1422
The Journal of Physical Chemistry, Vol, 83, No. 11, 1979
R. J. Kurland and 8.J. Marwedel
Fluoride Ion as a Nuclear Magnetic Resonance Probe of Galactose Oxidase. An Analysis of the Fluorine-I 9 Nuclear Magnetic Resonance Relaxation Rates Robert J. Kurland*+ and Beverly J. Marwedelt Bioinorganic Graduate Research Group, Departments of Chemistry and Biochemistry, State University of New York at Buffalo, Buffalo, New York 14214 (Received November 14, 1978) Publication costs assisted by the National Science Foundation
The temperature and frequency dependence of the 19FNMR spin-spin (l/Tz)and spin-lattice (l/Tl) relaxation rates of F in the presence of the copper-containingenzyme galactose oxidase have been analyzed. The magnitudes of the dipolar and scalar electron-nuclear interactions obtained from this analysis are both about four times smaller than those which have been determined previously for aqueous CuF'. The major contribution to the dipolar relaxation mechanism comes from unpaired electron spin in p orbitals centered at the bound F-; no more than 38% is due to the point-dipole interaction between the 19Fnucleus and unpaired electron spin centered at the enzyme Cu(I1). Pseudothermodynamic parameters for the binding of F- to the enzyme Cu(I1) site were determined: Kf = 6.9 x M-l at 50 "C, AHo = -4.2 X lo1 kJ mol-l. The smaller values for these superhyperfine and binding constants, compared to those for aqueous CuF+,are consistent with axial, rather than equatorial coordination to the Cu(I1) of the F- detected by these relaxation experiments.
Introduction The extracellular fungal enzyme galactose oxidase (E.C. 1.1.3.9) catalyzes the oxidation of many primary alcohols to the corresponding aldehydes.lB2 As possibly the only protein which contains but a single type 2 copper per m o l e ~ u l galactose e ~ ~ ~ oxidase (GOase) is of particular interest as a prototype for this type of copper site in other proteins. In our studies of water proton relaxation as a probe of the GOase Cu(I1) site, we found relatively small relaxation enhancements a t the maximum concentration of GOase that could be employed and no consistent effects due to substrate or Oz.5 We therefore sought to enhance the paramagnetic effects due to the Cu(I1) and focussed our efforts on fluoride ion in order to realize the following potential advantages over other NMR relaxation probes (water, halide ions) which have been used extensively. Since 19F has nuclear spin quantum number I = 1 / 2 , analysis of the relaxation rates would not be complicated by the quadrupolar effects present for other halide ions; moreover, the relaxation enhancement of F- bound to a paramagnetic metal ion should, from a priori considerations, be large; there will be a contribution to dipolar relaxation not only from the unpaired electron spin in orbitals centered a t the metal ion, but also from unpaired spin in fluorine centered p orbitals.6-8 The latter contribution may, indeed, be larger than the former,8 even though it has not been extensively considered in other studies utilizing F- as an NMR relaxation probe of paramagnetic metal lop rote in^.^-^^ Finally, the NMR sensitivity of 19Fis comparable to that for protons. We have used fluoride ion as a NMR relaxation probe to determine the binding constants of several substrates and products to GOase5J2and to elucidate the coordination chemistry of the Cu(I1) site. The 19FNMR relaxation results from CN- competition experiments,IZ combined with ESR data,13show that there are two coordination sites a t the GOase Cu(I1) available for exogeneous ligands: one corresponds to binding at an equatorial position, the other
* To whom correspondence should be addressed at Department of Chemistry, State University of New York at Buffalo, Buffalo, N.Y. 14214.
Grace Cancer Drug Center, Roswell Park Memorial Institute, Buffalo, N.Y. 14263. 0022-3654/79/2083-1422$01.00/0
to axial. Ions such as CN- and F- bind relatively strongly a t the equatorial position; F- also binds, but relatively weakly, a t the axial position. Quite probably neutral hydroxylic ligands, such as galactose, also bind weakly at the axial p0siti0n.l~ Only the F- which is axially coordinated is detected in these 19F NMR relaxation experiments since exchange between equatorially coordinated and bulk F- is slow; the equatorially coordinated F- is that which perturbs the observed ESR ~igna1.l~ In this paper we present an analysis of the temperature and frequency dependence of the 19FNMR relaxation rates of F- in the presence of GOase. The values for the relaxation and binding parameters derived from this analysis are consistent with the qualitative picture of F- coordination to the enzyme Cu(I1) which has been derived from other experiments, as outlined above.
