NMR of paramagnetic proteins Ivano Bertini1 and Claudio Luchinat2

1

Department of Chemistry, University of Florence, Via G. Capponi, 7, 50121 Florence, Italy, and

2

Department of Soil Science and Plant Nutrition, University of Florence, P.le delle Cascine 7,

50144 Florence, Italy

1. NMR as a spectroscopic tool 1.1. Signal detection and assignment 1.2. Information on the magnetic susceptibility tensor 1.3. Spin density delocalization 2. NMR as a structural tool 2.1 Contact shifts as structural constraints 2.2. MCPCSs as constraints 2.3. Nuclear relaxation enhancement-based constraints 3. Perspectives in NMR of paramagnetic molecules

NMR of paramagnetic proteins 1. NMR as a spectroscopic tool

1.1. Signal detection and assignment

Under favorable electronic relaxation times, the signals of nuclei nearby the metal ion are hyperfine shifted and undergo R1 and R2 enhancements, although not as large as to prevent detection. To optimize detection fast recycle times can be used by exploiting the large R1’s and by optimizing the experiments which are discussed below. The procedures for assignment are partly analogous to those used in diamagnetic systems and partly peculiar of paramagnetic systems. The available tools are summarized below: 1)

The signal intensity of proton spectra allow us to distinguish methyls from protons;

2)

NH groups can be recognized through exchange in D2O. In the spectra of CoCA of Figure

12a in Chapter 9

1

and of CuCoSOD (Figure 17 in Chapter 9) 2 the NH of coordinated histidines

have been assigned by recording the spectra in D2O. The comparison between the spectra in H2O and D2O often indicates which protons belong to His NH's. This procedure, however, should be used with caution since there may be other exchangeable protons which may experience pseudocontact shifts. 3)

R1 and R2 values depend on the inverse of the sixth power of the metal-nucleus distance.

This criterion can be qualitatively followed. However, ligand centered effects may give rise to pitfalls. For example in Figure 17 in Chapter 9 it is shown that the R1 values of His 46 of bovine CuCoSOD do not decrease when moving farther from the copper along the histidine ring

2-4

,

whereas it happens so for His 48 and in many other cases. 4)

1D steady state NOEs are a very powerful technique. Pioneered by La Mar

5-8

and then

widely exploited by our group, 1D NOEs provide a distance networking among protons which assists in the assignment and in mapping nuclei around the metal ions. The advantage of using steady state 1D NOEs with respect to 2D relies on the fact that NOEs depend on T1 of the observed signal whereas the broad signals with short T1 (e.g. few milliseconds) are simply saturated and

NOE (as difference spectra) is often measured on protons with longer T 1s. On the other hand, NOESY cross peak intensities depends on the T1 of both signals giving rise to the cross peak, and the broad signal plays a negative role 9,10. 5)

COSY spectra in the magnitude mode easily provide scalar connectivities. Care should be

taken to acquire the FIDs in COSY experiments for a time shorter than T 2 of the two connected protons. Scalar connectivities are also obtained from TOCSY spectra. TOCSY experiments are better performed at intermediate field strengths in order to minimize the problems due to the difficulty in adequately spin-locking the required spectral region. Together with NOEs, the scalar connectivities provide firm assignments. In NOESY experiments the mixing time should be of the order of T1. It should be noted that NMR spectra of paramagnetic proteins may experience sizable Curie relaxation. This relaxation mechanism depends on

r

(see Chapter 9) just like the proton-

proton dipolar relaxation mechanisms. This provides a cross term between the two mechanisms (cross correlation) which causes observation of M-COSY cross peaks in the presence of internuclear dipolar coupling only

11,12

. In Figure 1 the M-COSY spectrum of the cyanide

derivative of lignin peroxidase is shown 13. Lignin peroxidase is a heme protein of MW 38,000 Da. A COSY cross peak clearly appears between signals H and K, which have been subsequently assigned to two protons not scalar coupled (see inset of Figure 1).

Figure 1. 301 K, 600 MHz 1H NMR spectrum of the cyanide adduct of lignin peroxidase (A) and its NOESY (B) and magnitude COSY (C) maps. Cross peak 14 in the COSY map corresponds to two protons (H and K) that are not scalar but only dipole-dipole coupled 13.

The observation of a M-COSY cross peak inconsistent with scalar coupling has represented a puzzle for the authors 13. Also the unpredicted M-COSY cross peak between signals as broad as 800 Hz (see Figure 2) 14 has been a puzzle until this cross correlation effect was fully understood 12.

