Solution structure of the EcoRI DNA octamer containing 5-fluorouracil via restrained molecular dynamics using distance and torsion angle constraints extracted from NMR spectral simulations.

The self-complementary DNA octamer [d(GGAATUFCC)]2, containing the EcoRI recognition sequence with one of the thymines replaced by 5-fluorouracil (UF), was synthesized. Proton homonuclear two-dimensional nuclear Overhauser effect (2D NOE) and double-quantum-filtered correlation (2QF-COSY) spectra, as well as one-dimensional spectra at different temperatures, were recorded for the octamer. Consequently, all proton resonances were assigned. The thermally induced transition from the duplex to single strands has been followed, demonstrating the stability of the duplex containing 5-fluorouracil. Simulations of the 2QF-COSY cross-peaks by means of the programs SPHINX and LINSHA were compared with experimental data, establishing scalar coupling constants for the sugar ring protons and hence sugar pucker parameters. The deoxyribose rings exhibit a dynamic equilibrium of N- and S-type conformers with 75-95% populations of the latter. Two programs used for complete relaxation matrix analysis 2D NOE spectra, CORMA and MARDIGRAS, were modified to account for the influence of the fluorines on dipolar interactions in the proton system. Quantitative assessment of the 2D NOE cross-peak intensities for different mixing times, in conjunction with the program MARDIGRAS, gave a set of interproton distances for each mixing time. The largest and smallest values of each of the interproton distances were chosen as the upper and lower bounds for each distance constraint. The distance bounds define the size of a flat-well potential function term, incorporated into the AMBER force field, which was employed for restrained molecular dynamics calculations. Torsion angle constraints in the form of a flat-well potential were also constructed from the analysis of the sugar pucker data. Several restrained molecular dynamics runs of 35 ps were performed, utilizing 284 experimental distance and torsion angle constraints and two different starting structures, energy-minimized A- and B-DNA. Convergence to similar structures with a root-mean-square deviation of 1.2 A was achieved for the central hexamer of the octamer, starting from A- and B-DNA. The average structure from six different molecular dynamics runs was subjected to final restrained energy minimization. The resulting final structure was in good agreement with the structures derived from different molecular dynamics runs and showed a substantial improvement of the 2D NOE sixth-root residual index in comparison with classical and energy-minimized B-DNA. A detailed analysis of the conformation of the final structure and comparison with structures of similar sequences, obtained by different methods, were performed.     

Solution structure of [d(GTATATAC)]2 via restrained molecular dynamics simulations with nuclear magnetic resonance constraints derived from relaxation matrix analysis of two-dimensional nuclear Overhauser effect experiments

Two-dimensional nuclear Overhauser effect (2D NOE) spectra have been used as the experimental basis for determining the solution structure of the duplex [d(GTATATAC)]2 employing restrained molecular dynamics (rMD) simulations. The MARDIGRAS algorithm has been employed to construct a set of 233 interproton distance constraints via iterative complete relaxation matrix analysis utilizing the peak intensities from the 2D NOE spectra obtained for different mixing times and model structures. The upper and lower bounds for each of the constraints, defining size of a flat-well potential function term used in the rMD simulations, were conservatively chosen as the largest or smallest value calculated by MARDIGRAS. Three different starting models were utilized in several rMD calculations: energy-minimized A-DNA, B-DNA, and a structure containing wrinkled D-DNA in the interior. Considerable effort was made to define the appropriate force constants to be employed with the NOE terms in the AMBER force field, using as criteria the average constraints deviation, the constraints violation energy and the total energy. Of the 233 constraints, one was generated indirectly, but proved to be crucial in defining the structure: the cross-strand A5-H2 A5-H2 distance. As those two protons resonate isochronously for the self-complementary duplex, the distance cannot be determined directly. However, the general pattern of 2D NOE peak intensities, spin-lattice relaxation time (T1) values, and 31P nuclear magnetic resonance spectra lead to use of the A3-H2 A7-H2 distance for A5-H2 A5-H2 as well. Five rMD runs, with different random number seeds, were made for each of the three starting structures with the full distance constraint set. The average structure from all 15 runs and the five-structure averages from each starting structure were all quite similar. Two rMD runs for each starting structure were made with the A5-H2 A5-H2 constraint missing. The average of these six rMD runs revealed differences in structure, compared to that with the full set of constraints, primarily for the middle two base-pairs involving the missing cross-strand constraint but global deviations also were found. Conformational analysis of the resulting structures revealed that the inner four to six base-pairs differed in structure from the termini. Furthermore, an alternating structure was suggested with features alternating for the A-T and T-A steps.     

