallographic structure7 of the primary donor P in RC of R. sphaeroides with the two BChl a molecules PL and PM, the two axial ligands His L173 and His M202, the hydrogen bonding residue His L168, and the symmetry-related Phe at position M197, as well as the two Leu residues L131 and M160 in the vicinity of the 131-keto groups.
P and the radical anion of A, respectively. Stable charge separation is achieved when kPA is much larger than the rates for charge recombination, kAP and k/AP. In the native systems the charge separation is further stabilized by electron transfer from a secondary donor (e.g., a cytochrome11,12) to P•+. According to conventional theory13 the rate of electron transfer has a Gaussian dependence upon the free-energy difference between the final and initial states, ∆G0.14 Within the framework of this semiclassical treatment, the free-energy difference for charge separation is related to the oxidation potential of the primary donor, Vox, and the reduction potential of the acceptor, Vred, according to15-17
∆G0 ) F(Vox - Vred) + C
(2)
where F is the Faraday constant and C represents contributions to ∆G0 from the Coulomb attractive energy between radical ions as well as the energy difference between P0 and P* in the case of light-induced charge separation. As is evident from eq 2, the oxidation potential Vox is an important measurable quantity that determines the functional properties of P. A suitable system for studying pigment-protein interactions that influence Vox is the type-II RC of the purple bacterium Rhodobacter (R.) sphaeroides, because it can easily be purified,18 its X-ray structure is known,5-7 and the protein matrix can be selectively manipulated by site-directed mutagenesis.19 In this case, the primary donor is a dimer of BChl a molecules, PL and PM (Figure 2), each of which has specific interactions with certain amino acid residues of the two protein subunits, L and M.6,7 As a result, the energies of the highest occupied molecular orbitals (HOMO), φaL and φaM, of the two BChl moieties are different.20,21 Since P is an electronically coupled dimer, the oxidation potential of P is related to the energy of the HOMO, χ1, of the dimer, which in turn is a linear combination of φaL and φaM (Figure 3). Previous studies of site-directed mutants revealed that in RC of R. sphaeroides Vox can be varied between 410 and 770 mV, as compared with 500 mV in the wild type, by introduction or removal of hydrogen bonds from histidine residues to the 3-acetyl and 131-keto groups of PL and PM.22 Corresponding changes of ∆G0 according to eq 2 were used to explain the changes of ET rates observed in these mutants.22-26 These studies emphasized the role of interactions between the keto groups of the BChl macrocycles and certain amino acid residues in determining the redox properties of the pigments. To learn more about the dependence of Vox on the chemical nature of the amino acid residue interacting with the 131-keto
Figure 3. Two-orbital model of BChl a dimer (for details, see text).
group of a BChl, different series of mutants were constructed, in which Leu L131 or Leu M160 (see Figure 2) is exchanged to either Ser, Asn, Asp, Gln, Glu, or His.27 These mutants are expected to mainly affect the HOMO energy of only one dimer half. This particular situation allows for a theoretical analysis of the relationship between Vox and the distribution of the unpaired π-electron between PL and PM in the P•+ state.28-31 The latter is approximately represented by the spin population ratio FL/FM, which can be determined by using ENDOR/TRIPLE resonance spectrosopy.32,33 As has been shown previously for the M160 mutants, the experimental data can be fit to an analytical expression28-30 in which Vox is described as a function of FL/FM. The two independent fit parameters that could thus be determined were the HOMO energy of the unperturbed dimer half (i.e., aL in the case of the M160 mutants) and the resonance integral βD, which is responsible for the delocalization of the unpaired π-electron. In the present paper the studies by Artz et al.28 are extended to the corresponding L131 mutants as well as to two series of double mutants, in which the changes at positions L131 and M160 are combined with a change of Leu to His at positions M160 and L131, respectively. On the basis of the new experimental data, the limits of the theoretical model28,30 are discussed, and the electronic coupling between the dimer halves as well as the effect of the mutations on the HOMO energy of BChl a are estimated. II. Experimental Methods Strain Construction and Protein Isolation. Oligonucleotidedirected mutagenesis was performed following published procedures.19 The mutated genes were expressed in the R. sphaeroides deletion strain ∆LM1.1, which is derived from strain 2.4.1.34 The construction of the M160 mutants has been described.28,35 Cells were grown semi-aerobically under nonphotosynthetic conditions. RC were isolated by published procedures18,21,23,35 and finally obtained in 15 mM Tris/HCl (pH 8.0), 1 mM EDTA, 1 mM lauryl dimethylamine oxide. The wildtype RC were those from the deletion strain complemented with wild-type genes. Redox Titrations. The oxidation potential Vox was determined by electrochemical methods.17,22,36,37 The amplitude of the long-wavelength absorption of the P0 state around 866 nm was monitored while changing the ambient potential. The relative amount of P0 as a function of the potential was fit to the Nernst equation (n ) 1) using the absorption data combined from oxidative and reductive titrations.22
3228 J. Phys. Chem. B, Vol. 106, No. 12, 2002
Mu¨h et al.
ENDOR/TRIPLE Spectroscopy. EPR, ENDOR, and Special TRIPLE resonance spectra were recorded with a Bruker ESP 300E spectrometer as previously described,38 using ENDOR accessories and an ENDOR TM110 resonator of local design.39 The P•+ state was generated by in situ illumination of the samples with white light from a 150 W tungsten halogen lamp that was passed through 7 cm of water to reduce the light intensity for wavelengths λex g 1000 nm. In some cases edge filters were used to cut off light with λex < 600 nm. For some samples, the detergent was exchanged to 1 mM sodium deoxycholate by dialysis in order to avoid the formation of the second, detergent-induced conformation of the P•+ state.38,40 The proton hfc were determined by deconvolution of the Special TRIPLE resonance spectra,41 and the spin population ratio FL/ FM was calculated from the ratio of methyl proton hfc as described below.
