5 48 BIOCHEMICAL SOCIETY TRANSACTIONS

The electron paramagnetic resonance of metalloproteins

GRAHAM PALMER Department of Biochemistry, Rice University, P. 0. Box 1892, Houston, TX 77251, U.S.A.

E.p.r. is a spectroscopic technique that probes the environ- ment of a paramagnetic centre by defining tlie size and shape of the magnetic moment produced by the unpaired electron. and by characterizing any magnetic fields which might be produced by the parent molecule in the vicinity of the paramagnetic centre. In the context of our interests, these unpaired electrons are found either in selected transition metal ions or in certain organic free radicals. My talk will focus on the e.p.r. of biochemically interesting transition metal ions, for only these paramagnets exhibit a great variety of magnetic nionients. Organic radicals by contrast have identical magnetic moments (to within la). Notable examples of e.p.r.-active metalloproteins are listed in Table 1 and members of this Table will be discussed in detail by other contributors to this Colloquium.

As is the case with most forms of spectroscopy, e.p.r. measurements of paramagnetic metalloproteins ;ire made with one of two objectives in mind.

Conceptually the simplest. but by no means insignificant, is the ability of e.p.r. to provide a quantitative measure of the amount of paramagnetic species present in one's sample. In this instance. e.p.r. plays the same role as absorbance measurements in many other areas of biochemical research. The particular virtue of e.p.r. is that. for most systems, tlie intensity of the e.p.1. signal is independent of the chemical species so that a sample can be quantified without a priori knowledge of an 'extinction coefficient'. Such measure- ments occupy a large part of the e.p.r. method; iti general. they d o n o t require any special knowledge of the e.p.r. process (see Note 1 . Appendix 3 ) .

The second objective is to obtain insights into the structural domain i t i which the paramagnet resides. and t o characterize the local environment of the paramagnet by probing tlic interaction of local electric and magnetic fields with the unpaired electron( s ) of the transition metal ion.

This latter utilization of e.p.r. requires substantiallj, more understanding of tlie e.p.r. phenomenon than d o intensity measurements and the objective of this review is

Abbreviation used: HiPIP. high-potential iron protein.

to provide sonic insights into tlie inlportant pliysical processes that are a t work.

As a preamble t o tlie discussion. i t is important to note that the fundamental quantity that is studied in an e.p.r. nieasurenient is tlie magnetic moment ( p ) of the para- magnetic centre. Altliough the magnitude of p can be measured directly by magnetic susceptibility measurements. in e.p.r. we measure p indirectly via tlie paramcterg. which we can identify as the spectroscopic manifestation of the magnetic moment. Experimentally. g is obtained frolii tlie resonance relationship

hv = gOH, ( 1 )

where v is the spectrometer frequency (typically 0 Gliz) and H , is tlic magnetic field at the relevant feature in the e.p.r. spectrum (Fig. I ) ; h and 0 are I'lanck's constant and the Bohr (electron) magncton. respectively.

There are a number of advantages in using e.p.1. rather than magnetic susceptibility to characterize the magnetic moment. First, i t is a spectroscopic. not a bulk. teclinique and thus the individual contributions of all the paramagnets in one's sample can be separated: magnetic susceptibility provides only the gross magnetic monient of the sample. Second, tlie magnetic moment may have a shape. This can be characterized with difficulty from measurements of the magnetic susceptibility of single crystals: the same infor- mation can often be obtained easily from tlie c.p.1. spectrum of the polycrystalline sample (e.g. a frozen solution of a protein). Third. tlie interaction of the pata- magnet with local nuclear moments. and not-so-local electron moments. caii often be visualized i n tlic e.p.i-. spectrum: this is usually not possible with magnetic susceptibility. Last, but by no nie;ins least. e.p.1. nie:tsure- ments are lOO--lOOO-fold more sensitive. less affected by the presence of paramagnetic impurities and technically much easier t o perform (see Note 2. Appendix 2 ) .

As we will see. the g-factor can liavc as m a n y as t h e c values. each corresponding to a value obtained when tlie spectrometer magnetic field ( H , ) is parallel to one of three special directions in tlie molecule (Palmer, 1070). These special direct ions frequently correspond to structural ;IXCS and the g-values measured along these special directions are most commonly called g,.g, and g,. The orientation depen- dence of g has a profound effect on tlie shape of an e.p.r.

~ -~ ~ -. .- ..

Table 1. h'.p.r. properties of nietal ions found in biochemical sjuterns Modified from Palmer (1980).

Metal ion 1,'lectronic

configuration

3d5 3 d 5 3 d 5 3 d 5 , 3d6 ( 3 d 5 ) , ( 3 d 5 ) , 3d" 3d5(3d6) , 3d5 3d' 3d7 3d' 3d9 4 d'

Example ,q-values*

Cytochromcs c 3.8-0.5 P-450,,, + camphor 8- 1.8 Liposygenase 10-0.5 Spinach ferredosin 1.7-2.1 Aconitase 2-2.1 HiPII' 2-2.2 Bacterial ferredoxin 1.7- 2.1 Concanavalin A 2-6 Cobalamin ( B , 2 r ) 2.0-2.3

