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On the geometry and electronic properties of the FeS site of the two-iron ferredoxins
Volume 19, number 2
CHEMICAL PHYSICS LETTERS
15 March 1973
ON THE GEOMETRY AND ELECTRONIC PROPERTIES OF THE Fe-S SITE OF THE TWO-IRON FERREDOXINS J.A. HAGARMAN Department
of Chemistry,
and S.I. SHUPACK
Villanova University,
Villar~ova, Pennsylvania
Received 18 December
19085,
tX.4
1972
Semi-empirical LCAO MO theory has been used to calculate ground-state wavefunctions for modets of the osidized form of the two-iron ferredoxins. A large number of conformers were examined. Geometricaf variafions included Fe-Fe distance, Sb-Sb distance, and S,-Fe-S, angle. Ground-state wnveftinctions were used to caisuIate field-gradient tensors and subsequently quadrupolar splittings and asymmetry parameters. Best mode!s were determined from a reasonable fit of Mijssbauer results to experimental data.
Approximate ground-state wavefunctions for several geometric conformers of the active site (oxidized form) of the two-iron ferredoxins have recently been calculated by Loew and Steinberg [I, 21. Self-consistent extended Hiickel theory was used and the lowest total-energy conformer was taken as the best model. The wavefunction of this “best model” was used to determine room-temperature magnetic susceptibility and Mijssbauer constants (quadrupolar splitting QS, and asymmetry parameter 7)). A rough fit of the electronic spectrum of ferredoxin was included.’ In our work, we have attempted to determine a model structure for the active center (oxidized form) of the two-iron ferredoxin using a different approach, and have obtained quite different results. Rather than using total energy as the prime criterion of an acceptable model structure, we have chosen to correlate calculated Mijssbauer parameters with experimental data. The problems with total energies calculated by semi-empirical theory are well-documented [3,4], while calculations of properties dependent on oneelectron operators have been more successful [5,6]. Magnetic field Miissbauer spectroscopic measurements have been made on bcth the oxidized and reduced forms of the two-iron ferredoxins [7]. For the oxidized form, a single quadrupolar pair indicates equivalent iron atoms. A QS of 0.6 to 0.8 mm/set and an q of 0.5 5 0.3 at 4.2% have been reported [7].
4
Fig. 1. General model structure (from ref. [El) far the active cznter (oxidized form) of the two-iron ferredoxin. AZ Sc in J’Z plane, all Sb in xz plane, all S-Fe-S bond angks approximately tetrahedral.
We have begun with the general mode1 of Gibson et al. [8] (fig. 1) and have made systematic geometrical variations. Ground-state wavefunctions were calculated by the self-consistent charge and rqnfiguration (SCCC) technique of Ballhausen and Gray [9. lo]. Valence orbital ionization potentiais caiculated by the method of Anno [ 1 l] were used tbr diagonal hamiltonian elements. The off-diagonai terms were approximated by-the method of Cusachs [12J. Calculations were limited to models having two iron and six sul195
15 March 1973
CHEMICAL PHYSICS LETTERS
VoIume 19, number 2
phur atoms due to computer memory size. The four cysteine residues were accounted for by addition of two electrons to the model, comparable to 0.5 electron per residue. A similar approach has been used by Halton [6] for oxyhaemoglobin. Field-gradient tensors* were calculated from groundstate wavefunctions and used to determine quadrupolar splittings and asymmetry parameters by the formulas
large field-gradient-tensor components, V,, = 1.56, y, = -3.52, yVY= 1.95. These values are much too large to give an acceptable value for the quadrupolar splitting. The coordinate system used by Loew et al. [l] is different than that used in this study. They define the Fe-Fe axis to be the x coordhate. We feel that the major component of the field-gradient tensor, &, is probably along the Fe-Fe axis. The axial symmetry of our model, with the z axis along the Fe-Fe bond, fits preliminary results obtained for “g” tensor calculations on models for the reduced form of ferredoxin.
QS = 0.5 e V&Q( 1.0 + 77/3)]“, where I& > V, or VYY,--E is the charge on an electron, Q is the nuclear quadrupolar
moment
References
of the first
excited state of 57 Fe. A large number of geometric. conformers were studied by varying Fe-Fe and S,,-Sb distances as well as SC-Fe-S, bond angles within b_!, symmetry. The best fit of experimental Mijssbauer results was obtained at an Fe-Fe distance of 2.9 A, an S,--Sb distance of 3.0 A, and an SC-Fe-S bond angle of 90”. All bond lengths are 2.1 to 2.2 A. The &,-Fe-S, bond angle is approximately 90”. With this model, a QS of 0.48 and an Q of 0.59 were calculated. This geometry is quite different from the results of Loew et al., where an Fe-Fe distance of 4.2 A, an Sb--Sb distance of 2:08 8. an SC-Fe+ angle of 109”, and an Sb-Fe-Sb bond angle of 45 were found. A bond angIe of 90’ seems more reasonable in light of X-ray studies on other model systems [14, 15). Using our method, a calculation of the low-energy structure of Loew et al. produced a wavefunction which gave very
* Our method of calculating field-gradient tensorsagrces with ref. lj J, and appears to be diffzrcnt from the method of Loew et al.
