Electron Spin Polarization of the Oxidized Primary Electron Donor in

Fast time-resolved EPR spectroscopy is used to study electron spin polarization (ESP) in perdeuterated native, Fe2+-containing reaction centers (RCs) ...
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J. Phys. Chem. 1996, 100, 2430-2437

Electron Spin Polarization of the Oxidized Primary Electron Donor in Reaction Centers of Photosynthetic Purple Bacteria J. S. van den Brink,†,‡ T. E. P. Hermolle,§ P. Gast,† P. J. Hore,§ and A. J. Hoff*,† Department of Biophysics, Huygens Laboratory, Leiden UniVersity, P.O. Box 9504, 2300 RA Leiden, The Netherlands, and Physical and Theoretical Chemistry Laboratory, South Parks Road, Oxford OX1 3QZ, United Kingdom ReceiVed: August 11, 1995; In Final Form: October 24, 1995X

Fast time-resolved EPR spectroscopy is used to study electron spin polarization (ESP) in perdeuterated native, Fe2+-containing reaction centers (RCs) of photosynthetic purple bacteria. The spin-correlated radical pair(SCRP) model (previously used to simulate ESP observed in Fe-depleted RCs (Hore, P. J.; Hunter, D. A.; McKie, C. D.; Hoff, A. J. Chem. Phys. Lett. 1987, 137, 495) is extended to include the large anisotropy arising from the magnetic interactions between Fe2+ and the reduced primary electron-acceptor quinone (QA•-), which results in different quantization axes for the P•+ and the (QA•-Fe2+) spins. Using spectral simulations, it is shown that the ESP spectrum is solely due to the P•+ part of the spin-correlated radical pair [P•+(QA•-Fe2+)], whereas the rapid decay of the spin-polarized signal is due to spin-lattice relaxation of the (QA•-Fe2+) complex. The simulations are very sensitive to the relative orientation of the g matrices of P•+ and (QA•-Fe2+). Using orientation II of the g matrix of the oxidized primary donor P•+ (Klette, R.; To¨rring, J. T.; Plato, M.; Mo¨bius, K.; Bo¨nigk, B.; Lubitz, W. J. Phys. Chem. 1993, 97, 2015), the orientation of the g matrix of (QA•-Fe2+) is assessed. Finally, it is shown that the ESP spectrum of perdeuterated native, Fe2+containing RCs of Rhodopseudomonas (Rps.) Viridis is virtually identical to the spectrum obtained for perdeuterated native Rhodobacter (Rb.) sphaeroides, showing an AEA pattern (A denotes absorption and E emission). This result indicates that the magnetic axes of P•+ and (QA•-Fe2+) have (nearly) the same directions relative to one another in both species.

1. Introduction Fast electron-transfer reactions (τ < 1.0 ns) generally occur with conservation of electron spin angular momentum of the radicals involved, such that the resulting radical pair is formed with selectively-populated spin states, an effect known as electron spin polarization (ESP). In time-resolved electron paramagnetic resonance (EPR) experiments, this phenomenon is observed as a characteristic pattern of emissive and enhanced absorptive EPR transitions.1-6 The best-known example of ESP in the solid state, where the immobile radical pair exhibits anisotropic, but constant, magnetic and electronic interactions, is the spin-correlated radical pair (SCRP) [P•+QA•-] in reaction centers (RCs) of the photosynthetic purple bacterium Rhodobacter (Rb.) sphaeroides R26, in which the native Fe2+ (L ) 2, S ) 2) is chemically or biosynthetically replaced by diamagnetic Zn2+.4-12 In the RC, a process of fast charge separation from the excited primary electron donor 1P* gives rise to ESP in the radical pair [P•+QA•-], where QA is the first electron-accepting quinone. Simulations of ESP spectra, based on the known crystal structure of Rb. sphaeroides R2613,14 and (measured) g matrices of P•+ 15 and QA•-,16,17 revealed information on electronic and magnetic interactions in the RC-protein, essential for the elucidation of the relation between structure and function.10-12,18 The need for Zn2+-reconstitution has constrained the application of time-resolved EPR spectroscopy for studying ESP phenomena to RCs of Rb. sphaeroides R26, because the divalent Fe-ion cannot be removed readily from other bacterial RCs. Recently, however, ESP has been observed for native, Fe2+* To whom correspondence should be addressed. † Leiden University. ‡ Present address: Philips Medical Systems, 5684 PC Best, The Netherlands. § Physical and Theoretical Chemistry Laboratory. X Abstract published in AdVance ACS Abstracts, January 1, 1996.

0022-3654/96/20100-2430$12.00/0

containing RCs of Rb. sphaeroides.19-22 It now seems feasible to use ESP spectroscopy for a comparison of the magnetic properties of RCs of different purple bacteria, such as Rhodopseudomonas (Rps.) Viridis in which P consists of a different type of bacteriochlorophyll (viz., BChl a in Rb. sphaeroides and BChl b in Rps. Viridis), and QA is a menaquinone, as distinct from the ubiquinone-10 found in Rb. sphaeroides. The latter difference is manifest in the much stronger exchange interaction between the reduced intermediary acceptor bacteriopheophytin, I•-, and QA•- in Rps. Viridis.23 For this purpose, we first extend the SCRP model4,5,9 to include the magnetic anisotropy of the (QA•-Fe2+) complex,24 as a result of which the (QA•-Fe2+) spin will in general not be quantized along the external magnetic field. We show that previous attempts to simulate the [P•+(QA•-Fe2+)] ESP spectrum of perdeuterated RCs of Rb. sphaeroides R26 are incorrect, due to the neglect of this strong anisotropy of the g matrix of (QA•Fe2+).22 Specifically, there is no need to include polarization generated in the primary radical pair [P•+I•-]22 when the correct ESP theory is used. Using our extended theory, we simulate the ESP spectrum for perdeuterated, Fe2+-containing RCs of Rb. sphaeroides R26,19,21,22 using the lowest two Kramers’ doublets of the (QA•-Fe2+) complex.24 A good simulation, showing the experimentally observed AEA pattern (A denotes adsorption and E emission), can be obtained with either orientation I or II of the g matrix of P•+.15 Because recent W-band ESP results give preference to orientation II, we have used this orientation to deduce the orientation of the magnetic axes of (QA•-Fe2+). The fast relaxation of the ESP signal in native RCs is explained in the SCRP framework, and it is shown that although the spectrum is due to the P•+ part of the radical pair, its rapid disappearance is caused by relaxation of (QA•Fe2+). Finally, we discuss the ESP spectrum of perdeuterated RCs of Rps. Viridis, which closely resembles that of RCs of Rb. sphaeroides. From our spectral simulations, we conclude © 1996 American Chemical Society