Experimental Section Galactose oxidase was purified from the extracellular fluid of cultures of the fungus Dactylium dendroides by means of modified literature procedures.15 Protein concentrations are calculated from the 280 nm absorbance of solutions and enzyme activity was determined by means of a standard coupled assay reaction monitored a t 400 nm.'; Aqueous solutions of K F were stored or transferred in polyethylene or Kel-F equipment. Previous studies had shown that glass and polyvinyl chloride cause irreversible changes in the relaxation rates of aqueous fluoride solutions.8J6 In our own preliminary work we found that in the presence of lo4 M GOase, observed F- relaxation rates were identical for samples in glass, Delrin, and Kel-F tubes for a period of several hours after sample preparation. Over the 24-h period required for some of the NMR measurements, both glass and Delrin produced alterations in the solutions, as indicated by an increase in the "F NMR relaxation rates. Relaxation rates obtained for corresponding solutions in Kel-F sample tubes were reproducible over a 3-day period. The stock and sample solutions were kept a t p H 7.0 f 0.1 by addition of 0.05 M NaH2P04and NaOH solutions. The buffer solutions used in these experiments were made up from deionized, glass-distilled water which contained less than lo-@M Cu(II), according to tests by atomic 0 1979 American
Chemical Society
Fluoride as a NMR Probe of
Galactose Oxidase
absorption (limit of detection lo4 M). Buffers were passed through a CHELEX-1100 (BIO-RAD Laboratories) column to remove cupric ion impurity that might be present in the phosphate and base components. The GOase stock solutions were exhaustively dialyzed against Cu(I1)-free buffers to which lo-' M ethylenediaminetetraacetic acid had been added to ensure the complexation of any free cupric ion present due to enzyme decomposition. For the relaxation rate data reported here, fluoride concentrations were maintained a t 1015 M in order to eliminate variations in ionic strength as a factor in relaxation rate changes (it has been reported2 that GOase activity increases with increasing ionic strength). For those experiments where F- concentration was varied in order to obtain a preliminary estimate of the GOase-fluoride binding constant (see below), a 1.0 M ionic strength was maintained by addition of K,SO,; addition of this salt does not appreciably affect GOase activity.12 Fluorine-19 relaxation rates a t 26 and 56.4 MHz were measured by use of a Bruker B-KR 321s variable frequency pulsed NMR spectrometer. Field-frequency control a t the latter frequency was maintained via an external lock sample of paramagnetically doped water. Since this field-frequency control was not available a t the lower field of the 26-MHn experiments, the T, measurements at this frequency, for temperatures other than ambient, were not considered sufficiently reliable to be included in the data presented here (because of the incompatibility of the long averaging times required and field and temperature instability). Relaxation measurements a t 94.2 MHz were taken by use of a Varian XL-100 spectrometer with a Nicolet Technology Corp. TT-100 pulsed NMR accessory. For the 94.2-MHz measurements a D20 lock in an annular region of the sample was used for field-frequency control. The T1 relaxation times were obtained by use of the Carr-Purcell 180-t-90 pulse sequence,17and T2values by the Carr-Purcell, Meiboom-Gill methodla or from free induction decay curves. An approximate error range of f10% is assigned to the relaxation rate data, on the basis of error limits in the relaxation rate measurements, enzyme concentrations, and temperatures. (The errors from a standard propagation of errors treatment are less than this value for almost all of the data points.)
