Eur. J . Biochem. 88, 135-141 (1978)

Interpretation of the Mossbauer Spectra of the Four-Iron Ferredoxin from Bacillus stenrothermophilus Peter MIDDLETON, Dominic P. E. DICKSON, Charles E. JOHNSON, and James D. RUSH

Department of Physics, University of Liverpool

(Received October 14, 1977)

The Mossbauer spectra of both oxidized and reduced ferredoxin from Bacillus stearothrrmophilus have been analysed using computer fits to theoretical spectra obtained from a spin Hamiltonian. A consistent set of parameters was obtained from fits to spectra obtained over a wide range of temperature and magnetic field.

These results are interpreted in terms of a model for the active centre which is consistent with its electronic and magnetic properties in both redox states. In the model for the oxidized centre all four iron atoms have essentially the same valence, intermediate between ferric and ferrous, with one pair spin-up and the other pair spin-down. On reduction the extra electron goes predominantly to one pair of iron atoms which become ferrous with the other pair remaining substantially unchanged.

Using this model it is possible to obtain relationships between the spin Hamiltonian parameters for individual iron atoms and those for the coupled centre. This can give further insight into the relation between the observed electron paramagnetic resonance and Mossbauer spectra.

The ferrodoxin from Bacillus stearothermophilus belongs to the class of iron-sulphur proteins which contain one four-iron/four-sulphide centre per mole- cule. X-ray crystallographic studies on the ferrodoxin from Peptococcus aerogenes, which contains two such centres, show that each active centre consists of four iron atoms, each in a distorted tetrahedral environ- ment of three labile sulphur atoms and a fourth sulphur ligand from a cysteine residue of the amino acid chain [l]. The physicochemical properties of this ferrodoxin have previously been reported by Mullinger et al. [2]. The centre can exist in two redox states, C2- and C3-. When isolated it is in the oxidized form, Cz-, with formal valences 2 Fez+ + 2 Fe3+. On re- duction one electron is accepted by the centre which becomes C 3 - or formally 3 Fez+ + 1 Fe3'. No elec- tron paramagnetic resonance (EPR) signal is seen from the oxidized protein which shows the centre to have zero net spin; this is confirmed by its Mossbauer spectra in magnetic fields. The EPR spectrum of the reduced centre shows g values of 2.06, 1.93 and 1.89, and its Mossbauer spectra show the existence of positive and negative hyperfine fields within the centre which confirm the antiferromagnetic coupling be- tween the iron atoms [2].

While a considerable amount of information can be obtained from a qualitative interpretation of the

Ahhreviation. EPR, electron paramagnetic resonance

Mossbauer spectra of these proteins [3], the present work represents the next stage with computer fitting of the Mossbauer spectra. This fitting gives rise to certain constraints and the values of certain parameters which must be taken into account in any model for the electronic structure of the active centre. The ulti- mate goal of this work is to find this model.

COMPUTER ANALYSIS

In the presence of an applied magnetic field, H , the spin Hamiltonian for the active centre may be written :

where the first term is the electronic Zeeman inter- action, the second is the exchange interaction between the spins on the four iron atoms, the third is the hyper- fine interaction between thenuclear and electronic spins, the fourth is the nuclear Zeeman interaction and the last term is the nuclear quadrupole interaction. Si and Zi are the electronic and nuclear spins of each iron atom, Jij are the exchange couplings between electronic

136 Mossbauer Studies of Ferredoxin from Bacillus stearothermophilus

I Veloc i ty (mmis)

Fig. 1, Mdsshcuier spectrum ofreduiur.rd B. s tearothermophilus , ferre~~~in l i t 77 K showing the computer f i t to two components. The dashed line represents component a (Fe"'-FeZ") while the continuous line represents b (2 Fez+). The horizontal axis shows the velocity of the ?-ray source which is proportional to energy

spins, A , are the magnetic hyperfine couplings, Q is the nuclear quadrupole moment, and ( V , J L and v, are the principal components and asymmetry parameters of the electric field gradient tensors. p, fin, g,, and g, are the Bohr magneton, nuclear magneton, electronic g factors and nuclear g factor respectively.

