334

Biochimica et Biophysica Acta, 546 (1979) 334--340

© Elsevier/North-Holland Biomedical Press

BBA 47647 INTENSITY OF HIGHLY ANISOTROPIC LOW-SPIN HEME EPR SIGNALS

SIMON DE VRIES and SIMON P.J. ALBRACHT Laboratory of Biochemistry, B.C.P. Jansen Institute, University of Amsterdarn, Plantage Muidergracht 12, 1018 TV Amsterdam (The Netherlands)

(Received July 12th, 1978) Key words: Low-spin heine; EPR intensity

Summary A semi-empirical formula has been derived to calculate the concentration of low-spin heme compounds t h a t are highly anisotropic, i.e. 3 < gz ,( 4, and where information only on the g~ absorption is available.

Introduction EPR can be used for the determination of the concentration of paramagnetic species through comparison with a known standard. In the procedure developed by Aasa and V~inng°ard [1] the total intensity of a rhombic powder spectrum is calculated from the area under an isolated absorption peak in the first derivative spectrum. This area is related to the intensity of the signal through a proportionality factor which is a function of the three g values. Since in general only one or two g values can be detected in low-spin heme compounds with highly anisotropic EPR spectra especially if g~ is greater than 3.3, the concentration of these compounds could n o t be determined by EPR. Based on the expressions of the g values of low spin 3d s systems, derived by several authors [ 2--5 ], the proportionality factor of Aasa and V/~nng~rd can be rearranged into a form, t h a t is exclusively a function of g~. Since it is always possible to detect the gz peak, the concentration of low-spin heme compounds with highly anisotropic EPR spectra can now be determined by EPR. Materials and Methods Cytochrome c and the cyanide complexes of metmyoglobin and cytochrome c were prepared as described in the literature [6]. The concentration of cytochrome c was determined optically using ~--~reA~55°d--ox 21.1 mM -1 • cm -~ [7] and :

335 t h a t of m e t m y o g l o b i n according t o Ref. 8. EPR measurements and digitizing of EPR spectra were p e r f o r m e d as described in Ref. 9. EPR spectra were analyzed with a Du P o n t 310 Curve Resolver.

Results E P R t h e o r y o f low-spin 3d s s y s t e m s Many authors have derived expressions of the g values of low-spin heme comp o u nd s in terms of the wave-function coefficients [2--5]. Putting the orbital r e d u c t i o n factor k equal t o 1 and ge = 2, Griffith [3,10] calculated t h a t the sum of the squares of the three g values, S, maximally equals 16. If ge = 2.0023 this sum equals 16.018. For the derivation we put ge = 2. F r o m the expressions of the g values [11] it follows: A = ½~/2(½gz + B2) '/2

(I)

p2 = ~gz + 2B: + B(2gz + 4B2) 1/2

(2)

where p = ~/2A + B. The sum of the squares of the g values, S, can then be expressed: S = g~ + g~ + gz2 = 4p2(4 _ p 2 )

(2A)

By a calculation o f the wave-function coefficients from the experimental g values of low-spin hem e c o m p o u n d s and from the data in Ref. 5 it appeared t h a t 2 < C/B < 5 (C is a wave-function coefficient). Table I shows a calculation of S at different values of gz and B. In those

TABLE

I

CALCULATION O F gz A N D B

OF THE

SUM OF THE SQUARES

OF THE g VALUES

(S) AT DIFFERENT

VALUES

F r o m t h e v a l u e s g i v e n i n R e f . 5 i t a p p e a r s t h a t u s u a l l y B < 0 . 2 a n d 2 < C/B < 5 i n t h o s e l o w - s p i n h e i n e compounds having a set of g values comparable with experimental data. A good estimate for A from Eqn. 1 is A = 1/2(gz) 1/2, s i n c e B i s s m a l l . T h e m a x i m u m f o r B is B m a x = ( 1 - - A 2 ) 1/2, w h e n C = 0. A s 2 < C]B 5 and A 2 + B 2 + C z = 1 it follows that 0.2 Bma x < B < 0.45 Bma x. It can be seen in the table, that those v a l u e s o f S, c a l c u l a t e d f r o m E q n s . 2 a n d 2 A , w h i c h f u l f i l t h i s c o n d i t i o n ( u n d e r l i n e d v a l u e s ) a r e c l o s e t o 16. gz

3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0

A

0.866 0,880 0,894 0.908 0.922 0.935 0.949 0.962 0.975 0.987 1.000

Bma x

0.500 0.474 0.447 0.418 0.387 0.354 0.316 0.274 0.224 0.158 0.000

S B = 0

B = 0.04

B = 0.08

B = 0.12

B = 0.16

15.00 15.19 15.36 15.51 15.64 15.75 15.84 15.91 15.96 15.99 16.00

15.36 15.52 15.65 15.76 15.85 15.92 15.97 15.99 16.00 15.98 .

