Determination of the populations and structures of multiple conformers in an ensemble from NMR data: multiple-copy refinement of nucleic acid structures using floating weights.

A new algorithm is presented for determination of structural conformers and their populations based on NMR data. Restrained Metropolis Monte Carlo simulations or restrained energy minimizations are performed for several copies of a molecule simultaneously. The calculations are restrained with dipolar relaxation rates derived from measured NOE intensities via complete relaxation matrix analysis. The novel feature of the algorithm is that the weights of individual conformers are determined in every refinement step, by the quadratic programming algorithm, in such a way that the restraint energy is minimized. Its design ensures that the calculated populations of the individual conformers are based only on experimental restraints. Presence of internally inconsistent restraints is the driving force for determination of distinct multiple conformers. The method is applied to various simulated test systems. Conformational calculations on nucleic acids are carried out using generalized helical parameters with the program DNAminiCarlo. From different mixtures of A- and B-DNA, minor fractions as low as 10% could be determined with restrained energy minimization. For B-DNA with three local conformers (C2'-endo, O4'-exo, C3'-endo), the minor O4'-exo conformer could not be reliably determined using NOE data typically measured for DNA. The other two conformers, C2'-endo and C3'-endo, could be reproduced by Metropolis Monte Carlo simulated annealing. The behavior of the algorithm in various situations is analyzed, and a number of refinement protocols are discussed. Prior to application of this algorithm to each experimental system, it is suggested that the presence of internal inconsistencies in experimental data be ascertained. In addition, because the performance of the algorithm depends on the type of conformers involved and experimental data available, it is advisable to carry out test calculations with simulated data modeling each experimental system studied.