Relaxation-Matrix Formalism for Rotating-Frame Spin-Lattice Proton NMR Relaxation and Magnetization Transfer in the Presence of an Off-Resonance Irradiation Field

Magnetization transfer MRS

“…Thus, three-pool models have been discussed and mathematically analyzed. 29,30 Figure 5 shows schematically a three-pool model consisting of two Lorentzian pools, i.e. pool A of mobile spins being directly observed in the MR experiment, and Lorentzian pool B of semi-solid spins as well as a Gaussian pool C of solid spins.…”

1H magnetic cross‐relaxation between multiple solvent components and rotationally immobilized protein

“…Their approach using the projection operator method has been applied to the multiple spin bath problem in which the solid was treated as multicomponent (27,28 these studies were heat denatured egg albumin and bovine ocular lens, which are appropriately modeled with multiple solid components. For the protein gel samples in the present study.…”

Modeling Magnetization Transfer Using a Three-Pool Model and Physically Meaningful Constraints on the Fitting Parameters

“…Common practice is to replace the Lorentzian lineshape function which results from the Bloch formalism with a generalized lineshape function for the macromolecular component (39,44). In general, the lineshape of the macromolecular component is well approximated by a Gaussian,…”

“…The motions of these functional groups will be more restricted in cross-linked proteins and in lipid bilayers than in the solutions of the biopolymers and may range from picoseconds to microseconds. Initial estimates for T 1C will be taken from the literature based on the extraction of parameters from empirical MT data (39,41,44). The inverse of the MT linewidth provides an estimate of the lower limit for T 2C which is taken to be on the order of tens of microseconds.…”

“…The formulation of the coupled rate equations used to describe the transfer of nuclear magnetization within hydrated systems in the presence of a selective RF-saturation field and exchange and/or dipolar coupling has followed two general approaches, the use of modified Bloch equations (16,22,25,39,43,44) and the more general Redfield-Provotorov formalism (41). The Bloch equation description lends itself to simplicity with respect to interpretation, comparison between different models accounting for coupled populations and coupling mechanisms, and solving the system of coupled differential equations.…”