J. Phys. Chem. 1995, 99, 14217-14222
14217
A Theoretical Analysis of the 'H Nuclear Magnetic Relaxation Dispersion Profiles of Diferric Transferrin Ivano Beehi,**?Oleg Galas,+Claudio Luchinat," Luigi Messori,? and Giacomo Parigit Department of Chemistry, University of Florence, Via Gino Capponi 7, 50121 Florence, Italy, and Institute of Agricultural Chemistry, University of Bologna, Viale Berti Pichat IO, 40127 Bologna, Italy Received: January 26, 1995; In Final Form: June 27, 1995@
The magnetic field dependence of water proton relaxation rates of difenic transfenin solutions has been analyzed over the 0.01-200-MHz range. There is evidence of both fast and slow exchanging protons. The former provide the shape of the proton relaxation rate profile. The effect of ZFS and its disappearance when the Zeeman energy dominates the ZFS provide an inflection in the nuclear relaxation dispersion profile around 10 MHz. The experimental profiles can be quantitatively interpreted by taking into account (i) a rhombic ZFS of the iron(II1) ions, (ii) the change of the quantization axes along which the electron relaxation rates are defined on passing from the ZFS limit to the Zeeman limit, and (iii) the usual Zeeman limit field dependence of the electron relaxation rates.
Introduction Water proton longitudinal relaxation rates measured over a wide range of magnetic fields (nuclear magnetic resonance dispersion-NMRD) have proven to be very informative to describe the interaction of water with paramagnetic centers. The nuclear relaxation enhancements due to the presence of unpaired electrons were first calculated by Solomon in 1955 for the dipolar interaction' and by Bloembergen in 1957 for the contact interaction.* However, in the 1960s, it was soon realized that because of the splitting of the S manifold due to low-symmetry components, the above simple theories break d ~ w n . ~The -~ splitting of the S manifold can be due to zero field splitting (ZFS) when S > I12 andor to the interaction of the unpaired electrons with the metal nucleus spin. By the middle of the 1980s, it was shown that the effect of axial ZFS7-9 and of the hyperfine c o ~ p l i n g ~on. ' nuclear ~ relaxation can be treated within the Redfield limit'' by using the Kubo-Tomita formalism.l2 The theory of ZFS outside the Redfield limit was based on either the infinite-order perturbation theory for the electron spin relaxation' or the Liouville superoperator formalism. I 4 - l 7 Recently, the rhombicity of ZFS has been taken into consideration, first in the ZFS >> Zeeman limit183'9and then without this restriction;20corresponding theories and computer programs have been developed. Besides the intrinsic complexity of the theory, the difficulties in the interpretation of the NMRD profiles arise from the fact that it is often possible to fit the experimental data equally well with more than one set of parameters. Some aspects of this fundamental ambiguity were illustrated quite early by Koenigz' and Dwek.z2 Therefore, it is very important to understand how the theoretical parameters translate into the characteristic features of the experimental profiles in order to select the right set through physical considerations or independent methods. The splitting of the S manifold affects the NMRD profiles when the splitting is larger than or of the order of the Zeeman energy, provided that the electron-nucleus correlation time (7,) is long enough that ZFS >> fir,-'. These conditions are commonly met in the case of metalloproteins,' where z, is dominated by the electron relaxation time (re); a general
' University of Florence.
*
University of Bologna. @Abstractpublished in Advance ACS Abstracts, August 15, 1995.