Reaction Centers of Photosynthetic Purple Bacteria

J. Phys. Chem., Vol. 100, No. 6, 1996 2431

that the orientation of the g matrix of P•+ relative to the “effective” g matrix of (QA•-Fe2+) is virtually identical for the two species. 2. Theory The ESP spectrum observed for the radical pair P•+QA•- in Zn2+-reconstituted RCs of Rb. sphaeroides is well-understood in terms of the so-called spin-correlated radical pair model,5 which we first briefly summarize. For two radicals A and B whose electron spins are quantized along the direction of the external magnetic field (i.e., their spin-spin coupling is much weaker than the electronic Zeeman interaction, and their g-anisotropy is very small), the spin hamiltonian in the singlet-triplet (S-T) basis may be written in matrix form:9

|T+1〉 ω - J + 1/2d H) 0 0 0

(

|S〉

|T0〉

0 J Q 0

0 Q -J - d 0

|T-1〉 0 0 -ω - J + 1/2d

)

(1)

ω ) 1/2(gA + gB)µBB0/p

(2)

Q ) 1/2(gA - gB)µBB0/p

(3)

Here, gi is the g-value of radical i, µB the Bohr magneton, and B0 the magnitude of the magnetic field. The frequencies of the four allowed EPR transitions are:

ω13 ) [ω + Ω - (J - d)],

H ) µBB0T‚gA‚SA + µBB0T‚gB‚SB + SAT‚CAB‚SB

(6)

where the superscript T indicates transposition, and with the g matrices gA and gB given in a common reference frame, i.e., the crystal axes system, and

where J represents the (isotropic) electronic exchange interaction and d ) DAB(cos2ξ - 1/3). DAB is the magnitude of the (axial) dipolar interaction, and ξ is the angle between the vector connecting the two radicals and the magnetic field direction. ω and Q denote half the sum and half the difference of the Larmor frequencies of the two electrons in the absence of mutual interactions:

ω12 ) [ω - Ω - (J - d)],

between P•+ and QA•- (i.e., ∼2.8 nm), which results in a small dipolar interaction DAB ) -0.12 mT,10 and an isotropic exchange interaction of at most ∼1 µT.18 Thus, the presence of P•+ introduces only a small perturbation of the eigenstates and energy levels of (QA•-Fe2+), and the Kramers’ doublets may be considered as “effective S ) 1/2 radicals”, with g-values given by Butler et al.24 Using the above approximation, we have essentially reduced the problem of simulating the [P•+QA•-] ESP spectrum to the two-spin model summarized in eqs 1-5. The only complicating factor is that one of the radicals (the (QA•-Fe2+) part) is characterised by a highly anisotropic g matrix. Consequently, the “effective” spin of the (QA•-Fe2+) complex is in general not quantized along B0. This affects the “effective” magnitudes of the interactions J and d because the quantization axes of the two spins of the SCRP are no longer parallel. In this case, we must consider the Hamiltonian:

ω34 ) [ω - Ω + (J - d)]

CAB ) JI+D

where I denotes the unit matrix and D the dipolar coupling tensor. The spin-spin coupling CAB is minute compared to the energy separations of the Zeeman levels, which are dominated by the large g-anisotropy of (QA•-Fe2+). We may therefore neglect those components of the two-electron spin angular momenta that are not parallel to the respective quantization axes: the nonsecular parts of the electron-electron coupling are simply too weak to mix the widely separated Zeeman states of [P•+(QA•-Fe2+)]. We can therefore rewrite the Zeeman term in eq 6 for spin i as25

HZi ) µB|B0T‚gi|τiT‚Si

(4)

(8)

where τi is the quantization axis for spin i:

nT‚gi ) ) τi ) T gi |n ‚g | [nT‚g ‚g T‚n]1/2 T

ω24 ) [ω + Ω + (J - d)]

(7)

nT‚gi

nT‚gi

i

i

(9)

i

with n a unit vector directed along the external magnetic field B0. The spin-spin coupling term

with

Ω ) [(J + 1/2d)2 + Q2]1/2

(5)

It is seen that the EPR spectrum consists of two doublets, centered at fields p(ω ( Ω)/geµB, each with splitting 2p(J d)/geµB (ge denotes the free-electron g-value). In the polarized case, the transitions of each doublet are in antiphase, with equal amplitude.5 In native RCs, QA•- forms a magnetic complex (QA•-Fe2+) with the high-spin Fe2+ (L ) 2, S ) 2) and shows a highlyanisotropic EPR spectrum.24 Rigorous simulations of the ESP spectrum of the spin-correlated radical complex [P•+(QA•-Fe2+)] involving a three-spin Hamiltonian would be prohibitively time consuming. Butler et al.,24 however, showed that at ∼6 K the (QA•-Fe2+) spectrum is composed of two (nearly) equallypopulated Kramers’ doublets, which are well-separated in energy; i.e., they do not interact, and no transitions between the Kramers’ doublets are possible at X-band frequencies (9.2 GHz). Furthermore, the spin-spin interaction between P•+ and (QA•-Fe2+) is much weaker than all other terms in the Hamiltonian of the latter complex, because of the large distance

HC ) SAT‚CAB‚SB ) JSAT‚SB + SAT‚D‚SB

(10)

can now be rewritten in terms of effective exchange (Jeff) and dipolar (deff) couplings as

HC ) -Jeff(S2 - 1) + 1/2deff(3Sz2-S2)

(11)

where S ) SA+ SB is the operator for total spin, and

Jeff ) J

nT‚gA‚gBT‚n gAgB

(12)

with gi given in eq 9. Using26

D)

gAT‚0D‚gB ge2

(13)

where ge is the free-electron g-value, and 0D is the dipolar coupling in the absence of g-shifts and g-anisotropies, deff is

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van den Brink et al.

given by

deff )

nT‚gA‚gAT‚0D‚gB‚gBT‚n

(14)

gAgBge2

The difference in the expressions for Jeff and deff represents the different physical origins of the two interactions:26,27 the dipolar term originates from the magnetic interaction between the magnetic moments µi ()-µBgi‚Si) of the two radicals, whereas the exchange term represents the electronic interaction of the two electrons, which to first approximation equals the exchange integral