Hydrogenase 2-2.2 Plastocyanin 2-2.4

Cobalt-substituted proteins 1.8 6

Xanthine osidase 1.95-2.0

Nuclear spin

0 0 0 0 0 0 0

512 712 712 0

311- 511-

~~~-

Observation tempcraturc ( K )

~ ~ _ _ < 100 < 100 < 100

<50 <50 < 5 0 < 5 0

< 300 < 120 < 40 < 5 0

< 300 < 300

* The ranges shown cncompass bothg-anisotropy in a given system and the variation among proteins.

1985

EPR AND BIOCHEMISTRY '5 4'1

(a) Isotropic lbl Axial lcl Axial Id1 Rhombic

0 0 5

2 D 3 r i d

'q A A I

I , I I 1 8 1 I ( ( 1

- 9. ~ Sr g, g , ' r,RIFlm 9

, 9" * 3 - E-5 , s z < %

. - >

3 >

9 9 9.

Magnclic lield - Fig. I . Schematic representation of g-tensor and the conscquential e,p.r. spectra

The upper solid bodies show the geometric shapes associated with isotropic. axial (prolate and oblate) and rhombic magnetic moments (the last body proved t o be difficult to draw; it should be viewed as a rugby ball compressed about the equator, as if sotiieotie had sat on it). Underneath are shown the idealized absorption cut-ves (broken lines) and absorption curves with a finite linewidth. The corresponding e.p.r. derivative curves are shown on the bottom. The descending broken lines serve t o correlate the features in the absorption and derivative presentations.

spectrum and a n early responsibility of a budding e.p.r. spectroscopist is to be able t o identify the parent lineshape which arises because of difference i n the relative magnitudes

Three basic situations exist; these are sumtiiarired in Fig. I .

( I ) Tlie isotropic case i n which all three g-values are equal i n niagnitude: a single symmetric absorption curve is obtained. This is observed infrequently with transition nietal ions.

( 2 ) The axial case in which one g-value differs from the other two. The unique value is called gll. the pair of g- values is called gi. gll can either be larger [Fig. Ib. e.g. Cu(1I)l o r snialler (Fig. lc, e.g. low-spin Co(l1)J than g,.

(3) The rliotiibic case i n which all three g-values Iiave different iiiagnitudes 1e.g. Ni( 111). low-spin Fe( I l l ) ] .

With these lineshapes firmly committed to memory, we can now examine Fig. 2 which shows. in schematic fashion. the variety arid range of e.p.r. spectra to be found with nietalloproteins. The Figure (see Note 3, Appendix 2 ) documents several points:

( I ) T h e e.p.r. of transition metal ions can be observed over a wide range of magnetic fields. This can be contrasted with e.p.r. of frce radical species which all fall within the inverted triangle used to denote g = 2, and n.m.r. shifts which are usually quoted in parts per million and fall within tlie tip of the same arrow.

( 2 ) All four kinds of lineshapes (Fig. 1 ) are present (the g = 4.3 resonance of high-spin Fe(ll1) can exhibit vdriabk sliape including isotropic while the g = 2 resonance of 3-Fe clusters is only slightly distorted from isotropic character).

( 3 ) Both parent nuclei (Cu, Co. Mo. Mn) and satellite nuclei ( t l . N ) can give structure to the spectrum.

Tlie basic questions that now arise, and the question that

ofg,.g, arid g,.

forins the basis of this paper, are: 'What f'actor(s) are responsible for the great diversity in the e.p.r. spectra that is apparent in Fig. 2?'

The fundamental answer t o this question is that the ohserved variations reflect the differences in tlie size and shape of the local electric. and occasionally magnetic. fields which are present at the paramagnet in question.

Local electric fields originate in the electrons of the ligands which are the nearest neighbours of the paramagnet. They produce orbital contributions to the magnetic nioinent and. for S > I / ? . zero-field splittings. As these local electric fields are asymmetric in shape, reflecting the character and disposition of the ligands, the orbital magnetism and zero- field splitting are also asymmetric.

Local magnetic fields originate from (a) parent nuclei; these cause hyperfine interactions (e.g.. Cu): ( h ) satellite nuclei; these produce ligand hyperfine (also called super- hyperfine) interactions (e.g. N); and ( c ) satellite unpaired electrons; these give rise to the through-space dipolar inter- actions which affect the shape and/or relaxation of the paramagnet depending on distance and electron spin- relaxation time.

For our purposes the shifts in g-values that are docu- mented in Fig. 2 can be considered under four categories:

( l ) S = 1/2 , Ag<O.4 [e.g. Cu(ll), Ni(ll1). low-spin Co( 11). Mo(V)]

(2) S = 1/2, Ag > 0.4 (low-spin ferric liacnis) (3) S> 1/2 [e.g. Mn(ll), high spin Fe(l1l) and C o ( l l ) ] (4) Coupled-spin systems (irori-sulphur clusters)

Category(I)S=1/2, Ag <0.4 To understand the fundamental process which produces

g-shifts in S = 1/2 paramagnets, i t is desirable to be able to visualize the shape of the orbitals which contain tlie para-

Vol. 13

550 BIOCHEMICAL SOCl ETY TRANSACTIONS

g scale

9 7 6 4 3 3 0 2 1 5 I I 1 I I I

F e ( l l l j S 112 0

I - F e ( l l l ) S 512.E 0 "

F e ( l l l ) S - 5 / 2 €,O 113 n

Rhombtc ( S ~ 1 /2) Fe-S centres I +-

I V Axlal (S 1/21 Fe-S centres

Copper I I I j S 112, / = 3/2

Cobalt ( 1 1 ) S 112. / = 7 / 2

S 112. / = 3/2

Dominant features from 75% Molybdenum I V ) S - 112

Hyperfine ratelliter from 25%

Proton spltnmgr frequently observed a1 g and g

I = 512 isotopes

500 1500 2500 3500 4500 !

Magnetic field ( G )

Fig. 3. Diagrammatic presentation of e.p.r. spectrum com- monly observed with metalloproteins

The amplitudes of the boxes represent the appropriate features of the components of the relevant anisotropic g- values while the widths of the boxes denote the range of values associated with the respective feature. Vertically striped boxes imply that nuclear hyperfine is typically seen at this component of g . The stippled lone associated with Mo5+ denotes the hyperfine features associated with the (less abundant) isotopes having nuclear spin of 5/2. Modified from Palmer (1980). 1 G = 10-4T.

magnetic electron, namely the 3d-orbitals. These are depicted in any niodern text on inorganic chemistry (e.g. Cotton & Wilkinson, 1980). In addition, it is important t o recognize the symmetry properties of these orbitals and the Fact that their shapes are related by rotation about one or another axis, as summarized in Table 2. For example. rotation about z transforms dX2-,2 into d,,, and d,, into d,,, but does not transform d,i into any of the other four orbitals.

Because dX2.,,2 and d , are related to one another by a rotation about z , an appyied magnetic field, H, , directed along z can mix these two orbitals. This means that dX2cy2

1

Table 2. Rotational relationships of the real d-orbitals I.or rotations about: -

X Y z Initial d-orbital I.inal d-orbital

acquires a little of tlie character of d,, and, as a result. a path is made available for an electron present in dX2-,2 to circulate about z . Because of this circulation a current is created in the xy-plane and this circular current is equivalent to a magnet, tlie orbital magnetic moment, centred on the nucleus. The effect of this orbital niagnetic moment on tlie magnetic moment associated with tlie electron spin (p , ) can be visualized in either of two ways.

The first approach (Palmer. 1980) takes the point of view that the deviations of g from tlie free electron value reflect a change in the magnetic moment of tlie paraniag- netic electron and that this change is a nicasure of the contribution of the orbital magnetic moment ( p L ) to the total magnetic moment of the paramagnet.

I n the second approach we focus on the magnetic field associated with the circulation and tlie influence of this magnetic field on the spin. We write:

hv = g s H t ('0)