Figure 2. 300 K, 600 MHz 1H reference spectrum (top) and magnitude COSY spectrum of C. vinosum cytochrome c’ 14. Cross peaks 1 and 2 originate from cross-correlation effects 12. to the 1D NOE experiments are visible in (B) and (C) 15.

6)

NOE-NOESY spectra can be helpful in detecting NOE networks between broad and

hyperfine shifted signals and signals in the diamagnetic region of the spectrum

15

. The hyperfine

shifted signal is selectively saturated prior to recording the NOESY spectrum. The difference spectrum between the normal NOESY and the NOESY when a signal is selectively saturated

provides the NOE-NOESY spectra. In these spectra only the NOESY connectivities among signals giving NOE from the selectively saturated signal appear. An example is shown in Figure 3 15.

Figure 3. Portion of a 600 MHz, 310 K, 100 ms mixing time NOESY spectrum of the cyanide adduct of met-myoglobin (A) and of the NOE-NOESY spectra obtained upon saturation (300 ms) of a signal at 12.5 ppm (B) or of a signal at 26.1 ppm (C). The reference 1D spectrum (A) and 1D NOE spectra (B,C) are also reported. Only the NOESY cross peaks originating from signals responding

7)

The superweft pulse sequence is 180°- -90°-AQ

16

. If

is short with respect to T 1, a

negative signal is obtained; if is long a positive signal is obtained. For = ln2 T1 the intensity of a signal is zero. The idea is that of sending a train of pulses with a such that all the signals with e.g. T1 ≅ 200 ms have intensity zero and those with T1s close to this value have small intensities. Only fast relaxing signals have normal intensity because is of the order of 140 ms and the paramagnetic

protons with T1 < 10 ms completely recover. A superweft-NOESY, i.e. a superweft sequence followed by a NOESY sequence thus enhances the cross peaks between fast relaxing protons 17. 8)

Heteronuclear spectra are relatively easy to measure in paramagnetic systems. They connect

13C or 15N nuclei with protons, permitting the assignment of heteronuclei or of protons which are hyperfine broadened and shifted but still under the diamagnetic envelope. 13C-1H HMQC spectra of a ferredoxin containing the Fe 4S42+ cluster are shown in Figure 4

. Note that the Fe4S42+

18

cluster has a ground state S'=0, but the excited states are populated at room temperature and provide sizable paramagnetism 19-22.

Figure 4. Natural abundance

13

C-1H HMQC experiment performed on oxidized 8Fe8S ferredoxin

from C. acidi urici at 600 MHz proton Larmor frequency and 298 K. Cross peaks 1-16 refer to βmethylene groups of the eight cluster-coordinated cysteines and cross peaks 17-22 to six out of the eight α-CH groups 18.

9)

EXSY spectra could be helpful when there is a chemical equilibrium with a suitable

exchange rate between a paramagnetic and a diamagnetic state. EXSY spectra have been the first 2D spectra ever reported on the occasion of the investigations of a polyheme cytochrome 23. 10)

It would be nice to be able to state that hyperfine shifts have patterns typical of specific

residues, but it is not so. The pattern for each group depends on the metal ion and if there is pseudocontact shift it also depends on the other coordinated groups. However, analogies among similar systems may provide support to an independently obtained assignment. This holds especially for magnetic coupled systems which may reverse the sign of the shift depending on the magnitude of J/kT (see Figure 19 in Chapter 9). 11)

It may happen that a proton signal close to the paramagnetic center is broadened beyond

detection. In this case the protein can be grown with a specifically deuterated aminoacid and the 2H spectrum can be recorded. Since the magnetogyric ratio of 1H is 6.5 times larger than that of 2H, a 42-fold reduction in the line broadening is expected. In this way the signals of β-CH 2 protons of the cysteines coordinated to Fe3+ in oxidized rubredoxin could be detected (Figure 5) 24.

Figure 5. 2H NMR spectra of deuterium-labeled rubredoxin at 308 K, pH 6.0. The spectra of the αlabeled protein in the oxidized (A) and reduced (B) forms and the β-labeled protein in the oxidized (C) and reduced (D) forms are shown. Note the very large downfield shifts of the β-methylene hydrogens in the oxidized form 24.

Similarly, the β-CH 2 protons in the CuA fragment of cytochrome c oxidase from P. denitrificans have been detected (Figure 6) 25.

Figure 6. NMR spectra and assignment of the Cu A domain, schematically shown in the inset, from P. denitrificans (800 MHz, pH 5.6, 278 K) 25. The asterisks denote exchangeable NH signals from the coordinated histidines. The 100-500 ppm region of the spectrum is a 2H NMR spectrum. Signals a-d belong to β-CH2 protons of the two bridging cysteines. Signals a and c are not visible in the 1H spectrum. NOE connectivities are also shown 25.