Structure determination of [d(ATATATAUAT)]2 via two-dimensional NOE spectroscopy and molecular dynamics calculations

Proton homonuclear two-dimensional (2D) NOE spectra were obtained for the decamer [d(ATATATAUAT)]2 as a function of mixing time, and proton resonance assignments were made. Quantitative assessment of the 2D NOE cross-peak intensities was used in conjunction with the program MARDIGRAS, which entails a complete relaxation matrix analysis of the 2D NOE peak intensities, to obtain a set of upper and lower bound interproton distance constraints. The analysis with MARDIGRAS was carried out using three initial models: A-DNA, B-DNA and Z-DNA. The distance constraints determined were essentially the same regardless of initial structure. These experimental structural constraints were used with restrained molecular dynamics calculations to determine the solution structure of the decamer. The molecular dynamics program AMBER was run using A-DNA or B-DNA as starting model. The root-mean-square (rms) difference between these two starting models is 0.504 nm. The two starting models were subjected to 22.5 ps of restrained molecular dynamics calculations. The coordinates of the last 10.5 ps of the molecular dynamics runs were averaged to give two final structures. MDA and MDB. The rms difference between these two structures is 0.09 nm, implying convergence of the two molecular dynamics runs. The 2D NOE spectral intensities calculated for the derived structures are in good agreement with experimental spectra, based on sixth-root residual index analysis of intensities. A detailed examination of the structural features suggests that while the decamer is in the B-family of DNA structures, many torsion angle and helical parameters alternate from purine to pyrimidine, with kinks occurring at the U-A steps.     

Metropolis Monte Carlo calculations of DNA structure using internal coordinates and NMR distance restraints: An alternative method for generating a high-resolution solution structure

Summary A new method, a restrained Monte Carlo (rMC) calculation, is demonstrated for generating high-resolution structures of DNA oligonucleotides in solution from interproton distance restraints and bounds derived from complete relaxation matrix analysis of two-dimensional nuclear Overhauser effect (NOE) spectral peak intensities. As in the case of restrained molecular dynamics (rMD) refinement of structures, the experimental distance restraints and bounds are incorporated as a pseudo-energy term (or penalty function) into the mathematical expression for the molecular energy. However, the use of generalized helical parameters, rather than Cartesian coordinates, to define DNA conformation increases efficiency by decreasing by an order of magnitude the number of parameters needed to describe a conformation and by simplifying the potential energy profile. The Metropolis Monte Carlo method is employed to simulate an annealing process. The rMC method was applied to experimental 2D NOE data from the octamer duplex d(GTA-TAATG)·d(CATTATAC). Using starting structures from different locations in conformational space (e.g. A-DNA and B-DNA), the rMC calculations readily converged, with a root-mean-square deviation (RMSD) of <0.3 Å between structures generated using different protocols and starting structures. Theoretical 2D NOE peak intensities were calculated for the rMC-generated structures using the complete relaxation matrix program CORMA, enabling a comparison with experimental intensities via residual indices. Simulation of the vicinal proton coupling constants was carried out for the structures generated, enabling a comparison with the experimental deoxyribose ring coupling constants, which were not utilized in the structure determination in the case of the rMC simulations. Agreement with experimental 2D NOE and scalar coupling data was good in all cases. The rMC structures are quite similar to that refined by a traditional restrained MD approach (RMSD<0.5 Å) despite the different force fields used and despite the fact that MD refinement was conducted with additional restraints imposed on the endocyclic torsion angles of deoxyriboses. The computational time required for the rMC and rMD calculations is about the same. A comparison of structural parameters is made and some limitations of both methods are discussed with regard to the average nature of the experimental restraints used in the refinement.Abbreviations MC Monte Carlo - rMC restrained Monte Carlo - MD molecular dynamics - rMD restrained molecular dynamics - DG distance geometry - EM energy minimization - 2D NOE two-dimensional nuclear Overhauser effect - DQF-COSY double-quantum-filtered correlation spectroscopy - RMSD root-mean-square deviation To whom correspondence should be addressed.     