〈

| |

〉

e2 J ) - φA(1) φB(2) φ (2) φB(1) 4π0r A

(15)

The Hamiltonian of eq 11 shows that eq 1 is applicable to the spin-correlated radical pair [P•+(QA•-Fe2+)], when J is replaced by Jeff and d by deff. 3. Materials and Methods Deuterated cells of Rps. Viridis were grown anaerobically in modified Hutner medium,28 in which H2O was replaced by D2O. Deuteration was checked by monitoring the EPR line width of P•+, which decreased from 1.18 29 to 0.81 mT. RCs were isolated as described previously.30 On the sucrose gradient, an additional band was observed with λmax ) 336 nm, presumably containing carotenes. The RC-band appeared at the normal position in the gradient and was well-separated from the other bands. SDS-PAGE showed that pure RCs were obtained, with A280/A830) 2.6 (Aijk is absorbance at ijk nm). In order to observe transient P•+ in flash experiments on RCs of Rps. Viridis, the redox potential of the RCs must be adjusted to a state in which all cytochromes are oxidized, but P is not. This was done by adding a small volume of a 1:9 solution of K4Fe(CN)6/K3Fe(CN)6 to the concentrated RC solution prior to freezing in the dark. A typical sample had an A830 of 20 cm-1 and contained 60-70% (v/v) glycerol. Direct-detection EPR spectra were obtained using a modified Varian E-9 spectrometer operating at 9.2 GHz and equipped with a multipurpose TE102 cavity. Excitation of the RCs was performed with saturating laser flashes from a tunable optical parameter oscillator (OPO) consisting of a nonlinear β-BaB2O4 crystal, pumped with a Q-switched 355 nm Nd:YAG laser (Surelite I, Continuum). The excitation wavelength was 852 nm, with approximately 10 mJ/pulse and a pulse width less than 5 ns, at a repetition frequency of 10 Hz. The overall instrumental rise time was approximately 300 ns. Kinetic traces were averaged using a LeCroy 9410 150 MHz digital oscilloscope equipped with signal-averaging facility and were then stored in a personal computer for further analysis. Spectral simulations were performed on a Sun Sparc 2+ and a Silicon Graphics Personal Iris workstation. 4. Results and Discussion Figure 1 shows the ESP spectrum of perdeuterated native, Fe2+-containing RCs of Rps. Viridis, obtained at 300-600 ns after laser flash excitation of the RCs. Although slightly broader than the spectra of perdeuterated native, Fe2+-containing RCs of Rb. sphaeroides19,21 (presumably due to the difference in spin distribution over the P•+ dimer in the two species31), the characteristic AEA pattern, where A denotes enhanced absorption and E emission, is still discernible. The ESP spectrum of native Rb. sphaeroides R26 has been attributed to the P•+ part of the spin-correlated radical pair [P•+(QA•-Fe2+)],19,20 because the EPR spectrum of the polarized (QA•-Fe2+) radical is much too broad to be observed. A recent simulation of the spectrum,22

Figure 1. X-band (9.148 GHz) transient EPR spectrum (bold line) of perdeuterated native, Fe2+-containing RCs of Rps. Viridis at 6 K, obtained from kinetic traces at different field positions, showing ESP of [P•+(QA•-Fe2+)]. Points between 300 and 600 ns (10 ns resolution) from 10 different kinetic traces were averaged at each field position (microwave power, 1 mW). The dashed line shows the spectral simulation discussed in the text.

TABLE 1: Principal Values of the g Matrices of P•+ in Rb. sphaeroides R2615 and Rps. Wiridisa and of the Effective g Matrices of the Lowest Two Kramers’ Doublets of (QA•-Fe2+)24 Rb. sphaeroides R26 Rps. Viridis first doublet of (QA•-Fe2+) second doublet of (QA•-Fe2+) a

gx

gy

gz

2.003 32 2.003 20 1.77 1.83

2.002 53 2.002 54 0.62 4.68

2.002 10 2.002 06 1.89 1.70

Huber, M. Personal communication.

employing conventional SCRP theory, i.e., neglecting that the quantization axis of the effective spin of the (QA•-Fe2+) complex is different from B0,24,32 necessitated the introduction of an unrealistically large value for JPQ of 2.5 µT. We will show that the extended SCRP model, introduced in the Theory section to account for the g-anisotropies of P•+ and (QA•-Fe2+), yields accurate simulations of the ESP spectra of both Rps. Viridis and Rb. sphaeroides R26 RCs, without taking recourse to a large value for JPQ. We first concentrate on the simulation of the ESP spectrum of perdeuterated RCs of Rb. sphaeroides R26,21 because the magnetic properties of these RCs are known in much greater detail than those of RCs of Rps. Viridis. Orientation of the Magnetic Axes of P•+ and (QA•-Fe2+). RCs of Rb. sphaeroides R26. The g matrix for P•+ in Rb. sphaeroides R26 is available from single-crystal studies at the W-band (95 GHz);15 see Table 1. Four possible orientations were obtained, two of which could be excluded on the basis of theoretical considerations and previous ESP studies of Zn2+reconstituted RCs of Rb. sphaeroides R26.10,11 Simulations of X-band (9.2 GHz) and K-band (24 GHz) ESP spectra yield acceptable results for orientation I of gP only.10,11,18 However, a recent W-band (95 GHz) ESP study at 170 K,12 at which microwave frequency the shape of the spectrum is mainly determined by the g matrices of P•+ and QA•-, strongly suggests that orientation II of gP is correct. Because of the discrepancy of the results of the ESP simulations for Zn2+-substituted RCs at different microwave frequencies, we simulate the [P•+(QA•Fe2+)] ESP spectrum for both orientations I and II of gP. For (QA•-Fe2+), we use the “effective” g-values (see Table 1) of the lowest two Kramers’ doublets of the complex, which are almost equally populated at 6 K.24 The quinone spin probes the large zero-field anisotropy of the (S ) 2) Fe2+ and the magnetic axes of (QA•-Fe2+) are collinear with the magnetic axes of Fe2+.24 However, the orientation of the principal axes of the “effective” g matrix of the (QA•-Fe2+) complex in RCs of Rb. sphaeroides has not been determined experimentally. Theoretically,32 the directions of the magnetic axes of the six-

