Chapter 4
NMR
of Paramagnetic Systems
Magnetically Coupled Dimetallic Systems (Cu Co Superoxide Dismutase as an Example) Downloaded by MONASH UNIV on December 16, 2015 | http://pubs.acs.org Publication Date: June 21, 1988 | doi: 10.1021/bk-1988-0372.ch004
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Ivano Bertini , Lucia Banci1, and Claudio Luchinat
1Department of Chemistry, University of Florence, 50121 Florence, Italy 2Institute of Agricultural Chemistry, University of Bologna, 40126 Bologna, Italy Paramagnetic systems are widespread in macromolecules of biological relevance. A number of these contain dimetallic clusters with at least one paramagnetic center. The recent advances in obtaining H N M R spectra of paramagnetic macromolecules and in understanding the theory for electron -nuclear coupling will be presented, with emphasis on magnetically coupled dimetallic systems. The analysis of the H N M R spectra of Cu2Co2-superoxide dismutase will be presented in some detail to show how important structural and chemical information can be obtained using this approach. Other pertinent systems will be briefly discussed and the prospective uses of the technique will be critically evaluated. 1
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Dimetallic systems are common among metalloproteins and their characterization is important for understanding the nature of the interaction between the two metal centers. A dimeric unit may incorporate a metal ion that is a catalytic center and another one with some function, ranging from a structural role to regulation of enzymatic activity. Examples of such sites include erythrocyte superoxide dismutase (SOD), which contains copper(II) and zinc(II) ions, the latter being essentially structural and the former catalytic (1,2), and alkaline phosphatase, which has two zinc ions, one with a catalytic role and another one which is regulatory (3). The zinc ion can be replaced by several other metal ions, sometimes without a significant loss of enzymatic activity (4). Other examples of bimetallic systems include those formed by iron(II) and iron(III), e.g. the reduced Fe2S2 cluster in ferredoxins (5) and the mixedvalent dimetallic units contained in reduced uteroferrin (6,7), reduced acid phosphatases (6) and semimet-hemerythrin (7-9). This latter group of proteins have active sites which consist of a paramagnetic metal ion with fast electronic relaxation times (iron(II)) interacts with another paramagnetic metal ion with slow electronic relaxation times (iron(III)) (10). Such an interaction results in binuclear complexes with favorable N M R properties. 0097-6156/88/0372-0070$06.00A) © 1988 American Chemical Society
In Metal Clusters in Proteins; Que, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1988.
Downloaded by MONASH UNIV on December 16, 2015 | http://pubs.acs.org Publication Date: June 21, 1988 | doi: 10.1021/bk-1988-0372.ch004
4. BERTINI ET AL.
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NMR of Paramagnetic Systems
The proteins containing a zinc atom in the dimetallic unit can be manipulated in such a way as to achieve similar situations, like CuCo or C u Ni derivatives of CuZn native systems (1,11—14). The unpaired electron in an isolated copper(II) ion relaxes slowly, whereas the electrons of cobalt(II) and nickel(II) relax rapidly. The occurrence of magnetic coupling has a major effect on the electronic relaxation time of the slowly relaxing metal ion; its electronic relaxation times are largely reduced with the result that *H N M R signals of ligand protons can be readily observed, as in the case of metalloproteins containing only the fast-relaxing metal (10). The N M R parameters of the coupled system change with respect to the single ion systems, and such artificial metal pairs may provide a tool for the N M R investigation of slowly relaxing systems, like copper proteins, which would give rise to signals too broad for detection. In homodimeric systems like the oxidized form of Fe2S2 ferredoxins, the oxidized and reduced forms of hemerythrin, CU2CU2SOD etc., the magnetic coupling does not produce any major change in the electronic properties of the ions (15). We will discuss here the N M R parameters in paramagnetic systems and the effect of the magnetic coupling. One example will be discussed in detail, the CU2C02SOD system, and other relevant systems will also be mentioned. N M R Parameters in Paramagnetic Systems As far as paramagnetic systems are concerned, the relevant N M R parameters are the isotropic shift, i.e. the chemical shift minus the shift of an analogous diamagnetic system, and the T f and T enhancements ( T i and T ^ " ) (10). Such enhancements are due to the coupling between the unpaired electron(s) responsible for paramagnetism and the resonating nuclei. As will be shown in more detail, electronic relaxation times are very short compared to the nuclear relaxation times and the coupling provides further pathways for nuclear relaxation whose rate depends on the value of the electronic relaxation times, among other factors. 1
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The isotropic shift. The isotropic shift is the sum of two contributions: the contact and the dipolar contributions. The former is due to the presence of unpaired electron density on the resonating nucleus. The latter arises from the anisotropy of the magnetic susceptibility tensor, modulated by the distance between the unpaired electron and the resonating nucleus, and is also dependent on the orientation of the metal nucleus vector with respect to the principal axes of the magnetic susceptibility tensor. Some problems arise when the spin derealization is taken into account in calculating the dipolar coupling, but we will not address this problem except when strictly necessary. The effect of magnetic coupling on the above parameters is negligible as long as the energy levels arising from magnetic coupling are equally populated at the temperature of the experiment. If we consider, for example, two S = 1/2 electron spins, they give rise to two magnetically coupled S' = 0 and S' = 1 spin states. As long as the separation of these states, which is equal to J if the spin Hamiltonian for the interaction is written as H = J Si#S
2
(1)
is small compared to kT, they are equally populated regardless of the ferromagnetic or antiferromagnetic nature of the coupling. Under these
In Metal Clusters in Proteins; Que, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1988.