1.2. Information on the magnetic susceptibility tensor.

In low spin heme proteins with a histidine ligand and a cyanide, the orbital containing the single unpaired electron can be dxz, dyz or a linear combination of the two depending on the imidazole plane orientation with respect to the Fe-pyrrole nitrogen axes. CH3 depend on the above angle as reported in Figure 7.

26-33

The contact shifts of

Figure 7. Contact shift pattern for heme methyl groups in low spin iron(III) systems as a function of the orientation of the axial histidine ligand. The arrows indicate the direction of the π interaction. If two axial ligands capable of π interactions of comparable strength are present, the effective direction bisects the two π interaction vectors 29.

Since the contact shifts are the dominant contribution to the hyperfine shifts it follows that the shift pattern is immediately informative on the geometry of the axial ligand. If the shifts of 3 and 8 CH3 are larger than those of 1 and 5CH 3, it means that the imidazole plane is closer to the pyrrole Ipyrrole III axis, whereas the reverse is true if the shifts of 1 and 5CH3 are larger.

Another important information which can be obtained if extensive assignments are available is the anisotropy and directions of the magnetic susceptibility tensor

. Indeed, if a number of

signals is available which experience only dipolar interactions (e.g. protons several bonds away without

bonds) and pseudocontact shifts, and if a structural model is available, then

molecular axes to which r, 4,34-37

and

and the

are related can be obtained through Equation 9 in Chapter 9

. It is important to realize that pseudocontact shifts are observed only when there are low-lying

excited states and there are significant effects of spin-orbit coupling. This happens, for example, with low spin iron(III) 36-38, high spin cobalt(II)

4,34,35,39-41

, and lanthanides 42-49. It is also important

that the structural model is as close as possible to the actual structure in solution. The solid state structure or a structural model obtained from an analogous protein with known structure has been used

50

. We believe that solution structures determined with the help of pseudocontact shifts

provide the most reliable magnetic susceptibility anisotropy and principal directions of the tensor (see later). Our laboratory has been successfully engaged in providing programs which calculate the structure by minimizing simultaneously the classical constraints, e.g. NOEs, and pseudocontact shifts 51-54.

Figure 8. Orientation of the in plane χ tensor components in oxidized horse heart cytochrome c (along the x and y axes) and in its Met80Ala mutant lacking the axial methionine (pink vectors) 51,52

. In Figure 8 the tensor of Ala80 CytcCN

51

and CytcCN

52

are shown. The z direction in

Ala80 CytcCN is perpendicular to the average plane of the heme and the x and y directions are provided by the imidazole plane. In the case of cytochrome c, the other axial ligand, methionine, introduces i) a tilt of the z axis ii) a variation of the x and y axis due to its asymmetric π bonding.

Note that the NMR-based procedure here described to obtain information on the

tensor is the best

procedure to obtain this information.

The magnitude of the 13C shift of the CH 3 pendants of protoporphyrin IX can be related to the directions of the (molecular) magnetic x and y axes in the further assumption that z is perpendicular to the heme plane 29.

1.3. Spin density delocalization

The hyperfine shift is the sum of contact contribution, metal centered pseudocontact shift and ligand centered pseudocontact shift. The pseudocontact shift can provide in certain cases the tensor and orientation as discussed in Section 1.2. Then PCS can be calculated and subtracted from the total hyperfine shift experienced by nuclei experiencing PCS, CS and, when applicable, LCPCS. In Table 1 the calculated PCS for the heme moieties in lignin peroxidase 38, yeast cytochrome c horse heart cytochrome c

52

and cytochrome b 5

56

55

,

are reported, together with the sum of CS and

LCPCS. Similar estimates are available for cobalt(II)-containing proteins 35,39. From these and other data

57,58

, in a qualitative way we may predict the contact shifts induced by

high spin iron(III), high spin iron(II), low spin iron(III), cobalt(II), on Cys, His, Asp and Glu residues, which are common ligands of these metal ions (Figure 9).

Figure 9. Expected ranges of contact shifts for protons belonging to common ligands of iron and cobalt-containing systems.

2. NMR as a structural tool

Once the assignment and some interproton distances are obtained, structural information is available which permits the comparison of active cavities and active cavities in the presence of inhibitors and substrates. For example, the existence of a hydrogen bond between cyanide and the distal histidine in peroxidases (Figure 10) has been proposed through 1H NMR 50, and the inhibitor HCOO- could be mapped into the active site of Co-substituted CA (Figure 11) 59.