Reaction Centers of Photosynthetic Purple Bacteria coordinated Fe2+ are related to the positions of the ligands, forming a slightly-distorted octahedron.33,34 The main distortion is an elongation along one of the Fe-ligand vectors. Such a tetragonally-distorted octahedral complex possesses (at least) C4h-symmetry, with the unique magnetic axis (zFe) directed along the 4-fold-rotation axis, i.e., parallel to the elongated Fe-ligand vector.32,35 Single-crystal studies of (QA•-Fe2+) in RCs of Rps. Viridis36,37 indicated that, in this bacterium, zFeQ is indeed parallel to the axis connecting Fe2+ and the coordinating N-atom of one of the ligands (His L190).36 A tentative assignment of the orientation of the x-axis was also given on the basis of the singlecrystal results.36 It is not possible, however, to use the direction cosines obtained for Rps. Viridis directly in studies of Rb. sphaeroides R26, because the geometry and space group of the crystals are different for the two species.13,38 The crystal structures indicate, however, that the ligands of Fe2+ form a distorted octahedron in both Rps. Viridis and Rb. sphaeroides R26 with a high degree of architectural similarity,33,34,39,40 so that we expect that the orientations of the magnetic axes of the (QA•-Fe2+) complex in the two bacteria are quite similar. In our simulations, we use the dipolar interaction DPQ calculated with the point-dipole approximation for P•+ and QA•- and the PQ-distance from the crystal structure (rPQ ) 2.8 nm), which yields DPQ ) -0.12 mT. Furthermore, we use JPQ ) 0 for most simulations, because we have found that the shape of the ESP spectrum at the X-band of the radical pair [P•+(QA•Fe2+)] is much less sensitive to small values of JPQ than that of Zn2+-reconstituted RCs18 (see also below). Simulations obtained for the lowest two quartets of states of [P•+(QA•-Fe2+)], associated with the mS,Fe ) -2 and mS,Fe ) -1 levels, respectively, were added with equal weight, because the lowest two spin states of Fe2+ are almost equally populated at ∼6 K.24 For orientations I and II of gP, only minor differences are observed. The orientation of the magnetic axes of the (QA•Fe2+) complex was determined for both orientations of gP. We present the results for orientation II; for orientation I, the directions are only slightly different (by about (5°). ESP spectra were simulated using the method described previously.5,9 This calculation, which neglects modulation effects (quantum beats, transient nutations, or oscillations due to hyperfine couplings) is valid because the experimental spectra are obtained at low microwave power and with a time window of approximately 300 ns so that the influence of modulation effects is negligible. The shape of the spectrum does not change when the width of the time window or the delay after the exciting laser flash between 200 ns and 1 µs are varied (data not shown and results published previously19,21,22). Determination of the Orientation of gFeQ. Following the assignment of the z-axis of (QA•-Fe2+) by Evelo et al.,36 we first simulated the ESP spectrum of [P•+(QA•-Fe2+)] in RCs of Rb. sphaeroides R26,19,21 choosing zFeQ along the vector connecting Fe2+ to N2 of His L190. Because the x- and y-axes of (QA•-Fe2+) are not known, we calculated spectra for all possible orientations of these axes in the plane perpendicular to FefHis L190, see Figure 2A. For the line-broadening parameter of P•+, we used ∆BP ) 0.45 mT, corresponding to the line width of the stable radical in perdeuterated RCs of Rb. sphaeroides R26.41 It is seen that the experimentally observed AEA pattern is not reproduced for any of the orientations of the x- and y-axis of gFeQ corresponding to zFeQ along the vector FefHis L190, as proposed by Evelo et al.36 Subsequently, we followed the same approach to simulate the [P•+(QA•-Fe2+)] ESP spectrum, choosing zFeQ parallel to one of the other five iron-ligand vectors, i.e., directed toward either N2 of His L230, M219, and M266, or the carboxylate

J. Phys. Chem., Vol. 100, No. 6, 1996 2433

Figure 2. Simulated X-band ESP spectra of the SCRP [P•+(QA•-Fe2+)] of Rb. sphaeroides when the z-direction of the (QA•-Fe2+) complex is parallel to (A) the axis connecting Fe2+ and N2 of His L190 or (B) the axis connecting Fe2+ and N2 of His M266. A and B show simulations using orientation II of gP,15 in which the contributions of both the mS,Fe ) -2 and mS,Fe ) -1 doublets were added in equal proportion, and the x- and y-axes were rotated in the plane perpendicular to z. The experimentally observed AEA pattern cannot be simulated with the z-axis parallel to the Fe2+-ligand axis to His L190. Further parameters: microwave frequency, 9.207 GHz; ∆BP ) 0.45 mT.

oxygens of Glu M234. Figure 2B shows, as an example, simulations in which zFeQ was chosen parallel to the line connecting Fe2+ and N2 of His M266 and the x- and y-axes rotated in the plane perpendicular to zFeQ. The AEA pattern with correct relative amplitudes of the lowand high-field absorptive features21 could not be simulated for zFeQ parallel to the vector connecting Fe2+ to O2 of Glu M234 (not shown). Two possible solutions exist for each of the other z-axes, i.e., directed toward O1 of Glu M234, or N2 of His L230, His M219 (not shown), and His M266 (see Figure 2B). Thus, eight possible solutions exist when zFeQ is chosen parallel to one of the Fe2+-ligand vectors. Because gFeQ has almost cylindrical symmetry around its y-axis,24 the spectral simulations are very sensitive to the orientation of yFeQ, whereas the spectral shape does not change much while rotating around this axis. As an alternative approach, we therefore performed also a full-space grid search to determine all possible orientations of gFeQ, and found that a correct simulation is obtained for three directions of yFeQ only. These three directions are also obtained in the eight possible orientations of gFeQ mentioned above. To discriminate between the possible orientations of gFeQ, we assume that (at least) one of the other magnetic axes of (QA•Fe2+) is also (nearly) parallel to the vector connecting Fe2+ to one of its ligands. Because the simulations are sensitive mainly to the direction of yFeQ, we calculated the angle between the six Fe2+-ligand vectors and the y-axes of (QA•-Fe2+) corresponding to the simulations of the ESP spectrum of [P.+(QA•Fe2+)] obtained while choosing zFeQ parallel to an Fe2+fligand vector; see Table 2. Furthermore, we found in a recent study42 of the characteristic I•- EPR spectrum of RCs of Rps. Viridis23 that yFeQ is close to the vector connecting Fe2+ and I. The simulation parameters of the (QA•-Fe2+) EPR spectrum by Butler et al.,24 finally,

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van den Brink et al.