We now proceed to make approximations and assumptions in order to reduce the above general Hamiltonian to a readily soluble form while retaining a good representation of the active centre. Firstly we can say that the electronic spin exchange term is by far the largest such that the four electronic spins are coupled, under all normal experimental conditions, to give an effective net spin for the whole centre S = S1 + SZ + S3 + Sq. This gives S = 0 and S = '1, for the lowest coupled spin states of the oxidized and reduced centres respectively. In addition the electronic Zeeman term is assumed large compared with the last three terms so that the electronic and nuclear spins are decoupled. This enables the nuclear hyperfine problem to be solved using the effective field approxi- mation, that is treating the quantity S . A as an effec- tive field at the nucleus. In iron this means that the applied magnetic fields H must be large compared with 0.002 T.

In the case of the oxidized ferredoxin for which the total spin S = 0 the projections of the individual spins S , along the total spin are also zero and the first and third terms of the general Hamiltonian vanish. The resulting spin Hamiltonian used to describe each iron atom in the oxidized centre then becomes:

Q,= - PngnH I

with i = 1,2,3,4, which gives four Components of equal intensity in the Mossbauer spectrum if it is assumed that the recoil-free fraction is the same for all four iron atoms.

In the case of the reduced ferredoxin we have reduced the number of effective iron sites from four to two. This simplification is justified on evidence from three sources. Firstly, the spectrum taken at 77 K (Fig. 1) shows two resolved components which fit well to two doublets of equal linewidth and intensity. Secondly, spectra taken between 77 and 4.2 K show different relaxation behdviour for the two components [2]. Thirdly, previous spectra taken in applied magnetic fields have shown qualitatively the existence of two opposing hyperfine fields [2] again suggesting the presence of two sorts of iron atom within the reduced centre. In this situation the spin Hamiltonian for each of the two types of iron atom becomes:

f?i = f i H . g ' . S + S . A' i - I - fl,g,H. I

] (3) 5 V l 2 + --

~ I," - - + - ( Ix - Z,.) e 2 Q ( v Z Z ) 1 4 [ 4 3

with I = 1,2, where g' is the g tensor of the whole coupled centre, as measured by EPR, and A ; are the A tensors of the two different sorts of iron atom related to the spin of the whole centre, S = '1,.

The computer program used for fitting the applied field spectra is a modified form of that of Lang and Dale [4]. The program uses the spin Hamiltonian:

P. Middleton, D. P. E. Dickson, C. E. Johnson, and J . D. Rush 137

From this a theoretical spectrum is calculated from given parameters. These parameters are then iteratively varied until a minimum in x2 (the sum of the squares of the residuals between the calculated and experi- mental spectra) is obtained. The main modification was to enable the program to fit, iteratively, a spectrum with up to four components each resulting from a separate spin Hamiltonian of the above form.

The g and A tensors are assumed to have the same principal axis system as that of the electric field gradient tensor which is taken as the co-ordinate system for the calculation. In the case of a slowly relaxing paramagnetic material the theoretical spec- trum for each site is calculated in the following manner. A direction of the applied field is assumed and the electronic Zeeman problem is solved to find the quantum mechanical expectation value of the spin. This then replaces S in the Hamiltonian and the nuclear problem is solved using the effective field approximation to give a spectrum with up to eight lines. This procedure is carried out for both members of the electronic doublet and the resulting line spectra are added after multiplying by the appropriate Boltz- mann factors. The above procedure is repeated for a range of applied field directions appropriately dis- tributed over an octant of a sphere to accumulate the total array of absorption energies and intensities for a polycrystalline (frozen solution) sample. The number of field directions taken to form the average in the present work was 25, which gave the best compromise between computing time and accuracy of the calculated spectrum. The spectrum is then folded with a Lorent- zian lineshape. The theoretical spectra for each com- ponent are then added after multiplying by an area ratio parameter. A linear fit to the experimental spectra determines the parabolic background param- eters and the overall intensity of the theoretical spectrum. Finally this is compared with the experi- mental spectrum, x is calculated and the parameters are iteratively varied under chosen constraints until a minimum in x 2 is found.

