Electron spin relaxation of the electron paramagnetic resonance spectra of cytochrome c

9

Biochimica et Biophysics Acta, 621 (1980) 0 Elsevier/North-Holland Biomedical Press

9-N

BBA 38334

ELECTRON SPIN RELAXATION OF THE ELECTRON RESONANCE SPECTRA OF CYTOCHROME c

HAYWOOD

BLUM and TOMOKO

PARAMAGNETIC

OHNISHI

Johnson Research Foundation, Department of Biochemistry and Biophysics, School of Medicine, University of Pennsylvania, Philadelphia, PA 19104 (U.S.A.) (Received March 5th, 1979) (Revised manuscript received Key words: Cytochrome

August

6th, 1979)

c; ESR; Power saturation

Summary The progressive power saturation of the election paramagnetic resonance (EPR) spectrum of ferricytochrome c has been investigated in order to determine the spin-lattice relaxation time of the center. We have generalized the usual saturation treatments to include the effects of extended sample size and anisotropic g values as well as derivative spectra. We find that the results are consistent with a 2” power law in the temperature range 6-25 K. At temperatures above 25 K the relaxation time is too short for successful power saturation. Observation of the linewidth shows that the relaxation behavior continues as a first-order Raman process to 50 K.

Introduction The EPR responses of inhomogeneously broadened spin systems have been analyzed in the case where the spin packet linewidth is not necessarily insignificant relative to the inhomogeneous broadening. We have made three changes in our treatment of power saturation, extending earlier work [ 1,2] to include the anisotropic EPR spectra typical of biomolecules, including a correction for extended sample size, and giving the saturation curves for derivative spectra. In this paper we apply this formulation to ferricytochrome c, finding the low-temperature relaxation process to be consistent with a T’ Raman process. At higher temperatures, using linewidth broadening we are able to show that the relaxation time continues to follow a Raman process. The main purpose of this paper is to set out a formulation for the description of power saturation that can be applied in the analysis of relief from saturation through the use of extrinsic paramagnetic probes.

10

Materials and Methods Horse heart cytochrome c from Sigma Chemical Co., was used without further purification. Final concentration of cytochrome c in the 5.0-mm outer diameter EPR tubes was 0.3 mM. EPR-derivative spectra in the absorption mode were taken on a Varian E-109 EPR spectrometer used in homodyne mode with the microwave cavity exactly matched to the line. Low temperatures were achieved with an Air Products flowing helium transfer system. Temperatures were measured with calibrated carbon resistors and a thermocouple placed in the cold gas stream beneath the sample. Incident microwave power was read on the E-109 power dial. The calibration made at manufacture was taken as accurate. This is acceptable since we are not interested in absolute values of the spin-lattice relaxation time, T1. The precision microwave attenuator was checked on a non-saturating Varian ‘strong pitch’ sample at room temperature and found to be accurate to within a few percent. The 30 dB-switched microwave attenuator was found to be more than 10% off and low-power settings were corrected appropriately. The sample was in a 5 mm outer diameter quartz tube which fills the center of the TE 102 microwave cavity. Since the microwave magnetic field is not constant over the length of the tube, parts of the sample will saturate at different power levels. This will distort the saturation curves as discussed by Castner [2] so that the region near mild saturation is accentuated. In our analysis the effects of extended samples have been considered. The detailed relationship between incident power and resultant microwave magnetic field has been given [1,2]. Since the absolute value of T1 is not of deep interest we have not evaluated the parameters with extreme accuracy. For the conditions of these experiments we estimate that H1, the microwave magnetic field at the cavity center, is equal to 2.5 /JT (25 mG) when the incident microwave power, P, is 1 mW. On the other hand, for these experiments it is important that the relative sensitivity of the instrument remain constant throughout the experiment. This was monitored by substitution of the Varian ‘weak pitch’ sample for the experimental sample occasionally. The Varian standard was run at low power so that it remained unsaturated. The modulation frequency, vm, was 100 kHz. We found no change in the line shapes at any power or temperature from the usual EPR absorption spectrum when we reduced this frequency to low audio values. Since the signal/noise is better with higher modulation frequencies we used the standard value for this spectrometer. The basic condition which must be met to ensure slow-passage [3,4] conditions is given by Cullis (Ref. 5, Eqn. 40); namely,

ratio, H, is the modulation ampliwhere w, = 27rvm, y is the magnetogyric tude, and T2 is the spin packet linewidth, defined below. For our sample, T2 = lo-” s, T1 G 1O-2 s, H, = 0.5 mT (5 G), so that Eqn. 1 is amply satisfied.