TABLE 2: Angles between the Fe2+-Ligand Vectors and the Magnetic y-Axes of the (QA•-Fe2+) Complex for Which the Simulation of the [P•+(QA•-Fe2+)] ESP Spectrum Yields AEA When zFeQ Is Chosen Parallel to One of the Fe2+-Ligand Vectorsa angle ((5, deg)

HL190

HL230

HM219

HM266

EM234O1

EM234O2

FefI

FefQA

HL230(i) HL230(ii) HM219(i) HM219(ii) HM266(i) HM266(ii) EM234O1(i) EM234O1(ii)

74 77 61 17 95 64 77 67

(90) (90) 39 37 82 80 62 78

34 51 (90) (90) 49 34 59 50

80 82 40 38 (90) (90) 69 70

12 89 74 60 88 7 (90) (90)

65 33 37 68 32 69 28 42

13 74 80 73 71 12 77 72

43 52 81 79 55 45 64 84

a Two possible directions of yFeQ exist for four directions of zFeQ; the AEA pattern cannot be obtained using the other two directions of the Fe2+-ligand vector as z-axis. Also shown are the angles between the vector connecting Fe2+ and I•- and yFeQ, and between the vector connecting Fe2+ and QA and xFeQ. All angles are given in the first quadrant, because an intrinsic 180° ambiguity exists in our simulations. The preferred orientation of gFeQ is in boldface italics in the table, i.e., zFeQ is parallel to FefHL230 or FefHM266, and yFeQ is almost parallel to the vector connecting Fe2+ and O1 of EM234. (H denotes a histidine; E, a glutamate residue).

Figure 3. Simulated X-band ESP spectrum of [P•+(QA•-Fe2+)] in RCs of perdeuterated Rb. sphaeroides R26 showing the experimentally observed AEA pattern. We used orientation II of gP, and for the magnetic axes of (QA•-Fe2+) we chose zFeQ parallel to the axis between the Fe2+ and N2 of His M266 and yFeQ nearly parallel to the axis between Fe2+ and O1 of Glu M234 (to within ∼5°). Other parameters as in Figure 2. The open squares show the experimental spectrum for perdeuterated RCs of Rb. sphaeroides R26, recorded 400 ns after the exciting laser flash.21

indicate that the x-axis of (QA•-Fe2+) is close to the axis connecting Fe2+ and QA, because the dipolar part of the spinspin coupling between Fe2+ and QA•- has its largest component in that direction. Table 2 shows the angles between the vector FefI and the possible y-axes of (QA•-Fe2+) and between the vector FefQA and the possible x-axes of (QA•-Fe2+). All angles are shown in the first quadrant because an intrinsic 180° ambiguity exists in our simulation results (i.e., only the orientation of the g-axes is obtained, not the absolute directions). It is seen from Table 2 that two possible orientations of gFeQ fulfil the criteria that yFeQ is close to (i) a ligandfFe2+ vector and (ii) to the vector Fe2+fI. These orientations are characterized by zFeQ parallel to the vector connecting Fe2+ to either His L230 or His M266. For these two orientations, also the vector connecting Fe2+ and QA is closest to xFeQ (although still making an angle of approximately 45°, see Table 2). The two possible solutions are equivalent and complementary, because the vectors connecting Fe2+ to His L230 and His M266, respectively, are (almost) parallel and have opposite direction. On the basis of the results shown in Table 2, we choose to work with zFeQ pointing toward His M266. Thus, the experimental AEA spectrum19,21 is simulated correctly by choosing zFeQ parallel to the axis connecting the Fe2+ and N2 of His M266 and yFeQ parallel (to within ∼7°) to the line connecting Fe2+ and O1 of Glu M234 (see Figure 3). Table 3 shows the direction cosines between the principal axes of the effective g matrix as obtained from our simulations and the crystallographic reference frame. Figure 4 shows the directions of the magnetic axes of (QA•2+ Fe ) within the Fe-ligand structure. It also shows the deviation

Figure 4. Schematic drawing of the ligands surrounding the divalent Fe ion in Rb. sphaeroides R2633 and the magnetic axes frame of (QA•Fe2+). Also shown is QA•- to indicate the deviation between xFeQ and the vector Fe2+fQA•-.

TABLE 3: Direction Cosines of the g Matrix Axes (x, y, z) of the (QA•-Fe2+) Complex of Rb. sphaeroides R26 in the Crystallographic Reference Frame (a, b, c) a b c

x

y

z

-0.735 -0.678 -0.015

0.374 -0.425 0.824

-0.566 0.600 0.566

between xFeQ and the position of QA as determined from the dark-adapted crystal structure. From the above discussion, it follows that the orientation of the magnetic axes of the native Fe2+ is different from that of chemically-reconstituted Cu2+, in which case the z-axis was proposed to be parallel to the vector Fe2+fHis M219.35 This direction can be excluded for zFeQ because in that case the vector Fe2+fI is almost perpendicular to yFeQ, a result contradicted by evidence from our recent simulation of the [I•-QA•-Fe2+] split-line spectrum.42 Thus, our results indicate that substitution of the native metal-ion with other divalent metal-ions alters the positions of the coordinating ligands. Figure 3 shows that the relative amplitudes of the absorptive features in the simulated spectrum are close to those in the experimental spectrum (∼4.5), while the peak-to-peak separation of the absorptive features (∆BPP) in the simulated spectrum (∼0.80 mT) is close to the splitting observed 400 ns after the exciting laser flash (∼0.85 mT).21 The larger value of ∆Bpp ) 1.05 mT reported earlier19 for a spectrum obtained after ∼1.5 µs probably shows effects of spin-diffusion processes in the radical pair (see below). The simulations, of course, represent the spectrum immediately after the exciting laser flash (i.e., before any relaxation occurs). Especially noteworthy is that also the zero crossing of the simulated spectrum is at the correct position, i.e., g ≈ 2.0023.21,22 Interaction between Fe2+ and QA•-. As shown in Table 2, xFeQ makes an angle of ∼45° with the axis connecting Fe2+ and QA in the crystal structure for the two acceptable orientations