Structure determination of a DNA octamer in solution by NMR spectroscopy. Effect of fast local motions.

NMR structures of biomolecules are primarily based on nuclear Overhauser effects (NOEs) between protons. For the interpretation of NOEs in terms of distances, usually the assumption of a single rotational correlation time corresponding to a rigid molecule approximation is made. Here we investigate the effect of fast internal motions of the interproton vectors in the context of the relaxation matrix approach for structure determination of biomolecules. From molecular dynamics simulations generalized order parameters were calculated for the DNA octamer d(GCGTTCGC).d(CGCAACGC), and these were used in the calculation of NOE intensities. The magnitudes of the order parameters showed some variation for the different types of interproton vectors. The lowest values were observed for the interresidue base H6/H8-H2" proton vectors (S2 = 0.60), while the cytosine H5-H6 interproton vectors were among the most motionally restricted (S2 = 0.92). Inclusion of the motion of the interproton vectors resulted in a much better agreement between theoretically calculated NOE spectra and the experimental spectra measured by 2D NOE spectroscopy. The interproton distances changed only slightly, with a maximum of 10%; nevertheless, the changes were significant and resulted in constraints that were better satisfied. The structure of the DNA octamer was determined by using restrained molecular dynamics simulations with H2O as a solvent, with and without the inclusion of local internal motions. Starting from A- or B-DNA, the structures showed a high local convergence (0.86 A), while the global convergence for the octamer was ca. 2.6 A.     

Solution structure studies of d(AC)4.d(GT)4 via restrained molecular dynamics simulations with NMR constraints derived from two-dimensional NOE and double-quantum-filtered COSY experiments

The structure of d(AC)4.d(GT)4 is investigated by constrained molecular dynamics simulations. The constraints include proton pair distances derived from 2D NOE intensities by using the iterative relaxation matrix analysis algorithm MARDIGRAS and sugar pucker phases and amplitudes derived from double-quantum-filtered COSY spectra. Molecular dynamics runs on simulated intensity and distance sets as well as the experimental data were carried out to determine the effects of starting structure, distance constraint derivation, energy functions, and experimental errors on the end result. It was found that structural details could not be elucidated within about 1.5-A overall atomic deviation. This limitation is due in part to the accuracy of the experimental data but, more importantly, is attributable to the quantity of experimental constraints available and to imperfections in the force field utilized in the molecular dynamics calculations. Within the limits of the method, some structural characteristics of d(AC)4.d(GT)4 could be elucidated.     

Two-dimensional nuclear Overhauser enhancement investigation of the solution structure and dynamics of the DNA octamer [d(GGTATACC)]2

The resonances of nearly all 70 of the non-exchangeable protons of the duplex [d(GGTATACC)]2 in aqueous solution are assigned by proton two-dimensional nuclear Overhauser enhancement (2D NOE) spectra obtained in pure absorption phase at 500 MHz. Experimental and theoretical 2D NOE spectra are compared at each mixing time (100, 175, 250 and 400 ms) using two B-DNA structures: a standard B-form and an energy-minimized form. The GG and CC ends of the octamer duplex are well represented by the regular B-DNA structure. But large discrepancies from these models are observed for the 'TATA' box. All 2D NOE data are consistent with nanosecond correlation times, as indicated by non-selective proton spin-lattice relaxation times, but small variations in the correlation time are observed, suggesting that there are some local differences in mobility within the octamer duplex structure in solution.     

