An iterative fitting procedure for the determination of longitudinal NMR cross-correlation rates

We present a method to measure (15)N-(1)H dipolar/(15)N CSA longitudinal cross-correlation rates in protonated proteins. The method depends on the measurement of four observables: the cumulative proton-proton cross relaxation rates, the (15)N R(1) relaxation rate, the multiexponential decay of 2N(Z)H(N)(Z) spin-order, and multiexponential buildup of 2N(Z)H(N)(Z) spin-order. The (15)N-(1)H dipolar/(15)N CSA longitudinal cross-correlation rate is extracted from these measurements by an iterative fitting procedure to the solution of differential equations describing the coupled relaxation dynamics of the z-magnetization of the (15)N nucleus, the two-spin-order 2N(Z)H(N)(Z), and a two-spin-order term 2N(Z)H(Q)(Z) describing the interaction with remote protons. The method is applied to the microbial ribonuclease binase. The method can also extract longitudinal cross-correlation rates for those amide protons that are involved in rapid solvent exchange. The experiment that serves for extracting proton-proton cross-relaxation rates is a modification of 3D (15)N-resolved NOESY-HSQC. The experiment restores the solvent magnetization to its equilibrium state during data detection for all phase cycling steps and all values of NOE mixing times and is recommended for use in standard applications as well.