15.66 15.77 15.86 15.93 I~5,98 16.00 16.00 15.97 15.93 15.86 .

1 .~ R7 15,94 15,98 1~,00 15.99 15.96 15.91 15.83 15.73 15.61

15.99 1~;,00 15,99 15,95 15,89 ---15.38 --

.

.

336 c o l u m n s wherein 2 < C/B < 5 the sum of the squares of the g values equals or nearly equals 16. It is a fair a p p r o x i m a t i o n t h e n to put:

S = g~ + g~ + g~ = 16

(3)

if 3 < g z < 4 .

In tegra tion The p r o p o r t i o n a l i t y f a c t o r of Aasa and V/~nng~rd [1] can be written as follows: T = fi---

g~ + g~

1

g2

2 ,/2

(4)

S u b s t i t u t i n g g ~ +g2y = 1 6 - - g z 2 (Eqn. 3): T' = fl-~-" hv 2

.

16 -- g2 1 6 _ g z ~..+ ~gx 2

[1

(5) "

g2~1/2 y|

F Put R

J

_ g2x . g2y

Then, ifgx or gy equals zero, Rmi n = 0, so: T ~ x = ~__. 16 -- g~ hv 2 - [ 1 16--g2z] '/2

If g~ = g~, then R ~

Train=fl_. hv

2"

1

-

(6)

(16 _g~)2 4 • g~z , so:

16 --g~ 16 -- g~ (16 -- g~)2~ ,/2 ---'-~--+ -4~z "-]

(7)

Table II shows the values of T min and T max. Within the a p p r o x i m a t i o n t h a t S = 16, T rain and T max represent the e x t r e m e values of T at a fixed gz, i n d e p e n d e n t o f gy and gx. Since, then, the real value o f T is s o m e w h e r e b e t w e e n T rain and T max, the average is a better a p p r o x i m a t i o n t h a n T rain or T max alone. TAV = l(Tmin + Tmax)

(8)

For practical use TAv can be rearranged to: TAV

1 ~q I 1 2 1 -- ~ " 4-h (1 -- r) '/: + 2 ~ - - r

(9)

where q = 1 6 . 0 1 8 - - g ~ a n d r = q/g~. N o t e t h a t ge = 2.0023 has been introduced. The i n t e n s i t y of a low-spin h e m e signal with gz > 3 is t h e n calculated according to Aasa and V/inng~rd [ 1 ], b u t T M1 is replaced by T Av .

337 T A B L E II C A L C U L A T I O N O F T A V , T rain A N D T m a x A T D I F F E R E N T V A L U E S O F gz T m a x , T rain a n d T A V w e r e c a l c u l a t e d w i t h E q n s . 6, 7 a n d 8, in w h i c h t h e f a c t o r 1/u h a s b e e n o m i t t e d a n d 16 is r e p l a c e d b y 1 6 . 0 1 8 . D e v i a t i o n is d e f i n e d as + (1--Tmin/T A V ) X 100%. N o t e t h a t t h e d e v i a t i o n d e c r e a s e s w i t h i n c r e a s i n g gz values.

gz

Tmax

T min

T AV

D e v i a t i o n (%)

3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0

10.465 7.769 6.125 4.933 3.980 3.169 2.448 1.788 1.170 0.581 0.013

8.050 6.727 5.632 4.694 3.865 3.116 2.426 1.780 1.168 0.581 0.013

9.257 7.248 5.879 4.813 3.922 3.142 2.437 1.784 1.169 0.581 0.013

+ 13.0 __+7.2 -+ 4.2 -+ 2.5 + 1.5 __+0.8 + 0.5 + 0.2

Intensity of highly anisotropic low-spin heme EPR signals.

334 Biochimica et Biophysica Acta, 546 (1979) 334--340 © Elsevier/North-Holland Biomedical Press BBA 47647 INTENSITY OF HIGHLY ANISOTROPIC LOW-SPIN...
307KB Sizes 0 Downloads 0 Views