NMR study of the solution conformation of actinomycin D.

The solution conformation of actinomycin D, the Gram-positive antibiotic and DNA-binding drug, has been determined by 1H-NMR in deuterated dimethyl sulfoxide. The structure determination is based on the experimental data set of NOE restraints. Four structures were obtained from the distance geometry and restrained molecular dynamics calculation. The resultant structures satisfy the experimental restraints very well. These structures are found to be compatible with the X-ray crystal structures.     

The octamer motif in immunoglobulin genes: extraction of structural constraints from two-dimensional NMR studies.

Phase-sensitive two-dimensional nuclear Overhauser enhancement (2D NOE) and double-quantum-filtered correlated (2QF-COSY) spectra were recorded at 500 MHz for the DNA duplex d(CATTTGCATC).d(GATGCAAATG), which contains the octamer element of immunoglobulin genes. Exchangeable and nonexchangeable proton resonances including those of the H5' and H5" protons were assigned. Overall, the decamer duplex adopts a B-type DNA conformation. Scalar coupling constants for the sugar protons were determined by quantitative simulations of 2QF-COSY cross-peaks. These couplings are consistent with a two-state dynamic equilibrium between a minor N- and a major S-type conformer for all residues. The pseudorotation phase angle P of the major conformer is in the range 117-135 degrees for nonterminal pyrimidine nucleotides and 153-162 degrees for nonterminal purine nucleotides. Except for the terminal residues, the minor conformer comprises less than 25% of the population. Distance constraints obtained by a complete relaxation matrix analysis of the 2D NOE intensities with the MARDIGRAS algorithm confirm the dependence of the sugar pucker on pyrimidine and purine bases. Averaging by fast local motions has at most small effects on the NOE-derived interproton distances.     

Solution structure of phage lambda half-operator DNA by use of NMR, restrained molecular dynamics, and NOE-based refinement

The structure of a DNA decamer comprising the left half of the OR3 operator from bacteriophage lambda is determined in solution by using nuclear magnetic resonance spectroscopy and restrained molecular mechanics calculations. Nuclear magnetic resonance assignments for nonexchangeable protons are obtained by two-dimensional correlated and nuclear Overhauser effect (NOE) spectroscopies. Exchangeable proton resonances are assigned by one-dimensional NOE experiments. Coupling constant measurements from one- and two-dimensional experiments are used to determine approximate dihedral angles within the deoxyribose ring. Distances between protons are estimated by extrapolating distances derived from the time-dependent NOE intensities to initial mixing times. The sets of dihedral angles and distances form a basis for structure determination by restrained molecular dynamics. Separate runs start from classical A and from B DNA and converge to essentially identical structures (atomic root mean square difference of 0.8 A). The structures are improved by NOE-based refinement in which observed NOE intensities are compared to those calculated by using a full matrix analysis procedure. Final NOE residual (R) factors were less than 0.19. The resultant structures are generally B type in character, but display local sequence-dependent variations in dihedral angles and in the spatial arrangement of adjacent base pairs. Although the entire structure exhibits a small bend, the central core of the half-operator, which comprises the sequence-specific recognition site for cro repressor, is straight.     

Refinement of the NMR structures for acyl carrier protein with scalar coupling data

Structure determination of small proteins using NMR data is most commonly pursued by combining NOE derived distance constraints with inherent constraints based on chemical bonding. Ideally, one would make use of a variety of experimental observations, not just distance constraints. Here, coupling constant constraints have been added to molecular mechanics and molecular dynamics protocols for structure determination in the form of a psuedoenergy function that is minimized in a search for an optimum molecular conformation. Application is made to refinement of a structure for a 77 amino acid protein involved in fatty acid synthesis, Escherichia coli acyl carrier protein (ACP). 54 3JHN alpha coupling constants, 12 coupling constants for stereospecifically assigned side chain protons, and 450 NOE distance constraints were used to calculate the 3-D structure of ACP. A three-step protocol for a molecular dynamics calculation is described, in analogy to the protocol previously used in molecular mechanics calculations. The structures calculated with the molecular mechanics approach and the molecular dynamics approach using a rigid model for the protein show similar molecular energies and similar agreement with experimental distance and coupling constant constraints. The molecular dynamics approach shows some advantage in overcoming local minimum problems, but only when a two-state averaging model for the protein was used, did molecular energies drop significantly.     