Hi+ - H0 ) ai
(i ) L, M)
Note that the application of Koopmans’ theorem implies that upon removal of one electron from the system the remaining occupied spin orbitals do not change their energies, i.e., orbital relaxation is neglected (frozen orbital approximation). Next we consider the coupled dimer, in which the electrons of Pi are allowed to interact via Coulomb interaction with the electrons and the nuclei of Pj. The solution of the electronic problem of the coupled dimer yields another set of spin orbitals, where we denote by χ1 the HOMO of P with orbital energy E1, by χ2 the HOMO-1 of P with orbital energy E2, etc. Then the neutral state P0 and the singly oxidized state P•+ are represented by the Slater determinants
|P0〉 ) |χ1 χj1 χ2 χj2 ...χ2N χj2N〉 |P•+〉 ) |χ1 χ2 χj2 ...χ2N χj2N〉
III. Theory Basic Model. The relation between the oxidation potential of P, the distribution of the unpaired spin density of P•+ over the two dimer halves, and the energies of the two HOMO of PL and PM has been investigated in earlier work on the basis of a two-orbital model,28 which originates from a Hu¨ckel MO treatment of the ethylene dimer.20,42 To evaluate the limits of such a simple approach and for later reference, we shall derive this model here from a more general point of view. We first consider two BChl molecules named PL and PM, which interact differently with their respective protein environment but do not interact with each other. In this limit the solution of the electronic problem for the dimer within restricted Hartree-Fock theory43 yields two sets of spin orbitals, {φnL,φ h nL} and {φnM,φ h nM}, which are located on PL and PM, respectively. It is assumed that the two spin orbitals φni and φ h ni belonging to the same spatial orbital, but different spin states (spin up and spin down, respectively), have the same orbital energy ni (i ) L, M) and that intermolecular orbital overlap can be neglected. In the following we write n ) a for the HOMO, n ) b for the HOMO - 1 etc. (and n ) r for the LUMO, n ) s for the LUMO + 1 etc.). Then each redox state of the dimer, i.e., the neutral ground state and the two singly oxidized states, in which one electron is removed from the HOMO of PL or PM, can be written as
|P0LP0M〉 ) |φaLφ h aLφaMφ h aMφbLφ h bLφbMφ h bM ... φNLφ h NLφNMφ h NM〉 0 h aMφbLφ h bLφbMφ h bM ... φNLφ h NLφNMφ h NM〉 |P+ L PM〉 ) |φaLφaMφ
h aLφaMφbLφ h bLφbMφ h bM ... φNLφ h NLφNMφ h NM〉 |P0LP+ M〉 ) |φaLφ
(3)
Here we used a short-hand notation for normalized Slater determinants, in which the occupied spin orbitals are listed in the ket-symbol,43 and 2N is the number of electrons of one BChl moiety. The energy H of each determinant is given by the expectation value of the electronic Hamiltonian H ˆ LM of the uncoupled dimer. We introduce the following abbreviations:
ˆ LM|P0LP0M〉 H0 ) 〈P0LP0M|H
(6)
The energy W of each determinant is now given by the expectation value of the electronic Hamiltonian H ˆ D of the coupled dimer:
ˆ D|P0〉 W0 ) 〈P0|H ˆ D|P•+〉 W+ ) 〈P•+|H
(7)
Using again Koopmans’ theorem, we see that according to
W+ - W0 ) E1 ) - FV ox
(8)
the measured oxidation potential of the primary donor is directly given by the negative HOMO energy of P, -E1, within the frozen orbital approximation. In the following we shall give all energies in meV with the energy zero set to ENHE of the normal hydrogen electrode (NHE), so that all HOMO energies can directly be interpreted as oxidation potentials vs NHE and F can be neglected in numerical calculations (i.e., F ) 1). In general, each orbital of P is a linear combination of all occupied and virtual spin orbitals φni of both individual dimer halves. To simplify this problem, one may argue that only those spin orbitals which are close in energy to each other interact significantly. Then only pairwise interactions between the corresponding spin orbitals φnL and φnM of PL and PM have to be considered. If, in addition, the electronic coupling between φnL and φnM is weak (weak coupling limit44), the HOMO of P is essentially only a linear combination of the HOMO of PL and PM:
χ1 ) caLφaL + caMφaM
(9)
and similarly for χ2. The energies E1 and E2 are then given by: 20,28,42
E1,2 )
aL + aM ( 2
x(∆R2 ) + β 2
2 D
1 ) aL + (∆R (∆E) 2 (10)
with ∆R ) aM - aL and
0 0 ˆ LM|P+ HL+ ) 〈P+ L PM|H L PM〉
ˆ LM|P0LP+ HM+ ) 〈P0LP+ M|H M〉
(5)
(4)
It then follows from Koopmans’ theorem43 that the energy required to remove an electron from PL or PM (site potential) is simply given by
∆E ) E1 - E2 ) x∆R2 + 4β2D
(11)
where βD is the intermolecular coupling between φaL and φaM (cf. Figure 3). Equation 10 can be inserted into the secular equations to obtain the coefficients caL and caM in eq 9. Within the two-orbital model, the probability of finding the unpaired
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J. Phys. Chem. B, Vol. 106, No. 12, 2002 3229
electron of P•+ on Pi is given by the orbital population µi ) |cai|2 (i ) L, M) with µL + µM ) 1. It then follows for the orbital population ratio:28,29
( x( ) ) (
µL ∆R ) + µM 2βD
∆R2 +1 4β2D
2
)
∆R + ∆E 2βD
)
2
(12)
which is equivalent to
∆R ) βD
x x µL µM
µM µL
(13)
On the basis of these equations the energy difference between χ1 and φai can be calculated, resulting in a simple relationship between the measured oxidation potential of P and the orbital population ratio:
V ox ) -ai - βD
x
| |
µj caj ) -ai - βD µi cai
(i, j ) L, M) (14)
Relationship between Orbital Population Ratio and Measured hfc. Since in the P•+ state the unpaired electron is (in general) delocalized over PL and PM, it interacts via hyperfine couplings (hfc) with magnetic nuclei of both BChl molecules. The hfc can be measured by ENDOR and Special TRIPLE (ST) resonance spectroscopy.32,33 For protons the first-order resonance condition is
νST ) |νENDOR - νH| )
|| A 2
(15)
where νST is the swept Special TRIPLE frequency, νENDOR the resonance frequency observed in a corresponding ENDOR experiment, νH the Larmor frequency of a free proton in the applied B0 field, and A the isotropic hyperfine coupling constant of the respective proton in the molecule. The resonances are recorded as first-derivative spectra such as the one of P•+ in wild-type RC shown in Figure 4. Here, the resonance frequencies νST, from which the hfc constants A can be inferred according to eq 15, correspond to the zero-crossings of the individual resonance lines. Since there is usually a strong overlap of different lines, the spectra have to be deconvoluted, where each individual transition is assumed to have a Lorentzian line shape.41 For wild-type RC, the assignment of individual resonances to specific protons of the BChl a molecules has been achieved by comparison with monomeric BChl a•+ in organic solution45 and selective isotope labeling.46 Equivalent positions in PL and PM have been distinguished by experiments on RC single crystals20 and on the so-called heterodimer mutants,21,47 in which the spin is located on one dimer half. The most prominent hfc arise from the methyl protons at positions 21 and 121 as well as from the β-protons at positions 7, 8, 17, and 18 (Figure 1). The positive isotropic hfc constants A(21) and A(121) of the methyl protons are used in the present work to obtain information about the distribution of the unpaired electron of P•+ over the two BChl moieties.48 For the uncoupled dimer, the resulting electron density of state i (i ) 0, L, M; see eq 3) at position x is the sum of the density pi(x) of electrons with spin up and pji(x) of electrons with spin down, whereas the net spin density is given by
Qi(x) ) pi(x) - pji(x)
(16)
Figure 4. 1H-Special TRIPLE spectra (X-band) of light-induced P•+ in RCs of R. sphaeroides isolated from wild type and mutants with changes at position L131. The line positions for the protons at the 21and 121-methyl groups of PL and PM are indicated by solid and dashed lines, respectively. For assignment of hfc, see Table 1. In addition to the methyl signals, lines from β-protons at rings B and D are evident at νST g 3 MHz.
The isotropic hfc for a proton at position xH is proportional to Qi(xH).49 Within the restricted Hartree-Fock formalism, the 0 0 + net spin density of the states |P+ L PM〉 and |PLPM〉 is simply
Qi(x) ) |φai(x)|2
(i ) L, M)
(17)
if an electron is taken out of the spin orbital φ h ai as suggested by eq 3. To see how positive spin density occurs at the positions of the methyl protons, we represent φai as a linear combination of atomic orbitals (LCAO) φν
φai(x) )
∑ν diνφν(x)
(18)
The main contribution to φai comes from the 2pz orbitals located at the carbon and nitrogen atoms of the π-system of BChl a (Figure 1). However, due to hyperconjugation49 there are small but important contributions from the s orbitals of the methyl protons to the LCAO (eq 18), resulting in nonzero net spin densities Qi(21) and Qi(121) at the methyl protons and hence giving rise to the measurable isotropic hfc Ai(21) and Ai(121).50 For the coupled dimer, we assume that in the weak coupling limit the φai are neither changed due to the coupling nor affected by the mutations, i.e., the coefficients diν in eq 18 are constants. In this limit, the spin densities at the methyl protons are a direct measure of the orbital population µi. The validity of this approximation can be assessed from the intramolecular spin density ratio
3230 J. Phys. Chem. B, Vol. 106, No. 12, 2002
Ri )
Qi(121) Qi(21)
)
Ai(121) Ai(21)
(i ) L, M)
Mu¨h et al.