Theoretical Section The nuclear-electron hyperfine interaction responsible for 19F relaxation can be represented by the time-dependent H a r n i l t ~ n i a m : ~ ~ ~ ~ ~ Hl(t) = A , ( t ) I*S(t)+ I.A(t).S(t) (1) where the first term on the right-hand side of eq 1 represents the isotropic (Fermi contact) interaction and the second term the anisotropic hyperfine (dipolar) interaction. In a molecule-fixed principal axis coordinate system, with unit vectors i(t),j ( t ) , and k(t), the traceless dyadic A takes the form A(t) = A,(2kk - jj - ii) (2) if cylindrical symmetry is assumed. We emphasize that the constant A, in eql2 includes not only the contribution from unpaired spin in orbitals centered a t the Cu(I1) (Le., from the metal-ligand nucleus point-dipole interaction usually taken to be the major or sole contribution to the dipolar relaxation mechanism) but also the contribution from unpaired spin iin p orbitals centered a t the 19Fnucleus. The constant A, can be decomposed explicitly into contributions from metal and ligand centered pin:^,^ A, = D + A, + A, (3)
The Journal of Physical Chemistry, Vol. 83, No. 11, 1979
1423
where D gives the point-dipole contribution and A, and A, give the dipolar interactions due to unpaired spin in p, and p, orbitals, respectively, centered at the bound F-. The constant for the isotropic, scalar interaction can be decomposed into two terms, one representing a polarization of ligand J? ns electrons by unpaired spin in ligand p orbitals and the other, the remaining Fermi contact interaction. Following well-known p r o ~ e d u r e s ,the ~ ~ randomly fluctuating interaction represented in eq 1 and 2 can be used to derive expressions for the relaxation rates analogous to the Solomon-Bloembergen equations:
-
\
(4b) where TlP and TZpare the measured relaxation times, corrected for the effects of nonspecific binding (by subtraction of F- relaxation rates in the presence of apoenzyme, a t equivalent concentrations); TIMand T2M are relaxation times for F- bound to enzyme Cu(I1); T~~ is a correlation time for modulation of the hyperfine interaction; uI is the angular nuclear Larmor frequency; and p M is the fraction of F- bound to Cu(I1). The correlation time T~~ is given by 7,c-I = ~ ~ 8 + 1 ' 7M11, where T~~ is the spin-lattice relaxation time for the Cu(I1) unpaired electron and 7M is the mean lifetime of F- a t the Cu(I1) site. The use of eq 4a,b presupposes that exchange is fast between free fluoride in bulk solution and fluoride bound to the enzyme Cu(I1) and that only a single bound site is represented by eq 4a,b. A number of other assumptions and approximations have been made or are implicit in the derivation of eq 4a,b. Those pertinent to our analysis are the following: cylindrical symmetry for the anisotropic hyperfine tensor, A ; neglect of g tensor anisotropy; neglect of the term 7;l in the expression for 71;' on the basis that 7, is much larger than T M or 7lS,where T, is the rotational correlation time; neglect of terms of the form [ 1 + ws2~2:]-1 and [l + u~2722]-1 on the assumption that u97zeis much (here T~~ is the electron spin-spin regreater than lZ1 laxation time, T~~~ = 7 g 1 7M-l and us is the angular electron spin Larmor frequency); finally, the use of eq 1 as a starting point for the relaxation rate expressions is appropriate only if there is but one thermally populated Kramers multiplet, as is the case for C U ( I I ) . ~ ~ Equations 4a,b can be rearranged into a form more suitable for the analysis of the frequency and temperature dependence of the relaxation rates:
+
G o ' = PJ,2 =
--[+
5u
(1
-112 WI
~
3u
x ) TlP 2(1
+ x)
- 11
(5b)
where x = 5/4(Ai2/A,2) and CE is the analytical concentration of enzyme. The parameter u,which is obtained from measured relaxation rates, exhibits the temperature and frequency dependence of the correlation time r I cif IT^^ is appreciably larger than 0, since x should be temperature and frequency independent.
1424
The Journal of Physical Chemistry, Vol. 83,
No. 11, 1979
TABLE I: Relaxation Rates for F- in the Presence of Galactose Oxidase' temp, "C 50
freq, MHz 26.0b 56.4 94.2
0.321 0.361
2.57 2.69
26.0 56.4 94.2
0.233 0.228
0.516 0.628 0.734
2.20 2.72
30
26.0 56.4 94.2
0.141 0.138 0.138
0.381 0.370 0.441
2.13 2.11 2.70
20
26.0 56.4 94.2
0.0893 0.0796
0.255 0.225 0.226
2.02 2.34
26.0 56.4 94.2
0.0503 0.0444
0.152 0.130 0.118
2.08 2.16
10
V
uc
(UT,n) 0.855 0.986 1.15
40
R. J. Kurland and B. J. Marwedel
l/Tin = I/(T~,CE)(see text). Values taken for C, = 3.0 X MbC= ~ 1.015 M;values times (in units of M-' s-I). T , , values at 26.0 MHz and temperatures other than ambient have not been used. u = (T,,/T,, 1 / 2 ) ; (see text); ~ ~ " ( 9 4 . =2 )2.62 (10" value not used), uav(56.4) = 2.20.
