Relaxation of Two-Spin Coherence Due to Cross-Correlated Fluctuations of Dipole−Dipole Couplings and Anisotropic Shifts in NMR of ¹⁵N,¹³C-Labeled Biomolecules

Abstract

A comprehensive description is presented of the effects on two-spin coherences (i.e., superpositions of zero-and double-quantum coherences) of cross-correlation between the fluctuations of two different relaxation mechanisms in nuclear magnetic resonance (NMR). Dipole-dipole (DD) interactions between four nuclei and chemical shift anisotropy (CSA) of two of these nuclei are considered. Two complementary experiments have been designed for 15 N, 13 C-labeled proteins to quantify the effects of cross-correlation between the 13 C R -1 H R and 15 N-1 H N dipolar interactions on two-spin coherences involving 13 C R of the ith residue with the 15 N of the (i+1)th amino acid. Two other experiments allow one to quantify the effect of cross-correlation between the 13 C′ (carbonyl) CSA and the 13 C R -1 H R dipolar coupling on the relaxation of two-spin coherences involving the 13 C′ and 13 C R nuclei on the same residue of the protein. These experiments have been used to extract relevant cross-correlation rates in 15 N, 13 C-labeled human ubiquitin. These rates show a high degree of correlation with the backbone Ψ angles in proteins.

Detection of correlated dynamics on multiple timescales by measurement of the differential relaxation of zero- and double-quantum coherences involving sidechain methyl groups in proteins

“…Note, in writing Eqs. (5) and (6) we have assumed that the ZQC and DQC decays may be represented by single exponential functions, i.e., the secular approximation is valid. The validity of the secular approximation has been discussed in detail in the appendix (Appendix A).…”

“…(5). To estimate the first term corresponding to CSA/CSA cross-correlation accurately, estimates of the 13 C methyl and 13 C next shift tensors were required.…”

“…These measurements have revealed the existence of anisotropic motion in the protein backbone [3] and have allowed the estimation of hitherto inaccessible backbone dihedral angles [4][5][6][7]. They have also provided the means to determine the chemical shift tensor for backbone amide 15 N [8][9][10][11], 13 C a [12], and carbonyl 13 C 0 [13,14] nuclei in solution.…”

Theoretical Study of the Effective Chemical Shielding Anisotropy (CSA) in Peptide Backbone, Rating the Impact of CSAs on the Cross-Correlated Relaxations in l-Alanyl-l-alanine

“…Some of the CSA-DD cross-correlation mechanisms investigated in this work were also probed in recent NMR studies. [18][19][20]24,37,46 However, the majority of them were theoretically modeled in this work probably for the first time.…”

Correlated dynamics of consecutive residues reveal transient and cooperative unfolding of secondary structure in proteins

“…Recent methods development has made possible measurement of differential multiple-quantum (MQ) relaxation rates that report on correlated dynamics of different spin interactions (22)(23)(24). MQ relaxation rates can provide important structural information, because they depend on the angles relating the principal axis frames of the rank-two interaction tensors involved in the relevant relaxation mechanisms, which include the dipolar interaction and chemical shift anisotropy (25)(26)(27)(28)(29)(30). Another potentially important source of MQ relaxation is the correlated modulation of the (rank-zero) isotropic chemical shifts of multiple nuclei (19,21,(31)(32)(33)(34)(35).…”