11

Power saturation The effects of high-incident power applied at the resonant frequency have been considered in the earliest analyses of magnetic resonance spectra [ 61. In particular, Portis [l] and Castner [2] derive expressions for the power dependence of the EPR signal for inhomogeneously broadened resonance lines. Castner extends Portis’ treatment to the case where individual spin packets which make up the inhomogeneous line are not necessarily narrow relative to the overall linewidth. Cullis [5] has given an elegant treatment using a spin temperature approach. He discusses the meaning of the spin packet width in some detail. In this earlier work the overall line shape h (w - w,) is assumed to have a Gaussian distribution h(o - 00) = a- 1’2(Awc)-1 exp[-(w

- u~)~/Au&]

(2)

where AC+ is the Gaussian width and w. is the center of the distribution; that is, the EPR spectrum is taken to be isotropic in g value. The spectra which we must consider are, in general, anisotropic, possessing a g tensor with three principal g values, g,, gY , g,. Such a spectrum can be represented analytically [ 7,8]. Fig. 1 shows a computer simulation of the EPR absorption spectrum of a pmamagnetic center with rhombic symmetry. The envelope skeleton in the figure is calculated with no broadening. The envelope function assumes Gaussian broadening, as in Eqn. 2. If the unbroadened absorption envelope is given by H(U), then the actual envelope function f (w) is given by the convolution f(w) = y H(w’)h(o 0 The

broadening,

taken

(3)

as constant

\

I ,

in Fig. 1, can be mainly

ascribed

to

, L

1

,

I

\ I

9,

- w’)do’

%

gz

gr 0

gY0’

9x

Fig. 1. Computer simulation of EPR absorption enal of center with rhombic symmetry with gx = 1.9, gy = 2.1. gL = 2.3. Envelope skeleton has insignificant Gaussian broadening. Envelope is the same center with constant Gaussian broadening of 2.0 mT (20 G). Fig. 2. Illustration of EPR absorption signal with Gaussian broadening as in Fig. 1. Lorentzian spin packet is centered at w’.

12

‘g-strain’; that is, varying principal g values due to variations in the local crystalline fields of the proteins [9,10]. In general, the broadening will vary with g value. Additional inhomogeneous broadening mechanisms include hyperfine interactions and dipoledipole interactions among non-identical centers. If the individual spin packet line shape, g(w - w’) is Lorentzian g(0 - w’) = (T,/n)

1 1 + T&J - C&2

T2 is defined by AmLT2 = 1, where AC+ is the Lorentzian mum of g(w). The EPR absorption signal S(o) is then [ 21 proportional

s-

0

@‘f(a’)g(ti

width for half-maxito

- w’)dw’

1 ++ ny2H;2T,g(w--w')

Fig. 2 illustrates packets, g(w - o’), intractable but the on the EPR spectra

(5)

the envelope function f(w) with one of the Lorentzian spin centered at 0’. The task of calculating S(o) is analytically spectra can be computer simulated. Fig. 3 shows the effect of increasing the incident microwave power. In this figure

d Pjg. 3. Computer simulations of EPR absorption and derivative spectra versus applied microwave Power. Spectra corrected for extended sample size. Vertical axis., S/Pi/2. Conditions are: Gaussian linewidth of 2.0 mu (20 G); TV = 1.0. lo-6 s (= 5.6 G at g = 2). (A and B). isotropic center at g = 2; (C and D). rhombit center with gx = 1.9, gy = 2.1. gs = 2.3. (A and C), absorption; (B and D). derivative signals. p/p1/2 (defined in the text): (a) 0, (b) 1, (c) 10. (d) 100.