There is a danger when computer-fitting compli- cated spectra of finding an erroneous minimum in x 2 by allowing too much freedom in parameter space. This is especially true for the often broadened and noisy spectra obtained from biological compounds which are weak in iron. By using physical insight we can make further approximations in order to limit the number of variable parameters and so obtain a more reliable fitting procedure ; these are discussed in the next section. Ultimately the test for reliability and uniqueness is the consistency of the fitted param- eters from spectra obtained over a wide range of experimental conditions. This policy is successfully used in this work to produce a set of parameters which are consistent over the range of magnetic fields be- tween 0.05 and 6.0 T, applied both parallel and per-

>

't f w

3t I I I I I 1 I I

~4 -3 - 2 - 1 0 l 2 3 4 Velocity ( r n r n i s )

Fig. 2. Miisshauer spectru mid computer /its of oxidized B. stearo- thermophilus f iwedoxin ui 4.2 K in ( A ) zero ,field3 ( B ) 3.0 7 per- pendiculur and (C) 6.0 Tperpendiculur. The four-component spectra are also shown

pendicular to the axis of observation, and for the limits of both slow and fast relaxation (corresponding to liquid helium and liquid nitrogen temperatures).

RESULTS

The details of the sample preparation and Moss- bauer spectroscopy have been given previously [2].

O.dized Fervedoxin

Eqn (2) together with four chemical shift terms was used to fit the spectra of the oxidized protein. By constraining the areas and linewidths of the four component spectra to be equal, the number of variable parameters is reduced giving a well-behaved fitting procedure. Fig. 2 shows fitted spectra of the oxidized ferrodoxin taken at 4.2 K in perpendicular fields of 0, 3 and 6 T, and Table 1 gives the parameters ob- tained from these fits. They confirm that the centre has zero net spin in this state (complete antiferro- magnetic coupling) and the nearly equal chemical shifts confirm that all four iron atoms have very similar valence states. Although the iron atoms have formal valences of 2 Fe" + 2 Fe" , confirmed by the

138 Mossbauer Studies of Ferredoxin from Bacillus stearothermophilus

Table 1. Miisshauer parameters of oxidized B. stearothermophilus ferredoxin The chemical shifts 6 (relative to iron metal), the quadrupole split- tings LIEQ [= '/z QVzc (1 - 9 'h)] , and the full widths a t half maximum, I', are quoted in mm s- ' . The uncertainties a t 195 and 77 K are i- 0.01 or less. '1 is the asymmetry parameter. At 4.2 K the numbers in brackets give the standard deviations on the least significant digit of the mean parameters derived from fits to spectri obtained in a range of. applied fields

Temper- Iron 6 AEQ r '1 ature atom

K mm s - '