Figure 10. The H-bonding network in the active site of cyanide-bound peroxidases 50.

Table 1. Separation of pseudocontact and contact (with ligand centered pseudocontact) contributions to the hyperfine shift for horse heart cytochrome c at 293 K 52 and S. cerevisiae iso-1cytochrome c at 303 K

55

(A), and for rat microsomal cytochrome b5 at 313 K

56

and cyanide adduct

of phanerochaete chrysosporium lignin peroxidase at 301 K 38 (B). A horse heart cytochrome c

S. cerevisiae cytochrome c

Atom name

Residue name

PCS (ppm)

CS + LCPSC (ppm)

PCS (ppm)

CS + LCPCS (ppm)

Hα ε-CH 3 Hα Hδ2 Hε1 8-CH3 meso-δH 1-CH3 2-Hα 2-CH3 meso-αH 3-CH3 4-Hα 4-CH3 meso-βH 5-CH3 meso-γH

Met Met His His His Heme Heme Heme Heme Heme Heme Heme Heme Heme Heme Heme Heme

-0.03 ± 0.30 4.42 ± 1.4 4.28 ± 0.04 25.7 ± 0.45 12.9 ± 0.64 -1.86 ± 0.04 -9.06 ± 0.15 -4.38 ± 0.07 -4.73 ± 0.05 -3.09 ± 0.02 -6.31 ± 0.09 -1.15 ± 0.01 -2.70 ± 0.09 -1.37 ± 0.02 -10.63 ± 0.13 -4.86 ± 0.03 -6.25 ± 0.09

-0.29 -25.8 1.04 -1.20 -39.0 35.4 2.11 7.73 -1.8 -1.0 -1.6 30.1 -1.51 1.85 0.13 11.0 4.11

0.97 ± 0.63 3.43 ± 1.7 3.93 ± 0.09 21.5 ± 0.43 -0.79 ± 0.43 -0.96 ± 0.02 -5.36 ± 0.11 -2.94 ± 0.04 -4.28 ± 0.08 -3.17 ± 0.06 -6.77 ± 0.08 -1.18 ± 0.04 -1.53 ± 0.02 -0.46 ± 0.01 -5.58 ± 0.03 -3.54 ± 0.02 -5.88 ± 0.10

-22.6 1.29 2.40 -24.8 33.4 -1.48 7.46 -1.65 -0.43 -0.08 28.3 -2.00 -0.01 -2.43 11.0 4.27

B cytochrome b5 Atom name

Residue name

PCS (ppm)

CS + LCPCS (ppm)

NH Hα Hβ1 Hβ2 Hδ2 Hε1 NH Hα Hε1 8-CH3 meso-δH 1-CH3 2-Hα 2-Hβtrans 2-Hβcis meso-αH 3-CH3 4-Hα 4-Hβtrans 4-Hβcis meso-βH 5-CH3 meso-γH 7-Hα 7-Hα' 7-Hβ 7-Hβ' 6-Hα 6-Hα'

His39 His39 His39/His176 His39/His176 His176 His176 His63 His63 His63 Heme Heme Heme Heme Heme Heme Heme Heme Heme Heme Heme Heme Heme Heme Heme Heme Heme Heme Heme Heme

2.39 3.82 5.89 5.85

0.63 0.55 9.81 1.32

2.94 4.18 13.26 -2.82

2.19 0.76 -26.94 2.01

-1.54 -4.47 -1.71 -1.72 -11.84 -4.67 -2.66 -1.58 -2.66 -3.82 -1.50 -12.30 -5.88 -4.01

8.60 23.27 -10.01 -9.99 -0.60 15.97 -1.29 -1.61 -0.58 3.28 17.67 2.31 20.98 -1.42

-4.72 -2.79

16.30 13.07

lignin peroxidase CN PCS (ppm)

CS + LCPCS (ppm)

7.2 7.0 22.4 23.8

9.9 10.4 -10.5 -34.2

-1.1 -6.8 -5.8 -8.2 -3.8 -4.9 -15.1 -3.3 -0.2 -0.8 -0.6 -7.1 -6.0 -14.6 -4.6 -2.0 0.1 -0.8

17.7 3.5 2.7 7.8 -6.1 -5.6 6.4 30.5 5.3 -7.6 -9.4 4.0 5.5 8.0 11.3 7.2 -0.6 -2.2

Figure 11. Schematic representation of the binding mode of the inhibitor formate in the active site of carbonic anhydrase as deduced from NMR data on the cobalt(II)-substituted derivative 59.