[l] G.A. Loewand D.A. Steinberg, Theoret. Chim. Acta 23 (1971) 239. [ 21 G.A. Loew and D.A. Steinberg, Theoret. Chim. Acta 26 (1972) i07. I31J.R. de la Vega, Y. Fang and E.F. Hayes, Intern. J. Quantum Chem. 3S (1969) 113. 141 R.G. Parr, J. Chem. Phys. 19 (1951) 799.
I51 J.L.K.F.
de V&s,
C.P. Keijzers
and E. dc Boer,
Inorg.
Chem. 11 (1972) 1343. 161 h1.P. Halton, Theoret. Chim. Acta 24 (1972) 89. I71 W.R. Dunham, A.J. Benrden, I.T. Salmeen, G. Palmer, R.H. Sands, W.H. Orme-Johnson and H. Beinert, Biothem. Biophys. Acta 253 (1971) 134. 181 J.F. Gibson, D.O. Hall, J.H.M. Thornley and F.R. Watley, Proc. NatI. Acad. Sci. U.S. 52 (1966) 987. PI C.J. Ballhausen and H.B. Gray, Inorg. Chem. 1 (1962)
Ill.
IlO1 H.B. Gray and C.J. Ballhausen, J. Am. Chem. Sot. 85 (1963) 260.
IllI 1. Anno and S. Yoshiko, Theoret. Chim. Acta 18 (1970) 208.
[I21 L.C. Cusachs, J. Chcm. Phys. 43 (196.5) S137.
i131 H. Bcincrt and R.H. Sands, B&hem. Biophys. Res. Commun. 3 (1960) 41. [14] D.L. Stcvcnson and L.F. Dahl, J. Am. Chem. Sot. 89 (1967) 3721. [15] D. Coucouvanis, S.J. Lippard and J.A. Zubicta, J. Am. Chcm. Sot. 91 (1969) 761.
CHEMICAL PHYSICS LETTERS
15 March 1973
ON THE GEOMETRY AND ELECTRONIC PROPERTIES OF THE Fe-S SITE OF THE TWO-IRON FERREDOXINS J.A. HAGARMAN Department
of Chemistry,
and S.I. SHUPACK
Villanova University,
Villar~ova, Pennsylvania
Received 18 December
19085,
tX.4
1972
Semi-empirical LCAO MO theory has been used to calculate ground-state wavefunctions for modets of the osidized form of the two-iron ferredoxins. A large number of conformers were examined. Geometricaf variafions included Fe-Fe distance, Sb-Sb distance, and S,-Fe-S, angle. Ground-state wnveftinctions were used to caisuIate field-gradient tensors and subsequently quadrupolar splittings and asymmetry parameters. Best mode!s were determined from a reasonable fit of Mijssbauer results to experimental data.
Approximate ground-state wavefunctions for several geometric conformers of the active site (oxidized form) of the two-iron ferredoxins have recently been calculated by Loew and Steinberg [I, 21. Self-consistent extended Hiickel theory was used and the lowest total-energy conformer was taken as the best model. The wavefunction of this “best model” was used to determine room-temperature magnetic susceptibility and Mijssbauer constants (quadrupolar splitting QS, and asymmetry parameter 7)). A rough fit of the electronic spectrum of ferredoxin was included.’ In our work, we have attempted to determine a model structure for the active center (oxidized form) of the two-iron ferredoxin using a different approach, and have obtained quite different results. Rather than using total energy as the prime criterion of an acceptable model structure, we have chosen to correlate calculated Mijssbauer parameters with experimental data. The problems with total energies calculated by semi-empirical theory are well-documented [3,4], while calculations of properties dependent on oneelectron operators have been more successful [5,6]. Magnetic field Miissbauer spectroscopic measurements have been made on bcth the oxidized and reduced forms of the two-iron ferredoxins [7]. For the oxidized form, a single quadrupolar pair indicates equivalent iron atoms. A QS of 0.6 to 0.8 mm/set and an q of 0.5 5 0.3 at 4.2% have been reported [7].
4
Fig. 1. General model structure (from ref. [El) far the active cznter (oxidized form) of the two-iron ferredoxin. AZ Sc in J’Z plane, all Sb in xz plane, all S-Fe-S bond angks approximately tetrahedral.