- 26 MHz I--
a
The frequency dependence of rlC,which would arise from that of rlS,is not altogether well understood for Cu(I1) proteins. T h e Solomon-Morgan-Bloembergen formulationz2has been used to analyze the bound water spin-lattice proton relaxation for superoxide dismutaseZ3 and Cu(I1) carbonic a n h y d r a ~ e , but ' ~ an iterative calculation of the frequency dependence of the dominant correlation time at low field, r18,fits the observed data only qualitatively. Koenig has p r o p o ~ e that d ~ ~the ~ ~modulation ~ of the Cu(I1) anisotropic g tensor by ligand field fluctuations could serve as a mechanism for electron spin-lattice relaxation. The predicted frequency dependence of the electron spin-lattice relaxation rate for this mechanism plus others (dipolar, electron-nuclear scalar spin coupling, etc.) would take the form
where the first term, derived by analogy to that for nuclear spin-lattice relaxation by chemical shift ani~otropy?~ gives the contribution of g tensor anisotropy and the second, other sources of spin-lattice relaxation, and the r,, T', are correlation times. If the first term, due to g tensor anisotropy, dominates, then rlSshould decrease with increasing field (w,) until some limiting value is reached; if the second term dominates, then rlSwill increase with increasing field. If the two terms are comparable, one would expect a minimum in r I sat some field (a,)determined by the values of A , B, r,, and r', in eq 6. Results and Discussion Values of the observed, normalized relaxation rates, l/Tln = 1/(T&E) and l/Tzn= l / ( T & E ) , are given in Table I, along with the corresponding values of the parameter u. The relaxation rate values were obtained by interpolation from essentially linear plots of l/Tinvs. CE and In Tip vs. l/T.z6 The values of u appear to be approximately independent of temperature except possibly for the lower extreme, 10-20 "C, a t 94.2 MHz, so that an average value of u over the temperature range is taken, as listed in Table I.
I.....
0b
!
2
56 4 MHz 94 2 w i z
3
x
Figure 1. Plot of y = 3p,Aa2/CEvs. x = 5/4(Af/A82)calculated from eq 5b, text, and the values of u,, X (1 f 0.10) listed in Table I. The hatched region is that for acceptable solutions of xand y , corresponding to f10% error limits on the relaxation rates.
A 10% variation is assigned to the (presumably) temperature independent value of u obtained as the average over the temperature, in order to test the sensitivity of the subsequent analysis to errors in the relaxation rates. These values of u , a t a given temperature, are then used to calculate the quantity y = PMA?/CE as a function of x = 5/4 (Alz/A,2)via eq 5b; the intersection of two or more such bands for different frequencies wI should then give a region in which the values of x and y give solutions to eq 5a,b corresponding to the specified error limits. The results of such a calculation for the 30 "C data a t 26.0, 56.4, and 94.2 MHz are displayed in Figure 1. It is evident that a wide range of values for y lie in the region formed by the intersections of the curves for the three frequencies; thus y is quite sensitive to errors in the relaxation rates. On the other hand, the range of x. in the acceptable solution region is between 1.8 and 2.6 and is, therefore, not as sensitive to errors. Curves calculated a t 40 and 50 OC for the 56.4- and 94.2-MHz data are similar to those in Figure 1and give essentially the same range for acceptable values of x , 1.9 to 2.8. Accordingly a value of x = 2.35 is taken. With this value of x , the correlation time, rlC,a t 94.2 MHz may be calculated via eq 5a and the average value of u listed in Table I to give rlC(94.2 MHz) = 7.01 X s. The value of 1 a?rl> a t 56.4 MHz is too close to 1 to yield an accurate value of rlC;however, rlCat 56.4 MHz may be determined by use of eq 4a,b from the ratios of the observed relaxation rates a t a given temperature and different frequencies, if the parameter x and 71c (94.2 MHz) are known. The quantity pMcan be estimated from the dependence of the relaxation rates of fluoride concentration, CF, via the relation pM= KfCF/(1 4- KfcF). From the values of normalized relaxation rates a t 50 "C and a t several Fconcentrations an approximate value for Kf(50"C) = 0.061 is obtained. This value for Kf and the values for x , rlC(94.2 MHz), and rIc (56.4 MHz) can then be used to obtain a preliminary estimate for A: from the 50 "C relaxation data. This estimate for A: is used to obtain values for p~ a t lower temperatures and the resulting values for K f are fit to a Van't Hoff type relation, -R In K f = A + AHo/T.