Reaction Centers of Photosynthetic Purple Bacteria of gFeQ mentioned above; see also Figure 4. It has been argued that this axis may be different when QA is reduced, due to a possible displacement of the quinone upon reduction.43,44 In a previous communication, we showed evidence that only a minor reorientation of QA can occur upon reduction at room temperature.18 We could not exclude a displacement of QA along the line connecting P and QA. If we assume that xFeQ as determined here is the vector connecting Fe2+ and QA•- after displacement of QA•- along the vector connecting P and QA, we can estimate the position of QA in the reduced state (QA•-Fe2+) and compare it with its position before reduction as determined from the crystal structure.13,33 We find that under this assumption, the quinone moves ∼0.25 nm away from P•+ upon reduction. On one hand, such a displacement of QA corresponds well with the predictions of Kleinfeld et al., based on their analysis of the rate of recombination of P•+QA•-.43 On the other hand, however, a displacement away from P•+ seems to be contradicted by light-induced voltage changes measured by Brzezinski et al.,44 who found that one electron equivalent moves approximately 0.2 nm toward P upon formation of the chargeseparated state P•+QA•-. Furthermore, a sizeable displacement of QA upon reduction seems unlikely to occur at cryogenic temperatures. Therefore, we believe that it is more likely that the unexpected difference in the orientation of xFeQ and the vector connecting Fe2+ and QA•- shows that the anisotropic part of the coupling between Fe2+ and QA•- does not have a purely dipolar character (i.e., there is an anisotropic exchange contribution to the spin-spin coupling CFeQ).24 A full orientational EPR study of the (QA•-Fe2+) complex in combination with the orientation dependence of the spin-polarized spectrum of [P•+(QA•-Fe2+)] in single crystals of RCs of Rb. sphaeroides R26 is expected to provide conclusive evidence for our assignment of the directions of the magnetic axes. Relation with ESP in Zn2+-Substituted RCs. A noteworthy aspect of the simulations of the [P•+(QA•-Fe2+)] ESP spectra of perdeuterated native RCs of Rb. sphaeroides is that the linebroadening ∆BP of 0.45 mT gives the correct line width, whereas a much smaller line width had to be used for simulations of the ESP spectra of Zn2+-substituted perdeuterated RCs (viz., ∼0.33 mT).10 The line-broadening of ∼0.45 mT is close to the experimental (X-band) EPR line width of P•+ at Boltzmann equilibrium.41 The smaller value required for the simulations of the ESP spectra of Zn2+-substituted RCs has not been explained yet, but may be related to the above-mentioned inconsistencies between simulations of ESP spectra of Zn2+-substituted RCs at X-band (protonated RCs, 20 K18, and 77 and 285 K10), K-band (protonated RCs, 77 and 285 K10; perdeuterated RCs, 40 K11), and W-band12 (protonated RCs, 170 K; perdeuterated RCs 145 and 170 K), namely, that orientation I of gP gives a better simulation for X- and K-band,10,11,18 whereas W-band results can only be simulated with orientation II.12 Especially, the highfield emissive feature of the ESP spectrum of Zn2+-substituted RCs, which is mainly related to P•+, can only be simulated using gPII.45 We note that the principal g-values as determined at W-band are within the experimental error the same for 170 and 285 K 15 and that gPII determined at 285 K provides a very good simulation of the W-band ESP spectra at 145 and 170 K.12 Furthermore, we note that the ESP spectra of protonated Zn2+substituted RCs are practically identical at 77 and 285 K (Xand K-band measurements10) and at 5, 20, 80, and 290 K (Xband measurements7,9,18,46). It is, therefore, unlikely that the discrepancy of the simulation results at different microwave frequencies are caused by a change of the orientation of gP upon cooling. We believe that the fact that the overall line shape at lower microwave frequencies (X- and K-band) is better simu-

J. Phys. Chem., Vol. 100, No. 6, 1996 2435 lated with gPI is related to the severe cancellation of spectral components in Zn2+-reconstituted RCs. This hypothesis is corroborated by the fact that the dark line width of P•+ at X-band can be used for the simulations of the ESP spectrum of [P•+(QA•-Fe2+)], because the cancellation of spectral components is less severe in native, Fe2+-containing RCs. We presume that a more complete description of the (anisotropy of the) fieldindependent terms in the spin Hamiltonian (such as hyperfine interactions and the non-uniaxiality of the dipolar coupling) will solve the discrepancy at lower microwave frequencies between the experimental and simulated spectrum for gPII. Another noteworthy aspect of our simulations is that we obtain good fits for JPQ ) 0. This contrasts with the simulations of Morris et al.,22 who need an unrealistically large value of J (∼2.5 µT) to obtain agreement between their simulations and the experimental spectrum for perdeuterated native RCs of Rb. sphaeroides R26. Apparently, this large value of JPQ results from the neglect of the difference in quantization axes of the spins of P•+ and (QA•-Fe2+) on D; see eq 13.26,49 In our previous paper,18 we used |JPQ| ≈ 0.3 µT to simulate the X-band EPR spectra of Zn2+-substituted RCs of Rb. sphaeroides R26, a value which is approximately 2 orders of magnitude larger than estimated from the distance dependence of J.18,47,48 In the Theory presented in this paper, we explicitly separated the exchange and the dipolar interactions. The dipolar interaction for two anisotropic spins depends on the g matrices of the two spins, eq 13.26,49 The result is that D is no longer traceless, but contains an isotropic part, which cannot be distinguished from the isotropic exchange interaction in the spin Hamiltonian of eqs 6 and 7. For Zn2+-substituted RCs, |trace(D)| is of the order of 10 nT, much smaller than the isotropic interaction reported earlier18 and far too small to have a perceptible effect on the simulations of the ESP spectra of Zn2+-substituted RCs. RCs of Rps. Viridis. We have obtained the magnetic axis system of (QA•-Fe2+) in Rb. sphaeroides R26 using simulations within the framework of the extended SCRP model described above. The directions of these magnetic axes are very different from those proposed by Evelo et al.36 for (QA•-Fe2+) in RCs of Rps. Viridis. The ESP spectrum of [P•+(QA•-Fe2+)] in Rps. Viridis, however, is very close to that observed in Rb. sphaeroides R26, showing the characteristic AEA pattern, Figure 1. The ratio of the amplitudes of the high- and low-field absorptive wings is ∼8, a value slightly different from that in Rb. sphaeroides (∼4.5),21 and ∆Bpp is increased to approximately 1.5 mT. These small differences are well-explained by a somewhat larger line-broadening of P•+, corresponding with the observation that the dark line width of the P•+ signal in perdeuterated RCs of Rps. Viridis is approximately twice as broad as in perdeuterated RCs of Rb. sphaeroides R26. The observation that the experimental ESP spectra of [P.+(QA•-Fe2+)] in RCs of Rb. sphaeroides and Rps. Viridis are very similar strongly suggests that the relative orientations of the magnetic axes systems of P•+ and (QA•-Fe2+) are virtually identical in both species. The orientation of the z-axis of orientation II of gP in RCs of Rb. sphaeroides is almost perpendicular to the plane of the bacteriochlorophyll molecules.12,15 Considering the molecular homomorphy of the primary donor molecules in Rb. sphaeroides and Rps. Viridis, and the spin-density distribution, with the electron spin mainly localized at the BChlA dimer half in both bacteria at cryogenic temperatures,31,50,51 we presume that the orientation of the g matrix of P•+ in the latter species is similar to that of Rb. sphaeroides. The principal values of gP also are not very different for Rb. sphaeroides R26 and Rps. Viridis; see Table 1 (M. Huber, personal communication). Furthermore, the archi-