Structure refinement of oligonucleotides by molecular dynamics with nuclear Overhauser effect interproton distance restraints: application to 5' d(C-G-T-A-C-G)2

The solution structure of the self-complementary DNA hexamer 5' d(C-G-T-A-C-G)2 is refined by restrained molecular dynamics in which 192 interproton distances, determined from pre-steady-state nuclear Overhauser enhancement measurements, are incorporated into the total energy of the system in the form of effective potentials. First the method is tested by applying an idealized set of distance restraints taken from classical B-DNA to a simulation starting off from A-DNA and vice versa. It is shown that in both cases the expected transition between A- and B-DNA occurs. Second, a set of restrained molecular dynamics calculations is carried out starting from both A- and B-DNA with the experimental interproton distances for 5' d(C-G-T-A-C-G)2 as restraints. Convergence to the same B-type structure is achieved with the interproton distances equal to the measured values within experimental error. The root-mean-square atomic difference between the two average restrained dynamics structures (less than 1 A) is approximately the same as the root-mean-square fluctuations of the atoms.     

Solution conformation of purine-pyrimidine DNA octamers using nuclear magnetic resonance, restrained molecular dynamics and NOE-based refinement

The solution structures of two alternating purine-pyrimidine octamers, [d(G-T-A-C-G-T-A-C)]2 and the reverse sequence [d(C-A-T-G-C-A-T-G)]2, are investigated by using nuclear magnetic resonance spectroscopy and restrained molecular dynamics calculations. Chemical shift assignments are obtained for non-exchangeable protons by a combination of two-dimensional correlation and nuclear Overhauser enhancement (NOE) spectroscopy experiments. Distances between protons are estimated by extrapolating distances derived from time-dependent NOE measurements to zero mixing time. Approximate dihedral angles are determined within the deoxyribose ring from coupling constants observed in one and two-dimensional spectra. Sets of distance and dihedral determinations for each of the duplexes form the bases for structure determination. Molecular dynamics is then used to generate structures that satisfy the experimental restraints incorporated as effective potentials into the total energy. Separate runs start from classical A and B-form DNA and converge to essentially identical structures. To circumvent the problems of spin diffusion and differential motion associated with distance measurements within molecules, models are improved by NOE-based refinement in which observed NOE intensities are compared to those calculated using a full matrix analysis procedure. The refined structures generally have the global features of B-type DNA. Some, but not all, variations in dihedral angles and in the spatial relationships of adjacent base-pairs are observed to be in synchrony with the alternating purine-pyrimidine sequence.     

Solution structures of human transforming growth factor alpha derived from 1H NMR data

The 600-MHz 1H NMR spectrum of the des-Val-Val mutant of human transforming growth factor alpha (TGF-alpha) was reassigned at pH = 6.3. The conformation space of des-Val-Val TGF-alpha was explored by distance geometry embedding followed by restrained molecular dynamics refinement using NOE distance constraints and some torsion angle constraints derived from J-couplings. Over 80 long-range NOE constraints were found by completely assigning all resolved cross-peaks in the NOESY spectra. Low NOE constraint violations were observed in structures obtained with the following three different refinement procedures: interactive annealing in DSPACE, AMBER 3.0 restrained molecular dynamics, and dynamic simulated annealing in XPLOR. The segment from Phe15 to Asp47 was found to be conformationally well-defined. Back-calculations of NOESY spectra were used to evaluate the quality of the structures. Our calculated structures resemble the ribbon diagram presentations that were recently reported by other groups. Several side-chain conformations appear to be well-defined as does the relative orientation of the C loop to the N-terminal half of the protein.     