that is. the resonance relationship is t o be satisfied by the total magnetic field ( H t ) at the electron and this has contri- butions from the applied field ( H , ) together with the local field (Hloc) arising from the circulating electron. For tlie case when d,, is initially vacant tlie circulation produced results in a Hi,, which opposes If, ( the electron is shielded by the orbital field). To achieve resonance the intensity o f the applied field must be increased to compensate for the presence of Hi,, and the g-value calculated using eqn. ( 1 ) will be smaller than that calculated in tlie absence of Hi<,,. Conversely when d,, already contains a pair of electrons we can think of the circulation as moving an electron from d,, into the partly filled dx2.,1; this can be equated as tlie circulation of a positively charged vacancy (hole) o r the counter-rotation of an electron. In either case the resultant HI,, reinforces H,, and the value of H , needed to satisfy eqn. ( 2 ) is snialler than it would be if Hi,, were zero; we calculate ag-value greater than 2 .

In this picture. then. changes iii the value of g are a measure of the shielding or deshielding of the electron by the magnetic field produced by tlie paramagnetic current; by contrast the alternative approach (Palmer. 1'180) inter- prets changes in g as due to a change in the strength of the total magnetic moment of the electron.

There are three other factors to be considered. First, this circulation of the electron (or hole) is not necessarily facile. for in passing from dx2-,2 t o dxy tlie electron must over- come an energetic barrier (see Note 4. Appendix 2). As a consequence, the strength of the circulation and the niagni- tude of the associated magnetic nioment decreases with increasing difference in energy of the two participating orbitals.

Second, the magnitude of the orbital contribution

1985

EPR AND BIOCHEMISTRY 55 1

depends upon direction. From Table 2 we see that the orbital which combines with dX2.,2 to constitute the current loop is different along x . y and z . This has two consequences: ( 1 ) the intrinsic rotational strength depends upon which pair of orbitals is involved (Palmer. 1980) and (ii) the energy gap between different pairs of orbitals will usually be different.

Third, the magnetic field perceived by the electron is not simply a function of the orbital motion but increases with the size o f the atom; this dependence is characterized by the spin--orbit coupling constant (see Note 5. Appendix 2 ) . A. which specifies how this circulation appears as a magnetic field to the electron spin. The value of h is unique for each nucleus; it is a positive quantity ford' - d 5 .

These factors are quantified in ttie relationship

nih . g1 = g, + 1 = x , y ,

LlCI

where the first term on the right represents the contribution of p, and the second term quantifies pL or the shielding term. depending on one's point of view. n / A E is a measure of the intrinsic strength of the circulation. A E represents the energy gap between the particular pair of participating orbitals. In general. both n and A E change when the niolecule is observed along x, y and z ; consequently gi will also vary. This approach can be illustrated for Mo(V) i n Fig. 3 ; the qualitative betiaviour for other metal ions of biochemical interest arc shown in Appendix 1 (Fig. Al ) .

Category (2 ) S = 112. Ag > 0.4 The approach just described is adequate when deviations

of g f r o m 2 are small. This requires that A E be large (relative to h ) and the formal procedure proceeds on t h e assumption that the shape of the orbital which formally contains the unpaired electron is essentially unafcected by

light-cu-ordinate (dodccahcdroii)

Fig. 3. d-Orbital levelling for two geometries fovnd f o r molybdenum ( V )

The single electron is placed in the lowest level and the loops denote the current paths responsible for the orbital contributions tog,.g, and g,.

Vol. I3

t. 2

+ S111all Wlt l l 1113\1111311~

+ Axial rhoinh IC I I l O l l l l l l i

Cubic distort ion diatortioii d l \ l < N 11<111

Fig. 4. One-electron orbital levelling fo r the three tZg orbitals of low-spin F'e(l11) showing the changes in orbital

energy ajier axial and rhombic distortions The energy separations can be specified using either of the two parameters A and 13, or V and A. The actual orbital containing the paramagnetic electron is a mixture of these three orbitals with the composition of the mixture being determined by the relative magnitudes of A and B and A. the spin-orbit interaction constant (see Appendix 1 ).

iyrlinletry ( I ' = O . L # O ) (l'/LzO 7 5 ) ( 1 . 1 Oo'\

the process. When AL' is small. the energies of the relevant orbitals become comparable and eqn. ( 1 ) is clearly unsatisfactory. for the last term increases without limit. In these circumstances one must take into account the fact that the composition of the parent orbital is n o t simply one of our familiar d-orbitals but is a mixture with contri- butions from those orbitals energetically close to ttie parent; this mixture must now be explicitly considered. Unfortunately. this approach does not lead to an intuitively appealing picture.

The specific situation arises for low-spin haenis which have the energy levels shown in Fig. 4 (Palmer, 1979, 1'183). I n this case. the five valence electrons are acconi- rnodated in the three lowest d-orbitals, as shown. The energies of these orbitals differ only slightly. the relative energies being expressed in terms of two parameters ( A and H. or V and A) . If the haem is axially syninietric, typically due to a compression perpendicular to the haeni plane (i.e. along z), d,, and dyZ are destabilized equally by the amount A. Further distortion which leads t o an inequi- valence in the two in-plane axes ( x , y . a rbonibic distortion) leads to a separation of d,, and d,, which is quantified by the parameter V . ( I t is a conimon convention t o select x . y and z so that the ratio V / A does not exceed 2 : 3 . As long as this is true. the largest separation is between d,, and dx,. If, with the system of axes just employed. this inequality is not satisfied. one has the freedom t o change the directions labelled x. y and z to re-establish the condition. )

Formal analysis of this system (Taylor, 1977) shows tha t the magnetic moment is typically rhombic with the values of g,. g, and g, being completely specified by the niagni- tudes of either pair of energy parameters (in units of A). (See the Appendix for a number of useful relationships which can be derived from the formal analysis.)

One can use the measured g-values and eqns. ( 9 i ) and ( 9 j ) (see Appendix 1 ) t o obtain the magnitudes of V and A, a facility which has been exploited in a most creative way

5 52 BIOCHEMICAL SOCIETY TRANSACTIONS

1 2 1 2

O H b - C N

09 T 0 4 O 5 I

Pure axial I I 1 I 1 I I 0 1 2 3 4 5 6 7

Tetragotid field ( A j h )

Fig. 5. Crystal field correlation diagram for low-spin ferrihaenioproteins The Figure has been modified from that of Blumberg & Peisach (1971) to include data on cytochrome a from heart and yeast (a and y , respectively) and bis-iniidazole protohaem (Palmer, 1980). Calculations are carried out using the formulae and improper co-ordinate frame described in the Appendix. The abbreviations used are: P-450, J: P-450, M, rabbit liver microsonial cytochrome P-450; P-450. B. rat liver microsonial P-450; P-450, G, bacterial cytochrome P-450: Mb. 12.8. sperni whale niyoglobin, pH 12.8; Mb 10.1, sperm whale myoglobin, pH 10.1; a,. cytochrome a,; b 5 . 12-14, cytochrome b 5 , pH 12.1; b,, 12.1, cytochronie b 2 , P I 1 12.1;a3--N3. cytochrome a3 azide; Cat-N,, b , horse erythrocyte catalase a n d e ; a,-N,( i n ) . cytochrome a3 azide, minority component; Cat-N,, bl, beef liver catalase azide; b,. 4.9, cytochrome b,, pH4.9; b g , 6-10, cytochrome b 5 , pH 6-1O;c, cytochrome c ; HbR , haemoglobinRimrdale; C-CN, cytochrome c cyanide; Hb-CN, ferrihaemo- globin cyanide; a, cytochrome a; a-lm,, bis-imidazole haem a: a-lm,-HSO;. bis- iniidazole haem a bisulphite addition compound; a- lmz. 1 1.3, bis-imidazole haem a. pH 11.3; b-1111,. bis-iriiidazole protohaern. The analyses foi- CP. C-CN. and Hl -CN are based on two g-values, while all other points are based on three g-values. The vertical arrows on the upper boundary indicate that the last three compounds shown in Table 3 are well offscale at the values of the abscissa indicated.