(19)
which is expected to depend on the orientation of the 3-acetyl group,51 the ring geometry,21 and to a lesser extent on specific pigment-protein interactions such as axial ligation52 or hydrogen bonding.21 A hydrogen bond to the 131-keto group of either BChl moiety is found to increase Ri by approximately 10%.21 Therefore, in the L131 and M160 mutants both intramolecular spin density ratios are expected to be only approximately constant and close to the characteristic values found in the wild type, RL ) 1.44 and RM ) 2.35. The spin population of φai is defined as
Fi )
∫Qi(x) dx
AM(21) + AM(121)
(21)
Since µL + µM ) 1, it then follows that FL + FM ) 1 and that the sum of all methyl proton hfc
S ) [AL(21) + AL(121) + AM(21) + AM(121)]
(22)
should be a constant as well. Combining eq 21 with eq 14 results in a simple relationship between the measured oxidation potential of P and the spin population ratio
V ox ) -ai - βD
x
Fj Fi
(i, j ) L, M)
(23)
which is the model used by Artz et al.28 in its corrected form.29,30 Modeling of Electron-Phonon-Coupling. The structure of the neutral BChl a molecule differs from that of its cation radical. Since a redistribution of spin density between the two dimer halves is associated with a change of µL/µM via eq 21, the mutations studied here are expected to cause a change of the fraction of positive charge on Pi in the P•+ state, represented by the orbital population, µi. This should cause a significant change of the equilibrium coordinates of the nuclei due to the mutations in the state |P•+ 〉, but not in |P0〉. To model energetic relaxation of this kind, it is useful to introduce a set of normal coordinates q of the dimer that depend on the redox state of the individual dimer halves, i.e., on µi.30 As a consequence, all energies and energy differences in eqs 10 to 14 become a function of q, whereas βD is assumed to be independent of q. It is useful to distinguish between the energy difference ∆R of the localized states at their respective equilibrium coordinates and the actual energy difference ∆R′ of these two states at the equilibrium coordinates of the coupled dimer. Using the harmonic approximation for the dependence of the orbital energies on the nuclear coordinates, it can be shown that30
∆R′ ) ∆R + λ (µL - µM)
(25)
Within this framework, setting µi ) Fi, the following extension to eq 23 can be derived:30
V ox ) -ai + λF2j - βD
x
Fj Fi
(i, j ) L, M)
(26)
Note that the correction to the site energy ai scales with the spin population Fj of the HOMO of the remote dimer half Pj and vanishes, as expected, if the state is localized on Pi (Fj ) 0) or if electron-phonon coupling can be neglected (λ ) 0). IV. Experimental Results
∫QL(x) dx QL(21) + QL(121) ) ) ∫QM(x) dx QM(21) + QM(121) AL(21) + AL(121)
∆E ) x[∆R + λ(µL - µM)]2 + 4β2D
(20)
With the approximation of constant Ri, reflecting the constancy of the function Qi(x), we can write
µL FL ) ) µM FM
the energetic relaxation of the normal modes due to a complete charge transfer from µi ) 0 to µi ) 1. Then, eq 11 becomes
(24)
where λ is the total reorganization energy associated with the 0 0 + formal electron transfer from |P+ L PM〉 to |PLPM〉, representing
The 1H-Special TRIPLE spectra of the wild type and the L131 mutants are shown in Figure 4. The spectrum of the mutant LH(L131), in which a His residue is introduced in the vicinity of the 131-keto group of PL (cf. Figures 1 and 2), and the assignment of the observed resonances to protons of the two BChl macrocycles have been discussed in an earlier publication.21 For this mutant, four methyl proton hfc are detected that indicate a more symmetric distribution of spin density in P•+ as compared with the wild type. On the basis of the condition that the four methyl hfc are assigned to the two BChl moieties in such a way that intramolecular spin density ratios (eq 19) of RL ≈ 1.4 and RM ≈ 2.3 (see above) are obtained, the assignment depicted in Figure 4 results. The spectra of the other L131 mutants were analyzed in a similar manner after deconvolution of overlapping lines.41 In all cases the ratios RL and RM are found to be in the expected range, i.e., RL ) 1.5 ( 0.2 and RM ) 2.4 ( 0.4 (Table 1), which allows for a straightfoward determination of FL/FM. In all L131 mutants the distribution of spin between PL and PM is somewhat more symmetric than in the wild type. The opposite effect has been found earlier for the M160 mutants.28 For the double mutants with LH(M160), the effects of the different amino acid residues at position L131 on FL/FM are essentially the same as in the single mutants, but the additional mutation at position M160 results in an overall increase of FL/FM (Table 1). Similarly, the effects of the different residues at position M160 are qualitatively the same irrespective of whether there is a Leu or a His at position L131, but His L131 causes an overall decrease of FL/FM. Each of the mutations causes an increase of the oxidation potential of the primary donor, Vox (Table 1). The potential shift of the double mutants relative to wild type is, in general, approximately the sum of that of the individual mutations. Quantitatively, the effect of a certain amino acid substitution is similar in each case, with Ser causing the smallest increase in potential and His the largest, i.e., the order of residues with increasing potential is approximately
Lys < Ser < Asn < Asp < Gln < Glu < Tyr < His (27) Only Ser and Asn change their position for the L-side mutations. The same order is observed when comparing the values of FL/ FM (Table 1), but the differences between Ser and Asn are less pronounced. The data indicate a strong correlation between the oxidation potential and the spin population ratio. V. Discussion Effects of Mutations on Fit Parameters. There is a clear qualitative effect of the mutations on both oxidation potential
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J. Phys. Chem. B, Vol. 106, No. 12, 2002 3231
TABLE 1: Isotropic 1H-hfc Constants A (MHz; error: ( 30 KHz, if not stated otherwise) and Spin Population Ratios GL/GM of Light-induced P•+ and P/P•+ Oxidation Potentials Vox (mV; maximal error: ( 10 mV) for R. sphaeroides RC with Mutations at Residues Leu L131 and Leu M160
h
strain
AL(121)
AL(21)
AM(121)
AM(21)
RLd
RMd
Se
FL f
FL/FM g
Vox h
wild typea LK(M160)b LS(M160)b LN(M160)b LD(M160)b LQ(M160)b LE(M160)b LY(M160)b LH(M160)a LH(L131)a LE(L131) LD(L131) LQ(L131) LS(L131) LN(L131) LH(L131)+LN(M160) LH(L131)+LS(M160) LH(L131)+LD(M160) LH(L131)+LQ(M160) LH(L131)+LE(M160) LH(L131)+LH(M160)a LE(L131)+LH(M160) LD(L131)+LH(M160) LQ(L131)+LH(M160) LN(L131)+LH(M160) LS(L131)+LH(M160)
5.75 5.49 5.69 5.85 6.24 6.55 6.70 6.90 6.95 3.98 4.6c 5.16 5.21 5.22 5.29 4.16 4.3c 4.95 5.53 6.01 6.10 7.00 6.90 6.80 6.79 6.95
3.98 3.89 4.02 4.10 4.43 4.77 4.75 5.10 5.15 2.87 2.8c 3.25 3.25 3.30 3.4c 2.6c 2.6c 2.99 3.48 3.9c 3.97 4.36 4.40 4.52 4.70 4.77
3.24 3.44 3.30 3.10 2.75 2.25 2.15 1.75 1.70 5.42 5.0c 4.14 3.99 3.94 3.9c 5.69 5.71 4.95 4.33 3.9c 3.19 2.80 2.53 2.51 2.13 2.07
1.38 1.45 1.30 1.20 1.10 0.85 0.85 0.80 0.75c 2.33 2.4c 1.99 1.94 1.79 1.63 2.6c 2.6c 2.29 1.69 1.43 1.37 1.0c 1.0c 1.0c 0.8c 0.8c
1.44 1.41 1.42 1.42 1.41 1.37 1.41 1.35 1.35 1.38 1.64 1.59 1.60 1.58 1.56 1.60 1.65 1.66 1.59 1.54 1.54 1.61 1.57 1.52 1.44 1.45
2.35 2.37 2.54 2.58 2.51 2.65 2.53 2.19 2.27 2.33 2.08 2.08 2.06 2.20 2.39 2.19 2.20 2.16 2.56 2.72 2.36 2.80 2.53 2.51 2.60 2.60
14.35 14.27 14.31 14.25 14.52 14.42 14.45 14.55 14.55 14.60 14.80 14.54 14.39 14.25 14.22 15.05 15.21 15.18 15.03 15.24 14.63 15.16 14.83 14.81 14.44 14.59
0.68 0.66 0.68 0.70 0.74 0.79 0.79 0.82 0.83 0.47 0.51 0.58 0.59 0.60 0.61 0.45 0.45 0.52 0.60 0.65 0.69 0.75 0.76 0.76 0.80 0.80
2.11 1.92 2.11 2.31 2.77 3.65 3.82 4.71 4.94 0.89 1.00 1.37 1.43 1.49 1.57 0.82 0.83 1.10 1.51 1.86 2.21 2.99 3.20 3.23 3.89 4.08
503 511 514 527 539 544 546 558 563 578 555 544 551 535 535 591 584 606 619 623 621 615 600 600 583 594
a Hfc from ref 21. b Hfc and oxidation potential from ref 28. c Error of this hfc: (200 kHz. d eq 19. e eq 22. f F ) (A (21) + A (121))/S. g eq 21. L L L Oxidation potential from electrochemical titrations.
