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

Abstract

An analysis, based on the stochastic Liouville approach, is presented of the R(1)-NMRD or field dependent spin-lattice relaxation rate of amide protons. The proton relaxivity, displayed as R(1)-NMRD profiles, is calculated for a reorienting (1)H-(14)N spin group, where the inter spin coupling is due to spin dipole-dipole coupling or the scalar coupling. The quadrupole nucleus (14)N has an asymmetry parameter eta = 0.4 and a quadrupole interaction which is modulated by the overall reorientational motion of the protein. In the very slow reorientational regime, omega(Q)tau(R) >> 1 and tau(R) > or = 2.0 micros, both the dipole-dipole coupling and the scalar coupling yield a T(1)-NMRD profile with three marked peaks of proton spin relaxation enhancement. These peaks appear when the proton Larmor frequency, omega(I), matches the nuclear quadrupole spin transition frequencies: omega(1) = omega(Q)2eta/3, omega(2) = omega(Q)(1-eta/3) and omega(3) = omega(Q)(1 + eta/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, omega(1), 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 tau(R) = 400 ns, omega(2) and omega(3) are not resolved but become one relatively broad peak. At even faster reorientation, tau(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 T(1) NMRD dispersion. The low field part of it can be approximately described by a Lorentzian function: R(DD,SC)(0.01)/(1 + (omega(I)tau(R)3/2)(2)) whereas the high field part coincides with R(DD,SC)(0.01)/(1 + (omega(I)tau(R))(2)).