Analysis of error propagation from NMR-derived internuclear distances intomolecular structure of cyclo-Pro-Gly

Analytical expressions have been derived that translate uncertainties in di stance constraints (obtained from NMR investigations) into uncertainties in atom positions in the maximum likelihood (ML) structure consistent with th ese inputs, As a test of this approach, a comparison was made between test structures reconstructed by the new ML approach, which yields a single stru cture and a covariance matrix for coordinates, and those reconstructed by m etric matrix distance-geometry (MMDG), which yields a family of structures that sample uncertainty space. The test structures used were 560 polyhedra, with edges of arbitrary length containing up to 50 vertices, and one polyh edron, with 100 vertices; randomized distance constraints generated from th ese structures were used in reconstructing the polyhedra. The uncertainties derived from the two methods showed excellent agreement, and the correlati on improved, as expected, with increasingly larger numbers of MMDG structur es. This agreement supports the validity of the rapid analytical ML approac h, which requires the calculation of only a single structure. As a second t est of the ML method, the approach was applied to the determination of unce rtainties in the structure of a cyclic dipeptide, cyclo(DL-Pro-Gly) (cPG), derived from NMR cross-relaxation data. The input data were interproton dis tances calculated from NOEs measured for a solution of the peptide in 2:1 D MSO:H2O at -40 degrees C (so as to yield large negative NOEs), In order to evaluate effects of the quality of the input spectral parameters on the pre cision of the resulting NMR structure, information from the covalent geomet ry of cPG was not used in the structure calculations. Results obtained from the analytical ML approach compared favorably with those from the much slo wer random-walk variant of the Monte Carlo method applied to the same input data. As a third test, the ML approach was used with synthetic structural constraints for a small protein; the results indicate that it will be feasi ble to use this rapid method to translate uncertainties associated with a g iven set of distance restraints into uncertainties in atom positions in lar ger molecules. (C) 1998 Academic Press.