by Bluinberg & Peisach ( 197 I ), who measured the e.p.r of a large number of low-spin haem compounds and plotted their data on a graph such as that shown in Fig. 5 . In this graph the abscissa signifies the strength of the axial distortion (though there does not appear t o be a correlation between the magnitude of A and the basicity of the axial donor in families of related compounds; Walker et al.. 1984). The ordinate quantifies the degree t o which the ligand field departs from axiality; this could arise through intrinsic asymmetry in the porphyrin although it is currently suspected that it is the disposition of the axial ligands and their interaction with d, and d,, (and possibly porphyrin orbitals of 7r symmetry) that establishes the rhonibic distortion.

Blumberg & Peisach ( 197 1 ) found that their data fell in clusters: they defined five domains designated C. H, B. 0 and P. and they proposed that each domain represented a specific structural type. For example, the B domain was assigned to the bis-imidazole co-ordination. This concept has generated considerable interest in the e.p.r. of these compounds and a number of experimental and theoretical

developments have been spawned as a consequence. These are reviewed by Palmer (1979. 1983).

To a first, crude, approximation each of these domains can be identified by the value of the low-field g-value which ranges from about 3.05 for a C domain to about 2.5 for the P domain. However. a number of biochemically important haem proteins, notably the cytochromes from several electron-transport chains, exhibit values for gz- which are substantially larger than those used to construct Fig. 5 ; i n these compounds. g, and g, are not readily observed but both appear to have values very much less than 2. For example. the cytochromes b of the inner mitochondria1 membrane exhibit g,-values as large as 3.8 (Siedow et al., 1978); other examples are given in Table 3.

First attempts t o rationalize such large g-values within the basic formalism of the Blumberg ~-Peisach approach have relied upon the assumption of novel co-ordination combinations. notably bis-lysine and histidine-lysine (Brautigan et a/., 1977). However. the observation (Carter et al.. 1981) that similarly large g-values can be obtained in model compounds prepared with sterically hindered

1985

EPR AND BIOCHEMISTRY

imidazoles (e.g. 1.2-diniethylimidazole; Fig. 6) suggests that these highly anisotropic e.p.r. spectra reflect some kind of strain or distortion at the haeni centre and should not be taken as prima facie evidence for new co-ordination types.

There are two obvious possibilities for this distortion: (i) the length of the Fe-N(iniidazo1e) bond is shifted from its nornial value and the ligand field a t the haem is correspondingly different. It should be noted that the Fe-N bond lengths for hindered iinidazoles can be 0.01 nm smaller than those observed with unhindered imidazoles (Scheidt & Gouterman. 1983) although absolute values of such bond lengths may vary by as much as 0.04 nni; (ii) the in-plane (rhonibic) asymmetry is small.

zero ( i t . a = b ) g, asymptotically approaches a maximum

+j

2

Eqn. ( 9 i ) (see Appendix 1 ) shows that as V approaches

553

--

.

.-----

\ - Bis-l,2dirnethyl-,rn1dazole protohaern

Table 3. E.p.r. parameters for selected highly anisotropic low-spin haems

Abbreviations: PPIX, protohaem IX; TPP, iron tetraphenylporphin.

Compound (source) RX RY x,* Referencet

c-Type cytochromes c (heart) c , , ~ (Euglena) csll (Pseudomonas aeruKinosa) c1 (Rhodospirillum rubrum) cssa (Paracoccus detiitrificans) c, (heart) c , (yeast) Other cytochromes Liver microsomal h , Cytochrome f (spinach) Cytochrome h,,, (heart) Cytochrome b,,, (yeast) Cytochrome h,,, (heart) Cytochrome h,,, (yeast)

Model compounds Cytochrome c-cyanide Alkaline cytochrome c (fIis-Fe-Nllz) Metmyoglobin-pyridine PPI X- bis( p y rid ine) PPIX- bis( py rrole) PPIX-bis(buty1amine) PPIX-bis( 1.2-Mel-imidazole) TPP-bis( 2-Me-imidazole) TPP-bis(5 .6-Mez-benz~midazole) TTP-bis( 1 .2-Me2-itnidazole)

1.24 1.39

(1.25) 1.23 1

7

1

1.41 (1.6)

'I

7

'I

'?

0.93 1.50 1.17

<0.8 <0.8

1

3.48 3.399 3.432 3.40

2.24 2.05 2.05 2.1 1 2.06

? 7

2.22 2.07

?

? 1

7

1.89 2.06 2.19 1.35 0.9

? 1.6l(calc) - 1.74 (calc) 1.67 (calc) 1.67 (calc)

3.05 ( C )

3.48 v) 3.44 3.60 ( b ) 3.713 3.76 ( h )

*Values not reported designated by '?'. + References: ( a ) Salmeen & Palmer. 1968: ( b ) Ihut igan el al.. 1977: (c) Dwivedi e l a l . , 1979; (d ) De Vries ct al., 1979; ( e ) Ikeda ct al . , 1974; (f) Siedow et a / . , 1980; (R) Minis & Pcisach. 1976: ( 1 1 ) Walkcr ct al . . 1984; (i) A. L. Tsai & G. Palmer. unpublished work.

Vol. 13

554

iniidazoles defines one of the cubic axes of the ligand fields (see Note 6, Appendix 2). This being so, then the Cartesian orbitals d,, and d,, will always lie parallel t o and perpendicular t o the imidazole plane regardless of the absolute orientation of the imidazole; rhonibic e.p.r. spectra will result.

Almost all structural data reveal that the planes of unsubstituted imidazoles are close to being parallel, although the specific orientation is variable. Thus in bis( 1- methylimidazole) protohaem the (average) imidazole plane projects over a pair of opposite pyrrole nitrogens (Little et al.. 1975) while in cytochrome b5 the two iniidazoles arc symmetrically offset by about 15' from the p-S methine axis (Mathews et al., 1979). These two compounds exhibit almost identical e.p.r. spectra consistent with the idea that the imidazoles d o indeed define the in-plane cubic axes of the ligand field.

In striking contrast, the two planes of the two ligands in his( 2-methylimidazole) iron tetraphenylporphin are almost exactly 90" with respect to one another and lie approxi- mately over the two orthogonal methine-methine vectors (Kirner et al., 1978). With this geometry, the porphyrin is substantially puckered with the methine carbons displaced away from the methyl substituent on the imidazole. The e.p.r. of this compound is highly anisotropic with g, = 3.4 (Walkcr et al., 1984), providing support for the idea that these very large g-values reflect a symmetric ligand field a t the haem due t o a perpendicular orientation of the two axial ligands (see Note 7. Appendix 2).

Additional data are provided by the recent 0.18 nm structure of cytochronie c3 from Desulfovibrio vulgaris (lliguichi et al.. 1984). This protein contains four low- spin haeni centres, each with a pair of histidines as the axial ligands. The Fe---histidine bond lengths and imidazole porphyrin vectors for each haeni are depicted in Fig. 7 .

The e.p.r. spectrum for this protein exhibits three values (see Note 8, Appendix 2) for g,, 3.16, 2.95 and 2.71 (DerVartanian & LeCall, 1978), in the approximate intensity ratio of 1 : 2 : 1 .

1

His-70

(1.34

Fe

His-106 (Ig5

His-35 His-22 His.25 1 2 06 12.02 12.12

F e Fe Fe

12.06 1 1.88

His-52 His-34 His83

Fig. I . Schematic representation of the iron co-ordination in the four haem centres of cytochrome c3 from Desulfovi-

brio vulgaris The squares represent haem. with each corner denoting a pyrrole nitrogen; reading clockwise from top left the corners correspond t o pyrroles I - lV, respectively. The solid and broken lines denote the plane of the upper and lower imidazoles, respectively. Underneath is shown the reported Fe iniidazole-nitrogen bond lengths for each of the four haems. These data were obtained from Table 8 of Higuichi et al. (1 978).

BIOCHEMICAL SOClETY TRANSACTlONS

