Estimation of internuclear couplings in the solid-state NMR of multiple-spin systems. Selective spin echoes and off-magic-angle sample spinning

Longer-range distances by spinning-angle-encoding solid-state NMR spectroscopy

“…b Calculated as described in Ref. 25 (see ESI). c Determined from fitting the reference curve to eqn (3).…”

“…[1][2] In particular, protocols for the determination of three-dimensional structures of biomacromolecules rely upon establishing multiple distance constraints via the inherent inverse cubed dependence on the internuclear distance of a dipolar coupling between two nuclear spins. While utilising 25 dipolar couplings between nuclei with a short through-bond connectivity in the same or neighbouring amino acid residues is important for the assignment of the resonances, it is longerrange distances (> 4 Å) corresponding to inter-residue proximities between nuclei with no through-bond connectivity 30 that are key to determining the secondary and tertiary structure of a protein. [3][4][5][6][7] For isolated spin pairs in selectively labelled molecules, homonuclear dipolar couplings can be accurately determined, e.g., by double-quantum magic-angle spinning (MAS) 13 C 35 build-up.…”

“…As for previous (on-angle) MAS spin-echo experiments for 25 determining J couplings, 33-36 the spin-echo intensity, s(), is obtained by integration over the corresponding lineshape (after Fourier transformation with respect to the acquisition time, t 2 ). As discussed further in the ESI, this ensures that only in-phase lineshapes with their cosine spin-echo 30 modulation are considered, i.e., there is no contribution from anti-phase lineshapes which have a sine spin-echo modulation.…”

“…The calculation of the time shift, t s , due to the finite length of the refocusing pulse is 65 described in the ESI, using the procedure employed in Ref. 25 Note that the offset, , from the magic angle in eqn (1) is in radians, while the dipolar coupling constant, D, is in Hz:…”

“…Note that while the shortest C-C distances for the CO-C (2.57 Å) and CO-C Table 1 corresponds to a sum over multiple distances of 5.26 Å and longer. A further novel feature of this work is the recognition that the analytical expression for s(), eqn (1), defines a master 25 curve that depends on , D, and t s . This is illustrated by Fig.…”