+
The Journal of Physical Chemistry, Vol. 83, No. 11, 1979
Fluoride as a NMR Probe of Galactose Oxidase
TABLE 11: Calculated and Experimental Normalized Relaxation Ratesa and Correlation Times ( T ' c ) b -26.0 MHz 56.4 MHz 94.2 MHz temp, C
1/Tin
1lTzn
calcd 1 ' calcd 2d calcd 3e 40 exptl calcd '1 calcd 2d calcd 3e
0.335 0.312 0.313
0.853 0.922 0.857 0.859
0.208 0.214 0.211
30 exptl
O
50 exptl
T1C
1/Tin
1/T*n
5.41 5.03 5.04
0.321 0.353 0.321 0.341
0.986 0.998 0.963 0.962
0.573 0.574 0.589 0.579
5.41 5.56 5.02
0.233 0.220 0.218 0.227
0.147 0.124 0.139 0.137
0.386 0.342 0.383 0.377
5.41 6.05 4.99
calcd '1 calcd 2d calcd 3e
0.0713 0.0884 0.0854
0.253 0.196 0.244 0.235
10 exptl calcd 1' calcd 2d calcd 3e
0.0391 0.0558 0.0501
0.147 0.107 0.155 0.138
calcd 1' calcd 2d calcd 3e 20 exptl
1/Tin
TIC
1/Tzn
TIC
5.90 5.69 5.68
0.361 0.373 0.378 0.371
1.15 1.16 1.21 1.16
7.01 7.15 6.96
0.628 0.621 0.616 0.639
5.90 5.85 5.58
0.228 0.232 0.232 0.241
0.734 0.724 0.722 0.740
7.01 6.99 6.57
0.138 0.131 0.140 0.144
0.370 0.371 0.382 0.406
5.90 6.09 5.41
0.138 0.139 0.135 0.145
0.441 0.432 0.419 0.436
7.01 6.79 5.89
5.41 6.74 4.91
0.0893 0.0759 0.0805 0.0851
0.225 0.213 0.229 0.238
5.90 6.36 5.02
0.0796 0.0794 0.0755 0.0799
0.226 0.245 0.232 0.234
7.01 6.53 4.96
0.0503 0.0412 0.0471 0.0484
0.130 0.117 0.135 0.123
5.90 6.84 4.70
0.0444 0.0436 0.0422 0.0427
0.118
5.41 7.79 4.77
0.136 0.130 0.123
1425
7.01 6.70 4.31
For nuclear relaxation (see text and a l / T i n= l/(T,,CE:] (see text and Table 1);values times (in units of M-' s-I). eq 4a,b); values times 10" (in units of s). ' Calculation 1 values taken from temperature independent r I c values; 7 , c at 26 MHz obtained from an assumed w s z dependence, by use of T~~ values at 56.4 and 94.2 MHz; root mean square (rms) deviaCalculation 2 values taken by fitting T~~ t o eq 6; rms deviation tion between calculated and experimental values: 10.7%. between calculated and experimental values: 4.8%. See Table I11 for T~~ parameter values. e Calculation 3 values taken by fitting T I C to eq 6 arid adjusting A H for F--GOase binding; rms deviation between calculated and experimental values: 4.6%. See Table I11 for parameter values.
The values of Kf from this least-squares fit are used to derive new values for A,2 and T~~ (56.4 MHz). The zeroth order values of Aa2,T~~ (56.4 MHz), and K f ( q were sufficiently close to those obtained from one cycle of the iterative calculation outlined above that additional cycles were not required. The value of T~~ a t 26 MHz can be obtained from an arisumed w,2 dependence and the values of 7lCat 56.4 and 94.2 MHz. The values for the relaxation parameters thus derived are given in Tables I11 (calculation 1) and IV. The values of the normalized relaxation rates calculated via eq 4a,b from the parameters determined by the above analysis are compared in Table I1 (calculation 1)with the experimentally determined values. The agreement is good a t higher temperatures (30-50 " C ) but deviations greater than 10% are present for some of the low temperature values. The systemiatic character of the low temperature deviations is evident in the plot of relaxation rates vs. frequency given in Figure 2. At temperatures below 30 O C the experimental values of both 1/Tlpand l/TZp appear to decrease with iiicreasing frequency (negative slope) whereas the assumeld w,2 dependence would give, as shown, a positive slope. An additional discrepancy, not directly evident in Figure 2 or Table 11, is the following: at low temperatures (10 and 20 " C ) T~~ values calculated from the experimentally derived values of l/TlbIare consistently about 10-15% lower than the T~~ values Calculated from l/TzM(at the same temperature and frequency). This result suggests that the apparent value, (1/T2M)app,may include an exchange lifetime ( T M ) contribution: ( 1 / T 2 M ) a p p = l / ( T z M + T M ) . The approximate value of T~ required to give the observed differences, TM 5 X is consistent with the limits specified in Table IW.Unfortunately the differences in the values of TIC from 1/T I M and 1/T2M are too small (just outside the stipulated error range) for T M and its activation energy to be determined accurately. Since the correction for T M would be smalller still a t higher temperatures, it will
-
Figure 2. Plots of observed relaxation rates, l / T l p and l/T2,,, vs. frequency at several temperatures; T ~ is, assumed to follow an us2 dependence; points represent experimental relaxation rates: . , 50 OC;0,40 O C , A, 30 O C ; 0 , 20 O C ; 0 ,10 O C .