Besides the local structural and electronic information, NMR can today provide solution structures of paramagnetic metalloproteins in favorable cases. The assignment should be performed through TOCSY/COSY-NOESY spectroscopies. This procedure should lead to a number of distance constraints larger than 10-11 per residue. Sometimes much less, if any, NOEs are observed for residues very close to the metal ion. As two limiting cases, we can take the number of NOEs per residue for horse heart cytochrome c (Figure 12) inset) 60,61.

52

and oxidized 8Fe8S ferredoxin (Figure 12

Figure 12. NOEs per residue (black bars long/medium range, light grey sequencial, white intra residue NOEs) used to solve the solution structure of oxidized horse heart cytochrome c

52

. The

inset shows the total NOEs per residues used to solve the structure of oxidized (Fe4S4)2 C. pasteurianum ferredoxin

60,61

. Note the smaller number of NOEs compared to oxidized cytochrome

c and the lack of NOEs at positions closest to the clusters.

In the first case, paramagnetism does not reduce appreciably the number of NOEs even for residues close to the heme

52

, whereas in the second case an overall reduction, more marked in the

neighborhood of the clusters, is observed

61

. Even in the latter case, however, the quality of the

solution structure is reasonably good. At this stage a distance-geometry (DG) or a simulated annealing procedure provides a family of structures of the protein part. The metal ion (or the Fe nSn center) are treated by borrowing information from X-ray data on similar structures and imposing some links between the metal ion and the ligand atoms. In diamagnetic metalloproteins the scalar coupling between the metal nucleus and some protons provides an estimate of the dihedral angle

62-67

. This is not possible for

paramagnetic metal ions for which, however, new strategies are being established.

2.1. Contact shifts as structural constraints

New constraints based on the hyperfine coupling (contact, pseudocontact and relaxationbased) will be of great importance in locating the metal ion and in providing further constraints. The contact shift of a proton or a carbon in a moiety of the type shown in Figure 13, where the two above nuclei are separated from the metal by three bonds through the donor atom D, is related to the M-D-C-H or M-D-C-C torsion angle . The specific relationship depends on the metal ion and on the donor atom. This is analogous to what found by Karplus for the H-C-C-H moiety

68

. In the

case of an amine nitrogen as donor atom and nickel(II) as the metal ion the relationship is 69-71:

Figure 13. The M-D-C-H dihedral angle , where D is a metal donor atom. = A0 (cos2 + a cos + b)

(1)

which is analogous to the Karplus relationship. In the case of Fe4S42+ polymetallic centers the relationship between contact shift and the FeSCH or FeSCC torsion angle is 18,22 = A0 (sin 2 + a cos + b)

(2)

where A0 = 11.5 ppm for protons and 26.2 ppm for carbons, and a and b are -0.252Y and +0.322, respectively (Figure 14).

Figure 14. Karplus type relationship between the dihedral angle

as defined in Figure 32 (Fe-S-C-

H and Fe-S-C-C moieties) and the contact shifts of β-protons and α-carbons for cysteines coordinated to [Fe4S4]2+ clusters for a number of proteins 18,22.

The four iron ions are equivalent in the cluster. This relationship indicates that the mechanism of spin density transfer largely involves the -bonding p orbital of sulfur which is not available for an amine nitrogen donor. Although such a relationship should exist for any metal ion, it cannot be easily predicted from principles and enough experimental data should be available to obtain reliable A0, a and b parameters. Furthermore, the various examples require that the contact hyperfine coupling be constant. The fact that in Fe4S4 clusters for both HiPIPs and ferredoxins Equation 2 holds means that the hyperfine coupling is constant. As a consequence the structure of the cluster and the Fe-S bonds are the same over all the systems within the sensitivity of the technique, which is quite high. Note that the hyperfine shift has to be contact in origin, and this occurs when the PCS are negligible because the magnetic anisotropy is small. In FeS proteins pseudocontact shifts are small, the short electronic relaxation time being determined by magnetic exchange coupling. When

this is not the case, no relationship between the hyperfine shift and the torsion angle can be expected. However, if it is possible to separate the PCS from contact contributions, the relationship can still be looked for. For example, the α-CH 2 of propionates in protoporphyrin IX experience both contact and pseudocontact shifts. Their separation has been obtained in several cases (see later). The experimental dependence of the contact shift on the angle of the axis of the pz orbital of the pyrrole carbon and the CCH plane is given by 72: = A0 (cos2 + b)

(3)

It is clear that this is a precious information for solution structure refinements within series with the same A0. Even for a single case of a methylene proton pair with a single value of A0 the dihedral angles can be obtained, because there is a fixed angle between the two protons of the pair. When PCS are available, they represent an important tool to locate the metal ion within the protein frame

51,73

. This should also be done in conjunction with R1 and R2 enhancements due to

paramagnetism as explained in Chapter 9 61,74. As already mentioned, nuclear relaxation has been used extensively for structural information. In the next sections a detailed and updated analysis of PCS and nuclear relaxation is presented with respect to solution structure determination.