13

the Lorentzian and Gaussian linewidths are comparable. In Fig. 3, the EPR absorption or derivative signals shown have been divided by the square root of the power for reasons given below. At the center of an isotropic resonance line, Castner shows that the EPR absorption is given by S = l1/2(1 + t)-‘12 exp(a2t)

I

1 - $[a(1 + #“I

1 - 4(c)

(6) 1

where 4(x) is the error function G(x) = 2n-1’2 j

exp(--u2)du

l is a dimensionless t = wp,,,

=

parameter (7)

w,/q,2)2

where H, is the microwave

magnetic

field, H,,, is the value of H1 such that

microwave powers. a = (AwJAoG) is a and P and PI,, are the corresponding parameter which measures the degree of inhomogeneous broadening. Fig. 4A shows the inhomogeneous saturation curve derived by Castner, instead of the signal only. In a comreplotted with SIP"'asthe y-ordinate pletely inhomogeneous case the absorption signal reaches a maximum and remains constant as shown by Portis. The plot S/P"'on the other hand falls off as shown but not as rapidly as in the partly homogeneous case. At low powers, S/P1’2 is constant, which is the main virtue of this form of plot. We note that at case but 0.707 for the complete P = PI/29 S/P1j2 = 0.5 for the homogeneous inhomogeneous case. Thus one would rarely find that the measured power at which the experimental signal is one-half of its unsaturated value would correspond to P,,, as usually defined. Nevertheless, the use of the experimental parameter would be valid if the saturation curves remain unchanged in shape. Since the samples used in this study pass completely through the microwave cavity, the microwave field, H,, experienced by different segments of the sample will very sinusoidally from its maximum value at the cavity center to zero at each end of the cavity. Thus some parts of the sample will be more saturated than others. The actual signal will be the integrated average over the sample. This is shown in Fig. 4B. For P/PI ,2 << 1, there is very little change in the shape of the saturation curves, as one might expect (although the absolute magnitude of the low-power signal will be diminished by a factor of 2 relative to the case where H1 is constant over the sample). For P/PI,, > 1 the correction is important. Examination of the envelope function, shown in Fig. 2, immediately reveals that Eqn. 6 does not apply to centers with anisotropic g values. In the region near g,, for example, the envelope does not fall symmetrically on both sides of g,. In fact, the drop-off on the low-field side is compensated by a rise on the high-field side. This will cause the saturation behavior to be more inhomogeneous appearing for a given value of the parameter a. In the experimental situation actually encountered, magnetic field modula-

14

ID-

B

B

mrdas’

01.

e h

7

-a

2

x

001.

0 0

0.05 0.10 0.20 0.50 1.00

0.0011 001

0.1

Fig. 4. (A) Power saturation curves from EQ~. 6. The parametera is the ratio of the Lorentzian spin packet linewidth to the Gaussian envelope width, as defined by Eons. 4 and 2. respectively. P. the applied micro, WaVe Power. and _P1/2. the power corresponding to the microwave magnetic field H1,2 such that 1/4YH1/2 *(TIT~)"~ = 1. (B) Power saturation curves corrected for extended sample geometry. P. the maximum power at the cavity center.

0.00

&4

0.1

IO P/Ph

Ffg. 6. Calculated power saturation curves for a gs = 3.06 with Gaussian line shapes of width AH, (73 G). Plotted fs the hefght of the gr peak of Assumed values for T2 are shown. Values of the

paramsgnetic center with g valuer gx = 1.26. gy = 2.24, = 30 mT (300 G), AHy = 7.6 mT (75 G). AH, - 7.3 mT the derivative spectrum divided by (P/P1 a) vs. P/P1 ,Q. parameter a are calculated at g = 3.06 by (I = l/yTgLw,.

