401
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Gaponenko V, Sarma SP, Altieri AS, Horita DA, Li J, Byrd RA. Improving the accuracy of NMR structures of large proteins using pseudocontact shifts as long-range restraints. JOURNAL OF BIOMOLECULAR NMR 2004; 28:205-12. [PMID: 14752254 DOI: 10.1023/b:jnmr.0000013706.09264.36] [Citation(s) in RCA: 57] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/19/2023]
Abstract
We demonstrate improved accuracy in protein structure determination for large (>/=30 kDa), deuterated proteins (e.g. STAT4(NT)) via the combination of pseudocontact shifts for amide and methyl protons with the available NOEs in methyl-protonated proteins. The improved accuracy is cross validated by Q-factors determined from residual dipolar couplings measured as a result of magnetic susceptibility alignment. The paramagnet is introduced via binding to thiol-reactive EDTA, and multiple sites can be serially engineered to obtain data from alternative orientations of the paramagnetic anisotropic susceptibility tensor. The technique is advantageous for systems where the target protein has strong interactions with known alignment media.
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Affiliation(s)
- Vadim Gaponenko
- Structural Biophysics Laboratory, National Cancer Institute, P.O. Box B, Frederick, MD 21702-1201, USA
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402
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Bryce DL, Bax A. Application of correlated residual dipolar couplings to the determination of the molecular alignment tensor magnitude of oriented proteins and nucleic acids. JOURNAL OF BIOMOLECULAR NMR 2004; 28:273-287. [PMID: 14752260 DOI: 10.1023/b:jnmr.0000013701.16162.0c] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Residual dipolar couplings (RDC) between nuclear spins in partially aligned samples offer unique insights into biomacromolecular structure and dynamics. To fully benefit from the RDC data, accurate knowledge of the magnitude ( D (a)) and rhombicity ( R ) of the molecular alignment tensor, A, is important. An extended histogram method (EHM) is presented which extracts these parameters more effectively from dipolar coupling data. The method exploits the correlated nature of RDCs for structural elements of planar geometry, such as the one-bond (13)C'(i)-(13)C(i)(alpha), (13)C'(i)-(15)N(i+1), and (15)N(i+1)-(1)H(N)(i+1) couplings in peptide bonds of proteins, or suitably chosen combinations of (1) D (C1'H1'), (1) D (C2'H2'), (1) D (C1'C2'), (2) D (C2'H1'), (2) D (C1'H2'), and (3) D (H1'H2') couplings in nucleic acids, to generate an arbitrarily large number of synthetic RDCs. These synthetic couplings result in substantially improved histograms and resulting values of D (a) and R, compared with histograms generated solely from the original sets of correlated RDCs, particularly when the number of planar fragments for which couplings are available is small. An alternative method, complementary to the EHM, is also described, which uses a systematic grid search procedure, based on least-squares fitting of sets of correlated RDCs to structural elements of known geometry, and provides an unambiguous lower limit for the degree of molecular alignment.
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Affiliation(s)
- David L Bryce
- Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, MD 20892, USA
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403
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Wöhnert J, Franz KJ, Nitz M, Imperiali B, Schwalbe H. Protein alignment by a coexpressed lanthanide-binding tag for the measurement of residual dipolar couplings. J Am Chem Soc 2004; 125:13338-9. [PMID: 14583012 DOI: 10.1021/ja036022d] [Citation(s) in RCA: 164] [Impact Index Per Article: 8.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
A protein fusion construct of human ubiquitin with an N-terminal lanthanide binding tag (LBT) enables observation of long-range orientational restraints in solution NMR from residual dipolar couplings (RDCs) due to paramagnetic alignment of the protein. The paramagnetic lanthanide ions Tb3+, Dy3+, and Tm3+ are shown to bind to the LBT and induce different alignment tensors, in agreement with theory. RDCs, measured relative to the diamagnetic Lu3+, range from -7.6 to 5.5 Hz for Tb3+ and -6.6 to 6.1 Hz for Dy3+, while an opposite alignment tensor is observed for Tm3+ (4.5 to -2.9 Hz) at 800 MHz. Experimental RDCs are in excellent agreement with those predicted on the basis of the X-ray structure of the protein.