and spin population ratio. Each mutation causes an increase in the oxidation potential, with substitution by His leading to the largest change. As the oxidation potential increases, the ratio FL/FM systematically increases for the M-side mutations and decreases for the L-side mutations. To discuss this correlation in the framework of the theoretical model outlined in section III, it is necessary to make additional assumptions concerning the effects of the mutations on the involved parameters. There are three independent parameters, namely λ, ∆R, and βD (eq 25). Reorganization Energy. We shall assume that the mutations disturb only a few normal modes, such that the total reorganization energy λ can be considered to be constant. To avoid fitting with three free parameters, which yields ambiguous results, it is useful to keep λ fixed during the fitting.30 Realistic estimates of λ can be obtained from a theoretical analysis of FTIR data.53 A band at ∼2600 cm-1, corresponding to an energy difference of ∆E ≈ 320 meV, is characteristic of the dimeric P•+ state of the wild type. This band has been assigned to an electronic transition from χ2 to χ1 (cf. Figure 3), which involves a significant charge transfer, depending essentially on the parameters ∆R, βD, and λ. A theoretical analysis of this intervalance transition places the total reorganization energy in the range 100 meV < λ < 200 meV.54 Therefore, we set λ to 0, 100, and 200 meV. Energy Difference of Localized States. Possible effects of the mutations on ∆R can be seen from studies on so-called heterodimer mutants.37 The exchange of the axial ligand His M202 of PM (Figure 2) to Leu results in the loss of the central Mg ion of this cofactor and hence in the transformation of the BChl PM into the BPh DM. After oxidation of this heterodimer, the unpaired electron is located on the BChl-half, i.e., the state 0 |P+ L DM〉 is formed. Consequently, the measured oxidation potential Vox of such a heterodimer mutant corresponds to the HOMO energy of PL, if the coupling to DM and effects of the
mutation at position M202 on aL can be neglected. For the three heterodimer mutants HL(M202), HL(M202)+LH(L131), and HL(M202)+LH(M160), Vox was found to be 640 ( 10, 720 ( 15, and 655 ( 10 mV, respectively.37 It follows, that the introduction of His at position L131 stabilizes the HOMO of PL by 80 ( 18 meV, whereas the effect of His at position M160 on PL is only 15 ( 15 meV, i.e., within the error limits. We have thus two possibilities to model changes of ∆R: (a) Short-range model. We can neglect any effect of mutations near Pj on the orbitals of Pi, i.e., consider only short-range interactions of the mutated residues. In this case, the change of ∆R within each series of mutants is identical to the shift of aj, and eq 26 can directly be used as fitting relationship, where ai is a constant. (b) Long-range model. We can assume that a mutation near Pj changes ai by a certain fraction η of the shift of aj due to long-range effects of the mutated residues as has already been discussed in ref 28. With this assumption the following formula can be derived from eq 26:
V ox ) -ai + λ
βD
[
[ (x x x ) η (1 - η)
]
η 1 2 - F2i ) + (F2 - Fj,Leu F2 + (1 - η) i,Leu (1 - η) j Fi + Fj
Fj,Leu Fi,Leu
Fi,Leu 1 Fj,Leu (1 - η)
x] Fj Fi
(28) where Fj,Leu and Fi,Leu are the respective local spin populations for the case of a Leu residue near Pj within the mutant series.55 For η ) 0, eq 28 reduces to eq 26. This formula can only be used as fitting relationship if η is kept fixed during the fit and is assumed to be the same for each type of residue. The oxidation potentials of the heterodimer mutants suggest that 0 e η e 0.2.56 Electronic Coupling. The simplest way to treat the third independent fit parameter, βD, is to keep it constant, as has been
3232 J. Phys. Chem. B, Vol. 106, No. 12, 2002
Mu¨h et al.
TABLE 2: Results of Fitting the Experimental Data (Table 1) to Eq 28 with the Assumption that βD Is Not Affected by the Mutationsa λ ) 0 meV
a
λ ) 100 meV
λ ) 200 meV
η
-ai
βD
-ai
βD
-ai
βD
M160
0.0 0.1 0.2 0.2b
648 ( 13 606 ( 8 580 ( 6 573 ( 3
194 ( 21 133 ( 15 96 ( 11 80
660 ( 13 618 ( 9 592 ( 6 588 ( 2
227 ( 21 166 ( 15 128 ( 11 120
672 ( 13 630 ( 9 604 ( 6 604 ( 2
259 ( 21 198 ( 15 160 ( 12 160
M160 + LH(L131)
0.0 0.1 0.2 0.2b
693 ( 16 671 ( 13 655 ( 10 670 ( 4
97 ( 18 77 ( 14 62 ( 12 80
715 ( 17 694 ( 13 677 ( 10 686 ( 3
145 ( 18 125 ( 15 109 ( 12 120
738 ( 17 717 ( 14 700 ( 11 703 ( 3
193 ( 18 173 ( 15 157 ( 12 160
L131
0.0 0.1 0.2 0.2b
696 ( 22 666 ( 18 639 ( 14 628 ( 3
130 ( 18 109 ( 16 91 ( 13 80
718 ( 22 688 ( 17 661 ( 14 642 ( 3
177 ( 18 156 ( 15 138 ( 13 120
740 ( 21 710 ( 17 684 ( 14 657 ( 4
225 ( 18 204 ( 15 185 ( 13 160
L131 + LH(M160)
0.0 0.1 0.2 0.2b
741 ( 23 720 ( 20 699 ( 17 736 ( 4
78 ( 12 68 ( 11 59 ( 10 80
737 ( 22 715 ( 19 694 ( 16 749 ( 5
107 ( 12 97 ( 10 88 ( 9 120
732 ( 21 710 ( 18 689 ( 15 763 ( 6
137 ( 11 127 ( 10 118 ( 9 160
series
All energies are given in meV. The two parameters η and λ were kept fixed during the fitting. b In these cases, βD was also fixed.
