title: Nuclear magnetic relaxation by the dipolar EMOR mechanism: General theory with applications to two-spin systems.
abstract: In aqueous systems with immobilized macromolecules, including biological tissue, the longitudinal spin relaxation of water protons is primarily induced by exchange-mediated orientational randomization (EMOR) of intra- and intermolecular magnetic dipole-dipole couplings. We have embarked on a systematic program to develop, from the stochastic Liouville equation, a general and rigorous theory that can describe relaxation by the dipolar EMOR mechanism over the full range of exchange rates, dipole coupling strengths, and Larmor frequencies. Here, we present a general theoretical framework applicable to spin systems of arbitrary size with symmetric or asymmetric exchange. So far, the dipolar EMOR theory is only available for a two-spin system with symmetric exchange. Asymmetric exchange, when the spin system is fragmented by the exchange, introduces new and unexpected phenomena. Notably, the anisotropic dipole couplings of non-exchanging spins break the axial symmetry in spin Liouville space, thereby opening up new relaxation channels in the locally anisotropic sites, including longitudinal-transverse cross relaxation. Such cross-mode relaxation operates only at low fields; at higher fields it becomes nonsecular, leading to an unusual inverted relaxation dispersion that splits the extreme-narrowing regime into two sub-regimes. The general dipolar EMOR theory is illustrated here by a detailed analysis of the asymmetric two-spin case, for which we present relaxation dispersion profiles over a wide range of conditions as well as analytical results for integral relaxation rates and time-dependent spin modes in the zero-field and motional-narrowing regimes. The general theoretical framework presented here will enable a quantitative analysis of frequency-dependent water-proton longitudinal relaxation in model systems with immobilized macromolecules and, ultimately, will provide a rigorous link between relaxation-based magnetic resonance image contrast and molecular parameters.
authors.affiliation: Division of Biophysical Chemistry, Department of Chemistry, Lund University, P.O. Box 124, SE-22100 Lund, Sweden.
authors.forename: Zhiwei
authors.initials: Z
authors.lastname: Chang
authors.affiliation: Division of Biophysical Chemistry, Department of Chemistry, Lund University, P.O. Box 124, SE-22100 Lund, Sweden.
authors.forename: Bertil
authors.initials: B
authors.lastname: Halle
mesh_terms: D006878:Hydroxides / Q000737:chemistry*; D066244:Proton Magnetic Resonance Spectroscopy / Q000592:standards; D012015:Reference Standards; D013269:Stochastic Processes; D014867:Water / Q000737:chemistry*
chemical_list: D006878:Hydroxides; D014867:Water; C031356:hydroxide ion