A relaxation-matrix analysis of distance-constraint ranges for NOEs in proteins at long mixing times.

Long-mixing-time data (tau m > 200 ms) from NOE spectra have largely been ignored as a source of protein structural information due to the effects of spin diffusion on calculated interproton distances when using the two-spin approximation. An effective approach for incorporating spin-diffusion effects in an average way into refinements is to choose distance bounds based on distributions of distances observed in NOE back calculations on homologous proteins from a protein structure database. We have determined distributions of interproton distances characteristic of newly observed NOE cross peaks for the proteins crambin, PTI, and echistatin at long mixing times. A relaxation-matrix analysis was used to model the effects of spin diffusion. Constraint ranges were constructed from the interproton distance distributions which can be used in standard protein-refinement programs based on the two-spin approximation. Back calculations are also used to analyze constraint ranges typically used for protein structure determinations based on NOE spectra at shorter mixing times.