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 sim ulations or restrained energy minimizations are performed for several copie s of a molecule simultaneously. The calculations are restrained with dipola r relaxation rates derived from measured NOE intensities via complete relax ation matrix analysis. The novel feature of the algorithm is that the weigh ts of individual conformers are determined in every refinement step, by the quadratic programming algorithm, in such a way that the restraint energy i s minimized. Its design ensures that the calculated populations of the indi vidual conformers are based only on experimental restraints. Presence of in ternally inconsistent restraints is the driving force for determination of distinct multiple conformers. The method is applied to various simulated te st systems. Conformational calculations on nucleic acids are carried out us ing generalized helical parameters with the program DNAminiCarlo. From diff erent mixtures of A- and B-DNA, minor fractions as low as 10% could be dete rmined with restrained energy minimization. For B-DNA with three local conf ormers (C2'-endo, O4'-exo, C3'-endo), the minor O4'-exo conformer could not be reliably determined using NOE data typically measured for DNA. The othe r two conformers, C2'-endo and C3'-endo, could be reproduced by Metropolis Monte Carlo simulated annealing. The behavior of the algorithm in various s ituations is analyzed, and a number of refinement protocols are discussed. Prior to application of this algorithm to each experimental system, it is s uggested that the presence of internal inconsistencies in experimental data be ascertained. In addition, because the performance of the algorithm depe nds on the type of conformers involved and experimental data available, it is advisable to carry out test calculations with simulated data modeling ea ch experimental system studied.