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Affiliation(s)
- Jens Wöhnert
- Institut für Organische Chemie und Chemische Biologie, Center for Biomolecular Magnetic Resonance, Johann Wolfgang Goethe-Universität Frankfurt, Marie-Curie-Strasse 11, 60439 Frankfurt/M, Germany
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404
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Qu Y, Guo JT, Olman V, Xu Y. Protein structure prediction using sparse dipolar coupling data. Nucleic Acids Res 2004; 32:551-61. [PMID: 14744980 PMCID: PMC373331 DOI: 10.1093/nar/gkh204] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2003] [Revised: 12/10/2003] [Accepted: 12/10/2003] [Indexed: 12/17/2022] Open
Abstract
Residual dipolar coupling (RDC) represents one of the most exciting emerging NMR techniques for protein structure studies. However, solving a protein structure using RDC data alone is still a highly challenging problem. We report here a computer program, RDC-PROSPECT, for protein structure prediction based on a structural homolog or analog of the target protein in the Protein Data Bank (PDB), which best aligns with the (15)N-(1)H RDC data of the protein recorded in a single ordering medium. Since RDC-PROSPECT uses only RDC data and predicted secondary structure information, its performance is virtually independent of sequence similarity between a target protein and its structural homolog/analog, making it applicable to protein targets beyond the scope of current protein threading techniques. We have tested RDC-PROSPECT on all (15)N-(1)H RDC data (representing 43 proteins) deposited in the BioMagResBank (BMRB) database. The program correctly identified structural folds for 83.7% of the target proteins, and achieved an average alignment accuracy of 98.1% residues within a four-residue shift.
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Affiliation(s)
- Youxing Qu
- Computational Systems Biology Laboratory, Department of Biochemistry and Molecular Biology, University of Georgia, Athens, GA 30602, USA
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405
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Trivelli X, Bouillac S, Tsan P, Krimm I, Lancelin JM. NMR of redox proteins of plants, yeasts and photosynthetic bacteria. PHOTOSYNTHESIS RESEARCH 2004; 79:357-67. [PMID: 16328801 DOI: 10.1023/b:pres.0000017161.63661.9d] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/05/2023]
Abstract
NMR spectroscopy has evolved dramatically over the past 15 years, establishing a new, reliable methodology for studying biomacromolecules at atomic resolution. The three-dimensional structure and dynamics of a biomolecule or a biomolecular complex is only one of the main types of information available using NMR. The spectral assignment to the specific nuclei of a biostructure is a very precise reflection of their electronic environment. Any change in this environment due to a structural change, the binding of a ligand or the redox state of a redox cofactor, will be very sensitively reported by changes in the different NMR parameters. The capabilities of the NMR method are currently expanding dramatically and it is turning into a powerful means to study biosystems dynamically in exchange between different conformations, exchanging ligands, transient complexes, or the activation/inhibition of regulated enzymes. We review here several NMR studies that have appeared during the past 5 or 6 years in the field of redox proteins of plants, yeasts and photosynthetic bacteria. These new results illustrate the recent biomolecular NMR evolution and provide new physiological models for understanding the different types of electron transfer, including glutaredoxins, thioredoxins and their dependent enzymes, the ferredoxin-NADP oxidoreductase complex, flavodoxins, the plastocyanin-cytochrome f complex, and cytochromes c.
