In an exchanging system between major and minor species, the transverse paramagnetic relaxation enhancement rate observed on the resonances of the major species (Γ 2 (app) ) is dependent upon the exchange regime between the species. Quantitative analysis of PRE data in such systems typically assumes that the overall exchange rate k ex between the species is fast on the PRE time scale (k ex ≫ Γ2). Recently, we have characterized the kinetics of binding of the model protein ubiquitin to large (LUV) and small (SUV) unilamellar lipid-based nanoparticles or liposomes (Ceccon A, Tugarinov V, Bax A, Clore GM (2016). J Am Chem Soc 138:5789-5792). Building upon these results and taking advantage of a strong paramagnetic agent with an isotropic g-tensor, Gd(3+), we were able to measure intermolecular methyl carbon and proton PREs between paramagnetically-tagged liposomes and ubiquitin. In the limit of fast exchange (k ex ≫ Γ2) the ratio of the apparent proton to carbon methyl PREs, ((1)Hm-Γ 2 (app) )/((13)Cm-Γ 2 (app) ), is equal to the square of the ratio of the gyromagnetic ratios of the two nuclei, (γΗ/γC)(2). However, outside the fast exchange regime, under intermediate exchange conditions (e.g. when Γ2 is comparable in magnitude to k ex) the ((1)Hm-Γ 2 (app) )/((13)Cm-Γ 2 (app) ) ratio provides a reliable measure of the 'true' methyl PREs.
Keywords: Chemical exchange; Ligand binding; Liposomes; Paramagnetic relaxation enhancement; Protein-nanoparticle interactions.