Downloaded by MONASH UNIV on December 16, 2015 | http://pubs.acs.org Publication Date: June 21, 1988 | doi: 10.1021/bk-1988-0372.ch004
72
METAL CLUSTERS IN PROTEINS
circumstances the magnetic susceptibility is not altered by the magnetic coupling. Since the contact shift depends on the magnetic susceptibility, it should also remain unaltered. In other words, weak magnetic coupling does not change the contact contribution of a metal to the resonating nucleus and, if the nucleus interacts with two metal ions, the contact shift is strictly additive (16—18). This conclusion also holds in practice for the dipolar shift, although even small perturbations to the energy levels may change the orientation of the magnetic susceptibility tensor within the molecule, in principle. When J is of the same order of magnitude as kT, the magnetic susceptibility is reduced (if the coupling is antiferromagnetic) or enhanced (if the coupling is ferromagnetic) according to the Van Vleck equation. A n investigation of the temperature dependence of the shift may provide information on the value of J , if the hyperfine coupling is independently determined or assumed to be known (19) (although in principle the latter can also be parametrized). Longitudinal relaxation rates. This section considers separately the cases of homodinuclear and heterodinuclear systems. In the former case, an unpaired electron feeling another electron with the same spin lifetime should not affect the longitudinal relaxation rate, unless the new energy levels arising from the coupling provide additional electron relaxation mechanisms. The only example available in the literature that addresses this interaction is provided by CU2CU2SOD. Water N M R relaxation experiments show that the electronic relaxation time of copper at the native copper site is not affected by the presence of the copper ion at the zinc site, despite an antiferromagnetic coupling constant of 52 c m (20). The problem becomes more complicated when the magnetic coupling occurs between two different metal ions, one of which has a long electronic lifetime and the other has a short electronic lifetime. It is clear that, when the slow-relaxing electron starts feeling the fast—relaxing electron, the former may start exchanging energy with the lattice through the latter and thus increase its relaxation rate. The quantitation of this effect is a difficult matter. One approach applies perturbation theory to the slow—relaxing ion (21). Using Fermi's golden rule, the effect of the magnetic coupling on the electronic relaxation rate of the slow—relaxing metal ion (where (1) represents the slow—relaxing metal ion) can be calculated (21) to be -1
Tied) (J) = T ^ i ) (0) + ( J A ) Tied) (0) 2
(2)
2
a n
Tie(2) is not relevant as it is much smaller than Tied) 5 d Tied) (0) refers to the electronic spin—lattice relaxation time for the slow—relaxing metal ion in the absence of coupling. The approach seems quite reasonable for small J values. A J value of a fraction of 1 c m ' may account for large variations in Tie" . For example, in the case of low spin iron(III) interacting with copper(II), a J of 0.1 c m could account for the experimental increase in T ^ " of copper from 10 to 10 s" . For larger J values, equation 2 breaks down. However, by increasing J , the T ^ ' of the slow-relaxing electron is expected to approach that of the fast—relaxing electron, until eventually the two systems experience the same spin lifetime. In order to set some limits, we can tentatively propose that when J is smaller than (tiTied) ) (0) the magnetic coupling may be quite ineffective. When J is intermediate between (^Tie i))" (0) and TiTi 2) " K ) effect can be sizeable and in some 1
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In Metal Clusters in Proteins; Que, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1988.
