Modulation of the distance dependence of paramagnetic relaxation enhancements by CSA × DSA cross-correlation

doi:10.1016/j.jmr.2004.08.019

Journal of Magnetic Resonance

Volume 171, Issue 2, December 2004, Pages 233-243

https://doi.org/10.1016/j.jmr.2004.08.019 Get rights and content

Abstract

Paramagnetic metal ions with fast-relaxing electronic spin and anisotropic susceptibility tensor provide a rich source of structural information that can be derived from pseudo-contact shifts, residual dipolar couplings, dipole–dipole Curie spin cross-correlation, and paramagnetic relaxation enhancements. The present study draws attention to a cross-correlation effect between nuclear relaxation due to anisotropic chemical shielding (CSA) and due to the anisotropic dipolar shielding (DSA) caused by the electronic Curie spin. This CSA × DSA cross-correlation contribution seems to have been overlooked in previous interpretations of paramagnetic relaxation enhancements. It is shown to be sufficiently large to compromise the 1/r⁶ distance dependence usually assumed. The effect cannot experimentally be separated from auto-correlated DSA relaxation. It can increase or decrease the observed paramagnetic relaxation enhancement. Under certain conditions, the effect can dominate the entire paramagnetic relaxation, resulting in nuclear resonances narrower than in the absence of the paramagnetic center. CSA × DSA cross-correlation becomes important when paramagnetic relaxation is predominantly due to the Curie rather than the Solomon mechanism. Therefore the effect is most pronounced for relaxation by metal ions with large magnetic susceptibility and fast-relaxing electron spin. It most strongly affects paramagnetic enhancements of transverse relaxation in macromolecules and of longitudinal relaxation in small molecules.

Introduction

Enhanced relaxation of the nuclear spins surrounding a paramagnetic center constituted of one or several unpaired electrons presents one of the most obvious manifestations of paramagnetism [1]. The relaxation enhancement strongly depends on the distance between the nuclear and the electron spin. Since the effect can be observed for significantly longer distances than internuclear interactions, the measurement of paramagnetic relaxation enhancements (PRE) provides an attractive way of accessing long-range distance information between nuclear spins and paramagnetic centers. Consequently, paramagnetic compounds and metal ions have found wide-spread use as sources of long-range distance restraints for structure determination of molecules in solution [2], [3], as indicators of stable or transient intermolecular contacts in molecular biology [4], [5], [6], [7], [8], enzymology [9], drug discovery [10], [11], [12], [13], [14], and organic catalytic synthesis [15], [16], [17], and as probes to study the binding of non-magnetic ions like magnesium or calcium to receptors [18], [19], [20], [21]. In the presence of other, non-paramagnetic sources of nuclear relaxation, such as dipole–dipole and CSA relaxation, the net paramagnetic relaxation enhancement is usually determined as the difference in total relaxation rates between paramagnetic and diamagnetic molecules, i.e., in the presence and absence of the paramagnetic center.

With regard to NMR studies in solution, paramagnetic centers fall into two different classes. Nitroxide radicals and metal ions like Cu²⁺, Mn²⁺ or Gd³⁺ have an isotropic or, as in the case of Cu²⁺, nearly isotropic magnetic susceptibility [22]. Combined with the absence of low-lying excited states, these paramagnetic centers are characterized by slowly relaxing electronic spins which affect the surrounding nuclear spins through a dipolar (“Solomon”) mechanism [23].

The second class comprises metal ions with fast-relaxing electron spins [22]. The fast modulation of the stochastic dipolar interaction between electron and nuclear spins results in smaller PRE effects for the nuclear spins. Such paramagnetic centers are thus more compatible with high-resolution NMR spectroscopy. In addition, they usually possess anisotropic magnetic susceptibilities which generate pseudocontact shifts and cause an alignment of the molecule with respect to the external magnetic field [24]. Efficient electronic relaxation combined with a large Zeeman splitting creates a net magnetic moment (Curie spin) in thermal equilibrium. Interaction of the Curie spin with nuclear spins constitutes an additional mechanism of nuclear relaxation [25], [26]. It has been noted that the functional form of Curie-spin relaxation is analogous to that of CSA [27], [28]. This similarity was further emphasized by Bertini et al. [29] who pointed out that the Curie contribution can be viewed as an effect originating from the anisotropy of the dipolar shielding (DSA) caused by the electronic susceptibility at the site of the nucleus.

The enhancement of longitudinal and transverse nuclear relaxation is inversely proportional to the sixth power of the proton–electron distance for both Solomon and Curie-spin relaxation mechanisms. Therefore, the simultaneous presence of both mechanisms presents no impediment to the measurement of experimental distances. Deconvolution of the individual contributions requires the accurate knowledge of the electronic and molecular correlation times [22].

Unlike Solomon relaxation which depends on the electronic spin relaxation, Curie relaxation like diamagnetic relaxation mechanisms is caused exclusively by the rotational reorientation of the molecule, resulting in correlated spectral densities with respect to the diamagnetic relaxation. Cross-correlated relaxation between the Curie spin and the dipole–dipole interaction between two nuclear spins is a well-studied phenomenon [28], [30], [31], [32], [33], [34]. It results in differential line broadening of the doublet components observed for two scalar-coupled nuclear spins.

