Cross-correlated relaxation for the measurement of angles between tensorial interactions

Theory,experimental aspects, and use in structure calculation of cross-correlated relaxation rates measured on zero- and double-quantum coherences in liquid state NMR are presented. The relative size of the interaction depends on the projection angle between the two tensorial interactions. The tensorial interaction can be either a dipolar interaction or a chemical shift anisotropy relaxation mechanism (CSA). Effects of additional sources of relaxation on the cross-correlated relaxation rates are analyzed. Also, an easy-to-use formalism is given to manipulate different cross-correlated relaxation interactions. The application addresses measurement of the backbone angle psi in a protein by measuring dipole((15)N-(1)H)-dipole((13)C(alpha)-(1)H(alpha)) and CSA((15)N)-dipole((13)C(alpha)-(1)H(alpha)) cross-correlated relaxation rates. It is shown that ambiguities due to the 3 cos(2)θ-1 dependence of one cross-correlated relaxation rate can be overcome by measuring additional cross-correlated relaxation rates. The use of cross-correlated relaxation rates is demonstrated in structure calculations.