15

tion is used and subsequent phase-sensitive detection is employed at the modulation frequency. This causes the signal observed to be the first derivative of the absorption [ 51. The saturation behavior of the derivative signal, D, for small sample size and anisotropic g values is given by .p(l

mtw(o)

=

+ E)-l’2,

a = 0 (inhomogeneous

limit)

a >> 1 (homogeneous limit)

4_l’2(1+ .$>-2,

The effects of extended sample size and anisotropic lated. In Fig, 5 the height of the g, peak of a rhombic interesting to note that for intermediate cases the slope powers keeps increasing toward the homogeneous case, extended sample size and large H, [ll].

(9)

g values can be simusignal is plotted. It is of the curves for high a consequence of the

Cytochrome c Cytochrome c is a low-spin heme with rhombic g tensor. Its principal g values [ 10,121 are approximately 1.25, 2.25, 3.05. The low-field EPRderivative spectrum of horse heart cytochrome c is shown in Fig. 6, together with a computer simulation of the low-spin signal. The g = 1.25 signal which is very broad is not shown. The simulation assumes Gaussian line shape with width at g = 3.05 of 7.3 mT (73 G) and at g = 2.25 of 7.5 mT (75 G). The low-field part of the spectrum shows some degraded material at g = 4.2 and a high-spin rhombic signal at g = 6. Presumably this is derived from a modification of the cytochrome c protein moiety, weakening the crystal field at the heme. The saturation curves for the g = 3.05 cytochrome c signal were determined at various temperatures. The data (Fig. 7) were fit by the curves given in Fig. 5 with the parameter a approximately constant at 0.05. We see in Fig. 8 that over thetemperature range 6-25 K the data are well fit

Y

“P

0

loo0

n

4i2

m Magnetic

Fii

-em __--*num

of

lWSphSiQl-Ol

2.24 I

3coo

4ooo

(cod

Fip. 6. The x-band EPR absorption derivative spectrum at low magnetic field for cytochrome c in eolution. - - - - - -, computer eimuhtion affeumU principal g valuer of 1.25.2.24, and 3.05 with Gaupion tie *Dee of half-width 30 mT (300 G). 7.5 mT (76 G) and 7.3 mT (73 G). respectively. Concentxation of cytochrome c ie 300 pM. EPR conditions: T = 12 K; microwave power. 6 mW; modulation amplitude, 2.0 mT (20 G) at 100 kHz.

Fig. 7. Saturation curves for horse heart cytochrome c. Height of g = 3.05 peak divided by P112 versus microwave power, extended samples, at the indicated temperatures (0). Fits to the data using the computer-generated curves of Fig. 5 with o = 0.05. curves.

by a power law expression P1,2 a T5.’ . Since T2 remains constant, this is also the temperature dependence of T1. The expression found for T1 is unusual. It is, however, consistent with the results of Herrick and Stapleton [ 131, who measured the recovery from saturation of the low-spin cytochrome P-450 EPR signal, This direct measurement of T1 is fit by an expression of the form l/T1 = AT + CT’J,(O,/T) where 8n is the Debye parameters, and J,(&,/T)

Jn(x)

=

[

(e:‘$2

(10) temperature, is a transport

n = 2, 3, . . .

A and C are temperature-independent integral [ 14,151, defined as

(11)

Over the narrow temperature range 4-7 K, Eqn. 10 follows a T’ power law. Between 7 and 20 K a TSe5 power law fit can be made, with 8n = 75 K, as the effect of the transport integral becomes important. The first-order Raman process which goes as T’ in the low-temperature approximation eventually has a T? high-temperature limit [16], although other processes usually take over before this occurs. Using another indirect method based on rapid passage effects [ 3-51, Mailer and Taylor [ 171 reported a T’ temperature dependence for cytochrome c over the temperature range 8-18 K. From 4 to 8 K they found T1 to be constant. It is not possible for us to follow the saturation above 25 K since the available power is limited. However, we are able to measure the linewidth of the g = 3.05 signal, shown in Fig. 9. One can fit the linewidth over the limited temperature range available to us experimentally by a power law, T2.2. This temperature dependence is consistent with a continuation of the dominance of the first-order Raman process to 50 K. However, given the limited accuracy of these linewidth data, other theoretical analyses are possible. For example, one can fit the data equally well to a Resonant Raman or Orbach process [18] with an excited low-lying state 125 cm-* above the ground state. This energy would be consistent with the calcula-

17

uxxI-

IKXI-

P,,* (mW)

I(3.