2436 J. Phys. Chem., Vol. 100, No. 6, 1996

van den Brink et al.

TABLE 4: Direction Cosines of the g Matrix Axes (x, y, z) of the (QA•-Fe2+) Complex of Rps. Wiridis in the Crystallographic Reference Frame (a, b, c) a b c

x

y

z

-0.230 -0.965 -0.130

0.728 0.259 -0.635

0.646 0.051 0.762

tecture of the ligands of the divalent Fe ion is virtually identical in both species.34,40 Therefore, we expect that the orientation of the magnetic axes of (QA•-Fe2+) in Rps. Viridis is the same as that in Rb. sphaeroides. As mentioned before, this orientation of the magnetic axes of the quinone-iron complex deviates strongly from the directions obtained by Evelo et al. from their EPR study of (QA•-Fe2+) in RC crystals of Rps. Viridis,36 where the yFeQ axis makes an angle of approximately 69° with the Fe2+fI axis. The experimental data set of this work,36 however, did not cover a full set of angle-dependent EPR spectra, and therefore the assignment of the directions of the magnetic axes was not unambiguous. To check the above inferences regarding the orientation of the magnetic axes, we simulated the ESP spectrum of [P•+(QA•Fe2+)] in RCs of Rps. Viridis, using the directions of the dipolar and the g matrix axes calculated from the crystal structure.3840 For the directions of g , we used the convention introduced P by Norris et al. in their EPR single-crystal study of the triplet state of the primary electron donor, 3P.52 Because the unpaired electron of P•+ is localized mainly on the BChlA half of the dimer in Rps. Viridis,31 we can use the vectors NCfNA and NDfNB (IUPAC nomenclature) for xP and yP, respectively, so that zP is the normal to the plane of the macrocycle. We used an increased value of the line-broadening of P•+, ∆BP ) 0.80 mT, corresponding to the larger line width of P•+ in Rps. Viridis compared to that in Rb. sphaeroides. The broader P•+ line results in a decrease of the amplitude ratio of the absorptive wings. First, we tried a spectral simulation with the orientations of gFeQ proposed by Evelo et al.36 We consistently obtained an AE electron spin polarization pattern instead of the required AEA pattern. We then took the orientation of gFeQ obtained for Rb. sphaeroides (Table 3), with zFeQ parallel to the axis between the Fe2+ and N2 of His M266, and yFeQ nearly parallel to the axis between Fe2+ and O1 of Glu M234; see Table 4. This immediately gives the correct shape for the simulated ESP spectrum of [P•+(QA•-Fe2+)] in RCs of Rps. Viridis, see Figure 1 (dashed line). In a recent study of the EPR properties of photoaccumulated [I•-QA•-Fe2+] in RCs of Rps. Viridis,42 we found that the magnetic y-axis of Fe2+ must be close to the vector connecting Fe2+ and I•- in RCs of Rps. Viridis. The angle between the vector FefI and the y-axis obtained here is ∼12°. Thus, the orientations of the magnetic axes of the quinone-iron complex determined from the ESP spectrum of [P•+(QA•-Fe2+)] and from the X- and Q-band (steady-state) EPR spectra of [I•-QA•-Fe2+] are consistent. It follows that the magnetic axes of [QA•-Fe2+] for Rps. Viridis are identical to those of Rb. sphaeroides, with zFeQ parallel to the axis between Fe2+ and N2 of His M264 and yFeQ nearly parallel to the axis between Fe2+ and O1 of Glu M232. The direction of zFeQ can be rationalized when considering the position of the ligands, which form a tetragonally-distorted octahedron (see above). The crystal structure of Rps. Viridis40 shows that the axis FefHis L230 is elongated and should, therefore, be parallel to zFeQ, which is consistent with our findings. The close similarity in magnetic properties of the (QA•-Fe2+) complex for the two species agrees with the close similarity of the structure of Fe2+ and its ligands when comparing the crystal structures of Rb. sphaeroides and Rps. Viridis.34,40

Figure 5. Energy levels of the three radicals [P•+(QA•-Fe2+)] in the uncoupled representation. For clarity, the differences of the Zeeman interactions of P•+ and QA•- are greatly exaggerated. The levels acquiring large population in the SCRP model are shown in bold. Note that P•+QA•- is formed in a singlet configuration with the result that only the spin states containing the combinations Rβ and βR for P•+QA•are populated. The Orbach relaxation processes of the iron-quinone complex53 are indicated by arrows, with the solid arrows denoting the pure Fe2+ spin flips, and the dashed arrows the cross-relaxation of the QA•- and the Fe2+ spins.

