Elsevier

Chemical Physics Letters

Volume 300, Issues 3–4, 5 February 1999, Pages 429-434
Chemical Physics Letters

Influence of cross-correlation between the chemical shift anisotropies of pairs of nuclei on multiple-quantum relaxation rates in macromolecules

https://doi.org/10.1016/S0009-2614(98)01389-XGet rights and content

Abstract

The relaxation of multiple-quantum coherence due to intramolecular dipole–dipole and chemical shift anisotropy (CSA) relaxation mechanisms is described. It is shown that cross-correlation between the CSAs of the active spins can affect the relaxation of 1H15N two-spin coherences in the protein backbone. An experiment that enables this effect to be monitored is discussed. Data are presented for perdeuterated 15N-labelled human dynamic light chain 1 protein (hdlc1). An analysis of the results yields a value for the CSA of the active 1H.

Introduction

Recent years have seen an increase in interest in the measurement and analysis of NMR relaxation, much of it stimulated by the increasing availability of 15N- and 13C-labelled proteins. In addition to the conventional measurement of nuclear Overhauser enhancement to determine internuclear distances [1], relaxation studies of proteins in particular have been used to probe molecular dynamics 2, 3. More recently, measurements of the cross-correlation of different dipolar interactions have been used to determine the angle between them as well as to investigate local motion 4, 5, and measurements of dipolar–chemical shift anisotropy (CSA) cross-correlation have been used to measure chemical shift anisotropy 6, 7, 8, 9, 10, 11. Dipolar–CSA cross-correlation is also responsible for the production of relatively narrow linewidths in spectra produced by the TROSY experiment [12]compared with those produced by competing techniques. CSA–CSA cross-correlation has been predicted for zero- and double-quantum coherence [13]but has not been measured experimentally.

We report here experimental measurement and analysis of CSA–CSA cross-correlation in the 1H15N heteronuclear zero- and double-quantum coherences arising from Glutamine 27 of perdeuterated 15N-labelled protein hdlc1. It has come to our notice that Boyd is undertaking similar studies [14].

Section snippets

Theory

The time dependence of the density operator can be written in matrix form as 15, 16:dσ(t)dt=−{iH+Γ}{σ(t)−σ0},where H is the time-independent nuclear spin superoperator, Γ is the relaxation superoperator, σ(t) is the density operator at a time t, and σ0 is the density operator at equilibrium. For convenience the density operator is often expanded as either single-transition operator, or the product of shift operators. Here we adopt the latter approach. The diagonal elements of Γ give the

Experimental methods and results

The pulse sequence used to measure the relaxation of 1H15N heteronuclear zero- and double-quantum coherence is shown in Fig. 1. Sensitivity is maximised by both exciting and detecting 1H magnetisation. The essential features of CSA–CSA cross-correlation may be demonstrated by the transverse relaxation behaviour of the backbone 1H15N group of Glutamine 27 of a fully 15N-labelled and perdeuterated, except for the amide protons, sample of the protein hdlc1 in H2O [24]. Glutamine 27 is in an

Discussion

The calculation of values for both ΓklC and ΔσH has been made by making a number of approximations. The model free spectral density function given in Eq. (14)makes the assumption that molecular motion is isotropic; this is often not the case and consequently J(ω) may vary with orientation [27]. However, since the angle between the 1H15N vector and the principal axis of the 15N CSA tensor is relatively small (∼220) any variation of J(ω) between the two will also be small and can usually be

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