be neglected in the other calculations outlined below. In any case, the inclusion of TM would not account for the apparently anomalous frequency dependence of 1/TIMand l/TzMa t low temperatures. Our initial assumption that T,, the rotational correlation time, is much greater than T ~ is C justified by the values derived for the latter (Tables I1 and IV). The StokesEinstein relation gives an estimate for T , of about s for GOase (molecular mass, 6.8 X lo4 daltons). Moreover the lack of a strong temperature dependence for T~~ is ; ~ T ~ - that ~ , consistent with a small contribution to T ~ from is to say, 7M-l is much smaller than T ~ and ; ~ so the approximate equality T~~ T~~ will hold in the frequency range 26-94 MHz. Then the frequency dependence of T~~ should , for example, by eq 6. follow that of T ~ as~ given, In order to account for the positive slope of ilC vs. frequency above and the negative slope below 30 "C, both terms in eq 6 must be taken into account, and one or both of the correlation times for electron spin relaxation, T,, T ' ~ , must be taken as temperature dependent. Even though the use of eq 6 to fit T~~ will yield smaller deviations ~
1426
The Journal of Physical Chemistry, Vol. 83, No. 7 1, 1979
TABLE 111: Parameters for Correlation Time Calculations' calculation
~b
2c
3d
AN"/Re ( K ) -5.33 X -5.33 X l o 3 -4.15 X l o 3 103 Af 0 2.88 x 10-3 4.47 x 10-3 Bf 1.47 x 0.886 x l o 2 ' 1.24 x 10" 102' r V (30 oC)f 4.63 X lo-'? 4.24 X ~ ' ~ ( oC)f 3 0 1.29 X 1.77 X 1.66 X lo-'* 10-12
-1.59 x 1 0 3 6.61 x 103 0 -1.03 x 103 o E act /Rg ' Values for A,', A,', and K , at 50 C (Table 111) used to determine 1 / T , M , ~ / T , Mr;I c assumed to follow eq 6. Calculation 1 : temperature independent r I c values at 56.4 and 94.2 MHz from analysis in text; r I c at 26 MHz determined from an assumed u s 2 dependence (A = 0 in eq 6) by use of T~~ values at 56.4 and 94.2 MHz. A, B, r v , and rIV (eq 6 ) and Eact/R, EIact/R chosen to f i t r l C values at 10 and 50 " C from experimental 1/T,, l / T 2 p values, and A N " set as for calculation 1. A$ adjusted to give E',,/R = 0 (for T ~ ' ) : A, B, T~ and r i V(eq 6 ) and values at 10 EaCtIR adjusted t o fit r I c from 1/T, , l/!Z'2p and 50 ' C. e Enthalpy change for &-GOase binding. Parameters for eq 6. g Activation energies for assumed temperature dependence of r v , r t V :rv = 72 exp(Eact/RT), rrV= T ' ' ~exp(EactIRT). Eact
O
TABLE I V : Relaxation Parameters for GOase-Cu( 11) F- and Aqueous CuF' parameter
GOase-Cu(I1) F- '
CuF+(aq)b
Aa Ai AiIA,
1.89 X l o s s - ' 2.59 x l o s s - ' 1.37 to l o - 9 sc 6.87 x lO-"s (94.2 MHz) (50 "C) 5.65 X 1 0 - ' o s (56.4 MHz) (50 C) 5.01 X lO-''s (26.0 MHz) ( 50 a C) 0.0689 M-l (50 "C)
8.2 x 1 0 8 s - ' 1.0 x 109 s-1 1.3
rMd 71s
KF
s
>2.5 X lO-''s (10.75 MHz)
1.0M-' (25 "C)
' This analysis; see text. Reference 8. Limits placed for T M - ~