computer program has been recently developed by us to analyze the experimental profiles under these conditions.20 Here we attempt the interpretation of the NMRD profiles of diferric transfemn according to the outlined strategy. The NMRD curves of iron transfemn were first reported in 1969 by Koenig et al.;3 a contribution from slow exchanging protons was soon suggested, together with a contribution from fast exchanging proton^.^ In recent years, significant progress has been made in the understanding of the biochemistry of iron transferrin and in the elucidation of the structural features of its iron binding sites. In particular, Bakerz3and L i n d l e have ~~~ solved the X-ray structure of this family of proteins and determined the local structure of the metal environment to a good resolution. In both sites, the metal is hexacoordinated to two tyrosine residues, one histidine, one aspartate, and to the bidentate synergistic anion (bicarbonate) in a distorted octahedral geometry. No solvent molecule is directly coordinated to the metal. We have now re-recorded the experimental NMRD profiles of diferric serum transfemn over a wider magnetic field range and attempted their full interpretation in light of the recent advancements both in NMRD theories and structural knowledge of the system. Remarkably, we have found that the contribution to NMRD from the fast exchanging protons has a peculiar profile which is ascribed to static ZFS. The inclusion of a rhombic component of the static ZFS is shown to be necessary for the theoretical reproduction of the experimental data, as well as of an up to now never described magnetic field dependence of the electron relaxation time.
Materials and Methods Human serum transferrin was purchased from Sigma Chemical Co. as apoprotein and was used without further purification. Protein solutions for NMRD studies were about 1 mM. Diferric transferrin was prepared by addition of a stochiometric amount of a standard iron(II1) chloride solution to apotransfemn in the presence of 20 mM sodium bicarbonate, at pH 7.4. The concentrations of apotransfenin and difemc transferrin were determined spectrophotometricallyas previously reported.25The C-terminal monofenic transfemn was prepared by addition of 1 equiv of iron(II1) to apotransfenin to pH 6.0. The pH was then raised to 7.4 with sodium hydroxide.
0022-365419512099-14217$09.00/0 0 1995 American Chemical Society
14218 J. Phys. Chem., Vol. 99, No. 39, 1995
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Figure 1. Water proton NMRD profiles of the diferric transferrin solution at different temperatures (0 = 278 K, 0 = 283 K, + = 288 K, * = 293 K, 0 = 298 K, A = 303 K, 0 = 308 K) over the 0.01200-MHz interval.
The longitudinal spin relaxation rates of water protons in the 0.01 -50-MHz range were measured at different temperatures using a Koenig-Brown field cycling (FC) relax~meter*~.~' and at 90 and 200 MHz using the inversion recovery method on Bruker CXP90 and Bruker MSL200 instruments, respectively. The estimated errors on the individual data points were usually lower than 1% for the measurements performed on the FC relaxometer and lower than 5% at 90 and 200 MHz. The paramagnetic contribution to the water proton relaxation rates has been calculated by subtracting the values of proton relaxivities for a sample of apotransferrin from those for difenic transferrin at the same concentration and the same temperature. For the data obtained at the relaxometer, the errors in the paramagnetic enhancement values-subtracted quantities-are in the range 2-3%, being maximal at the lowest field and lowest temperature because the relaxivities of diferric transferrin and apotransferrin solutions are maximal under these conditions. The errors in paramagnetic enhancements at 90 and 200 MHz were still lower than 5% because at these frequencies the diamagnetic relaxation was dispersed. The results are shown in Figure 1.
Theoretical Section The description of relaxation phenomena, caused by the dipolar and contact interaction with the electron spin (9, through -the Kubo and Tomita formalism'2 allows the inclusion of a realistic description of the electronic spin system in terms of its appropriate static spin Hamiltonian. In general, the static electron spin Hamiltonian for molecules where a metal nucleus is not magnetic can be written as
+
H = pBS.g.B0 D(S: - S(S
+ 1)/3) + E(Sx2- S):
(1)
where Bo is the static magnetic field, g is the electron g tensor, and D and E are the axial and rhombic components of the zero field splitting tensor. As a result,20 we obtain for the field dependence of TIM-]a function which contains many unknown parameters TIM-
1-
-
where the summation is over all the transitions of the electron spin system,fi and gi are the coefficients of the spectral density terms, we,;is the difference between the eigenvalues of the static electron spin Hamiltonian (l), w~ is the nucleus Larmor frequency, r is the distance between electron and nuclear point dipoles, a is the constant of contact interaction, 0 and p are the polar angles which specify the position of the investigated nucleus in the molecular coordinate frame, /?and y are two of the three Euler angles which describe the orientation of the molecular coordinate frame with respect to the laboratory one (they are not explicitly present in Hamiltonian (1) because the electron spin operator in the Zeeman term is written in the laboratory coordinate frame, while the electron spin operators in the ZFS terms are written in the molecular coordinate frame which diagonalizes the ZFS tensor), and zc is the correlation time of the relaxation process. At the initial state, a single z, is considered. In turn, we depends on the parameters which characterize the Hamiltonian in eq 1