done in refs 28 and 30, and to use eq 26 or 28 directly as fitting relationship. This treatment implies that any effect of the mutations on the electronic coupling between the HOMO of PL and PM can be neglected. However, it cannot be excluded that βD is changed by the mutations due to a perturbation of the HOMO or structural rearrangements of the dimer. Besides the assumption of constant βD, another possibility of fitting the data is given by the fact that the position of the intervalence transition53 was found to be essentially unchanged at least in the M160 mutants as well as LH(L131) and LH(L131) + LH(M160).57,58 Within the two-orbital model, in which ∆E is assigned to the maximum of the intervalence band, this suggests that ∆E is constant within a range of about 20 meV. Combining eqs 11 and 13 and setting µi ) Fi yields βD ) ∆ExFLFM. This result is independent of λ and reduces to the well-known relation βD ) ∆E/2 for ∆R ) 0. It is thus possible to substitute βD in eq 26 or 28 and to use ∆E as a fit parameter. Within the short-range model, the data can indeed be fitted in this way (not shown). However, realistic values of ∆E (i.e., 300 ( 40 meV) are only obtained for λ ) 0, but not for all four series of mutants. Considering realistic values of λ (see above)54 results in an overestimation of ∆E by up to 430 meV. Similar problems occur within the long-range model. Therefore, we prefer to use βD instead of ∆E as the relevant fit parameter. Fitting Results. Short-Range Model. According to the shortrange model without electron-phonon coupling (eq 23), the oxidation potential of the primary donor, Vox, can be related to the square root of the spin population ratio Fj/Fi (j ) L for L131 mutants, j ) M for M160 mutants) by a linear dependence with two parameters, the slope βD and the site energy ai, that is related to the zero-intercept (Figure 5). For all four series of mutants, the data can be well described by such a linear dependence, but with different values of βD ranging from 78 to 194 meV (Table 2, η ) 0, λ ) 0). Note that this range of βD values is larger than the uncertainty of each individual value. Interestingly, the βD values are smaller for the double mutants than for the single mutants. This could indicate that the change of His to Leu at either position lowers the electronic coupling between the dimer halves. However, since a His mutant is part of each mutant series, such a change of βD is not in agreement with the initial assumption. Therefore, the original model28 is
Figure 5. Correlation of Vox and (Fj/Fi)1/2 for the four series of mutants. Experimental data are represented by symbols: 2 L131 mutants (j ) L), 3 L131 mutants combined with LH(M160) (j ) L), b M160 mutants (j ) M), O M160 mutants combined with LH(L131) (j ) M). (A) Fits to eq 26 with λ ) 0 (solid), 100 (dashed), and 200 meV (dotted), showing the effect of electron-phonon coupling within the short-range model. (B) Fits to eq 28 (λ ) 0 meV) with η ) 0 (solid), η ) 0.2 with variable βD (dashed) and η ) 0.2 with βD ) 80 meV (dotted), demonstrating the effect of considering long-range interactions without electron-phonon coupling.
not able to yield a quantitatively consistent description of the experimental data. It has already been noted by Reimers et al.30 for the M160 mutants, that the electron-phonon correction to the site energy
Pigment-Protein Interactions
J. Phys. Chem. B, Vol. 106, No. 12, 2002 3233 TABLE 3: Site Energy Differences (∆r, ∆r′) and Shifts (∆Eai) as Calculated from the Fit Parameters Eai in Table 2 (η ) 0.2, βD Fixed) and the Measured Spin Populations µi ) Gi (eq 24)a λ) 0 meV
λ) λ) 100 meV 200 meV
wild type
∆Rb 55 ( 5 54 ( 4 ∆R′ c 55 ( 5 90 ( 4 βD (fit)d 80 120 βD (ENDOR)e 72 ( 7 118 ( 6 βD (FTIR)f 140-185 145-175
LH(L131)
∆Rg ∆R′ c βD (fit)d βD (ENDOR)e βD (FTIR)f
-42 ( 5 -42 ( 5 80 360 ( 43 140-190
-44 ( 5 -50 ( 5 120 429 ( 43 140-185
-46 ( 5 -58 ( 5 160 497 ( 43 140-185
Figure 6. Same experimental data as in Figure 5, but together with fits to eq 28 (η ) 0.2) for either λ ) 0 meV, βD ) 80 meV (solid), λ ) 100 meV, βD ) 120 meV (dashed) or λ ) 200 meV, βD ) 160 meV (dotted).
LH(M160)
∆Rh 163 ( 5 ∆R′ c 163 ( 5 βD (fit)d 80 e βD (ENDOR) 92 ( 3 βD (FTIR)f 103-155
161 ( 6 227 ( 6 120 128 ( 4 110-135
159 ( 7 291 ( 7 160 164 ( 2 65-90
ai according to eq 26 causes some nonlinearity of the relationship between Vox and (Fj/Fi)1/2 (Figure 5A, η ) 0). As expected, this effect increases with increasing spin density on Pj. The differences between the fits for λ ) 0 and λ * 0 are, however, not significant in view of the scattering of the experimental data. The magnitudes of the site-energies ai are somewhat increased, with the exception of the L131 + LH(M160) mutants. The range of fitted βD values is not significantly diminished compared to the case with λ ) 0, while the absolute βD values are increased. This shows that the neglect of electron-phonon coupling may lead to an underestimation of the electronic coupling βD, but is not responsible for the differences of this parameter between the four series of mutants. Long-Range Model. Fitting the data to the long-range model without electron-phonon coupling (eq 28, λ ) 0) shows that both fit parameters, ai and βD, are decreased with increasing η (Table 2). Interestingly, the range of βD values is decreased to about 65 ( 23 and 37 ( 18 meV for η ) 0.1 and 0.2, respectively, indicating that the neglect of long-range interactions could to a large extent be responsible for the differences of the fitted electronic coupling. This suggests that for η ) 0.2 a fit with the same βD value for all four series of mutants should be possible in agreement with the initial assumption. This is indeed the case, although fixing βD to the average value of 80 meV (Table 2) yields a less satisfying fit of the experimental data (compare dashed and dotted curves in Figure 5B). Similar results are obtained for λ * 0, i.e., the range of βD values mainly depends on η and to a lesser extent on λ. Consequently, fits with η ) 0.2 and fixed βD can be performed (Table 2), but again are somewhat less accurate (Figure 6). Interpretation of Fit Parameters. Site Energies and Site Energy Shifts. The quality of the data in Table 2, obtained for η ) 0.2 and the same constant βD for all series, can be assessed from a comparison with other experiments. Information about the orbital energy aL is obtained from the oxidation potentials of the heterodimer mutants37 (see above). The values of -aL ) 604 and 703 meV obtained from the M160 and M160 + LH(L131) series for λ ) 200 meV are reasonable estimates for the oxidation potentials of the HL(M202) and HL(M202) + LH(L131) mutants. For λ ) 0 and 100 meV, the corresponding values of -aL are lower by ∼30 and ∼15 meV, respectively. The fit parameters thus underestimate the oxidation potentials of the heterodimers by about 30 to 60 meV, but it must be taken into account that the loss of the central Mg2+ from PM could affect -aL. A better approach is to compare the estimates for
LH(L131) + LH(M160)
∆Ri 66 ( 6 ∆R′ c 66 ( 6 βD (fit)d 80 βD (ENDOR)e 81 ( 8 βD (FTIR)f 140-185
63 ( 6 101 ( 6 120 124 ( 8 140-175
60 ( 7 136 ( 7 160 167 ( 9 135-170
98 ( 4 107 ( 6
99 ( 4 106 ( 8
site energy shift due ∆aLj to Leu f His ∆aMk
97 ( 5 108 ( 5
53 ( 5 125 ( 5 160 164 ( 7 140-165
a To check the consistency of the model, ∆R values were used to calculate βD from the ENDOR data on the basis of eq 13 and compared with the βD values used in the fit. Alternatively, βD was calculated from eq 25 to check consistency with FTIR data. b ∆R ) aM(L131) aL(M160). c eq 24. d Table 2. e Calculated from ∆R’ on the basis of eq 13 with ∆R replaced by ∆R’ and µi by Fi. f Estimated from ∆R’ on the basis of eq 25 with 320 meV e ∆E e 340 meV.56,57 g ∆R ) aM(L131) - aL(M160+LH(L131)). h ∆R ) aM(L131+LH(M160)) aL(M160). i ∆R ) aM(L131+LH(M160)) - aL(M160+LH(L131)). j ∆ k aL ) aL(M160) - aL(M160+LH(L131)). ∆aM ) aM(L131) aM(L131+LH(M160)).