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Affiliation(s)
- Xavier Trivelli
- Laboratoire de RMN Biomoléculaire associé au CNRS, Université Claude Bernard - Lyon 1, Domaine Scientifique de La Doua, Ecole Supérieure de Chimie Physique Electronique de Lyon, 69622, Villeurbanne, France
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406
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Ding K, Louis JM, Gronenborn AM. Insights into Conformation and Dynamics of Protein GB1 During Folding and Unfolding by NMR. J Mol Biol 2004; 335:1299-307. [PMID: 14729345 DOI: 10.1016/j.jmb.2003.11.042] [Citation(s) in RCA: 70] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
Abstract
Understanding protein stability requires characterization of structural determinants of the folded and unfolded states. Many proteins are capable of populating partially folded states under specific solution conditions. Occasionally, coexistence of the folded and an unfolded state under non- or mildly denaturing conditions can be observed by NMR, allowing us to structurally probe these states under identical conditions. Here we report on a destabilized mutant of the B1 domain of protein G (GB1) whose equilibrium unfolding was systematically investigated. Backbone amide residual dipolar couplings (RDCs), the tryptophan Nepsilon-H resonance and the amide nitrogen transverse relaxation rates (R2s) for varying pH values and different temperatures were measured. The backbone amide RDCs indicate that prior to complete unfolding, two melting hot spots are formed at the turn around T11, L12 and K13 and the N terminus of the helix at A24 and T25. The RDCs for the low pH, thermally unfolded state of GB1 are very small and do not indicate the presence of any native-like structure. Amide nitrogen transverse relaxation rates for GB1 in the folded state at different temperatures exhibit large contributions from exchange processes and the associated dynamics display considerable heterogeneity. Our data provide clear evidence for intermediate conformations and multi-state equilibrium un/folding for this GB1 variant.
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Affiliation(s)
- Keyang Ding
- Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, NIDDK, Building 5, Room 130, Bethesda, MD 20892, USA
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407
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Nabuurs SB, Spronk CA, Vriend G, Vuister GW. Concepts and tools for NMR restraint analysis and validation. ACTA ACUST UNITED AC 2004. [DOI: 10.1002/cmr.a.20016] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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408
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Annila A, Permi P. Weakly aligned biological macromolecules in dilute aqueous liquid crystals. ACTA ACUST UNITED AC 2004. [DOI: 10.1002/cmr.a.20020] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
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409
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Kramer F, Deshmukh M, Kessler H, Glaser S. Residual dipolar coupling constants: An elementary derivation of key equations. ACTA ACUST UNITED AC 2004. [DOI: 10.1002/cmr.a.20003] [Citation(s) in RCA: 98] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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410
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Meiler J, Baker D. Rapid protein fold determination using unassigned NMR data. Proc Natl Acad Sci U S A 2003; 100:15404-9. [PMID: 14668443 PMCID: PMC307580 DOI: 10.1073/pnas.2434121100] [Citation(s) in RCA: 99] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/02/2003] [Indexed: 11/18/2022] Open
Abstract
Experimental structure determination by x-ray crystallography and NMR spectroscopy is slow and time-consuming compared with the rate at which new protein sequences are being identified. NMR spectroscopy has the advantage of rapidly providing the structurally relevant information in the form of unassigned chemical shifts (CSs), intensities of NOESY crosspeaks [nuclear Overhauser effects (NOEs)], and residual dipolar couplings (RDCs), but use of these data are limited by the time and effort needed to assign individual resonances to specific atoms. Here, we develop a method for generating low-resolution protein structures by using unassigned NMR data that relies on the de novo protein structure prediction algorithm, rosetta [Simons, K. T., Kooperberg, C., Huang, E. & Baker, D. (1997) J. Mol. Biol. 268, 209-225] and a Monte Carlo procedure that searches for the assignment of resonances to atoms that produces the best fit of the experimental NMR data to a candidate 3D structure. A large ensemble of models is generated from sequence information alone by using rosetta, an optimal assignment is identified for each model, and the models are then ranked based on their fit with the NMR data assuming the identified assignments. The method was tested on nine protein sequences between 56 and 140 amino acids and published CS, NOE, and RDC data. The procedure yielded models with rms deviations between 3 and 6 A, and, in four of the nine cases, the partial assignments obtained by the method could be used to refine the structures to high resolution (0.6-1.8 A) by repeated cycles of structure generation guided by the partial assignments, followed by reassignment using the newly generated models.
