3164
JACQUES RUEBEN
Electron Spin Relaxation in Aqueous Solutions of Gadolinium(II1). Aquo, Cacodylate, and Bovine Serum Albumin Complexes by Jacques Reuben1 Department of Biophysics and Physical Biochemistry, University of Pennsylvania School of Medicine, Philadelphia, Pennsylvania 19104 (Received April 6,1971) Publication costs borne completely by The Journal of Physical Chemistry
Electron spin relaxation rates of gadolinium(II1) complexes in aqueous solution were obtained from epr spectra at 9.14 and 34.2 GHz. The aquo ion and the complexes with cacodylate and with bovine serum albumin were investigated at several temperatures. The results are analyzed in terms of correlation times characteristic of processes modulating the zero-field splitting of Gd(III), using the relaxation matrix given by Hudson and Lewis. Theoretically predicted features of temperature and frequency dependence of the epr line width have been recognized in the experimental results. From the relative values of the zero-field splitting constant it appears that the immediate environment of Gd(II1) bound to the protein is more symmetric than that of the aquo ion. Comparison between the zero-field splitting constants, the correlation times, and their activation energies for the three complexes studied suggests that: (a) the zero-field splitting effecting electron spin relaxation is transient to a large extent; (b) for the “small” complexes the processes governing electron spin relaxation may be identified with rotational diffusion of, solvent impact upon, and inversion of the complex. A mechanism involving metal-ligand interactions coupled to slower motions of the whole polypeptide chain is suggested to account for the electron spin relaxation observed in macromolecular systems.
Introduction
Experimental Section
Electron spin relaxation rates of paramagnetic ions (and other free radicals) are often implied as indicators of molecular dynamics in the liquid state. A theory of electron spin relaxation converging into a simple closed expression for the relaxation rate as a function of frequency and correlation time has been given by Bloembergen and Morgan.2 Subsequently it has been found that for an exact representation the appropriate relaxation matrix has to be used and solved numerically. Recently, Hudson and Lewis presented the theory of electron spin relaxation of *S ions, e.g., gadoliniurn(II1) in s o l u t i ~ n . ~From the literature review given in their article4 it appears that the available epr data on Gd(II1) in solution are too limited to provide an experimental test of the theory let alone to allow any conclusions to be drawn regarding the processes leading to electron spin relaxation. I n this paper we present the results of an epr study of aquogadolinium(II1) and its complexes with cacodylate (dimethylarsinate) and with bovine serum albumin (hereafter referred to as BSA). This study was carried out in conjunction with an investigation of the suitability of Gd(III) as a Paramagnetic probe in proton relaxation studies of biological macromolecules, which has been e1seU’here‘6 A’easurements were done at two microwave frequencies and several temperatures. The results are used to examine the theory and draw conclusions regarding the processes effecting electron spin relaxation in solutions and the ion envirorlment in the ‘Omsymmetry Of the plexes.
Epr spectra aL 9.14 GHz were recorded with a Varian E-3 spectrometer. Spectra a t 34.2 GHz were obtained with a Varian Rlodel V-4503 spectrometer equipped with a Model V-4561 microyave bridge. The solutions were contained in quartz capillary tubes. Temperature control was achieved by flowing precooled or preheated nitrogen using the Varian temperature control accessories. The temperature in the cavity was measured before and after each recording and was found to be constant to within h0.3”. A modulation amplitude of 4 G at 100 kHz and microwave powers of 20-40 mW \yere used to record the derivative of the absorption mode. Depending on the line width, different sweep widths (scan ranges) were used. The accuracy of the line width measurements is estimated to range between i5 G for the narrowest lines and f 15 G for the widest. KO detailed line shape analysis was performed, but using the ‘Lmoment” criterion6 the lines were found to be Lorentzian to a good approximation. The peak-to-peak line width of the derivative of the absorption mode, A H , expressed in units of
The Journal of Physical Chemistry, Val, 76,No.20, 1972
(1) Career Investigator Fellow of the American Heart Association, Feb 1969-Jan 1971. To whom all correspondence should be addressed at The Weizmann Institute of Science, Rehovoth, Israel. (2) N. Bloembergen and L. 0 . Morgan, J . Chem. Phys., 34, 892 (1961). (3) A. Hudson and G. R . Luckhurst, Chem. Rev., 69, 191 (1969). (4) A. Hudson and J. TV. E. Lewis, Trans. Faraday SOC.,6 6 , 1297 (1970). ( 5 ) J. Reuben, Biochemi,stry, lo, 2834 (1971). (6) C. p. poole, Jr., “Electron Spin Resonance,” Interscience, New York, N. Y., 1967, Table 20-7, p 806.
