Accurate measurement of longitudinal paramagnetic relaxation enhancement through division after subtraction

Paramagnetic relaxation enhancement (PRE) provides valuable distance constraints with respect to unpaired electron for the structural and dynamic characterization of biomolecules. While transverse PRE (Γ ₂) has been widely used, its quantitative interpretation is often confounded by chemical exchange and other factors. In contrast, longitudinal PRE (Γ ₁), though much smaller in magnitude than Γ ₂, is a more faithful reporter of electron-nuclei distances. In this work, we introduce the division after subtraction (DAS) approach, which utilizes a synchronized sampling scheme to analytically cancel out common-mode artifacts. We validate this approach using site-directed covalent labeling and solvent PRE systems, and demonstrate improved accuracy compared to standard separate fitting routine. DAS is particularly effective for labile residues, where traditional nonlinear regression breaks down due to solvent-mediated effects. The enhanced precision with DAS in Γ ₁ measurement allows for more rigorous investigation into biomolecular conformational landscape, thus providing a powerful complement to Γ ₂-based PRE methodology.