In general, the inverse of
tcis
the sum of few terms
for dipolar interaction and
for contact interaction, where re, tr,and zm are the electron relaxation, the rotational, and the chemical exchange correlation times, respectively. There is general agreement2*that the water proton relaxation rate caused by the paramagnetic metal is essentially dipolar in nature in macromolecules, even when the water is bound to the metal center. We could not reveal any effect due to contact interaction. If the proton interacting with the paramagnetic center can exchange with the protons of bulk water, the effect of the exchange rate (t,-') on the measured T1-l is governed by the following equation:
T,-l = m&T,,
+ 'J1 + Tldia-'
where mf is the molar fraction of the interacting protons with respect to solvent protons and Tldia-' is the contribution of diamagnetic relaxation. Sometimes, as in the case of diferric transferrin, one finds that the electron relaxation time (re)is field dependent. The theory for field dependence of re in the presence of static ZFS is not available yet. A model is available when there is not static ZFS, but an instantaneous ZFS is generated by solvent collisions:29 Ie'
-
+ (7)
I
where (B2) is the average quadratic transient ZFS, zv is the correlation time for the electron relaxation, S is the electron spin quantum number, and wsis the electron Zeeman frequency. We have calculated te-'also by using in the place of osthe calculated f ' / 2 electron transition frequency, we,in the presence of static ZFS. This is reasonable because it has been shown
'H NMRD Profiles of Diferric Transferrin that the other electronic transitions have negligible intensity? In any case, the results are practically identical. Recently, a general computer program has been developed20 to calculate the paramagnetic contribution in TI-' along the above guidelines, in slowly rotating systems. Of course, more than one kind of proton interacting with the paramagnetic center can be analyzed.
J. Phys. Chem., Vol. 99, No. 39, 1995 14219 51
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Results and Discussion The experimental 'H NMRD profiles of diferric transferrin aqueous solutions, at various temperatures, are shown in Figure 1. Noticeably, all profiles exhibit two inflections between 0.01 and 15 MHz, the first centered around 0.2 MHz and the second starting around 10 MHz. As usual, the first inflection is due to the wedispersion, which corresponds to the transition. Such dispersion provides an approximate value of the correlation time of 1 x s. The second inflection is attributed by us to the transition from the dominant ZFS limit to the dominant Zeeman limit. Because it occurs at a proton Larmor frequency close to 10 MHz, we can estimate a D value of -0.2 cm-'. In the ZFS limit, the quantization axes are determined by the internal molecular field described by the ZFS tensor, and nuclear relaxation, for the half-integer electron spin, is dominated by the electronic transitions in the lowest Kramer's doublet only.8.9.17,30~31 In the Zeeman limit, the usual Solomon equation holding, all five electronic transitions equally contribute to nuclear relaxation, and the electron quantization axis is determined by the direction of the extemal magnetic field. This gradual passage from one limit to the other is revealed by NMRD as an inflection centered at hw, D. We will show that this passage can be theoretically reproduced as has been predicted for the axial ZFS by Sharp.31 The consequence of this observation is that for ZFS within the NMRD accessible range of the electron Zeeman energies (-10 cm-') the magnitude of ZFS can be estimated by NMRD. Noteworthy, from inspection of Figure 1, we observe that the ratio between the values of the relaxation rates before and after the we dispersion is smaller than 10/3, the characteristic ratio obtained considering only the Zeeman term in the static Hamiltonian (1); we also observe that the relaxation rates invariantly increase between 20 and 50 MHz and then decrease. This bell-shaped relaxivity profile between 20 and 200 MHz may be explained as a consequence of the field dependence of
re. Upon comparing the NMRD profiles at various temperatures, one notices that for temperatures > 20 "C, relaxivity markedly increases with increasing temperature. For slowly rotating molecules, rc coincides with the electron relaxation time (which has been set to be around 1 x s; r,,,is usually much longer than re and cannot influence the correlation time). The electron relaxation time is temperature dependent, and its dependence may be viewed like an activation process and described by the Arrhenius law. The proton relaxation rates are proportional to re;thus, by assuming only one kind of relaxing protons, one would expect to observe a decrease of the proton relaxation rates with increasing temperature. According to this reasoning, we can state that the unusual temperature dependence observed in the NMRD profiles of diferric transferrin probably implies the occurrence of relevant exchange processes around the metal site as previously suggested by Koenig and S~hillinger.~ The X-ray structure of diferric t r a n ~ f e r r i n demonstrates ~~.~~ that the polypeptide chain is folded into 2 lobes, each containing some 330 amino acids and a single iron-binding site. The iron ions are se arated by numerous chemical bonds and are situated about 40 apart.
