Magnetic susceptibility in paramagnetic NMR Ivano Bertini a , Claudio Luchinat b, * , Giacomo Parigi b a CERM and Department of Chemistry, University of Florence, via L. Sacconi, 6, I-50019 Sesto Fiorentino, Italy b CERM and Department of Agricultural Biotechnology, University of Florence, p.le delle Cascine 28, I-50144 Florence, Italy Accepted 20 January 2002 Contents 1. Introduction .................................................................. 250 2. Magnetic moments, magnetization, magnetic susceptibility ................................ 250 2.1. The Curie law ............................................................. 250 2.2. Saturation at high ®eld ...................................................... 252 2.3. The origin of anisotropy ..................................................... 252 2.4. Tensor representation ....................................................... 253 2.5. The direction of km l ........................................................ 254 2.6. Diamagnetic susceptibility .................................................... 255 3. The pseudocontact shift .......................................................... 255 3.1. Relevant equations ......................................................... 255 3.2. Solving protein structures with pseudocontact shifts: theoretical considerations ............. 259 4. The contact shift ............................................................... 260 5. Curie relaxation ................................................................ 261 5.1. Curie relaxation in the case of isotropic magnetic susceptibility ........................ 261 5.2. Curie relaxation in the case of anisotropic magnetic susceptibility ....................... 262 6. Cross-correlation between dipolar and Curie interactions .................................. 262 7. Orientation tensor .............................................................. 263 7.1. Partial orientation effects on nucleus±nucleus coupling ............................... 265 7.1.1. The case of magnetic ®eld induced order ................................... 265 7.2. Partial orientation effects on the dipolar shift ...................................... 267 7.2.1. The case of magnetic ®eld induced order ................................... 268 7.3. Partial orientation effects on the contact shift ...................................... 269 7.4. Residual dipolar couplings in the presence of paramagnetic and diamagnetic anisotropy ...... 269 7.5. Partial orientation with both external and internal orienting agents ...................... 269 8. Conclusions .................................................................. 270 Acknowledgements ................................................................ 271 References ...................................................................... 271 Keywords: Paramagnetism-based constraints; Protein solution structure; Magnetic susceptibility; Pseudocontact shift; Residual dipolar coupling; Cross-correlations Progress in Nuclear Magnetic Resonance Spectroscopy 40 2002) 249±273 0079-6565/02/$ - see front matter q 2002 Elsevier Science B.V. All rights reserved. PII: S0079-656502)00002-X www.elsevier.com/locate/pnmrs * Corresponding author. Fax: 139-055-4574-253. E-mail addresses: bertini@cerm.uni®.it I. Bertini), luchinat@cerm.uni®.it C. Luchinat), parigi@cerm.uni®.it G. Parigi).