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Affiliation(s)
- Jens Meiler
- Department of Biochemistry and Howard Hughes Medical Institute, University of Washington, PO Box 357350, Seattle, WA 98195-7350, USA
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411
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Permi P. Measurement of residual dipolar couplings from 1Halpha to 13Calpha and 15N using a simple HNCA-based experiment. JOURNAL OF BIOMOLECULAR NMR 2003; 27:341-349. [PMID: 14512731 DOI: 10.1023/a:1025866606252] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Novel NMR pulse schemes for simultaneous measurement of 1D(C)alpha(H)alpha and 2D(NH)alpha residual dipolar couplings in proteins is presented. We show that 2D(NH)alpha coupling can be very useful for protein structure determination. The 2D(NH)alpha coupling can be measured from 15N dimension with good accuracy on a slowly relaxing TROSY resonance, utilizing HNCA-TROSY-based experiments, which concomitantly supply large 1D(C)alpha(H)alpha coupling. The dynamic range of 2D(NH)alpha coupling is comparable to 1D(NC') coupling, but instead, it also serves non-redundant information on the course of protein backbone, thanks to rotational degree of freedom with respect to peptide bond. The HNCA-TROSY-based experiments are optimal for measuring residual dipolar couplings at high magnetic fields owing to absence of rapid transverse relaxation of carbonyl carbon. The reliability of the proposed approach was tested on 15N/13C human ubiquitin. A very good correlation with ubiquitin solution as well as crystal structure, for both 1D(C)alpha(H)alpha and 2D(NH)alpha couplings, was obtained.
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Affiliation(s)
- Perttu Permi
- NMR Laboratory, Structural Biology and Biophysics Programme, Institute of Biotechnology, P.O. Box 65, University of Helsinki, FIN-00014, Helsinki, Finland.
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412
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Hu W, Zhang Z, Chen Y. A high sensitivity 3D experiment for measuring Calpha-Halpha residual dipolar coupling constants. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2003; 165:248-252. [PMID: 14643706 DOI: 10.1016/j.jmr.2003.08.008] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
A new sensitivity improved approach is presented to measure the Calpha-Halpha scalar and dipolar coupling constants in 13C/15N-labeled proteins using a HA(CA)CONH scheme. The proposed experiment has significantly higher sensitivity than the previously published (HA)CA(CO)NH sequence, and provides accurate and straightforward measurements of the scalar and residual dipolar coupling constants. The sequence is easy to implement, and has been demonstrated on the C-terminal domain of the human Ku-80 protein (152 amino acid residues). On average, sensitivity is improved by 40% for both isotropic and anisotropic samples. The sensitivity enhancement is more pronounced for structured regions than unstructured regions, with an average of 50-60% enhancement being observed in the well-structured regions of the protein.
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Affiliation(s)
- Weidong Hu
- Division of Immunology, Beckman Institute of the City of Hope, Duarte, CA 91010, USA.
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413
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Haliloglu T, Kolinski A, Skolnick J. Use of residual dipolar couplings as restraints inab initio protein structure prediction. Biopolymers 2003; 70:548-62. [PMID: 14648765 DOI: 10.1002/bip.10511] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
NMR residual dipolar couplings (RDCs), in the form of the projection angles between the respective internuclear bond vectors, are used as structural restraints in the ab initio structure prediction of a test set of six proteins. The restraints are applied using a recently developed SICHO (SIde-CHain-Only) lattice protein model that employs a replica exchange Monte Carlo (MC) algorithm to search conformational space. Using a small number of RDC restraints, the quality of the predicted structures is improved as reflected by lower RMSD/dRMSD (root mean square deviation/distance root mean square deviation) values from the corresponding native structures and by the higher correlation of the most cooperative mode of motion of each predicted structure with that of the native structure. The latter, in particular, has possible implications for the structure-based functional analysis of predicted structures.
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Affiliation(s)
- Turkan Haliloglu
- Polymer Research Center and Chemical Engineering Department, Bogazici University, Bebek 80815, Istanbul, Turkey
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414
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Kateb F, Piccioli M. New Routes to the Detection of Relaxation Allowed Coherence Transfer in Paramagnetic Molecules. J Am Chem Soc 2003; 125:14978-9. [PMID: 14653719 DOI: 10.1021/ja038101v] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
Abstract
A new pulse sequence is proposed to measure cross correlation rates between 1H Curie spin relaxation and 1H-15N or 1H-13C dipole-dipole coupling (%@mt;sys@%Gamma%@sx@%H,HX%@be@%CS,DD%@sxx@%%@mx@% ) in paramagnetic systems. The new sequence has been conceived to obtain quantitative measurements of cross correlation rates in the close proximity to the paramagnetic center, preventing the loss of information due to fast transverse relaxation. The approach was tested on the dicalcium protein calbindin D9k in which Ca2+ has been substituted at site II with Ce3+. At variance with previously reported experiments, all peaks observed in HSQC experiments tailored to paramagnetic signals give quantitative estimates of %@mt;sys@%Gamma%@sx@%H%@ital@%,%@rsf@%HX%@be@%CS%@ital@%,%@rsf@%DD%@sxx@%%@mx@% . This is crucial to refine the immediate proximity of the metal ion.
