Fig. 1: Method for the detection of LLC-based transfer in proteins.

a Energy level diagram of spin states characteristic to a J-coupled two-spin-1/2 system. Thermal magnetisation is a population imbalance between the outer states, while long-lived coherences are superpositions between the singlet state and the central triplet states. Inset: glycine backbone highlighting the H^α2,3 protons denoted (I,S) and the mirror plane \({\sigma }_{h}^{{Gly}}\) which interconverts the two spins. b The 1D/2D pulse sequences used to excite multiple narrow bands of the protein’s proton spectrum centred around the targeted Gly-H^α resonances and sustain LLC’s during transfer. The initial phase offset between the two components of the 90° dual-frequency pulse can be adjusted to generate either long-lived coherences (‘LLC’ experiment), or classical transverse coherence (reference ‘REF’ experiment). (see “Materials and Methods” section). c Signal decay of the LLC versus transverse magnetisation during the spin-lock period (\({\tau }_{{mix}}\)) measured at \(1/{J}_{{IS}}^{{Gly}}\) intervals for Gly117 residue. d Excitation profile of the 90° dual-frequency pulse used to excite LLCs (red) and standard transverse coherences (black, shifted). Residual z-axis magnetisation is shown in blue. The y-axis shows normalised magnetisation excited for each nuclear spin. e Graphic representation of the LLC-ROE magnetisation transfer in a sphere surrounding the two glycine protons H^α2 (green) and H^α3 (blue) highlighting the stereospecific interaction of neighbouring protons. Depending on relative distances to the two (I,S) methylene protons, surrounding spins K will display either negative (when they are found in the space region closer to H^α2, outlined in green) or positive ROE build-up curves (when they are found in the space region closer to H^α3, outlined in blue). f Numerical simulations (notebook provided in Supplementary Note 3) highlighting the dependence of maximum expected transfer towards a third spin K via rotating-frame Overhauser effects (ROE), starting from \({\rho }_{{LLC}}^{0}={I}_{x}-{S}_{x}\) (red) compared to \({\rho }_{{REF}}^{0}={I}_{x}+{S}_{x}\) (black), the rotational correlation time increases. The transfer from LLC gradually increases and surpasses the classical ROE transfer. Structural parameters of the three-spin-1/2 system are provided as an inset.