195 1 0.37 1.08 0.29 2 0.37 0.83 0.29 3 0.37 0.70 0.29 4 0.37 0.55 0.29

77 1 0.43 1.36 0.27 2 0.43 1.07 0.27 3 0.43 0.86 0.27 4 0.42 0.57 0.27

... ._ . .-

~~~ ~~ . . .- ~~~~~~~~ ____

~. . . .. .._ ~~

4.2 1 0.42 ( 1 ) + 1.50 (6) 0.27 ( I ) 0.7 (1) (applied 2 0.43 (2) + 1.20 (3) 0.27 (1) 0.7 (1) fields) 3 0.42 (2) + 1.10 (9) 0.27 (1) 0.9 (1)

4 0.42 (2) +0.66 (1) 0.27 (1) 0.9 (1)

1

- 0 ." C 0 ._ c

L a 0 u)

: 1

0

1

intermediate values of the chemical shifts [3], the valence electrons must be delocalized to produce equal charge densities at the four iron nuclei. The differences in the quadrupole splittings for the four iron atoms implies a small inequivalence of the charge distribu- tions at each iron site. The fits were insensitive to the asymmetry parameters and only an estimate for each site was obtained.

Reduced Fevvedoxin

Eqn (3), together with two additional chemical shift terms, was used to fit the spectra of the reduced protein with g;, g; and g: set equal to 2 for both components since calculations showed the Mossbauer spectra to be insensitive to any anisotropy. By con- straining the areas and linewidths of the two com- ponents to be equal (cf. Fig. l), the number of variable parameters is significantly reduced.

Fig. 3 shows spectra of the reduced ferrodoxin at 4.2 K in various magnetic fields applied both parallel and perpendicular to the axis of observation, fitted as described above. It can be seen that the overall splitting of component b (the ferrous-like component

I I I I I I I I I I I I I I

A D

I 1 1 I I 1 I 1 1 I I I 1 I

-6 - 4 - 2 0 2 4 6 -6 - 4 - 2 0 2 4 6 Velocity (rnmls)

Fig. 3. Miissbauer spectra and computer fits of reduced B. stearothermophilus ferredoxin at 4.2 K in perpendicular applied magnetic fields of ( A ) 0.05 T, ( B ) 3.0 T and ( C ) 6.0 T and parallel applied magnetic fields of (0) 0.1 T, ( E ) 3.0 T and ( F ) 6.0 T. The dashed line represents component a while the continuous line represents b

P. Middleton, D. P. E. Dickson, C. E. Johnson, and J. D. Rush 139

Table 2. Miissbauer parameters of reduced B. stearothermophilus ,firredosin Component a is Fe3' -Fe2', component b is 2 Fe2+. Values of A' are given in mm s- ' and refer to the "Fe ground state; to obtain values in MHz multiply by 11.625 mm s- ' . Numbers in brackets for values at 4.2 K are explained in Table 1

Temperature Com- 6 AEQ r 'I A: AI A; ponent

~

K m m s m m s

195 a 0 44 1 1 3 0 28 b 0 53 1 54 0 35

77 a 0 49 1 2 0 0 36 b 0 59 184 0 36

- - ~ _ _ _ _ _ ~~- - ____ ~ _ _ ~ - - ~~ -

4 2 (applied rl 0 so (2) + 1 32 (6) 0 78 (9) - 2 73 (12) - 2 80 (7) - 2 40 (12) fields) b 0 5s (2) + 1 89 (6 ) 0 32 (4) + 2 28 (5) + I 16 (14) f O 74 (7)

which has the larger chemical shift and quadrupole splitting together with more anisotropic A values) in- creases as the applied magnetic field is increased while the splitting of component a (the more ferric-like component) decreases. This confirms the existence of two opposing fields within the centre.

The parameters corresponding to these fits are given in Table 2. The hyperfine coupling constants A' are those of the ground ( I = 1/2) 57Fe nuclear state; positive A ' values correspond to a positive internal field at the nuclei and vice versa. Although reasonable fits to the low-temperature spectra could be obtained with a negative sign for the principal component of the electric field gradient for component b, this pos- sibility is ruled out by the spectra obtained in large fields at higher temperatures which correspond to the case of a fast relaxing paramagnet where the hyper- fine field averages zero. These spectra can only be fitted with a positive sign. Fig. 4 shows just such a fit to a spectrum measured at a temperature of 133 K and in a field of 6 T perpendicular to the y-rays. The splitting of the lower energy line into three and the higher energy line into two by the field identifies the lower energy line as arising from the I ml = k ' 1 2 > ex- cited level, and hence shows that the electric field gradient is positive for both sites. The linewidths were held equal during the fit and gave a value of 0.35 mm s- ', and the chemical shifts and quadupole splittings are consistent with those found at 195 K in zero field (Table 2). The rather large values of linewidths found in the high-temperature spectra results from the assumption that the atoms in each pair are identical. Relaxing these conditions would not provide any more reliable values of 6 and d EQ for each atom, and would not alter the conclusion that the electric field gradient is positive. Thus the parameters given appear to constitute a unique set of values for the Mossbauer and spin Hamiltonian parameters which is confirmed by the consistency in the values of these parameters resulting from fits to spectra obtained over a wide