3165
ELECTRON SPINRELAXATION IN AQUEOUSSOLUTIONS OF GADOLINIUM(III)
1000:
gauss is related to the electron spin transverse relaxation time, Tze,by
l/Tze = (qfl7r3”’/h)AH
800600-
(1)
Crystallized bovine serum albumin, obtained from Pentex, Inc., was dissolved in 0.05 M tetramethylammonium cacodylate buffer at pH 6.3. Insoluble material was removed by centrifugation. The concentration was determined from the absorbance at 280 mp using 0.66 as the absorbance of 1 mg/ml per cm and a molecular weight of 69,000.’ Solutions of GdCL were prepared from a 1 M stock solution made by reacting Gd&a (from Alfa Inorganics) with dilute hydrochloric acid. To maintain ionic strength all solutions were made 0.1 M in tetramethylammonium chloride. Computations were done on the PDP-6 computer of the Medical School computer facility.8 The facility kindly provided a subroutine for matrix diagonalization based on the Jacobi method.
Results Epr measurements were performed on three solutions. Solution A was 80 m M GdCL at pH 3. No concentration or pH dependence of the epr line width was observed in the ranges 2-80 mM GdCla and 3-6.5 pH units. Solution B was 8 mM GdCla in the cacodylate buffer at pH 6.3. Solution C was 0.94 mM GdC13 and 0.4 m M BSA in the cacodylate buffer at pH 6.3. A binding study by proton relaxation methods has shown that BSA has four independent and equivalent binding sites for Gd(I1I) with an apparent dissociation constant of 1.3 X M at 300°K and pH 6.3.5 Thus in solution C almost all the Gd(II1) is bound to the protein. The peak-to-peak line widths of the epr spectra are graphically presented in Figure 1 plotted against the inverse absolute temperature. The following general features are apparent. For the three systems investigated the line width at the lower frequency is larger than that at the higher frequency. At 9.14 GHz the line width decreases with increasing temperature, whereas at 34.2 GHz it increases or shows a maximum. The results obtained with GdCla (solution A) are in good agreement with those reported by Marianelli for a 25 m M solution of Gd(C104)sa9 It seems safe to assume that in both cases Gd(II1) exists as the fully hydrated ion. However, in presence of cacodylate the epr line of Gd(II1) is much broader. Formation of strong complexes between lanthanides and anions is well known10and has also been detected by nmr.11p12 Also the proton relaxation rates due to Gd(II1) in presence of cacodylate were found to be lower than those in its absence suggesting water substitution by the anion.6 With a more than sixfold excess of cacodylate and at the relatively high pH of 6.3 it can be assumed that practically all the gadolinium is complexed and the
4002 300v)
0
2a
200100: 80-
603:2 3:3 3:4 3:5 3:6 317 IO3/ TPK“ Figure 1. Peak-to-peak line widths of the epr spectra of Gd(II1) as a function of inverse absolute temperature a t two frequencies (in GHz): Aquo Gd(III), solution A-0, 0 ; Gd(II1)-cacodylate, solution B-0, m; Gd(II1)-BSA, solution C-A, A. Curves are calculated (see text).
epr spectrum of solution B corresponds to the Gd(II1)cacodylate complex. I n order to quantitatively analyze the results, the relaxation matrix for spin 7/z systems given by Hudson and Lewis was used.4 These authors assumed that the dominant line broadening mechanism for an ion is provided by the modulation of the zero-field splitting by a process with a characteristic time 7. The transverse relaxation rate is given by
l/TZ,
= -ZM(U,T)
(2)
where Z is the inner product of the zero-field splitting tensor (in rad2 set+) and M(u,T)is the relaxation matrix, w being the electron Larmor frequency (cf. ref 4). In general the epr line of Gd(II1) is composed of four transitions of different intensities and line widths. A numerical solution of the relaxation matrix shows, however, that only one of these lines is significant in the observed spectrum, the others having a total contribution of, e.g., less than 6% at 9.14 GHz and T lo-” see. The relaxation matrix was diagonalized numerically for the two frequencies and for different values of 7.