8:
0.01
0.10
I .00 10.00 Proton Lannor Frequency (MHz)
100.00
Figure 2. Analysis of the 'HNMRD data at 278 K according to a model with axial ZFS. The respective parameters are re = 1.43 x s, D = 0.2 cm-I, 19 = 0" (solid line), 30" (dashed line), 60" (dotted line), 90" (dotted-dashed line). The distances between the protons
and the paramagnetic center have been adjusted in each profile separately.
No evidence of magnetic coupling is present in the EPR spectra, which are typical of isolated high-spin iron(III).33,35-43 Furthermore, we have recorded the relaxivity profile of the C-terminal monoferric transferrin at 278 K (not shown). The obtained paramagnetic enhancement of water proton relaxivity is equal to half of that of diferric transferrin under the same experimental conditions within the experimental error. This confirms that we are allowed to neglect also a weak coupling of the electron spins of iron ions which, in principle, could influence the electron and therefore the proton relaxation rates. With this in mind, we have tried to analyze quantitatively the experimental profiles. In our calculations we have assumed that (1) the two paramagnetic centers present in the diferric transferrin molecule are essentially equivalent as supported by several independent methods3*and are not magnetically coupled and (2) in each site there are protons interacting with the paramagnetic center and in fast exchange with the bulk solvent protons, plus protons, close the paramagnetic center, slowly exchanging with bulk protons. All calculations were performed with g equal to the free electron g factor because the ground state for high-spin iron(111) is 9. In the simulations of the EPR spectra of ferric transferrins, the value of g is usually assumed to be close to 2.00 and isotropic.33 For the analysis, we have treated independently the TI-'dependence on a constant re and the TI-' dependence on a field-dependent re. This has been made possible by an effective field dependence of re above 15 MHz. The profiles were simulated by assuming either axial (A) or rhombic (B) ZFS. I. Analysis within an Axial ZFS Model. The analysis of the experimental NMRD profile up to 15 MHz according to a model implying an axial ZFS is shown in Figure 2 for the 278 K case. The positions of the two inflections in the experimental NMRD curves are properly reproduced by setting the values of re and D to around s and 0.2 cm-', respectively. The angle 6 between the direction of the metal nucleus-proton vector and z axis of the molecular coordinate frame determines both the ratio between the values before and after the We dispersion and the shape of the inflection caused by ZFS.34In order to reproduce the profiles up to 1 MHz, we had to select angle values around 90"; with such values, however, the behavior at the frequencies of the second inflection could not be reproduced (see Figure 2). It follows that the parameters
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available in an axial ZFS model cannot be adjusted to satisfactorily simulate the whole experimental profiles. 11. Analysis within a Rhombic ZFS Model. From Figure 3, it can be easily seen that the ratio between the values before and after the we dispersion can match the experimental values by adding a rhombic component, E, to the ZFS while still keeping a "good" shape of the ZFS inflection. We fitted the data by assuming the same values for the parameters r, D, E, 0, and p, at each temperature and a temperature dependence for z, of the type re-' = kle-kz'T. We assumed that there are two protons interacting with the
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paramagnetic center and in the fast exchange regime, probably corresponding to a water molecule. In any case, a different number of protons would only change the value of the distance between the protons and the paramagnetic center. The fittings on the parameter tm have been performed separately for each temperature assuming one proton to be in the slow exchange regime. If n protons instead of one are in the slow exchange regime, we must consider correspondingly the value of tmto be equal to n times the value obtained assuming n = 1. We noted that the temperature dependence of zm is well described by the Arrhenius law, with constants kl = 6.58 x 10l6 s and k2 = 8418 K, where zm-' = kle-k2/T. The best fitting up to 15 MHz is shown in Figure 4, and the corresponding parameters are shown in Table 1A. From the fitting of this low-field part, we have found a value of D = 0.2 cm-' and an E D ratio close to the maximum allowed These values of ZFS parameters are reasonably consistent with the values of D (0.15-0.32 cm-I) and E/D (0.22-0.325) obtained from other technique^.