the change in energy ∆aL due to the LH(L131) mutation. A value of ∆aL between 92 and 103 meV is obtained, which is essentially insensitive to the chosen value of λ (Table 3) and is in excellent agreement with the experimental value of 80 ( 18 meV. Assuming that the other ai values obtained in this way provide reasonable estimates of site energy differences as well, we predict that the shift ∆aM due to the LH(M160) mutation is slightly larger, i.e., between 98 and 113 meV. This is in agreement with the experimental finding that the spin distribution in the double mutant LH(L131) + LH(M160) is slightly more asymmetric than in the wild type. If both His mutations would increase the respective site potential by exactly the same amount, no difference in FL/FM should be observed with respect to the wild type, provided βD remains unaffected. The ai values from each pair of mutant series can be used to calculate the site energy difference ∆R for the mutants LH(L131), LH(M160), LH(L131) + LH(M160), and the wild type, which are each contained in two series. For instance, the value aL obtained from the M160 single mutants and aM from the L131 single mutants should correspond to the site energies of the wild type, resulting in ∆R ) 55 ( 5 meV (Table 3). In this way the consistent result is obtained that ∆R is increased in the LH(M160) mutant, decreased in LH(L131), and approximately restored in the double His mutant (Table 3). Electronic Coupling. A consistency check is provided by eq 13 with µi ) Fi. It allows for a calculation of βD from the values of ∆R as calculated from ai in Table 2 and the spin population
3234 J. Phys. Chem. B, Vol. 106, No. 12, 2002 ratio. The calculated value of βD should agree with the corresponding value of βD used in the fit. Note that for λ * 0, eq 24 has to be taken into account. We can, for example, estimate from FL/FM ) 2.11 for the wild type and the data for the L131 and M160 mutants that βD ≈ 70, 120, and 160 meV for λ ) 0, 100, and 200 meV, respectively. These values are in excellent agreement with the fitted average value of βD (Table 3). Similar agreement is obtained for the three mutants with the exception of LH(L131), for which βD (ENDOR) is severely overestimated. In the latter case, the small deviation of the spin population ratio from symmetry must be taken into account, which implies a large relative error of the calculated βD value (the errors given in Table 3 only originate from the uncertainty of the fitted ai values). It follows that, in general, the results from the fits with constant βD and η ) 0.2 are consistent with the ENDOR data, both with and without electron-phonon coupling, at a reasonable degree of accuracy. On the basis of the ENDOR data alone, βD is estimated to be between 80 and 160 meV. InterValence Transition. To see whether electron phonon coupling is important, we have calculated βD in an alternative way by using eq 25 and the published FTIR data.57,58 Assuming that the intervalence transition53 is not strongly affected by the mutations, we placed ∆E between 320 and 340 meV in the calculations. In general, a better agreement with the βD values used in the fits is obtained for λ ) 100 or 200 meV than for λ ) 0 meV (Table 3). As expected, electron phonon coupling has to be taken into account in order to reach consistency with the FTIR data, and earlier estimates of the reorganization energy54 are corroborated. Then, βD has to be placed between 120 and 160 meV. Limits of the Model. Our MO model of P implicates several assumptions, which may limit the interpretation of the data. The most important approximation is the identification of the spin population ratio FL/FM with the orbital population ratio µL/µM (eq 21), which in turn is based on three assumptions: (i) The oxidized state |P•+〉 of the coupled dimer can be described as a linear combination of only the ground state determinants of the 0 0 + localized states |P+ L PM〉 and |PLPM〉, i.e., no configuration interaction occurs. This assumption has been questioned on the basis of semiempirical calculations, indicating mixing of the ground state with higher electronic states of different spin multiplicity.59 Of particular importance is the coupling to the 3 3 + so-called tripdoublet states |P+ L PM〉 and |PLPM〉, giving rise to a -1 tripdoublet band at 8000 cm (1250 nm) of P•+. Mixing with these states can cause significant deviations of FL/FM from µL/ µM as has recently been shown by DFT studies.60 In principle, such an effect can be modeled by using a four-state model,61 but then more independent parameters have to be determined. This is only possible on the basis of additional experimental data like the exact position and intensity of the tripdoublet band or transient ENDOR spectra of the triplet state of P,62 which have not been studied so far in the L131 and M160 mutants. (ii) The coefficients diν in eq 18 are constants. A readjustment of these coefficients due to the mutations cannot be excluded. This could cause a change of the degree of hyperconjugation, making the application of eq 21 problematic. (iii) Spin polarization can be neglected. This is a critical assumption, since the presence of the unpaired spin will surely lift the degeneracy of each pair of spin orbitals φni and φ h ni. Although this effect may be negligible on the energy scale, it could affect the net spin densities Qi(xH) at the proton positions.50 A more rigorous quantum-chemical treatment of these effects requires the detailed knowledge of the mutant structures (of P•+)
Mu¨h et al. including hydrogen bond distances, which may be obtained from a combined quantum mechanical/molecular mechanical approach as proposed by Hutter et al.63 Such elaborated calculations are beyond the scope of the present work. Relationship between Site-Energy Shifts and Amino Acid Properties. In principle, the site-energy shift ∆ai caused by a certain mutation in the vicinity of the 131-keto group of Pi can be calculated from the measured oxidation potential and the spin population ratio on the basis of eq 26, if the parameters βD and λ are known. We have performed such calculations, but in view of the limits of the theoretical model, we shall not discuss them quantitatively. We just note that the order of residues with increasing ∆ai is essentially the same as that with increasing Vox, i.e., the order of residues in eq 27 can also be applied to the site energies. Therefore, we can discuss the effects of the different residues on the HOMO of BChl a on the basis of the measured oxidation potentials. All amino acid residues considered in this work are more polar than the native Leu residue, are potential hydrogen bond donors, and cause an increase of the site potential. The stabilization of the HOMO of BChl a most probably arises from a favorable interaction of the introduced NH- or OH-dipole with the partially negative charge of the 131-keto oxygen of the respective BChl moiety. This interaction in turn depends on the distance between the dipole and the keto group, i.e., the size of the amino acid side chain, and hence might be correlated with the hydrogen bond strength. Indeed, a correlation between the size of the side chain and the potential shift is observed (cf. eq 