To the best of our knowledge, the effects of cross-correlation between Curie and CSA relaxation have never been assessed. The present paper examines their relevance for determination of electron–nucleus distances by measurements of paramagnetic relaxation enhancements.

Section snippets

Theory

The evolution of the density matrix can be described by $\frac{d}{d t} σ_{i} = - i ω_{i} σ_{i} + \sum_{j} Γ_{i, j} (σ_{j} - σ_{j}^{eq}),$ where σ_i are the matrix elements of the density operator, $σ_{i}^{eq}$ their corresponding equilibrium values and ω_i their oscillation frequencies [35]. The elements of the relaxation supermatrix Γ_i, j are functions of the Hamiltonian terms H^μ responsible for relaxation, where μ identifies a particular relaxation mechanism. The elements of the relaxation supermatrix can readily be calculated when each of the Hamiltonian

Results and discussion

The contribution of the CSA × DSA cross-correlation rate $R_{1, 2}^{CSA \times DSA}$ to the R₁ and R₂ relaxation rates of a nuclear spin I depends on the distance r between the nuclear and electronic spin and on the relative orientation of the CSA and DSA tensors. In the case of axially symmetric CSA and DSA tensors $R_{1, 2}^{CSA \times DSA} \propto ξ_{CSA} \cdot ξ_{DSA} \cdot P_{2} (\cos θ^{CSA, DSA}) \propto γ_{I}^{2} B_{0}^{2} Δ σ_{I}^{CSA} Δ σ_{I}^{DSA} \cdot P_{2} (\cos θ^{CSA, DSA}) \propto \frac{P_{2} (\cos θ^{CSA, DSA})}{r^{3}},$ where γ_I is the magnetogyric ratio of nucleus I, B₀ is the magnetic field and $Δ σ_{I}^{CSA}$ and $Δ σ_{I}^{DSA}$ denote the

Conclusions

Metal ions with fast relaxing electronic spins and large, anisotropic susceptibilities present a rich source of long-range structural restraints, including distance and angular information. Anisotropic susceptibility tensors are a prerequisite for the observation of pseudocontact shifts and molecular paramagnetic alignment in the magnetic field. In addition, the average susceptibility enhances the relaxation rates of the nuclear spins in a distance-dependent fashion, providing a relaxation

Acknowledgments

We thank Prof. Jozef Kowalewski for valuable discussions and for a critical reading of the manuscript. G.P. thanks the EU for a postdoctoral fellowship within the Research Training Network on Cross-Correlation (HPRN-CT-2000-00092). G.O. thanks the Australian Research Council for a Federation Fellowship. Financial support by the Australian Research Council is gratefully acknowledged.

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CommunicationModulation of the distance dependence of paramagnetic relaxation enhancements by CSA × DSA cross-correlation

Abstract

Introduction

Section snippets

Theory

Results and discussion

Conclusions

Acknowledgments

Structure

Struct. Fold Des.

J. Inorg. Biochem.

J. Magn. Reson.

Chem. Phys. Lett.

J. Magn. Reson.

J. Magn. Reson.

J. Magn. Reson.

Prog. NMR Spectrosc.

Nuclear and Electron Relaxation: The Magnetic Nucleus-Unpaired Electron Coupling in Solution

Paramagnetic constraints: an aid for quick solution structure determination of paramagnetic metalloproteins

Concept Magn. Reson.

Paramagnetism-based restraints for Xplor-NIH

J. Biomol. NMR

Utilization of site-directed spin labeling and high-resolution heteronuclear nuclear magnetic resonance for global fold determination of large proteins with limited nuclear Overhauser effect data

Biochemistry

A new method to detect long-range protein–RNA contacts: NMR detection of electron–proton relaxation induced by nitroxide spin-labeled RNA

J. Am. Chem. Soc.

EDTA-derivatized deoxythymidine as a tool for rapid determination of protein binding polarity to DNA by intermolecular paramagnetic relaxation enhancement

J. Am. Chem. Soc.

The ATCUN domain as a probe of intermolecular interactions: application to calmodulin–peptide complexes

J. Am. Chem. Soc.

Paramagnetic cobalt(II) as a probe for kinetic and NMR relaxation studies of phosphate binding and the catalytic mechanism of Streptomyces dinuclear aminopeptidase

Inorg. Chem.

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J. Am. Chem. Soc.

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Biochemistry

Comprehensive 2D 1H NMR studies of paramagnetic lanthanide(III) complexes of anthracycline antitumor antibiotics

Inorg. Chem.

Lanthanides: Chemistry and Use in Organic Synthesis

Solution versus solid-state structure of ytterbium heterobimetallic catalysts

J. Am. Chem. Soc.

Communication
Modulation of the distance dependence of paramagnetic relaxation enhancements by CSA × DSA cross-correlation

Comprehensive 2D ¹H NMR studies of paramagnetic lanthanide(III) complexes of anthracycline antitumor antibiotics