4. BERTINI ET AL.
73
NMR of Paramagnetic Systems
cases an attempt of evaluation can be made according to equation 2. When J >> hTie(2)' (0)? expect that the electronic relaxation times of the two systems are equal. More quantitative treatments are difficult to envisage owing to the presence of other effects, such as zero field splitting, which introduce additional parameters. However, the above semiquantitative considerations can guide us in developing new strategies to investigate bimetallic systems through N M R . In principle, there are several contributions to nuclear T i ; however, the dipolar coupling term often dominates (10,22). The dipolar contribution depends on the reciprocal of the sixth power of the distance between the resonating nucleus and the relaxing electron, on the square of the magnetic moments associated with the unpaired electrons (g /iB S(S+l)) and with the nucleus (7N h ), on the magnetic field as expressed by the Larmor frequencies, u\ and afc, and finally on the correlation time for the electronnuclear coupling (r ) (Solomon equation, equation 3 (23)): 1
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Downloaded by MONASH UNIV on December 16, 2015 | http://pubs.acs.org Publication Date: June 21, 1988 | doi: 10.1021/bk-1988-0372.ch004
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7g g§ Mj> S(S+1) ' TlM
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7r
R
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3r„
c
•+ u|7-2
ftf
" 15 [4iJ
1 +
(3)
1 + J\tIj
The correlation time is determined by the fastest motion among those capable of inducing a change in the interaction energy between the nuclear and electronic magnetic moments. The most common of these motions are the electronic relaxation itself (r ), the molecular tumbling (r ), and the chemical exchange between a group containing the resonating nucleus and another containing the paramagnetic metal ion (r ). The Solomon equation (equation 3) holds in the so-called Redfield limit, i.e. when the electron is always in equilibrium with the lattice and the motions inducing electronic relaxation are faster than the electronic relaxation itself. It has been shown that, as far as nuclear relaxation is concerned the electron—lattice system behaves as if this were always the case, even if the mechanism for electronic relaxation is not known (24). Under these circumstances the following relation holds: s
r
m
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rc' = TV + i r + TV *
(4)
If we restrict this discussion to nuclei belonging to coordinated ligands, the exchange rate seldom makes a significant contribution to the correlation rate. The molecular tumbling rate may contribute in small complexes (rr" a 3 x 10 s" for the hexaaqua complexes at room temperature), but never in macromolecules (rr" ~ 10 s for spherical molecules of M W 30,000). The electronic relaxation rate varies from 10 to 10 s' depending on the distribution of the energy levels. It may also vary with the magnetic field, as it occurs with manganese(II), gadolinium(III) and nickel(II) (the latter for magnetic fields larger than 0.1 T ) . The concept of r is not straightforwardly related to electronic T i or T . A t low magnetic fields T i and T are presumably equal, whereas at high magnetic fields nuclear relaxation is determined by T i . T i and T are defined with respect to the direction of the external magnetic field. However, when there is a strong zero field splitting the molecular axes are independent of the external magnetic field and is possible that r is a combination of T i and T . The rationale for understanding nuclear T f in weakly magnetically coupled dimers is that metal ions with large r which interact with metal 1
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In Metal Clusters in Proteins; Que, L.; ACS Symposium Series; American Chemical Society: Washington, DC, 1988.
2 e
74
METAL CLUSTERS IN PROTEINS 1
ions with small rs" induce an increase of the latter values and thus a decrease in nuclear relaxation rates. The equations relating nuclear relaxation and r should take into consideration that each new orbital arising from magnetic coupling has different S' quantum number and different hyperfine coupling with the resonating nucleus. Recalculation of these effects results in a correction factor to the Solomon equation (23). These values, now available in the literature, are 1/2 for each homonuclear couple and, for example, 3/8 for Cu and 7/8 for Co in the C u - C o couple. When J is of the order of kT, the coefficients should be calculated by using the same procedure (17) and taking into account the Boltzmann distribution of the occupied levels.
Downloaded by MONASH UNIV on December 16, 2015 | http://pubs.acs.org Publication Date: June 21, 1988 | doi: 10.1021/bk-1988-0372.ch004
s
Transverse relaxation. The contributions to transverse relaxation are contact, dipolar and Curie type (10,25,26) in origin. The contact contributions are meaningful only for heteronuclei directly bound to the paramagnetic metal ion, and for protons only when r is relatively very long. In the example we are going to discuss next the contact contribution is negligible. Dipolar coupling is sizeable and of the same order of magnitude as dipolar nuclear T i . A n equation similar to equation 3 describes the interaction, and the changes in cases of magnetic coupling are the same as for T i . Curie relaxation deserves some comments. In the classical dipolar coupling mechanism, the difference in population of the various electronic spin states is neglected. Although small, this difference provides a permanent magnetic moment associated with the molecule. The nucleus sees this magnetic moment in different positions according to the rotational correlation time (25,26). In macromolecules r is small and its effect on T2" is large; it has been shown that its effect on T f is negligible. Of course Curie relaxation increases with the magnetic field, which increases the difference in population among the electronic spin levels. Indeed this contribution is proportional to the square of the magnetic field, just like the magnetic susceptibility. Since the coupling is still dipolar in nature, it can provide structural information. In practice the linewidth, which is equal to (TTT^)" , is measured at various magnetic fields, i.e. 90-500 MHz, and is plotted against the square of the magnetic field. At high magnetic fields the data are on a straight line because Curie relaxation is the dominant term. The intercept at zero magnetic field provides the other contributions to the linewidth at high magnetic fields. A n approximate equation to describe Curie relaxation is (25,26) s
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T
, _ i r " 0 l ^ I 47T "* ~ 2M ~ r
A