27). Furthermore, carboxylic acids such as Glu and Asp cause larger potential shifts than the corresponding amides Gln and Asn, respectively, since the (OH-O) bonds formed by the acids are stronger than the (NH-O) bonds formed by the amides. The largest effects are observed for aromatic residues, but this is probably also related to the ability to form hydrogen bonds rather than to a ππ interaction between the BChl macrocycle and the aromatic side chain. An experimental test of the role of hydrogen bonding is provided by vibrational spectroscopy, since the C ) 0 stretching frequency is sensitive to this interaction. A frequency shift of ∆ν(C ) 0) ≈ -15 cm-1 or larger is an indicator of hydrogen bonding, whereas smaller shifts are assumed to be due to unspecific solvent effects.64-66 The M160 mutants have been investigated by use of both FTIR spectroscopy on chromatophores58 and FT Raman spectroscopy on isolated RC.31 Both studies showed clear evidence for hydrogen bond formation to the 131-keto group of PM in the Asp, Gln, Glu, and His mutants, but for the cases of Ser and Asn, weakly hydrogen bonded keto groups have been proposed.58 In the case of the L131 mutants there are at least indications for hydrogen bonds to the 131keto group of PL from His, Glu, and Asp.67 Although the order of residues with increasing ∆ν(CdO) is somewhat less clear due to spectral overlap, eq 27 is essentially corroborated. This indicates a strong correlation between the hydrogen bond strength and the HOMO energy and hence a prominent role of hydrogen bonding in the pigment protein interactions studied in this work. VI. Summary and Conclusion We have shown that the (revised) model of Artz et al.,28 which is based on a simple two-orbital model of the primary donor of bacterial RC,20,42 provides a reasonable description of the observed relationship between the P/P•+ oxidation potential Vox and spin population ratio FL/FM of P•+ in RC of R. sphaeroides with changes at positions L131 and M160 (Figure 2). However,
Pigment-Protein Interactions to be consistent with FTIR data and the assumption of a constant electronic coupling βD between the HOMO of PL and PM, the model must be extended to include both electron-phonon coupling as proposed by Reimers et al.30 and long-range interactions. On the basis of this interpretation of the experimental data, βD is on the order of 120 to 160 meV, while the reorganization energy associated with a complete charge transfer from PL to PM is about 100 to 200 meV, corroborating earlier estimates.54 Exchanging the native Leu residue at either position L131 or M160 to His stabilizes the HOMO of the adjacent BChl moiety by about 100 meV, in reasonable agreement with measurements on heterodimer mutants.37 The effects of other residues at these positions are smaller according to eq 27. The new data also reveal the limits of the simple theoretical approach. Problems arise from the neglect of configuration interaction and spin polarization, which could complicate the relationship between the model parameters and the spin density distribution. Furthermore, slight changes of βD due to the mutations cannot be excluded and could contribute to the observed variation of this parameter between different series of mutants. Therefore, the physical significance of the longrange parameter η, which has to be introduced to obtain quantitative consistency within the error limits, is not fully clear at present. The presented simple model is only a first approach to explain the correlation between Vox and FL/FM but still allows for estimates of site-energy shifts due to pigment-protein interactions. A more rigorous treatment of P•+ including various orbital interactions is possible by numerical methods, but calculations of such large molecules remain a challenge. The presented results will hopefully trigger further experimental and theoretical work on the primary donors in other photosynthetic reaction centers of bacteria and plants and related supramolecular systems with a significant valence electron delocalization. Acknowledgment. We thank Drs. M. Plato (FU Berlin, Germany) and E. Nabedryk (CEA Saclay, France) for insightful discussions and for providing unpublished material. This work was supported by a grant from the USDA (1999-01753), by DFG (Sfb 498), EU (FMRX-CT98-0214), and Fonds der Chemischen Industrie (to W.L.). References and Notes (1) Abbreviations: BChl, bacteriochlorophyll; BPh, bacteriopheophytin; DFT, density functional theory; ENDOR, electron nuclear double resonance; EPR, electron paramagnetic resonance; FTIR, Fourier transform infrared; hfc, hyperfine coupling; HOMO, highest occupied molecular orbital; LCAO, linear combination of atomic orbitals; LUMO, lowest unoccupied molecular orbital; NHE, normal hydrogen electrode; P, primary donor; RC, reaction center; TRIPLE, electron nuclear nuclear triple resonance. (2) Allen, J. P.; Williams, J. C. FEBS Lett. 1998, 438, 5-9. (3) Blankenship, R. E. Photosynth. Res. 1992, 33, 91-111. (4) Deisenhofer, J.; Epp, O.; Sinning, I.; Michel, H. J. Mol. Biol. 1995, 246, 429-457. (5) Feher, G.; Allen, J. P.; Okamura, M. Y.; Rees, D. C Nature 1989, 339, 111-116. (6) Ermler, U.; Fritzsch, G.; Buchanan, S. K., Michel, H. Structure 1994, 2, 925-936. (7) Stowell, M. H. B.; McPhillips, T. M.; Rees, D. C.; Soltis, S. M.; Abresch, E.; Feher, G. Science 1997, 276, 812-817. (8) Jordan, P.; Fromme, P.; Witt, H.-T.; Klukas, O.; Saenger, W.; Krauss, N. Nature 2001, 411, 909-917. (9) Zouni, A.; Witt, H.-T.; Kern, J.; Fromme, P.; Krauss, N.; Saenger, W.; Orth, P. Nature 2001, 409, 739-743. (10) Woodbury, N. W.; Allen, J. P. In Anoxygenic Photosynthetic Bacteria; Blankenship, R. E., Madigan, M. T., Bauer, C. E., Eds.; Kluwer Academic Publishers: Dordrecht, Netherlands, 1995; pp 527-557. (11) Mathis, P. Biochim. Biophys. Acta 1994, 1187, 177-180. (12) Nitschke, W.; Dracheva, S. M. In Anoxygenic Photosynthetic Bacteria; Blankenship, R. E., Madigan, M. T., Bauer, C. E., Eds.; Kluwer Academic Publishers: Dordrecht, Netherlands, 1995; pp 775-805.
J. Phys. Chem. B, Vol. 106, No. 12, 2002 3235 (13) Marcus, R. A.; Sutin, N. Biochim. Biophys. Acta 1985, 811, 265322. (14) According to a recent interpretation by Tachiya,15 the Gaussian distribution of ET rates originates from a Gaussian distribution of the local electrostatic potential. (15) Tachiya, M. J. Phys. Chem. 1993, 97, 5911-5916. (16) Chanon, M.; Hawley, M. D.; Fox, M. A. In Photoinduced Electron Transfer; Fox, M. A., Chanon, M., Eds.; Elsevier: Amsterdam, Netherlands, 1988; pp 1-59. (17) Watanabe, T.; Kobayashi, M. In Chlorophylls; Scheer, H., Ed.; CRC Press: Boca Raton, 1991; pp 287-315. (18) Feher, G.; Okamura, M. Y. In The Photosynthetic Bacteria; Clayton, R. K., Sistrom, W. R., Eds.; Plenum Press: New York, 1978; pp 349386. (19) Williams, J. C.; Taguchi, A. K. W. In Anoxygenic Photosynthetic Bacteria; Blankenship, R. E., Madigan, M. T., Bauer, C. E., Eds.; Kluwer Academic Publishers: Dordrecht, Netherlands, 1995; pp 1029-1065. (20) Lendzian, F.; Huber, M.; Isaacson, R. A.; Endeward, B.; Plato, M.; Bo¨nigk, B.; Mo¨bius, K.; Lubitz, W.; Feher, G. Biochim. Biophys. Acta 1993, 1183, 139-160. (21) Rautter, J.; Lendzian, F.; Schulz, C.; Fetsch, A.; Kuhn, M.; Lubitz, W.; Lin, X.; Williams, J. C.; Allen, J. P. Biochemistry 1995, 34, 81308143. (22) Lin, X.; Murchison, H. A.; Nagarajan, V.; Parson, W. W.; Allen, J. P.; Williams, J. C. Proc. Natl. Acad. Sci. U.S.A. 1994, 91, 10265-10269. (23) Lin, X.; Williams, J. C.; Allen, J. P.; Mathis, P. Biochemistry 1994, 33, 13517-13523. (24) Allen, J. P.; Williams, J. C.; Graige, M. S.; Paddock, M. L.; Labahn, A.; Feher, G.; Okamura, M. Y. Photosynth. Res. 1998, 55, 227-233. (25) Rautter, J.; Lendzian, F.; Lin, X.; Williams, J. C.; Allen, J. P.; Lubitz, W. In The Reaction Center of Photosynthetic Bacteria - Structure and Dynamics; Michel-Beyerle, M.