In haems I , 3 and 4 the imidazoles are almost co-planar and lie close t o a niethine-methine vector (a , y lor 1 and 3, 0, 6 for 4). As all of the reported g-values are less than 3.2, the haenis are far from axiality and thus it would appear that the imidazoles are defining the co-ordinates of the ligand field. Haems 1, 3 and 4 can be assigned to the e.p.r. features a t 2.95 (twice) and 2.71. The dihedral angle between the planes of the imidazoles in haeni 2 is 64"; thus haetn 2 should be closest t o axial and presumably associated with the largest g-value. 3.1 0: in the model compound (Kirner et al., 1978) a dihedral angle of 88" corresponded to a gvalue of 3.4 (Walker et al., 1984). However, because the e.p.r. in cytochronie c3 has not been quantified, the possibility arises that this protein exhibits e.p.r. in the range g = 3.1-4.0, wliich has not yet been detected (see Note 9. Appendix 3). Clearly this protein presents a remarkably useful system with which to evaluate the role of the axial ligands in dictating the magnitude of the g-tensor.

g-strain and its effects on the shape of e.p.r. spectra. g-strain is the name given to those processes that niodulate the magnitude of g,, g, and g,. These processes are believed t o result in intrinsic microheterogeneity at the paramagnet by producing varkdtions in bond angles and bond lengths. As a consequence g,, for exaniplc. does not have a unique value but a distribution of values, usually taken as Gaussian, centred on the nominal value.

This phenomenon has two striking consequences. First. the e.p.r. of species with very anisotropic g-values exhibit equally anisotropic linewidths; this is demonstrated very clearly with cytochrome c (Fig. 8). This anisotropy in line- width arises because e.p.r. spectra are not recorded versus a linear energy scale (see Note 10, Appendis 2) but a linear field scale. The latter is proportional to reciprocal energy. Consequently, a fixed increment in g results in only a small change in H, when H, is small but a large change in H , when H, is large. For cytochrome c the width of the low-field peak (g,) is about 140G ( 1 C = T); this is

. - - - _ _ _ _ _ - _ - - _ - _ _ - 2600 3400 4200 5000 51

. - - - _ _ _ _ _ - _ - - _ - 2600 3400 4200 5000 51

- _ - - _

30 Magnetic field ( G )

Fig. 8. Experimental e.p.r. spectrum of horse-heart cyto- chrome c recorded at 10 A'

The solid line shows the direct spectrometer output with the g-values indicated (the frequency was 9.34 GHz). The broken line shows the absorption envelope obtained by numerical integration. Note the extremely small amplitude with associated large width at g,. From I'almer (1983). 1 G = T.

1985

EPR AND BIOCHEMISTRY 555

equiv;~lent to a spread of g-values of about 0.7. The same spread of g-values at the high-field trough (g,) results in a width of about 900 G. The observed width is close to this value; Hagen (1981) has been able t o reproduce quite closely the e.p.r. of cytochrome c simply by assuming that g-strain controls the linewidth.

A second consequence of gstrain, observed when g, is at its axial limit. has recently been described by Salerno (1984). As g, cannot exceed this limit, the Gaussian distri- bution in g, is truncated and only manifests itself ~ i i the high-field side. As a consequence. the e.p.r. begins very abruptly and the e.p.r. envelope is very asymmetric. as illustrated by the isolated cytochrome b from yeast (Fig. 6). As g, moves upfield from its limiting value, the abrupt low-field edge beconies rounded and the high-field envelope

can develop a shoulder (the reflected position of the distri- bution no longer overlaps the direct position). Salerno concludes from his analysis that earlier evidence for multiple cytochronie b's in mitochondria1 complex 111 (De Vries el al., 1979) is an artefact of these lineshape pheno- mena and should be discounted.

Category (3) S > 112 (namely S = 512) For paramagnets containing inore than one unpaired

electron [e.g. high-spin Fe(IlI), Mn(I l ) ] the interaction between the paramagnetic electrons and the ligand field leads to differences in the energies of the spin substates (M, = 2 1/2, k 3 / 2 , * 5/2) even in the absence of a magnetic field. This effect is called the zero-field splitting. At first sight it is surprising that an electric field can affect the

P' 5 /2

3/2

1 /z

1 12

3/2

5 /2

When H, I12 ::I;;; Selection rule

AMz = * 1

Spin microstates

S

+ + + + + + + + 4-2 + + + -k + 5 1 2

lc) Large ZFS ID b h u )

H parallel to haem normal

M,

5 /2

3/2

1 /2

Small projection on Ho;Sll = 2

HR = f i CMr 112) [D(3coS2R 1 ) I (For a transition from M, . M, 1 )

M, H R ~ /?(O -0) 5 /2 2 0 D - 500 G 3/2 D for Mnl I I) 1/2 0 1/2 D H - 9 8 / ( h U )

-3/2 2 0

H perpendicular to haem normal

Large projection on Ho: gi = 6

Fig. 9 . Etiergy levels atid e.p.r. of g = 512 with varying degrees o f zero-field splitting (ZFS)

( a ) In the absence of splitting (D = 0) a single isotropic e.p.r. line is observed. ( b ) With a small splitting, five lines, the fine structure components, are centred at g = 7. (c) When the zero-field splitting is large, a highly anisotropic signal is observed from the lowest ( M , = I/') component.

V O l . 13

556 BIOCHEMICAL SOCIETY TKANSACTIONS

electron spin, but this is an indirect process which arises as a consequence of tlie requirement that electrons with the same spin cannot occupy the same space (Pauli's Principle). Thus alternative configurations such as ( t t t t t , M, = 5/2), in which all five unpaired electrons have the Same spin orientation, and (t t t l l , M, = l/2), in which the five unpaired electrons have the maximum number of opposite spins, differ in that the motion of the individual electrons in the former configuration is constrained more severely than it is in the latter.

In rigorously octahedral ligand fields (usually met only in contrived situations in solid-state physics) this charac- teristic of the M, = f 1 / 2 configuration cannot be exploited, for all directions are equivalent. !lowever, as the symmetry of tlie ligand field is lowered the greater flexibility of the M, = f 1/2 configuration becomes more and more signifi- cant and the electrons of the * 1/2, f 3/2 and f 5/2 configurations will adopt slightly different spatial distri- butions and acquire different energies; it is this difference in energies that causes the zero-field splitting.

For example, when the axial ligand field weakens. the f 1/2 state can more easily elongate along the z-axis; the resultant charge distribution is quadrupolar in shape with tlie charge density at tlie poles ( t z ) greater than that of the equivalent sphere while that around the equator is less than tlie equivalent sphere. This asymmetric charge density can interact with tlie electric field (actually the gradient of the electric field) and change its energy. Conversely, when the axial field strengthens, the charge flows away from the poles toward the equator. and the sign of the quadrupolar charge distribution is reversed. These two alternatives result in zero-field splittings of opposite sign (see Note 11, Appendix 2).

The e.p.r. for S = 5/2 is thus very sensitive to small departures from cubic symmetry. For purely axial distortions, the magnitude of this splitting is quantified by the parameter D , the zero-field splitting constant (Fig. 9a); this is analogous t o the parameter A in the S = 1 / 2 case. In the simplest (idealized) case, D = 0. the levels converge to a common origin when H,, is zero and a single e.p.r. resonance is observed at g = 9- (Fig. 9a). Each transition satisfies the e.p.r. selection rule, AM, = * 1, and the levels are equally separated at all values of H,.

With values of D smaller than the microwave quantum (hu) a small, zero-field. splitting in the energy levels occurs (Fig. 96). If the f 1/2 states lie lowest, then D is said t o be negative. Values of M, that differ by only 1 can now be resolved. It should be recognized that the individual lines in this spectrum d o not have separate g-values but rather are zero-field splittings. or fine-structure, on the parent e.p.r.; the relationship between D and the separation of the e.p.r. lines is given in eqn, (10) (see Appendixl).