Relaxation of the Polarized Signal. The spin-polarized EPR signal of P•+ in Rb. sphaeroides was shown to decay rapidly, with a time constant of approximately 20 µs at 6 K.20 This decay time is very close to the measured T1 of the (QA•-Fe2+) complex53 and much faster than the relaxation of P•+ in RCs frozen in the charge-separated state (∼10 ms54). It is unlikely that the fast polarization decay can be attributed to spin-lattice relaxation of P•+, enhanced by its interaction with the fast relaxer (QA•-Fe2+),20 because the coupling between P•+ and (QA•-Fe2+) is much too small for such a large enhancement (see above). We therefore consider the origin of the rapid decay of the P•+ polarization in closer detail. In Figure 5, we show the energy levels (in the uncoupled representation) of the lowest two quartets of states, which correspond to the mS ) -2 and mS ) -1 states of Fe2+ that are populated at ∼6 K. Considering the relaxation mechanism of the Fe2+QA•- complex as an Orbach-type relaxation process,53 we can distinguish two types of relaxation (see Figure 5): (i) relaxation of Fe2+ (S ) 2), where the orientation of the Fe2+ spin changes without inducing a spin flip of the quinone radical (∆mS,Fe ) (1, ∆mS,Q ) 0; solid arrows) and (ii) (enhanced) cross-relaxation of the quinone spin, where a spin flip of both the Fe2+ and the quinone spins occurs (dashed arrows). Figure 5 shows that a flip of the Fe2+ spin only connects states with (nearly) equal population, because it does not affect the spin correlation of P•+ and QA•-. Such a change in spin state of Fe2+ will change the effective g-value of the quinone-iron complex24 and thus will modulate the splitting of the two P•+ lines (as follows from eqs 12 and 13), without affecting the polarization pattern or the amplitudes of the spectral components. Process i on its own cannot account for the rapid decay of the polarisation of P•+, but its modulation of the splitting could result in the observed increase in ∆Bpp with time (see above). Cross-relaxation of the quinone and Fe2+ spins, i.e., process ii, connects highly-populated spin states with nonpopulated spin states. In the coupled representation of the SCRP model, this implies transfer of polarization from the two states with singlet character to the two triplet states with mS ) (1. Thus, cross-relaxation of the quinone spin rapidly destroys the initial population difference of the SCRP. It follows that the decay of the ESP signal of P•+ directly probes cross-relaxation within the (QA•-Fe2+) complex, which, as mentioned, is about 3 orders of magnitude faster than the spin-lattice relaxation of P•+ as measured in RCs frozen in the charge-separated state.53,54 A third process possibly destroying ESP (and used to explain

Reaction Centers of Photosynthetic Purple Bacteria the temperature dependence of the decay of P•+ by Morris et al.22) is exchange narrowing,55 which occurs if the correlation time τe of the quinone electron spin is much less than the splitting, i.e., τe , 0.2 µs. Because the T1 of the complex at ∼6 K is approximately 2 orders of magnitude longer,53 the exchange-narrowing process apparently does not contribute much to the decay of the P•+ polarization. 5. Conclusions The short-lived transient EPR signal observed in native, Fe2+containing RCs of the photosynthetic purple bacteria Rb. sphaeroides R26 and Rps. Viridis is described well with the theory of the spin-correlated radical pair, when the deviation between the quantization axis of the effective spin of the (QA•Fe2+) complex and the magnetic field direction, caused by the strong g-anisotropy of (QA•-Fe2+), is properly taken into account. More specifically, the ESP pattern (AEA) of P•+ could be simulated well with orientation II of the g matrix of P•+ 12,15 and JPQ ) 0. The unrealistically-large value of JPQ ≈ 2.5 µT, reported by Morris et al.,22 results from the neglect of the magnetic anisotropy of (QA•-Fe2+). We assessed the orientation of the magnetic axes of the (QA•Fe2+) complex in Rb. sphaeroides R26 and Rps. Viridis and conclude that for both species zFeQ is parallel to the axis between the Fe2+ and N2 of His M266 (M264 in Rps. Viridis) and yFeQ almost parallel to the axis between Fe2+ and O1 of Glu M234 (M232 in Rps. Viridis). The rapid decay of the ESP signal is discussed in terms of the relaxation of the quinone-iron complex, and we show that it probes the cross-relaxation of QA•- and Fe2+. Acknowledgment. This work was supported by the Netherlands Foundation of Chemical Research (SON), financed by the Netherlands Organization of Scientific Research (NWO), by a Twinning Grant of the European Community (Grant SC1*CT90-0569), and by a British Council Fellowship (to J.S.v.d.B.). The authors thank Dr. J. A. Weil (University of Saskatchewan, Canada) for helpful discussions, Mr. A. J. de Wit for growing the bacteria, and Ms. S. J. Jansen for biochemical assistance and purification of the RCs. We are indebted to Dr. M. C. Thurnauer for sending us the manuscript by Morris et al. prior to publication. J.S.v.d.B. gratefully acknowledges the hospitality of Corpus Christi College and the Physical and Theoretical Chemistry Laboratory during his stay in Oxford. References and Notes (1) Muus, L. T., Atkins, P. W., McLauchlan, K. A., Pedersen, J. B., Eds. Chemically Induced Magnetic Polarization; Reidel: Dordrecht, The Netherlands, 1977. (2) McLauchlan, K. A.; Steiner, U. E. Mol. Phys. 1991, 73, 241. (3) Hoff, A. J. Q. ReV. Biophys. 1984, 17, 153. (4) Stehlik, D.; Bock, C. H.; Petersen, J. J. Phys. Chem. 1989, 93, 1612. (5) Hore, P. J. In AdVanced EPR, Applications in Biology and Biochemistry, 1st ed.; Hoff, A. J.; Ed.; Elsevier: Amsterdam, 1989; p 405. (6) Snyder, S. W.; Thurnauer, M. C. In The Photosynthetic Reaction Center; 1st ed.; Deisenhofer, J., Norris, J. R., Eds.; Academic Press: New York, 1993; Vol. II, p 285. (7) Hoff, A. J.; Gast, P.; Romijn, J. C. FEBS Lett. 1977, 73, 185. (8) Tiede, D. M.; Dutton, P. L. Biochim. Biophys. Acta 1981, 637, 278. (9) Hore, P. J.; Hunter, D. A.; McKie, C. D.; Hoff, A. J. Chem. Phys. Lett. 1987, 137, 495. (10) Fu¨chsle, G.; Bittl, R.; Van der Est, A.; Lubitz, W.; Stehlik, D. Biochim. Biophys. Acta 1993, 1142, 23. (11) Van der Est, A.; Bittl, R.; Abresch, E. C.; Lubitz, W.; Stehlik, D. Chem. Phys. Lett. 1993, 212, 561. (12) Prisner, T. F.; Van der Est, A.; Bittl, R.; Lubitz, W.; Stehlik, D.; Mo¨bius, K. Chem. Phys. 1995, 194, 361. (13) Allen, J. P.; Feher, G. Proc. Natl. Acad. Sci. U.S.A. 1984, 81, 4795.

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