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.

[1]  R. Fletcher.  Practical Methods of Optimization , 1988 .

[2]  T. James,et al.  A theoretical study of distance determinations from NMR. Two-dimensional nuclear overhauser effect spectra , 1984 .

[3]  D. Gorenstein.  Conformation and Dynamics of DNA and Protein-DNA Complexes by 31P NMR , 1994 .

[4]  Ashok Kumar,et al.  Probability assessment of conformational ensembles: sugar repuckering in a DNA duplex in solution. , 1995, Biophysical journal.

[5]  T. James,et al.  Structure and dynamics of a DNA.RNA hybrid duplex with a chiral phosphorothioate moiety: NMR and molecular dynamics with conventional and time-averaged restraints. , 1995, Biochemistry.

[6]  V. Zhurkin,et al.  Different families of double‐stranded conformations of DNA as revealed by computer calculations , 1978 .

[7]  T. James,et al.  Insights into the dynamic nature of DNA duplex structure via analysis of nuclear Overhauser effect intensities. , 1998, Biochemistry.

[8]  M. Kennedy,et al.  Solution-state structure of a DNA dodecamer duplex containing a Cis-syn thymine cyclobutane dimer, the major UV photoproduct of DNA. , 1998, Journal of molecular biology.

[9]  G. Varani,et al.  The stereospecific assignment of H5' and H5'' in RNA using the sign of two-bond carbon-proton scalar couplings , 1993 .

[10]  V. Zhurkin,et al.  Systematic study of nuclear Overhauser effects vis-à-vis local helical parameters, sugar puckers, and glycosidic torsions in B DNA: insensitivity of NOE to local transitions in B DNA oligonucleotides due to internal structural compensations. , 1992, Biochemistry.

[11]  B. Borgias,et al.  Two-dimensional nuclear Overhauser effect: complete relaxation matrix analysis. , 1989, Methods in enzymology.

[12]  H. Kalbitzer,et al.  Relax, a flexible program for the back calculation of NOESY spectra based on complete-relaxation-matrix formalism. , 1997, Journal of magnetic resonance.

[13]  Nikolai B. Ulyanov,et al.  [4] Statistical analysis of DNA duplex structural features , 1995 .

[14]  A. Brünger,et al.  Conformational variability of solution nuclear magnetic resonance structures. , 1995, Journal of molecular biology.

[15]  W. V. van Gunsteren,et al.  Time-averaged nuclear Overhauser effect distance restraints applied to tendamistat. , 1990, Journal of molecular biology.

[16]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[17]  T. James,et al.  Small structural ensembles for a 17-nucleotide mimic of the tRNA T psi C-loop via fitting dipolar relaxation rates with the quadratic programming algorithm. , 1998, Biopolymers.

[18]  B. Borgias,et al.  MARDIGRAS : a procedure for matrix analysis of relaxation for discerning geometry of an aqueous structure , 1990 .

[19]  M. Delepierre,et al.  NF-kappa B binding mechanism: a nuclear magnetic resonance and modeling study of a GGG --> CTC mutation. , 1999, Biochemistry.

[20]  S. Landy,et al.  Dynamical NOE in multiple-spin systems undergoing chemical exchange , 1989 .

[21]  A. Bianucci,et al.  Nuclear magnetic resonance structure of d(GCATATGATAG). d(CTATCATATGC): a consensus sequence for promoters recognized by sigma K RNA polymerase. , 1998, Biochemistry.

[22]  G. L. Kenyon,et al.  A potential gene target in HIV-1: rationale, selection of a conserved sequence, and determination of NMR distance and torsion angle constraints. , 1992, Biochemistry.

[23]  M. Sundaralingam,et al.  Conformational analysis of the sugar ring in nucleosides and nucleotides. A new description using the concept of pseudorotation. , 1972, Journal of the American Chemical Society.

[24]  R. Levy,et al.  Determining local conformational variations in DNA. Nuclear magnetic resonance structures of the DNA duplexes d(CGCCTAATCG) and d(CGTCACGCGC) generated using back-calculation of the nuclear Overhauser effect spectra, a distance geometry algorithm and constrained molecular dynamics. , 1990, Journal of molecular biology.