2.2. MCPCSs as constraints

MCPCS as obtained from Equation 9 in Chapter 9, can be rewritten as:

dip av

=

pc

{[

1 1 = 24 5 2 ri

zz

−

(

xx

+

yy

)](3(ri ⋅ rz )2 − ri2 )+ 3(

xx

−

yy

)((ri ⋅ rx )2 − (ri ⋅ ry )2 )} (4)

Equation 4 contains the position vectors of nuclei i in the laboratory axis system, while the principal directions of the

tensor in the same axis system are given by rx , ry and rz. Equation 4 has

as unknown as well as the reference axis system of the

and

tensor. If the polar coordinates of

nuclei were known with respect to the laboratory axis system, then the two axis systems can be

related by three direction cosines. So the unknowns are two relative to relative to the

anisotropy and three

directions. But a structure is needed in order to define the polar coordinates of

nuclei in the laboratory axis system. For small or relatively small molecules a straightforward procedure has been attempted to build a model which satisfies directly Equation 4. Actually, the first idea to describe a structure through a family of conformers was applied to mononucleotides (Figure 15)

75,76

. This, however, is not a successful procedure for proteins also because the number

of PCSs is too small to lead to a structure. In our lab two strategies have been designed to exploit the potentialities of PCSs.

Figure 15. Historical illustration showing a family (two extremes and the average) of structures for AMP derived with the aid of pseudocontact shifts from a lanthanide ion

75,76

. Two orthogonal

projections are shown.

1)

from a NOE-derived structure the 5 parameters of

are obtained. A distance-geometry

protocol is then used to refine the structure by simultaneously minimizing the errors on NOEs and PCSs. The new structure has a different set of the 5 the 2)

parameters. The procedure is repeated until

parameters do not vary significantly any more 51. Structure determinations based on simulated annealing protocols require as input parameters

the NOEs, PCSs and the

anisotropies. A structure is searched which minimizes the error on

NOEs and PCSs. A final set of 5

parameters is obtained.

3)

PCSs can be used as constraints together with NOEs on MD programs which are devoted to

minimize the molecular energy. They can be introduced at any stage of the refinement. The protocol provides also the definitive set of 5 parameters 53. The 5 parameters approach requires that the position of the metal ion is somehow assumed. For example in heme proteins the iron ion can be bound to the heme by following the knowledge on X-ray structures. But our final goal is that of independently locating the metal ion in the protein frame. Therefore the two above approaches have the variant with 8 parameters: 5 defining the

anisotropy and 3 defining the coordinates of the

metal ion. Note that the PCSs are long range constraints because they decay as r-3. Of course only those protons are taken into consideration which are separated from the metal ion by a number of chemical bonds such that the occurrence of contact shift (and consequently LCPCSs) can be ruled out. Then the allowed errors in calculated PCSs are better taken proportional to the PCSs themselves. This avoids giving excessive weight to protons near the metal ion, and takes into account possible failures of the MC model. As already stated, the PCSs are determined as the difference between the measured chemical shift and the chemical shift of the diamagnetic analogue. If the diamagnetic chemical shifts are not known, they can be calculated from the Amber program

77

. In this case the indetermination in

evaluating PCSs is relatively large (ca. 0.5 ppm for CHs and 1.0 ppm for NHs). Another possibility has been suggested which is based on the temperature dependence of the chemical shifts. In the diamagnetic case it is assumed that there is no temperature dependence, which then is effective only for the PC calibration. The proportionality constant K between PCS and PCS for a given system is determined for some protons experiencing large

PCS for which the exact knowledge of the

diamagnetic reference is of little importance. The other ∆PCS can then be used to determine the unknown PCS through the same proportionality constant 73. When giving the parameters of

anisotropy, we have to remember that we are dealing with

a family of structures. Each family member has its own set of 5 (8) parameters. They can be averaged at the end or calculated on the average structure. In Figure 16 the structures without and with PCS are shown for the cyanide adduct of the Met80Ala mutant of horse heart cytochrome c and in Figure 17 the variation of RMSD per residue 51.

Figure 16. Stereo drawings of the family of solution structures for the Met80Ala mutant of oxidized horse heart cytochrome c obtained without (top) and with (bottom) the use of pseudocontact shifts 51

.

