✍ Scribed by C. Galli; Jennifer B. Innes; Donald J. Hirsh; Gary W. Brudvig
No coin nor oath required. For personal study only.
The method of microwave progressive power saturation If log(S/P 1/2 ) is plotted versus log P, two linear regions is commonly used to evaluate electron spin-relaxation times are obtained that intersect at P Å P 1/2 (see Fig. ). It is of paramagnetic centers in biological systems (1-3). Often, possible to calculate T 1 T 2 from an experimental measurethe aim is to determine the locations of paramagnetic centers ment of P 1/2 (2). in biomolecules by analyzing spin-relaxation enhancements Equation [1] is not strictly applicable to determine relaxdue to long-range spin-spin interactions. The objective of ation times of spins with dipolar coupling. In deriving the this Note is to point out that the empirical expression used to saturation expressions, it is assumed that all spins at resoanalyze saturation data is incorrect for cases where dipolenance saturate equivalently; that is, all the spins have the dipole interactions contribute significantly to the spin relaxsame value for the product T 1 T 2 . If, however, a dipolar ation and can lead to significant errors in the determination relaxation mechanism is significant and the molecules are of spin-relaxation times. We present a simple procedure for immobilized, the spins will saturate nonuniformly because determining the dipolar contribution to the spin relaxation each spin's T 1 T 2 will depend on the orientation of its molecuof a protein radical from microwave progressive power satular axes with respect to the external magnetic field. As deration data.
tailed below, the effect is particularly significant for radicals The empirical expression used to fit saturation data is in proteins. For example, consider an enzyme with two spins buried EPR Derivative Signal Amplitude in the protein matrix at a fixed distance r apart, one of which is a slowly relaxing radical and the other a rapidly relaxing Å S Å KP 1/2 /[1 / (P/P 1/2 )] b /2 ,
[1] species. This situation is typical for redox-active metalloproteins which frequently contain a slowly relaxing organic where K is a constant, P is the microwave power, P 1/2 is the radical coupled to a rapidly relaxing metal center ( 6-10). microwave power at half-saturation, and b is the inhomoge-Consider further the usual case where the two spins are far neity parameter. Equation [1] follows from the work of Portis enough apart that the EPR lineshape of the radical is unaf-(4) and Castner (5) who derived expressions for the suscepfected by the dipole-dipole interaction, but the radical does tibility, x, as a function of microwave power. The functional have enhanced spin relaxation. Due to the large dimensions form of the saturation expression depends on whether the of the protein and the fact that organic radicals are usually EPR lines are homogeneously or inhomogeneously broadburied, intermolecular spin-spin interactions are often negliened. For a first-derivative spectrum, b Å 1 in the inhomogegible, especially at the submillimolar protein concentrations neous limit and b Å 3 for the homogeneous limit. Intermedinormally used for EPR measurements. Therefore, protein ate cases are treated empirically by allowing b to be a fitting parameter. The logarithmic form of Eq. [1] is a convenient systems often have long-range spin-spin interactions beway to present experimental data tween a discreet pair of spins at a fixed distance and relative orientation. EPR saturation measurements of the radical frolog(S/P 1/2 ) Å log(K) 0 (b/2)log[1 / (P/P 1/2 )]. [2] zen in a glass will sample a random distribution of molecular orientations in the magnetic field owing to the small g value and hyperfine anisotropy of radicals. However, the magni-
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