I!o-

0 .I - d

’ 4

8

IO

I5

20 2 5

‘OL

T(K)

T(K)

Fig. 8. Values of PI/~ vs. temperature for the g = 3.05 peak of cytochrome the power saturation data to the curves of Fig. 5, as shown in Fig. 7.

c. PII

is found from fi tsl 3f

Fig. 9. Linewidth increase vs. temperature for the 8 = 3.06 peak of cytochrome c (0). Using the approximate formulation that mT = (ITS + AHLGR2 )1’2 , where UT, MT(u), and ULGR are the total. low temperature, and Lorentaian contributions to the linewidth. respectively. we can derive the open circles through which the indicated line can be drawn with temperature dependence T2’2.

tions of Mizuhashi [ 191 for hemoglobin azide; that is, the splitting of the d,, and 4, orbit& by the rhombic field must be about 150 cm’ in order to produce the anisotropic g values observed. Other theoretical treatments [20-221 predict levels at higher energies (above 600 cm-‘). In recent resonance Raman measurements on cytochrome c [23] low-lying excited states were found only between 750 cm-’ and 1300 cm-‘, tending to exclude the possibility of an Orbach process. However, it is extremely difficult for the resonance Raman spectrometer to scan below 200 cm-‘. Conclusion We have seen that expressions derived for isotropic inhomogeneously broadened spectra, when suitably modified, apply to the more general case of rhombic symmetry. The electron spin-lattice relaxation time is dominated by a T’ Raman process. Acknowledgements This work was supported by NIH grants GM-12202 National Science Foundation grant PCM-7316779. References 1 Port& A.M. (1963) Phys. Rev. 91,1071-1078 2 Castnar. T.G. (1959) Phys. Rev. 116.1506-1515

and GM-25052

and by

18 3 Portis, A.M. (1955) 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Magnetic Resonance in Systems with Spectral Distributions,

Technical

Note No.1,

S.M. Scaife Radiation Laboratory, University of Pittsburgh Weger, M. (1960) BeII Syst. Tech. J. 39.1013-1112 CuRis, P.R. (1976) J. Magn. Resonance 21.397-416 Bloembergen. N.. Purcell. E.M. and Pound, R.V. (1948) Phys. Rev. 73. 679-713 Kneubuhl. F.K. (1960) J. Chem. Phys. 33,1074-1078 Poole, C.P. (1964) Electron Spin Resonance pp. 825-836. John Wiley and Sons, New York Eisenberger, R. and Pershan, P.S. (1967) J. Chem. Phys. 47,3327-3333 Mailer. C. and Taylor, C.P.S. (1972) Can. J. Biochem. 50. 1048-1065 Hyde, J.S. (1960) Phys. Rev. 119.1492-1495 Hori. H. and Morimoto. H. (1970) Biochim. Biophys. Acta 200.581-583 Henick. R.C. and Stapleton, H.J. (1976) J. Chem. Phys. 65.4778-4785 Rogers, W.M. and Powell. R.C. (1958) NatI. Bur. Stand. (U.S.A.). Circ. 695 Scott, P.L. and Jeffries. C.D. (1962) Phys. Rev. 127,32-60 Abragam. A. and Bleaney, B. (1970) Electron Pammagnetic Resonance of Transition Ions, p. 556. Ciarendon Press, Oxford Mailer, C. and Taylor, C.P.S. (1973) Biochim. Bioghys. Acta 322.195-203 Orbach. R. (1961) Proc. R. Sot. Lond. A264.458484 Misuhaahi. S. (1969) J. Phys. Sot. Jap. 26.468-492 Harris, G. (1968) Theor. Chim. Acta 5.379-397 SaImeen. I. and Palmer. G. (1968) J. Chem. Phys. 48.2049-2052 Zerner. M.. Gouterman, M. and Kobayashi, H. (1966) Theor. Chim. Acta 6.363-400 Adar, F. (1978) J. Phys. Chem. 82.230-234