Larger values of D ( 2 D > hv) (Fig. 9c) lead to a separation in the zero-field spin-states sufficiently large that. for commonly available magnetic fields. the selection rule ( A M , = f 1 ) is only satisfied by the M, = k I / ? levels. Values of D range from about 2 c m - ' in the iron dioxy- genases t o about 10 cni-' in haem proteins.

With H , parallel t o D (Fig. 9c) the projection of M, along H , is small; a single resonance is seen at g = 2. flowever, when H , is perpendicular to D a somewhat unique circumstance arises.

Normally. one expects tlie unpaired electrons to align along the magnetic field regardless of the orientation of the molecule in the magnetic field. However, when the elec- trons gain an energetic advantage from their interaction with the ligand field, the electrons stay aligned (quantized) along the symmetry axis of the ligand field and d o not maintain their orientation along H, as the molecule is rotated in the magnetic field. Thus with H , perpendicular

to the symmetry axis of the ligand field. If,, 'sees' a spin component that is much larger than was seen with H , parallel to D (Fig. 9c); this large magnetic moment can be accounted for by assigning a larger g-value to tlie resonance. i.e. gl = 6. Justification of this value requires solving the relevant quantum mechanical formulae. In general gL = 2 S t I .

With symmetries lower than axial. a second parameter E (analogous to u) is used to describe the rliombic distortion; then gl splits into g, and g,. When E/D = 1/3 (3 V / A = 2 / 3 ) the limiting values for the g-values are Y.7, 0.5. 0.6: the first of these has been observed in the rubredoxins although the other two components have yet to be detected. Formulae for the g-values expected for small valucs of l</D are given in Appendix 1 [eqns. (106) t o (1Oc)J.

In these highly distorted compounds e.p.r. can also be observed from excited states, most commonly that which is formally labelled M, = f 3 / 2 . When E/D exceeds 0.30 (and D > 1 cm-'). all three g-values for this excited state rapidly approach 4.27. the limiting value when h'/D = 1/3; as a consequence, a relatively isotropic e.p.r. absorption is observed in the neighbourliood of 1500 G. This signal is diagnostic o f high-spin iron in a strongly rliombic site; such systems appear naturally but also seem t o be the fate of iron adventitiously present in a biosysteni. Because this resonance arises from an excited state. decreasing tlie temperature will depopulate this level and lead to ;I loss of the g = 4.3 resonance: at the same time t h e g = 9.7 feature characteristic of the ground state will grow i n intensity.

Category ( 4 ) Coupled-spin systems Most reduced iron -sulphur clusters exhibit e.p.r. spectra

which have at least two g-values smaller than 2. These signals are usually called tlie g = 1.94 signals. Sucli signals are difficult to rationalize in ternis of niononuclcar iron and it is now recognized that these resonances arc diagnostic of a coupled-spin system. Although these signals were first observed in iron -sulphur clusters (Ormc-Johnson bi Sands, 1973), they are not uniquely associated with sucli species for similar signals can be demonstrated in half-reduced (semi-met) haemerythrin (Muhoberacet al.. 1Y80) and in the purple acid pliosphatases (DeBrunner et al.. 1083). (One might also predict that similar signals will be denionstrated in half-reduced ribonucleotide reductase.)

The resonance is associated with a paramagnetic centre which contains. as a minimum, one high-spin Fe(l l l ) and one high-spin Fe( 11). Normally, an applied magnetic field would cause the unpaired electrons of both iron centres to orient parallel with the field. However, when the two metal centres are coupled to one another sucli that the spins on one iron are constrained t o be antiparallel to the spins on the other, only the resultant spin is required to align itself with the field. The (antiferromagnetic) coupling of S = 5/2 and S = 4/2 produces a resultant state with a net spin (S') of 1/2. When S' is parallel t o H,,, so are the five electrons on the ferric ion; however, the electrons on the ferrous ion will then be aligned in opposition to H,. The observed magnetic moment (and hence the observed g- factor) will reflect this opposition of the two sets of electrons and will have a magnitude weighted by the relative contributions of these two sets to the resultant. These weighting factors can be deduced by application of the classical Lande formula for evaluating the contributions of individual spin systems to a coupled spin (this is normally seen in the context of evaluating a J arising from tlie coupling of L plus S) and lead to the essential result (Gibson e f al., 1966):

gi = 7/3gi (Fe+3)-4 /3gj (Fe+2) i , j = x, J?, z (4)

1985

EPR AND BIOCHEMISTRY 557

which emphasize that tlie observed g-values arise from the opposition of the gvalues 011 the ferric and ferrous ions. As g for Fe3+ = 2.0 and the g-values for Fe2+- 2L2.4. the observed g-values fall at 7 or below.

With iron sulphur clusters one of the three gvalues is found t o be larger than 2 (2.01-2.06); however, with tlie purple acid phosphatase and semi-met haemerythrin all three values are smaller than 2. With haenierythrin (Stenkamp ct 01.. 1084) and possibly with the phosphatase there is no sulphur in the co-ordination site and it is plausible that an orbital contribution from the fraction of unpaired spin on one o r mure of the sulphur atoms produces the ‘anonia- lously high’ g-value in the iron-sulphur clusters.

There are a number of important cases in which two paramagnetic ions, each with an odd number of electrons. are coupled to yield an even-spin system: the binuclear centre o f cytoclironie oxidase. which comprises a S = 5/2 haeni arid a S = I/’ copper. is a case in point (Palmer e f al.. 1970). Provided the strength of the coupling is greater than g/3H (- 0.3 cni-’). then the resultant spin system will probably not exhibit any e.p.r. I t must be emphasized that this coupling cannot be broken thermally (unless the protein is denatured): only magnetic fields sufficiently strong to negate the coupling between the two centres will allow tlic individual paramagnets to exhibit their intrinsic c . p. I. spe c t rum.

Thc ejyects of local magnetic fields o n the e.p.r. spc’c- trzrtn. The simplest case is provided by a paramagnet wliicli possesses a nucleus with a nuclear moment (e.g. Cu. Mn. Co. Mo). This nucleus then makes a contribution t o the niapnetic field present at the electron:

A , the Iiyperfine interaction constant. specifies the niagnitude of tlic interaction between the electron and nucleus in energy units (see Note 1 1 , Appendix 9) (it is common practice to quote A in c n - I ) , g is the electron g- value a t the place i i i tlie spectrum where tlie hyperfine interactioti is studied and MI is tlie nuclear analog t o M,. F o r example, for Cu I = 3/2 and MI can have the values 3 / 9 , I/‘. - I / ? . - 317. Consequently, HI,, will also have four values and the parent e.p.r. will be split into four coniponents of essentially equal intensity.

1:vcii though the nucleus can be viewed as spherically symmetric, the interaction between the electron and the nucleus is aiiisot ropic. This arises because the hyperfine interaction is also composed of two parts, an isotropic component whicli reflects a contact interaction between electron and nucleus and an asyninietric component arising from a spatial interaction. As the paramagnetic electron resides in an orbital with specific directional properties, the spatial interaction is also directional. For an electron con- filled t o a single ‘pure’ orbital the anisotropic component is axial 2.4, = - A , = - A y : when the electron orbital is composed of two o r more orbitals, the anisotropic component can have rhombic symmetry. As an example we can consider tlie case of a Cu( 11) species which tiasg, = 9.3, A , = 0.02 C I I ~ - ’ . g, (=g,) = 2.05. A , (= A , ) = 0.001 cni-’. The splitting in G at g, is proportional t o 0.02/2.3, that at g , to 0.001/2.05; the values are approximately 100 and 10G. respectively. The isotropic contribution is 1/3 ( A , + A , + A, ) = 0.0073 cii1-l: thus the anisotropic components are 0.02 ~ 0.0073 for A , and 0.001 - 0.0073 for A,x and A , . The results are in the ratio 2 . - 1. - 1 as advertised.