Figure 17. RMSD/residue for the family of solution structures for the Met80Ala mutant of horse heart cytochrome c obtained without (squares) and with (circles) the use of pseudocontact shifts. Both backbone atoms (A) and heavy atoms (B) are shown 51.

2.3. Nuclear relaxation enhancement-based constraints

The development of a protocol for solution structure determination requires an analysis to define the boundaries of validity of the protocol. We rely on MC relaxation and on Equation 15 in Chapter 9 as the main source of R1 relaxation enhancement. In principle the equations for R2 should

be equally good. The atoms taken into consideration are only those which do not experience any contact shift, to decrease LC effects. The effect of ca. 40% delocalization onto the donor atom on the nuclear relaxation of nuclei at different distances from the metal ion and for different

s

is

reported as compared to a purely metal-centered situation in Figure 18.

Figure 18. Calculated line broadening of a proton at variable distance from a complex constituted by a metal and four ligands at 2.0 Å in a square planar arrangements. The calculations are for dipolar and Curie broadening at 500 MHz by an S = 5/2 spin with

s

of 2 × 10 -10 s, in the

assumption of no electron delocalization (pure metal centered) and with 10% delocalization on each of the four ligands for the proton perpendicular to the donor plane (along z) and in the donor plane along a metal-donor vector (along x) or bisecting two metal-donor vectors (along xy). Note that the ligand centered contribution causes a non negligible linewidth enhancement when the proton is on a metal-donor axis, a sizably smaller enhancement when bisecting two metal-donor axes, and even a small linewidth reduction when perpendicular to the donor plane.

It appears that for

s

< 10-11 s and nuclei 5 Å far from the metal ion, delocalization can be

disregarded. In other words any structural constraint based on nuclear relaxation for atoms closer than 5 Å to the metal ion (and about 3 Å from the donor atoms) should be discarded or analyzed

with care. Neglect of delocalization induces a constraint shorter than the actual distance, and this may lead to a wrong structure. Another important aspect about paramagnetic relaxation regards the definition of T1. T1 is defined as the time constant for the exponential recovery of magnetization after a perturbation. In a two-proton system I-J, the return to equilibrium of nucleus I after a perturbation is

d Iz = dt

where t is the time,

I

I

( I (∞ ) − z

)

I z (t ) +

IJ

( J (∞) − z

J z (t )

)

(5)

is a relaxation constant and σIJ is called cross relaxation, i.e. it is the

parameter which describes the transfer of magnetization from nucleus I to nucleus J (see Chapter 5). If σIJ = 0, Equation 5 represents an exponential whose time constant is -1. Since

IJ

is ≠ 0, and

indeed this is needed to observe NOEs, then the longitudinal magnetization recovery is not exponential. As a matter of fact, in a non-selective T1 experiment, i.e. where all nuclei are perturbed, the recovery of magnetization looks like an exponential within experimental error. Even the calculated magnetization recovery is quasi exponential. This is important in this context, because it allows us to define an effective T1dia for each proton. For a protein of MW 10,000, T 1dia is of the order of 500 ms 78. Nuclear magnetization recovery in paramagnetic proteins has another

term in Equation 5,

which is the paramagnetic relaxation due for instance to Equation 15 in Chapter 9. This term is absolutely exponential. This term contains the metal-nucleus distance as long as the relaxation is metal centered in nature. A procedure that is used in our laboratory in order to utilize these data is that of subtracting the average of all R1's smaller than 10 s-1. It is not important to know the exact diamagnetic value of each proton, but it is appropriate to subtract a R1 value that is equal or larger that the actual value. In this way R1para becomes equal or smaller than the actual value, and the constraint is equal or longer than actual. For safety reasons we always want a loose constraint, which is however still helpful for solution structure determination as an upper distance limit. We have also afforded the problem of cross relaxation with respect to the use of R1 as constraints. Cross relaxation tends to equalize the R1 of two coupled nuclei

79,80

. This may tend to

equalize the distances from the metal ion of two protons which indeed are not equidistant. Cross

relaxation is efficient when the two nuclei (protons) are close, e.g. when they are geminal. Despite this limitation is true in principle, in practice the problem is minor because in some algorithms the two geminal protons are treated as a single pseudoatom, whereas if the two protons are stereospecifically assigned and NOEs were available, one constraint would violate the overall structure. Then either the constraint is discarded or the constraint corrected through a full relaxation matrix analysis which allows the calculation of cross relaxation 61. After these theoretical considerations, we may consider how to measure T 1's. First of all T 1 should be measured through non selective experiments, i.e. we want to equally perturb all the nuclei in such a way as to decrease the effect of cross relaxation