Solution structure of [d(GCGTATACGC)]2.

The solution structure of the alternating pyrimidine-purine DNA duplex [d(GCGTATACGC)]2 has been determined using two-dimensional nuclear magnetic resonance techniques and distance geometry methods. Backbone distance constraints derived from experimental nuclear Overhauser enhancement and J-coupling torsion angle constraints were required to adequately define the conformation of the inter-residue backbone linkages and to avoid underwinding of the duplex. The distance geometry structures were further refined by back-calculation of the two-dimensional nuclear Overhauser enhancement spectra to correct spin-diffusion distance errors. Fifteen final structures for [d(GCGTATACGC)]2 were generated from the refined experimental distance bounds. These structures all exhibit fully wound B-form geometry with small penalty values (< 1.5 A) against the distance bounds and small pair-wise root-mean-square deviation values (typically 0.6 A to 1.5 A). The final structures exhibit positive base-pair inclination with respect to the helix axis, a marked alternation in rise and twist, and are shorter and wider than classical fiber B-form DNA. The purines were found to adopt a sugar pucker close to the C-2'-endo conformation while pyrimidine sugars exhibited significantly lower pseudorotation phase angles in the C-1'-exo to C-2'-endo range. The minor groove cross-strand steric clashes at pyrimidine-purine steps that would exist in pure B-DNA are attenuated by an increased rise at these steps (and an increased roll angle at TpA steps). Concomitantly the backbone torsion angles of the pyrimidine moieties have larger gamma values, larger epsilon values, and smaller zeta values than the purines. The structures generated by distance geometry methods were also compared with those obtained from restrained molecular dynamics with empirical force-field potentials. The results indicate that the nuclear magnetic resonance/distance geometry approach alone is capable of elucidating most of the salient structural features of double-stranded helical nucleic acids in solution without resorting to empirical energy potentials and without using any structural assumptions from crystallographic data.     

How accurately can oligonucleotide structures be determined from the hybrid relaxation rate matrix/NOESY distance restrained molecular dynamics approach?

The accuracy and precision of structures derived from a combined hybrid relaxation rate matrix/NOESY distance restrained molecular dynamics methodology were examined with simulations that included typical experimental errors. NOESY data were simulated for a DNA dodecamer duplex, d-(CGCGAATTCGCG)2, with added volume error of approximately 20% and low-level thermal noise. Distances derived from a hybrid relaxation matrix analysis of the NOE data were used as constraints in molecular dynamics driven structural refinements of several initial model geometries. The final structures were compared against results obtained from the traditional isolated two-spin approximation treatment of these NOESY volumes and also against refined structures that employed error-free data. Results show that the structures derived from the relaxation rate matrix analysis of the NOESY data are more accurate than those derived from a simple two-spin approximation analysis and it is possible to achieve refinement to the level of simulated experimental error. Results may be significantly improved with the use of either more accurately measured NOESY volumes or additional matrix-derived constraints. Many of the helical parameters and backbone torsional angles may be accurately reproduced by the hybrid matrix methodology.     

Effect of bulky lesions on DNA: solution structure of a DNA duplex containing a cholesterol adduct

