Perspective: revisiting the field dependence of TROSY sensitivity

The discovery of the TROSY effect (Pervushin et al. in Proc Natl Acad Sci USA 94:12366-12371, 1997) for reducing transverse relaxation and line sharpening through selecting pathways in which dipole-dipole and CSA Hamiltonians partially cancel each other had a tremendous impact on solution NMR studies of macromolecules. Together with the methyl TROSY (Tugarinov and Kay in J Biomol NMR 28:165-172, 2004) it enabled structural and functional studies of significantly larger systems. The optimal field strengths for TROSY have been estimated to be on spectrometers operating around 900 MHz (21.14 T) for the ¹H_N TROSY (Pervushin et al. in Proc Natl Acad Sci USA 94:12366-12371, 1997) while the aromatic ¹³C (¹³C_aro) TROSY is posited to be optimal at around 600 MHz (14.09 T) (Pervushin et al. in J Am Chem Soc 120:6394-6400, 1998b; Pervushin in Q Rev Biophys 33:161-197, 2000). The initial rational was based on the consideration of where the quadratic B₀ field dependences of the TROSY relaxation rates reach a minimum. For sensitivity consideration, however, it is interesting to estimate which field strengths yield the tallest peaks. Recent studies of ¹⁵N-detected TROSYs suggested that maximal peak heights are expected at 1.15 GHz (27.01 T) although the slowest relaxation rates or longest transverse relaxation times T₂ are indeed expected around 900 MHz (21.14 T) (Takeuchi in J Biomol NMR 63:323-331, 2015; Takeuchi et al. in J Biomol NMR 64:143-151, 2016). This was based on the fact that the heights of Lorentzian lines are proportional to B _o^3/2 * T₂ (B_o). Thus, multiplying the parabolic T₂(B_o) dependence with the increasing function of B _o^3/2 shifts the maxima of peak-height field dependence from the T₂ maximum at 900 MHz to higher fields. Moreover, besides shifting the peak height maximum for ¹⁵N TROSY, this analysis yields estimates for optimal peak heights for ¹H_N detected TROSY to 1.5 GHz, and to 900 MHz for ¹³C-detected ¹³C_aroTROSY as is detailed below. To our knowledge, this aspect of field dependence of TROSY sensitivity has not been in the attention of the NMR community but may affect perspectives of NMR at ultra-high fields.