I +

1.0 1 1 I

1

-4 -3 - 2 -1 0 1 2 3 4 Velocity ( r n r n i s )

Fig. 4. ikliicshuuer spectrum of reduced B. stearothermophilus. f&ri>- doxin at 133 K in a perpendicular applied magnetic ,field of 6.0 T. The dashed line represents component a while the continuous line represents b. This spectrum confirms that both iron species have a positive quadrupole splitting

range of applied magnetic fields and at different temperatures.

DISCUSSION

The computer analysis described above confirms the model for the four-iron centres of iron-sulphur proteins that has been proposed previously by Dick- son et al. [5] as a result of a more qualitative inter- pretation of the Mossbauer spectra of Clostridium pasteurianum ferredoxin and Chromatium high-poten- tial iron-sulphur protein. In this model the C2- centre of oxidized ferredoxin contains two spin-up iron atoms and two spin-down iron atoms. There is fast

140 Mossbauer Studies of Ferredoxin from Bacillus stearoihermophilus

Fig. 5. Model for the C3- ctintre of' the reduced fcrredoxin in an upplied field showing ihe magnetic moments of the jhur irons atoms. The open circles represent the labile sulphur atoms and the hatched circles represent cysteiuyl sulphur atoms. The dashed line indicates the fast hopping or delocalization of the sixth 3d electron between the spin-up pair of ferriclferrous atoms

hopping or delocalization of the sixth 3d electrons between each pair of iron atoms and all iron atoms have an effective valence Fe2f+. On reduction the centre gains one 3d electron which goes to the pair of spin-down iron atoms. Thus the C3- centre of the reduced ferredoxin has one pair of high-spin (S = 2) Fe2 * atoms which have their magnetic moments directed antiparallel to an applied magnetic field and thus give the positive and anisotropic A' values de- noted by for component b in Table 2. The other is a high-spin Fe3'-Fe2+ pair of iron atoms which have their magnetic moments directed parallel to the applied field. These have negative values of A' (component a in Table 2). The sixth 3d electron is shared between these two iron atoms so that they appear essentially equivalent. Any sharing of electrons between the spin- up and spin-down iron atoms is inhibited by the Pauli exclusion principle. The centre has a total spin S = '/, .

This model for the C 3 - centre is shown in Fig. 5. It indicates the arrangement of spins resulting from the coupling between the four irons atoms. It does not explain the details of this coupling, although it is presumably 90 O superexchange through the sulphur atoms that gives rise to the dominant antiferro- magnetic interaction. However from the spin arrange- ment of Fig. 5 it is possible to obtain further informa- tion on the relationship between the g and A values related to the spins of the individual iron atoms and the g' and A' values which are measured experi- mentally by EPR and Mossbauer spectroscopy. The following analysis is an extension of that given by Johnson et al. [6] for the simpler case of the two coupled spins in the two-iron ferredoxins. A com- pletely general solution of the problem of four coupled spins is not possible and the simplification implicit

in the model of Fig.5 represents an essential inter- mediate state in the analysis.

centre we have the iron atoms forming two pairs a and b such that:

From this model for the S =

s a = S l + s 2 s b = s 3 + s 4 s a $ s b = s . ( 5 ) The electronic Zeeman term in the spin Hamiltonian [Eqn (I)] for the two iron atoms in pair a can be written

f lH ' ga ' S a = f l H ' (81 . S1 + g2 . S2) (6)

and thus the pairwise g factors are given by

(7)

and similarly for pair b. The spins of the two pairs can be coupled together giving

and so finally we obtain

From the model shown in Fig.5, and for simplicity neglecting the equivalence between atoms 1 and 2 (pair a), we have S1 = 512, S2 = 2, S3 = 2, S4 = 2, Sa = 912 and s b = 4. The terms in brackets can then be evaluated to give

I 55 44 4 4 g = -g1 + -g2 - -g3 - -&. 27 21 3 3 (10)

