Unlocking Gd(III) Anisotropy: Determining the Zero-Field Splitting Axes to Enhance Spin-Label Structural Analysis

The zero-field splitting (ZFS) of Gd(III) complexes is central to magnetic resonance applications, influencing nuclear relaxation in MRI and NMR, electron spin relaxation in EPR, and the performance of Gd-based spin labels for structural biology applications. However, determining the molecular-frame orientation of the ZFS tensor is experimentally and computationally demanding for Gd(III) chelate complexes in frozen solution, where structural and dynamic heterogeneity complicates orientation determination. Here, we introduce an experimental strategy that enables direct determination of the ZFS tensor orientation in Gd(III) complexes using ¹⁹F and ¹H orientation-selective (OS) electron-nuclear double resonance (ENDOR). For the commonly used spin labels Gd-DO3A and Gd-PyMTA, we determined the molecular-frame orientation of the ZFS, necessary for quantitative analysis of the Gd(III) anisotropy. This allowed for a dual-mode analysis of Gd-F ENDOR spectra, where electron-nuclear distances can be accurately extracted from measurements at the Gd(III) central transition, while the Gd-F vector orientation is determined using OS-ENDOR on high-|m_S| transitions. Accordingly, we determined the location of Gd-DO3A labels in two ¹⁹F-containing proteins and showed that utilizing existing rotamer libraries substantially overestimates the label's conformational distributions. The experimentally determined ZFS orientations are further compared to theoretical predictions of a simple molecular modeling calculation based on the electric-field-gradient tensor. Our results provide a platform for improved structure determination with Gd-based labels and offer valuable benchmarks for improving quantum-chemical predictions of ZFS tensors.