Theory of water-proton spin relaxation in complex biological systems

In complex biological systems (e.g. gels, cross-linked proteins and biological tissues), the longitudinal spin relaxation of water protons is primarily induced by exchange-mediated orientational randomization (EMOR) of intra- and intermolecular magnetic dipole-dipole couplings. The chemical exchange processes that dominate the magnetic relaxation dispersion (MRD) typically occur on a time scale of microseconds or longer, where the conventional perturbation theory of spin relaxation breaks down. In this thesis, we have systematically studied water proton MRD in different immobilized model spin systems corresponding to different exchange cases. In the study of a dipolecoupledspin-1/2 pair which exchanges with bulk water proton spins, we presented the first treatment of dipolar MRD outside the motional-narrowing regime based on the stochastic Liouville equation for the EMOR mechanism. Moreover, we obtained simple analytical expressions which generalize the well-known Solomon equations. Then we studied the asymmetric exchange case for the two-spin system, when the spin system is fragmented by the exchange. Some new and unexpected phenomena showed up in this case. Notably, the anisotropic dipole couplings of nonexchanging 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 splitsthe extreme-narrowing regime into two sub-regimes. Then we extended our studies to a macromolecule-bound threespin system, where one, two, or all three spins exchange with the bulk solution phase. In contrast to the previouslystudied two-spin system with a single dipole coupling, there are now three dipole couplings so relaxation is affected by distinct correlations as well as by self-correlations. Moreover, relaxation can now couple the magnetizations with threespin modes and, in the presence of a static dipole coupling, with two-spin modes. In another study of the three-spin system in which the relaxation is induced by rotational diffusion, we calculated longitudinal relaxation rate of this model system in arbitrary geometry and with arbitrary rotational dynamics. In this study, we found that the odd-valued spectral density function influences longitudinal relaxation, which is at variance with conventional wisdom. Based onthese studies, we have constructed a multi-spin dipolar EMOR relaxation theory based on stochastic Redfield equations with generalizations. This theory yields a quantitative molecular description of tissue-water relaxation and thus provides a rigorous link between relaxation-based magnetic resonance image contrast and molecular parameters