81

. The measurement of the return to

equilibrium after a non selective perturbation is relatively easy on hyperfine shifted signals. Attention has to be paid to have the same 90° pulse all over the spectral width. Sometimes the use of shaped pulses can be advised. In some cases, several T1 experiments are performed by placing the carrier frequency at different position in the spectrum. In any case, the experiment has to be largely non selective. For overlapping signals, 2D NOESY following a non selective 180° pulse and a variable time delay provide cross peaks on the column corresponding to a diagonal signal with variable intensities that provide the T1 for that signal . From these, T1 values can be obtained. If and/or

15

N

13

C-enriched proteins are available, then heteronuclear spectra can be measured in short

times. Again, a 180°- - sequence before the heteronuclear 2D sequence provides cross peak intensities (on the column!) depending on , which provide T1's. R2 data do not suffer from cross relaxation and non-exponentiality problems, and can be used e.g. through Equations 16 or 20 in Chapter 9 in a straightforward way. However, R2 values of diamagnetic nuclei are larger than R1, and the paramagnetic enhancement is relatively smaller. Then, smaller is also the number of R2 data which can be used. R2 as structural constraints have been used in the case of a dinucleotide with a Pt complex containing a nitroxyl radical 82. In summary, nuclear relaxation can be used for localizing the metal ion within the protein frame. Relatively few constraints can already be helpful for this purpose; so the extensive use of R1 and R2 is precious in refining a solution structure in the neighborhood of the paramagnetic center(s). In Figure 19 the solution structure of the (Fe 4S4)2 ferredoxin from C. pasteurianum in the neighborhood of cluster II with and without the use of 69 R1 constraints is shown.

Figure 19. Family of solution structures of oxidized C. pasteurianum (Fe 4S4)2 ferredoxin in the neighborhood of cluster II obtained without (A) and with (B) 69 R1 constraints. Note the better resolution of the cluster and the resolution of some backbone conformational ambiguities 61.

The variation in RMSD per residue is shown in Figure 20 61.

Figure 20. RMSD per residue (backbone, top; heavy atoms, bottom) of the family of solution structures of oxidized C. pasteurianum (Fe 4S4)2 ferredoxin with and without 69 R1 constraints 61. It appears that the clusters are now better defined, as well as the residues close to the paramagnetic centers. R1 constraints are particularly helpful when the NOEs per residue are relatively few, as in this case (see inset of Figure 11).

Note that paramagnetic relaxation-based constraints can be treated as normal NOEs owing to the r-6 dependence. Actually, they can be calibrated just like NOEs. A positive property of these

constraints is that they are long range, as the magnetic moment of the electron is about 658 times that of the proton. It is clear that relaxation based constraints help in locating the metal ion within the protein frame. If then PCSs are available, the location of the metal ion becomes quite reliable and successful. This has been done in locating cerium(III) in the calcium binding site of a fragment of calmodulin 73.

3. Perspectives in NMR of paramagnetic molecules

The understanding of the basic phenomena of NMR of paramagnetic molecules is nowadays rather deep. The experiments can be mastered with the simulations by including nuclear relaxation. It is also possible sometimes to affect electron relaxation itself by changing coordination number, ligand field strength or by introducing exchange magnetic coupling. The results range from the classic info on structure and mobility of the proteic/organic part to the electronic structure of the metal ion itself. The use of structural constraints deriving from the hyperfine coupling in protocols regarding the structural determination in solution of biomolecules is a most recent and noticeable result. It has been recently noted that myoglobin-cyanide is partially oriented in solution owing to its anisotropic magnetic susceptibility between

83,84

. This effect produces a non zero dipolar coupling

15

N and 1H of NH groups, which in turn depends on the orientation of the NHs with

respect to the molecular axis determination

85

. This observation can be used in protocols for solution structure

86

. It is possible that the effects of partial orientation become more and more

important with the availability of large magnetic fields. Starting from this idea, the magnetic field dependence of PCS of anisotropic lanthanide containing molecules has been addressed. The following equation has been derived in the case of axial anisotropy 87:

pc

=

1 12 r

3

(

|| −

⊥

 B02 3cos2 − 1 1 + 3  10 0 kT

)(

)

(

||

−

⊥

)

(6)

This effect is, however, masked by the non-linearity of with B0 when B0 becomes very large. This effect, which is known as Brillouin effect in molecular magnetism, is larger and of opposite sign with respect to that arising from partial orientation 87.

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