-E., Ed.; Springer-Verlag Publishers: Berlin, 1996; pp 37-51. (26) For the case of the ET from cytochrome c2 to P•+ it has been noticed that there is also a small effect of the mutants on the electronic coupling between donor and acceptor due to the redistribution of the unpaired electron on P•+ (see ref 25). (27) In addition, Leu M160 has been exchanged to Lys and Tyr (see ref 28). (28) Artz, K.; Williams, J. C.; Allen, J. P.; Lendzian, F.; Rautter, J.; Lubitz, W. Proc. Natl. Acad. Sci. U.S.A. 1997, 94, 13582-13587. (29) In ref 28 an error has occurred in eq 2, where ∆R/2 has been replaced with ∆R. As a consequence, eq 5 of this reference as well as the corresponding formulae in ref 31 are also incorrect. The correct formulae are given in this work and in ref 30. (30) Reimers, J. R.; Hughes, J. M.; Hush, N. S. Biochemistry 2000, 39, 16185-16189. (31) Ivancich, A.; Artz, K.; Williams, J. C.; Allen, J. P.; Mattioli, T. A. Biochemistry 1998, 37, 11812-11820. (32) Lubitz, W. In Chlorophylls; Scheer, H., Ed.; CRC Press: Boca Raton, 1991; pp 903-944. (33) Lubitz, W.; Lendzian, F. In Biophysical Techniques in Photosynthesis; Amesz, J., Hoff, A. J., Eds.; Kluwer Academic Publishers: Dordrecht, Netherlands, 1996; pp 255-275. (34) Paddock, M. L.; Rongey, S. H.; Feher, G.; Okamura, M. Y. Proc. Natl. Acad. Sci. U.S.A. 1989, 86, 6602-6606. (35) Williams, J. C.; Alden, R. G.; Murchison, H. A.; Peloquin, J. M.; Woodbury, N. W.; Allen J. P. Biochemistry 1992, 31, 11029-11037. (36) Moss, D. A.; Leonhard, M.; Bauscher, M.; Ma¨ntele, W. FEBS Lett. 1991, 283, 33-36. (37) Allen, J. P.; Artz, K.; Lin, X.; Williams, J. C.; Ivancich, A.; Albouy, D.; Mattioli, T. A.; Fetsch, A.; Kuhn, M.; Lubitz, W. Biochemistry 1996, 35, 6612-6619. (38) Rautter, J.; Lendzian, F.; Lubitz, W.; Wang, S.; Allen, J. P. Biochemistry 1994, 33, 12077-12084. (39) Zweygart, W.; Thanner, R.; Lubitz, W. J. Magn. Reson., Ser. A 1994, 109, 172-176. (40) Mu¨h, F.; Rautter, J.; Lubitz, W. Biochemistry 1997, 36, 41554162. (41) Tra¨nkle, E.; Lendzian, F. J. Magn. Reson. 1989, 84, 537-547. (42) Plato, M.; Lendzian, F.; Lubitz, W.; Mo¨bius, K. In The Photosynthetic Bacterial Reaction Center II; Breton, J., Verme´glio, A., Eds.; Plenum Press: New York, 1992; pp 109-118. (43) Szabo, A.; Ostlund, N. S. Modern Quantum Chemistry; McGrawHill Publishing Company: New York, 1989. (44) Within the Hu¨ckel MO model of the ethylene dimer considered by Plato et al.20,42 the weak coupling limit is defined by 10βD e βL ) βM, where βD is the intermolecular resonance integral of the dimer and βL, βM are the intramolecular resonance integrals of the individual dimer halves. In the context of the present paper, this definition is equivalent to the condition that the coupling between two corresponding spin orbitals φnL and φnM is not larger than about 1/10 of the energy difference between the HOMO φai and the LUMO φri of one dimer half.
3236 J. Phys. Chem. B, Vol. 106, No. 12, 2002 (45) Lubitz, W.; Lendzian, F.; Plato, M.; Scheer, H.; Mo¨bius, K. Appl. Magn. Reson. 1997, 13, 531-552. (46) Lendzian, F.; Gessner, C.; Bo¨nigk, B.; Plato, M.; Mo¨bius, K.; Lubitz, W. In Research in Photosynthesis, Vol. I; Murata, N., Ed.; Kluwer Academic Publishers: Dordrecht, Netherlands, 1992; pp 433-436. (47) Huber, M.; Isaacson, R. A.; Abresch, E. C.; Gaul, D.; Schenck, C. C.; Feher, G. Biochim. Biophys. Acta 1996, 1273, 108-128. (48) The hfc of the β-protons at positions 7, 8, 17, and 18 depend on the dihedral angle between the CH-bond axis and the π plane and are thus sensitive to thermal motion and structural heterogeneity of the saturated rings B and D (Figure 1). For the protons at positions 21 and 121, this angular dependence is averaged out due to rapid rotation of the methyl groups, making the hfc less sensitive to structural perturbations and mainly dependent on the distribution of spin density in the π system. Therefore, we make use here only of the methyl proton hfc. (49) Atherton, N. M. Principles of Electron Spin Resonance; Ellis Horwood PTR Prentice Hall: New York, 1993. (50) There are also contributions to the net spin densities Qi(21) and Qi(121) from spin polarization, which is neglected in the present model. In this context, spin polarization refers to differences between the spin orbitals φni and φ h ni, resulting in nonzero net spin density (eq 16) even if both spin orbitals are occupied. This has to be distinguished from polarization effects in transient EPR/ENDOR spectroscopy, referring to non-Boltzmann population of spin energy levels. (51) Ka¨ss, H.; Rautter, J.; Zweygart, W.; Struck, A.; Scheer, H.; Lubitz, W. J. Phys. Chem. 1994, 98, 354-363. (52) Schulz, C.; Mu¨h, F.; Beyer, A.; Jordan, R.; Schlodder, E.; Lubitz, W. In Photosynthesis: Mechanisms and Effects, Vol. II; Garab, G., Ed.; Kluwer Academic Publishers: Dordrecht, Netherlands, 1998; pp 767-770. (53) Breton, J.; Nabedryk, E.; Parson, W. W. Biochemistry 1992, 31, 7513-7520.
Mu¨h et al. (54) Reimers, J. R.; Hush, N. S. Chem. Phys. 1996, 208, 177-193. (55) For the two series of single mutants, the Leu case is the wild type, e.g., FL,Leu/FM,Leu ) 2.11 (cf. Table 1), whereas for the two series of double mutants the Leu case is the respective single mutant with a His residue near Pi. Note that in eq 28 the parameter ai also corresponds to the Leu case. (56) In principle, the error limits of the oxidation potentials from ref 37 allow for η values as large as 0.5. However, such large long-range effects seem to be unrealistic. (57) Nabedryk, E.; Allen, J. P.; Taguchi, A. K. W.; Williams, J. C.; Woodbury, N. W.; Breton, J. Biochemistry 1993, 32, 13879-13885. (58) Nabedryk, E.; Breton, J.; Allen, J. P.; Williams, J. C. In Spectroscopy of Biological Molecules: Modern Trends; Carmona, P., Navarro, R., Hernanz, A., Eds.; Kluwer Academic Publishers: Dordrecht, 1997; pp 107108. (59) Reimers, J. R.; Hush, N. S. J. Am. Chem. Soc. 1995, 117, 13021308. (60) Reimers, J. R.; Hutter, M. C.; Hughes, J. M.; Hush, N. S. Int. J. Quantum Chem. 2000, 80, 1224-1243. (61) Scherer, P. O. J.; Fischer, S. F. Chem. Phys. Lett. 1997, 268, 133142. (62) Lendzian, F.; Bittl, R.; Lubitz, W. Photosynth. Res. 1998, 55, 189197. (63) Hutter, M. C.; Hughes, J. M.; Reimers, J. R.; Hush, N. S. J. Phys. Chem. B 1999, 103, 4906-4915. (64) Krawczyk, S. Biochim. Biophys. Acta 1989, 976, 140-149. (65) Nabedryk, E.; Allen, J. P.; Taguchi, A. K. W.; Williams, J. C.; Woodbury, N. W.; Breton, J. Biochemistry 1993, 32, 13879-13885. (66) Mattioli, T. A.; Williams, J. C.; Allen, J. P.; Robert, B. Biochemistry 1994, 33, 1636-1643. (67) Nabedryk, E., personal communication.
