A set of cross-correlated relaxation experiments to probe the correlation time of two different and complementary spin pairs

Intrinsically disordered proteins (IDPs) defy the conventional structure-function paradigm by lacking a well-defined tertiary structure and exhibiting inherent flexibility. This flexibility leads to distinctive spin relaxation modes, reflecting isolated and specific motions within individual peptide planes. In this work, we propose a new pulse sequence to measure the longitudinal ¹³C${}^{\prime }$ CSA-¹³C${}^{\prime }$-¹³C${}^{\alpha }$ DD CCR rate ${\Gamma }_z^{C^{\prime }/C^{\prime }{C}^{\alpha }}$ and present a novel 3D version of the transverse ${\Gamma }_{xy}^{C^{\prime }/C^{\prime }{C}^{\alpha }}$ CCR rate, adopting the symmetrical reconversion approach. We combined these rates with the analogous ${\Gamma }_{xy}^{N/NH}$ and ${\Gamma }_z^{N/NH}$ CCR rates to derive residue-specific correlation times for both spin-pairs within the same peptide plane. The presented approach offers a straightforward and intuitive way to compare the correlation times of two different and complementary spin vectors, anticipated to be a valuable aid to determine IDPs backbone dihedral angles distributions. We performed the proposed experiments on two systems: a folded protein ubiquitin and Coturnix japonica osteopontin, a prototypical IDP. Comparative analyses of the results show that the correlation times of different residues vary more for IDPs than globular proteins, indicating that the dynamics of IDPs is largely heterogeneous and dominated by local fluctuations.