Exactly the same considerations arise for the interaction between an electron and a satellite nucleus. although the magnitude of the effect. especially the spatial component. is smaller. F o r example. the splitting. in G. of an electron

Vol. 13

by a distant proton is given by

28 g - ( 3 cos2 8 - I ) /r3 (6)

In this case, 6 is the angle between the line connecting tlie electron and proton and the direction of the magnetic field and r is the length of that line in A ( 1 A = 0.1 nm): g is theg-value for the electron at that orientation.

Finally, we will consider tlie consequences of having multiple paramagnets in the same protein molecule. In such a case, extraordinarily complex e.p.r. will be observed provided that (i) the molecule moves slowly with respect to the strength of tlie magnetic interaction between the two

Resonance position when Hd,p = 0

Fig. 10. Geometric relationship (a) o f two spins interacting via the classical dipole-dipole interaction and ( 6 ) the

resultant e.p.r. absorption The solid line and dashed lines represent the e.p.r. of spin 1 influenced by tlie population of spin 2 with M, = + 1/2 and - 1 /2 , respectively. The dotted line denotes the total e.p.r. absorption of spin 1 . ( c ) The derivative curve corresponding to the dotted line of ( b ) .

558 BlOCHEMlCAL SOCIETY TRANSACTIONS

centres (expressed in frequency), and (ii) the distance between the two centres is not too great.

The principles involved are readily appreciated from consideration of the simplest case, namely a protein containing two S = 1/2 species, each with an isotropic g factor; for concreteness let the distance between the two centres be 1 0 A. We focus first of all on the magnetic field at spin 1 produced by spin 2 (Fig. lOa) and equate H,,,, with Hap, the dipolar field a t spin 1. Because S = 1/2 and g = 2 the field a t spin 1 produced by those spins 2 with M, = + 1/2 is

1 SO00 3 P - - (1-3 c0s2e)-- ___ 4 r3 r3 (1 -3 cos3 0) (in G) (7)

There are two limiting conditions. When 0 = 0” and spin

Appendix 1 : some useful formulae and relationships (1) For low-spin ferric haems, the electron is found in an orbital derived from d,,. which can be described as a mixture of the d,,, d,, and d,, in proportions a. b and c . namely;

a-d,, + bad,, +cad,,

This new orbital differs in energy from dyz by an amount E/X = - (b + c)/2a. The magnitude of this quantity is a measure of the degree of mixing that has occuired.

For this modified orbital we have Taylor (1977):

g, = 2 [(a + b)’ - c’] , (()a 1

(‘)b) g, = 2 [(a + c)’ - b’]. 2 lies ‘north or south’ i f spin 1, &p = - 3 0 G and Hi =

molecules are so oriented, hence the intensity a t a’ is small.

g, = 7 [a’ - ( b + c)’] , ( oc H,, - 30. This is the location a’ in Fig. 10(b). Not many

When e = 90” and spin 2 lies ‘east-west’ of spin 1, Hdip = 15 G; this is the location b‘ in Fig. 10. As many molecules can lie on the equator, the intensity from this orientation is large. The envelope produced by summing over all orientations is then given by the solid line in the Figure.

However, in 50% of the molecules spin 2 has the

g, -g, (‘Id . c = ____ , , b = 2 a = - g -g, g, + g D D D ‘

with

If a’ + b2 + c’ = 1 (i.e. assuming n o covalency) tlicn:

= [8(g, +g, - g x ) ~ 112

g : + g i + d = 16 opposite, M, = - 1/2, orientation and so, in-one-half of the molecules, spin 1 eoxperiences a dipolar field of oposite sign. 0 = 0” and 0 = 90 leads t o the points a and b, respectively, and the overall envelope is given by the broken line. The total e.p.r. absorption due t o spin 1 is then given by the dotted line. As, in this example, spins 1 and 2 are identical, the effects of spin 1 upon spin 2 are the same as those just described and the e.p.r. absorption envelope for spin 2 is identical t o that for spin 1. The resultant e.p.r. derivative curve is shown in Fig. lO(c). In this simple case the distance from a t o a’ (Fig. 1Oc) will be 60G; this value can be inserted into eqn. (4) t o yield (twice) the distance between the two centres.

In real life this simple pattern is rarely observed. First, the g-values of the participating centres are usually aniso- tropic so that the e.p.r. spectrum in the absence of inter- action already has a complicated envelope. Second, the two species are rarely identical. This can be due t o intrinsically different metal ions, or spin-states, or g-tensors, or simply different orientations of the two g-tensors from two other- wise identical paramagnets.

Finally, the value of r may be sufficiently large that a discrete splitting is not obtained and all that can be observed is a small increase in the linewidth of the e.p.r. spectrum. Zweier (1983) has examined this situation and his formula for the distance. r , can be rewritten

and

_ - A A -

where AH is the measured broadening of the e.p.r. line of spin 1 and g = (g, + gy + g,)’” is the root-mean-square g-value for spin 2 . Assuming that a 1 G broadening is the smallest that can be reliably measured (Zweir, 1983), this formula implies that distances of about 20 A can be detected when the perturbing paramagnet has a spin of 1/2 and close t o 40 when the perturbing paramagnet has a spin of 5 / 2 .

I thank F. Ann Walker for providing me with a preprint of her work, and R. Cammack, P. Knowles, C . Reed and T. Vanngard for discussion o n the content of the manuscript. The research in my laboratory is supported by grants from the National Institutes of Health (GM 21337) and the Welch Foundation (C-636) .

a + c b + c 2b 7a A = E(,vz) - ~ ‘ ( x z ) = - -

~ + b b S c 2C ? a B = E(yz) - fqx-y) = __ - ~

V h - _ - A ,

Note: when using eqns. (9h) and ( 9 9 to make entries on Blumberg-Peisach graphs, gx, g, and g, should be assigned as -gm,, gm, and -g-., respectively. For a proper co- ordinate system (Palmer, 1979) g,,g, and g, correspond t o gmim gmid and gmax.

From eqns. (9a), (9b) and (9c) it follows that: ( I ) With a = 1, b = c = 0 and g, = gy = g, = 2 (2) With a = b = c = (0.33)”’, g, = g, = gz = 2 (3) With a’ = b2 , (a’ < 0.5)

g, = 12a’-2 (9i)

(9k) g, = g, = 1 - 20’ - (4a* - ~a4)’” (4a’ - 8a4)’’*

Whena’ = O.S,g, = 4,gx = g, = 0

( 2 ) S = 5/2 systems (i) D <hv In this case, the resonance field, H,, for a transition from

1985

EPR AND BIOCHEMISTRY 559

M , to M , - 1 is given by (Zweier. 1983):

H, = H , - (M, - 1 /2) [D(3 cos2 0 - 1 )] (1 Oa)

H , is the resonance field when D = 0 (= hv/gfi) and 0 is the angle between the magnetic field and the axis of D. For example. the value of D for Mn” is about - 500 G so that the e.p.r. will be spread over the range 1500-6000G a t X-band. These limiting values are obtained when 0 = 0. whereupon eqn. (loa) reduces t o H , = H , + 1000 ( M , - 1 / 2 ) . Furthermore with frozen samples, which contain randomly oriented molecules, all values of 0 will be present and individual niolecules will exhibit a spead of e.p.r. absorption which falls inside these limiting values: as a consequence. the e.p.r. tend t o be diffuse and badly defined.

(ii) D > hv For g, -g, < 2 the following simple relations apply

( l o b )

(10c)

( 104

( 10e)

(Slappendel et al., 198 1 ):

g, = 6 + 24 E/D - 79 ( E 2 / D 2 )

g, = 6 - 24 E/D - 79 (E2/D2)

g, = 2 - 3 4 ( E 2 / D Z )

g, -g, = 48 iE /D)

