A molecular theory of relaxation and magnetization transfer: Application to cross‐linked BSA, a model for tissue

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Abstract
Homogeneous soft tissue, as regards its magnetic relaxation properties, is well‐modeled by solutions of cross‐linked protein (see Koenig and Brown, Prog. NMR Specfr. 22,487 (1991)). Interactions at the solute‐solvent interface alter the hydrodynamics of solvent water, and also couple the solute and solvent proton Zeeman energy reservoirs, giving hydrodynamic and cross‐relaxation contributions to water proton relaxation that respond differently to deuteration of solvent. We report measurements of the magnetic field dependence of 1/T1, of water protons in cross‐linked bovine serum albumin (BSA), for partially deuterated solvent and, in order to separate these two contributions, of 1/T1, of deuterons. The major experimental finding is that, in addition to recently identified water‐binding sites on protein (covering ∼0.2% of the surface) with water lifetimes of about 1 μs, there is another group of sites with lifetimes of about 23 ns, covering ∼2% of the surface, which are evident in both proton and deuteron data. In addition, we have formulated a theory of interfacial proton‐proton magnetic interactions which—with these four parameters, plus two that quantify the protein‐water coupling at each site—can account for all the proton and deuteron data, in both native and cross‐linked BSA.