We have begun with the general mode1 of Gibson et al. [8] (fig. 1) and have made systematic geometrical variations. Ground-state wavefunctions were calculated by the self-consistent charge and rqnfiguration (SCCC) technique of Ballhausen and Gray [9. lo]. Valence orbital ionization potentiais caiculated by the method of Anno [ 1 l] were used tbr diagonal hamiltonian elements. The off-diagonai terms were approximated by-the method of Cusachs [12J. Calculations were limited to models having two iron and six sul195
15 March 1973
CHEMICAL PHYSICS LETTERS
VoIume 19, number 2
phur atoms due to computer memory size. The four cysteine residues were accounted for by addition of two electrons to the model, comparable to 0.5 electron per residue. A similar approach has been used by Halton [6] for oxyhaemoglobin. Field-gradient tensors* were calculated from groundstate wavefunctions and used to determine quadrupolar splittings and asymmetry parameters by the formulas
large field-gradient-tensor components, V,, = 1.56, y, = -3.52, yVY= 1.95. These values are much too large to give an acceptable value for the quadrupolar splitting. The coordinate system used by Loew et al. [l] is different than that used in this study. They define the Fe-Fe axis to be the x coordhate. We feel that the major component of the field-gradient tensor, &, is probably along the Fe-Fe axis. The axial symmetry of our model, with the z axis along the Fe-Fe bond, fits preliminary results obtained for “g” tensor calculations on models for the reduced form of ferredoxin.
QS = 0.5 e V&Q( 1.0 + 77/3)]“, where I& > V, or VYY,--E is the charge on an electron, Q is the nuclear quadrupolar
moment
References
of the first
excited state of 57 Fe. A large number of geometric. conformers were studied by varying Fe-Fe and S,,-Sb distances as well as SC-Fe-S, bond angles within b_!, symmetry. The best fit of experimental Mijssbauer results was obtained at an Fe-Fe distance of 2.9 A, an S,--Sb distance of 3.0 A, and an SC-Fe-S bond angle of 90”. All bond lengths are 2.1 to 2.2 A. The &,-Fe-S, bond angle is approximately 90”. With this model, a QS of 0.48 and an Q of 0.59 were calculated. This geometry is quite different from the results of Loew et al., where an Fe-Fe distance of 4.2 A, an Sb--Sb distance of 2:08 8. an SC-Fe+ angle of 109”, and an Sb-Fe-Sb bond angle of 45 were found. A bond angIe of 90’ seems more reasonable in light of X-ray studies on other model systems [14, 15). Using our method, a calculation of the low-energy structure of Loew et al. produced a wavefunction which gave very
* Our method of calculating field-gradient tensorsagrces with ref. lj J, and appears to be diffzrcnt from the method of Loew et al.
[l] G.A. Loewand D.A. Steinberg, Theoret. Chim. Acta 23 (1971) 239. [ 21 G.A. Loew and D.A. Steinberg, Theoret. Chim. Acta 26 (1972) i07. I31J.R. de la Vega, Y. Fang and E.F. Hayes, Intern. J. Quantum Chem. 3S (1969) 113. 141 R.G. Parr, J. Chem. Phys. 19 (1951) 799.
I51 J.L.K.F.
de V&s,
C.P. Keijzers
and E. dc Boer,
Inorg.
Chem. 11 (1972) 1343. 161 h1.P. Halton, Theoret. Chim. Acta 24 (1972) 89. I71 W.R. Dunham, A.J. Benrden, I.T. Salmeen, G. Palmer, R.H. Sands, W.H. Orme-Johnson and H. Beinert, Biothem. Biophys. Acta 253 (1971) 134. 181 J.F. Gibson, D.O. Hall, J.H.M. Thornley and F.R. Watley, Proc. NatI. Acad. Sci. U.S. 52 (1966) 987. PI C.J. Ballhausen and H.B. Gray, Inorg. Chem. 1 (1962)
Ill.
IlO1 H.B. Gray and C.J. Ballhausen, J. Am. Chem. Sot. 85 (1963) 260.
IllI 1. Anno and S. Yoshiko, Theoret. Chim. Acta 18 (1970) 208.
[I21 L.C. Cusachs, J. Chcm. Phys. 43 (196.5) S137.
i131 H. Bcincrt and R.H. Sands, B&hem. Biophys. Res. Commun. 3 (1960) 41. [14] D.L. Stcvcnson and L.F. Dahl, J. Am. Chem. Sot. 89 (1967) 3721. [15] D. Coucouvanis, S.J. Lippard and J.A. Zubicta, J. Am. Chcm. Sot. 91 (1969) 761.