The quadrupole enhanced 1H spin–lattice relaxation of the amideproton in slow tumbling proteins

Abstract

An analysis, based on the stochastic Liouville approach, is presented of the R₁-NMRD or field dependent spin–lattice relaxation rate of amide protons. The proton relaxivity, displayed as R₁-NMRD profiles, is calculated for a reorienting ¹H–¹⁴N spin group, where the inter spin coupling is due to spin dipole–dipole coupling or the scalar coupling. The quadrupole nucleus ¹⁴N has an asymmetry parameter η = 0.4 and a quadrupole interaction which is modulated by the overall reorientational motion of the protein. In the very slow reorientational regime, ω_Qτ_R ≫ 1 and τ_R ≥ 2.0 μs, both the dipole–dipole coupling and the scalar coupling yield a T₁-NMRD profile with three marked peaks of proton spin relaxation enhancement. These peaks appear when the proton Larmor frequency, ω_I, matches the nuclear quadrupole spin transition frequencies: ω₁ = ω_Q2η/3, ω₂ = ω_Q(1 − η/3) and ω₃ = ω_Q(1 + η/3), and the quadrupole spin system thus acts as a relaxation sink. The relative relaxation enhancements of the peaks are different for the dipole–dipole and the scalar coupling. Considering the dipole–dipole coupling, the low frequency peak, ω₁, is small compared to the high field peaks whereas for the scalar coupling the situation is changed. For slow tumbling proteins with a correlation time of τ_R = 400 ns, ω₂ and ω₃ are not resolved but become one relatively broad peak. At even faster reorientation, τ_R < 60 ns, the marked peaks disappear. In this motional regime, the main effect of the cross relaxation phenomenon is a subtle perturbation of the main amide proton T₁ NMRD dispersion. The low field part of it can be approximately described by a Lorentzian function: R^DD,SC(0.01)/(1 + (ω_Iτ_R)²) whereas the high field part coincides with R^DD,SC(0.01)/(1 + (ω_Iτ_R)²).