^^,^^-^^ The above theoretical analysis of the NMRD profiles of difemc transferrin reveals that the resulting parameters may be roughly classified into two groups. The first group (re,D) includes those parameters that are responsible for the main features of the profile, the second group (E, r, 0,p, tm) those that determine the relative amplitude of each feature. We have seen that and D control the position of the fist two inflections. 111. The Field-Dependent re Region. The solid lines in Figure 4 have been obtained by assuming that the electron relaxation time is field independent and by fitting the experimental points from low fields up to 15 MHz. Above 15 MHz, the bell-shaped T1M-I profile forces us to include a fielddependent t e into the theoretical approach. The results obtained
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Figure 4. Best fitting analysis of the IH TI-' NMRD profiles of the diferric transfemn solution at different temperatures over the 0.01-15-MHz interval with tefield-independent parameter (solid lines) and extrapolation up to 200 MHz imposing eq 7 for field dependence of t e(dash lines). (A) 278 K, (B) 283 K, (C) 288 K, (D)293 K, (E) 298 K, (F)303 K, ( G ) 308 K. The corresponding parameters are reported in Table 1A.
'H NMRD Profiles of Diferric Transferrin
J. Phys. Chem., Vol. 99, No. 39, 1995 14221
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Figure 5. Best fitting analysis of the 'H T1-I NMRD profiles of the diferric transferrin solution at different temperatures over the 0.01-2-MHz interval (solid line): (A) 278 K, (B) 293 K, (C) 308 K, (D) 283 K, (E) 288 K, (F) 298 K, (G) 303 K. The corresponding parameters are reported in Table 1C. Dotted lines indicate the best fitting from 50 to 200 MHz obtained with the parameters reported in Table 1B. TABLE 1: Parameters which Account for the Experimental Water Proton NMRD Profiles of Diferric Transferrin A: 0.01- 15 MHz ~~~~
D,cm-I 2.286 x 10-10e513'T 0.2 has
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303 308 218 283 288 293 298 1.45 1.40 1.36 1.32 1.28 1.24 1.21 0.206 0.113 0.091 0.053 0.028 0.015 0.011
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283 288 293 298 303 308 1.35 1.35 1.30 1.25 1.15 1.10 r, = r:, ns 0.35 0.34 0.33 0.32 0.31 0.305 0.30 rm/n:ms 0.206 0.113 0.091 0.053 0.028 0.015 0.011 Considering two protons in fast exchange. For the dashed lines in Figure 4, the parameters of eq 7 are (E2)= 0.0325 cm-I and t v= 1.82 x 10-11e-513'rs.n is the number of protons in slow exchange. T, K rx,ns
218 1.40
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using eq 7 for a field dependence of t, are shown in Figure 4 as dashed lines, the previous values for the other parameters being the same. It appears that the fitting is very poor, in that the w1 dispersion occurs too early to allow for a substantial
increase of TIM-I around 100 MHz. In other words, the parameters of Table 1A do not account for the high-field part. Equation 7 should probably be trusted when Zeeman > 5 ZFS, Le., at least for the experimental points at 50,90, and 200 MHz. If we try to fit only the points at 50,90, and 200 MHz with the Solomon equation and eq 7, indeed the pattern of the three points is reproduced with the parameters presented in Table 1B. The two fittings yield a difference in the value of the parameter r, which is well outside its uncertainty. IV. An Attempt to Reconcile Low-Field and High-Field Fittings. Between the high-field and low-field approaches, one has to choose which is more reliable, Le., which approximations have indeed been made in the two cases, although they are generally accepted. Indeed, at magnetic fields tending to zero, in a rhombic ZFS case, we have three electron relaxation times: along the x axis (zJ,along the y axis (t,,), and along the z axis (zz) for the relaxation of the S,, S, and Sz components of electron spin S34(see refs 44 and 45 for the axial ZFS limit). Here x , y , and z are the axes of the molecular coordinate frame which diagonalizes the ZFS tensor. zx, z,, and trare transformed into t e l along the extemal magnetic field and t e 2 orthogonal to it according to the variation of the quantization axes on passing from the ZFS limit to the Zeeman limit. Generally, this aspect has always been neglected: in the absence of ZFS at low magnetic fields, zel = ze2, and at large magnetic fields, nuclear relaxation depends only on t e l . That is why a single re is considered as we have done in the preceding sections. We have introduced in the program described above three values for ,z, z,, and z, which, in general, can be all different. Because of the symmetry of the molecular field in an axial ZFS case, zx = z,, and in a case of maximal rhombicity (E/D= l/3), t, = z.,
14222 J. Phys. Chem., Vol. 99, No. 39, 1995
Since the rules of transformation of tx,t),and t, for the passage from the ZFS limit to the Zeeman limit are not known, we fitted the relaxivity profiles up to 1-2 MHz of proton Larmor frequency where ZFS L 10-fold Zeeman. We assumed E D = '13, r = 4 8,, and the values of t m from Table 1A. The theoretical profiles together with experimental points are shown in Figure 5 and the parameters are presented in Table 1C. The results are encouraging because now the parameters r and t m assume the same values both in the low- and in the high-field regions. This theoretical analysis leads us to rethink our previous interpretations of low magnetic field TIM-I values even in the case of the occurrence of the hyperfine coupling of the electrons with magnetic nucleus, Le., everytime there is an internal field of the molecule. While this success may be taken as an a posteriori confirmation of the validity of the assumption of two t values at low field, the assumption itself will need further experimental support. We can only stress again that, using the existing theories, we found no other way to obtain a satisfactory fitting of low- and high-field data using the same r and t mvalues. The obtained r value of 4 8, is indicative of the presence of fast exchanging water not directly bound to the metal. This water is still associated with the protein in such a way as to experience the same reorientational time and, therefore, with the correlation time for the interaction with the paramagnetic center dominated by the electronic relaxation time.
Concluding Remarks The analysis of the water proton NMRD profiles of diferric iron transferrin has taught us the following: 1. There are two sets of protons, one in slow and the other in fast exchange, both of them interacting with the paramagnetic center. 2. The fast exchange protons are at about 4 8, from iron nucleus. 3. The above results can be obtained with a D of about 0.2 cm-I and E/D G l/3. These results are consistent with those obtained from the analysis of the EPR spectra.33135-43 4. There is evidence of a continuous change of the electron relaxation time with increasing magnetic field. At low magnetic field, there is a transition from electron relaxation along the directions of the internal molecular field to the electron relaxation along the directions which are parallel and perpendicular to the extemal magnetic field. At magnetic fields above 35 MHz there is a variation of the electron relaxation time of the type of that described in eq 7.29 5. Although conceptually required$5 it is possible that the two sets of electron relaxation times relative to internal or external quantization axes are, in general, not so different and their differentiation has insignificant effects. In the present case, for the first time, this differentiation is required.
Acknowledgment. This work has been partially financed by Consiglio Nazionale delle Ricerche. The financial support for O.G. and G.P. by Bracco S.p.A., Milan, Italy, is also gratefully acknowledged. References and Notes (1) Solomon, I. Phys. Rev. 1955, 99, 559. (2) Bloembergen, N. J . Chem. Phys. 1957, 27, 575,
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