The last relationship holds quite well even at higher distortions. For example. the gvalues for P-450 arc 8, 3.7 and 1. Exact solution of the relevant quantum mechanical formulae reveals E/D = 0. I . The above approximate formula yields a value of 0.09.

For values of E/D less than 0.1, exact solutions for the g-values in graphical form have been given by Slappendel et al. (1981), while Aasa (1970) has published graphical solutions at selected values of E/D as a function of D.

Appendix 2 : Notes (1) It should be noted that accurate procedures for

quantification require two pieces of information. First, all the g-values of the paramagnet should be known. If the paramagnet contains only a single unpaired electron, this is a sufficient requirement. For paramagnets with S> 1/2 it is also necessary to know the zero-field splitting constant and whether the resonance arises from a spin-multiplet ground state (e.g. the g = 6 resonance of high-spin haems) or from an excited state (e.g. the g = 4.3 resonance of high- spin, non-haem ferric ion). Furthermore, in these latter cases it is not always possible to establish the total width of a spectrum so that integration of the prominent features may lead t o a serious underestimation of the species in question.

(2) Rather than make this comparison too one-sided, it should be recognized that magnetic susceptibility measure- ments quantify even-spin systems (S = 0, 1, . . .) just as readily as odd-spin systems (S = I / ? , 3 / 2 , . . .). e.p.r., on the other hand, is only routinely applied t o odd-spin systems.

(3) This Figure is not comprehensive. The most conspicuous omissions are Mil, the Iiigh-potential iron protein ‘HiPIP’ resonance of certain 4-iron FeS clusters, and iron dioxygenases.

(4)An analogy can be made t o the activation energy of chemical reactions. However, it must be noted that this orbital circulation is not a thermally driven process but is driven by the applied magnetic field.

( 5 ) So far, we have dealt with a planetary system revolving around the nucleus. To get more insight into spin-orbit coupling we have to change to a planetary system revolving around the paramagnetic electron (an ‘anti-Galilean’ transformation). This electron sees the nucleus and all the other electrons circulating about it, and the current thus created results in a maenetic field a t the

Y

electron. If the other electrons were absent it would be easy ___ ~ ____ t o see that the magnitude of this current would increase

directly with the atomic number ( Z ) of the nucleus. Conversely, if the other electrons completely separated the nucleus from the paramagnetic electron then the size of the circulating current would be independent of atomic number.

Because the (paramagnetic) electron is a cloud and not a x’ xv yJg!;*-;:[fJ::....;p g x . g y and point. experiences part of it lies much inside more the of shell the of nuclear the other charge. electrons Thus,

I \ .* , ‘8 the actual charge perceived by the paramagnetic electron increases with nuclear charge but falls between the two extreme cases just outlined. and the efficacy of the orbital motion in producing a magnetic field a t the paramagnetic electron increases with atomic number.

(6) Traditionally, the cubic axes of the ligand field are assumed to lie along pyrrole-pyrrole directions. In this alternative co-ordinate system. imidazoles that are co- linear with opposing methine bridges should not lower the ligand field symmetry. However, when both histidines are aligned to be parallel to either pyrroles I L I l l or IILIV, d,, and d, interact differently with the lone pairs on the

Square Elongated Flattened co-ordinating iniidazole nitrogens and a rhombic ligand planar octahedron tetrahedron field splitting is produced (Fig. 4). Cullll C u ( l l ) . Co(l l l . Ni( l l l1 C u l l l l (7) Recent X-ray data on bis(2-methylimidazok) octa-

ethylporphinato iron (HI) suggest that the spin-state of a haem can also be modulated by the rotational orienta- tion of the axial ligands (Geiger et al,, 1983).

(8) The published spectra show an additional feature a t g = 2.4 which is too weak (relative to the other com- ponents) to represent one haem; furthermore, a g-value of 2.4 is unprecedented for bis-imidazole co-ordination.

(9) It should be recognized that the transition probability

, ‘I ,‘r 92

, . I,. 2 . -. I , I , \ \

# I ._ r,. - gx. 9” *:’ 9x. g y

xz, v z - - - - - - - - - - - - - - .

/- ,+ Fig. A l . d-Orbital levelling for three geometries found for

copper (11) ( 3 d ) The ninth electrons are plrced in the uppermost level and the loops denote the current paths responsible for the orbital contributions t o g,,gy and g,. For Co(l1) and Ni(ll1) only seven electrons are used in filling up the levels.

Vol. 13

560 BIOCHEMICAL SOCIETY TRANSACTIONS

(intensity) a t g, is determined by g , plus g,. When g, approaches 4, g, and g , approach 0 (see Appendix 1) and thus the e.p.r. intensity in this low-field region will be very small relative to that when the value of g, lies between 2.4 and 3.1.

( 10) Recall that optical absorption bands are expected t o be symmetric when recorded on linear energy scale; in practice these spectra are recorded on a linear wavelength scale. When these bands are sufficiently broad, the asymmetry becomes apparent.

( 1 1 ) This phenomenon is analogous t o the nuclear quadrupole interaction found in n.m.r. In the electron case the effect is characterized formally by second-order effects of spin-orbit coupling. The formal analysis however is not readily amenable to a physical picture.

(12) The following approximations are useful: 1 cni-’ - 30 GHz - 10000 G (at g = 2).

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Electron-paramagnetic-resonance studies using pre-steady-state kinetics and substitution with stable isotopes on the mechanism of action of molybdoenzymes

ROBERT C. BRAY and GRAHAM N. GEORGE School of Chemistry and Molecular Sciences, University of Sussex, Brightoti BN1 9QJ, Sussex, U. K.

Much of molecular enzymology is concerned with eluci- dation of enzymic reaction mechanisms dependent on detection and identification of transient intermediates in their catalytic reactions. In cases where such intermediates have distinct e.p.r. spectral properties, e.p.r. is potentially a good method for their investigation. This is well exempli- fied by studies of the Very Rapid molybdenum (V) e.p.r. signal-giving species from xanthine oxidase.

What are the limitations of e.p.r. in the detection of transient intermediates? Firstly, as normally used, the method is relatively slow. Long spectrometer time constants and slow scanning are employed t o filter out noise from the spectra. Furthermore, in e.p.r. flow experiments it is difficult (Piette, 1964; Klinies et a f . , 1980) to keep the

Abbreviation used: IXAFS, extended X-ray absorption fine structure.

dead-space between mixing and detection points small. Nevertheless under the favourable conditions applying with xanthine oxidase, Swann & Bray (1972) succeeded in using continuous flow to scan in 1 s the spectrum of Mo(V) in the enzyme, 8 0 m s after it was mixed with its substrate. xanthine. The extension t o e.p.r. stopped-flow was. how- ever, not attempted, since the dead-time could not readily be reduced, and the turnover time (l/kat) for oxidation of xanthine is about 60 ins. Though e.p.r. stopped-flow experiments using normal ‘good’ substrates of xanthine oxidase would thus be very difficult and perhaps uninformative, on the other hand, as will be described below. such studies, using ‘poor’ substrates, are eminently practicable and have recently provided important new information.

An alternative way of performing fast kinetic studies by e.p.r. was put forward by Bray (1961). This method. known as ‘rapid freezing’ (though i t might perhaps better have been called ‘quenched flow’), allows the preparation of a series of samples, each frozen at a particular reaction time (from about 3 ms upwards) after mixing two reagents

1985