A ferric atom has g values which are isotropic and equal to 2 since it is in a spherically symmetrical spin state and the orbital contribution is zero. A ferrous atom has g values that are anisotropic with gZ = 2 and gX,? = 2 + A (assuming axial symmetry) as a result of the additional orbital contribution. Putting these single-atom g values in Eqn (10) gives

This gives the single set of g' values with an average of less than 2 that is observed experimentally by EPR [2].

The A' values for the spin of the coupled centre can be related to the A values for the spins of the individual iron atoms by considering the hyperfine interaction terms in the spin Hamiltonian [Eqn (l)] :

S1 . A1 . I1 = S, . Aal . I 1 (12) where Aal is the hyperfine coupling tensor for atom 1 related to the spin of pair a.

Thus, as before

P. Middleton, D. P. E. Dickson, C. E. Johnson, and J. D. Rush 141

Then coupling the pairs together gives finally

for the A’ values of each iron atom related to the spin of the centre. The terms in brackets are the same as those in the relationship for the g’ values [Eqn (9)]. A; and A; are negative and experimentally it is ob- served that A; % Ai as they both correspond to pair a of the computer fits. A; and A4 are positive and equal corresponding to pair b of the computer fits.

The values of A1,2,3,4 are those for individual ferric and ferrous iron atoms in a tetrahedral sulphur environment. Using the values obtained by Schulz and Debrunner [7] for the protein rubredoxin which con- tains only one iron atom, the above treatment gives a set of A’ values of (3.17, 1.29, 4.74) for pair b, the, ferrous pair. It is more difficult to know how to treat the ferrous/ferric pair, but taking averages gives A’ values of - 3.89 which will be more isotropic than for the ferrous pair. Comparison with experimental data (Table 2) indicates that the theoretical values are too large by about 50% but that the predicted anisotropy is approximately correct. Thus the simple spin-coupling model described gives qualitative agree- ment with measured data for the C3- centre. It should be emphasized that the x, y and z axes relate to the electric field gradient and may be different for every protein and possibly also for each redox state. There- fore the A:, A: and A: in the different proteins do not necessarily correspond to each other.

An alternative approach would be to use the ex- perimental A values found for B. s ~ e u ~ @ ~ h e ~ m @ ~ h ~ i u s ferrodoxin and for rubredoxin, to give the factors in brackets in Eqn [14] and hence the same factors in Eqn (9) for the whole centre g’ values. This yields g’ values near to 2 but with large errors resulting from the many uncertainties involved.

CONCLUSIONS

Computer analysis of Mossbauer spectra as dc- scribed in this paper can allow a considerably more complete description of the system than is possible with a qualitative interpretation. In the present work the model for the active centre of B.stearothermo- philus ferredoxin has been found to be fully consistent with the fitted spectra. Although the basic features of this model were previously inferred from a quali- tative inspection of the spectra [ 5 ] , the confirmation of the model that has resulted from a computer analysis gives one confidence in using the model for further calculations. For many systems computer-fitting of the spectra may present the only possibility of inter- pretation.

The authors wish to thank Professor D. 0. Hall and Drs R. N . Mullinger, R.Carnmackand K. K.RaoofKing’sCollege, University of London for preparing the 57Fe-enriched protein samples used in the present work. J. D. Rush would like to thank the Science Research Council for a Research Studentship. This work is sup- ported by the Science Research Council.

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3. Cammack, R., Dickson, D. P. E. & Johnson, C. E. (1977) in Iron-Sulphur Proteins (Lovenberg, W., ed.) vol. 3 , pp. 283- 330, Academic Press, New York.

4. Lang, G. & Dale, B. W. (1974) Nucl. Instrum. A4ethod.Y 116,

5. Dickson, D. P. E., Johnson, C. E., Thompson, C. L., Cammack, R., Evans, M. C. W., Hall, D. O., Rao, K. K . & Weser, U. (1974) J . Phys. (Paris) 35, 0-343-346.

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P. Middieton, D. P. E. Dickson, C. E. Johnson, and J. D. Rush, Department of Physics, University of Liverpool, P.O. Box 147, Liverpool, Great Britain, L69 3BX