The three-dimensional solution structure of two DNA decamers of sequence d(CCACXGGAAC)-(GTTCCGGTGG) with a modified nucleotide containing a cholesterol derivative (X) in its C1 '(chol)alpha or C1 '(chol)beta diastereoisomer form has been determined by using NMR and restrained molecular dynamics. This DNA derivative is recognized with high efficiency by the UvrB protein, which is part of the bacterial nucleotide excision repair, and the alpha anomer is repaired more efficiently than the beta one. The structures of the two decamers have been determined from accurate distance constraints obtained from a complete relaxation matrix analysis of the NOE intensities and torsion angle constraints derived from J-coupling constants. The structures have been refined with molecular dynamics methods, including explicit solvent and applying the particle mesh Ewald method to properly evaluate the long range electrostatic interactions. These calculations converge to well defined structures whose conformation is intermediate between the A- and B-DNA families as judged by the root mean square deviation but with sugar puckerings and groove shapes corresponding to a distorted B-conformation. Both duplex adducts exhibit intercalation of the cholesterol group from the major groove of the helix and displacement of the guanine base opposite the modified nucleotide. Based on these structures and molecular dynamics calculations, we propose a tentative model for the recognition of damaged DNA substrates by the UvrB protein.     

Experimental and theoretical studies of the conformational perturbations induced by an abasic site

The three-dimensional structure of the natural undecamer duplex d(CGCACACACGC). d(GCGTGTGTGCG) has been determined by the combined use of NMR spectroscopy and restrained molecular dynamics (rMD) and also by molecular mechanics calculations using the JUMNA program without experimental distance constraints. Both procedures have also been used to model the abasic structure d(CGCACOCACGC).d(GCGTGTGTGCG), where 'O' indicates a modified abasic site: 3-hydroxy-2-(hydroxymethyl) tetrahydrofuran. For the natural duplex, 134 interproton distances have been obtained by complete relaxation matrix analysis of the NOESY cross-peaks intensities, using MARDIGRAS software. These distances along with 100 torsion angles for sugar ring and additional data derived from canonical A and B-DNA, have been used for structures refinement by restrained molecular dynamics. Comparison of the natural oligomer with the abasic structure obtained earlier by NMR/rMD (Y. Coppel, N. Berthet, C. Coulombeau, Ce. Coulombeau, J. Garcia and J. Lhomme, Biochemistry 36, 4817-4830, 1997) confirms that the creation of an abasic site, in this sequence context, leads to marked helix kinking. It is also shown that the JUMNA procedure is capable of reproducing the overall structural features of the natural and damaged DNA conformations without the use of experimental constraints.     

A geometric arrangement algorithm for structure determination of symmetric protein homo-oligomers from NOEs and RDCs

Nuclear magnetic resonance (NMR) spectroscopy is a primary tool to perform structural studies of proteins in physiologically-relevant solution conditions. Restraints on distances between pairs of nuclei in the protein, derived from the nuclear Overhauser effect (NOE), provide information about the structure of the protein in its folded state. NMR studies of symmetric protein homo-oligomers present a unique challenge. Using X-filtered NOESY experiments, it is possible to determine whether an NOE restrains a pair of protons across different subunits or within a single subunit, but current experimental techniques are unable to determine in which subunits the restrained protons lie. Consequently, it is difficult to assign NOEs to particular pairs of subunits with certainty, thus hindering the structural analysis of the oligomeric state. Computational approaches are needed to address this subunit ambiguity, but traditional solutions often rely on stochastic search coupled with simulated annealing and simulations of simplified molecular dynamics, which have many tunable parameters that must be chosen carefully and can also fail to report structures consistent with the experimental restraints. In addition, these traditional approaches rarely provide guarantees on running time or solution quality. We reduce the structure determination of homo-oligomers with cyclic symmetry to computing geometric arrangements of unions of annuli in a plane. Our algorithm, disco, runs in expected O(n2) time, where n is the number of distance restraints, potentially assigned ambiguously. disco is guaranteed to report the exact set of oligomer structures consistent with the distance restraints and also with orientational restraints from residual dipolar couplings (RDCs). We demonstrate our method using two symmetric protein complexes: the trimeric E. coli diacylglycerol kinase (DAGK) and a dimeric mutant of the immunoglobulin-binding domain B1 of streptococcal protein G (GB1). In both cases, disco computes oligomer structures with high precision and also finds distance restraints that are either mutually inconsistent or inconsistent with the RDCs. The entire protocol DISCO has been completely automated in a software package that is freely available and open-source at www.cs.duke.edu/donaldlab/software.php.