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Affiliation(s)
- Fathia Kateb
- Magnetic Resonance Center, University of Florence, Via L. Sacconi 4, 50019 Sesto Fiorentino, Italy
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415
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Millet O, Hudson RP, Kay LE. The energetic cost of domain reorientation in maltose-binding protein as studied by NMR and fluorescence spectroscopy. Proc Natl Acad Sci U S A 2003; 100:12700-5. [PMID: 14530390 PMCID: PMC240681 DOI: 10.1073/pnas.2134311100] [Citation(s) in RCA: 97] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2003] [Indexed: 11/18/2022] Open
Abstract
Maltose-binding protein (MBP) is a two-domain protein that undergoes a ligand-mediated conformational rearrangement from an "open" to a "closed" structure on binding to maltooligosaccharides. To characterize the energy landscape associated with this transition, we have generated five variants of MBP with mutations located in the hinge region of the molecule. Residual dipolar couplings, measured in the presence of a weak alignment medium, have been used to establish that the average structures of the mutant proteins are related to each other by domain rotation about an invariant axis, with the rotation angle varying from 5 degrees to 28 degrees. Additionally, the domain orientations observed in the wild-type apo and ligand-bound (maltose, maltotriose, etc.) structures are related through a rotation of 35 degrees about the same axis. Remarkably, the free energy of unfolding, measured by equilibrium denaturation experiments and monitored by fluorescence spectroscopy, shows a linear correlation with the rotation angle, with the stability of the (apo)protein decreasing with domain closure by 212 +/- 16 cal mol-1 per degree of rotation. The apparent binding energy for maltose also shows a similar correlation with the interdomain angle, suggesting that the mutations, as they relate to binding, affect predominantly the ligand-free structure. The linearity of the energy change is interpreted in terms of an increase in the extent of hydrophobic surface that becomes solvent accessible on closure. The combination of structural, stability, and binding data allows separation of the energetics of domain reorientation from ligand binding. This work presents a near quantitative structure-energy-binding relationship for a series of mutants of MBP, illustrating the power of combined studies involving protein engineering and solution NMR spectroscopy.
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Affiliation(s)
- Oscar Millet
- Departments of Biochemistry, Medical Genetics and Microbiology, and Chemistry, and Protein Engineering Network Centers of Excellence, University of Toronto, Toronto, ON, Canada M5S 1A8; and Programme in Structural Biology and Biochemistry, Hospital for Sick Children, Toronto, ON, Canada M5G 1X8
| | - Rhea P. Hudson
- Departments of Biochemistry, Medical Genetics and Microbiology, and Chemistry, and Protein Engineering Network Centers of Excellence, University of Toronto, Toronto, ON, Canada M5S 1A8; and Programme in Structural Biology and Biochemistry, Hospital for Sick Children, Toronto, ON, Canada M5G 1X8
| | - Lewis E. Kay
- Departments of Biochemistry, Medical Genetics and Microbiology, and Chemistry, and Protein Engineering Network Centers of Excellence, University of Toronto, Toronto, ON, Canada M5S 1A8; and Programme in Structural Biology and Biochemistry, Hospital for Sick Children, Toronto, ON, Canada M5G 1X8
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416
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Pintacuda G, Hohenthanner K, Otting G, Müller N. Angular dependence of dipole-dipole-Curie-spin cross-correlation effects in high-spin and low-spin paramagnetic myoglobin. JOURNAL OF BIOMOLECULAR NMR 2003; 27:115-132. [PMID: 12913408 DOI: 10.1023/a:1024926126239] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
The (15)N-HSQC spectra of low-spin cyano-met-myoglobin and high-spin fluoro-met-myoglobin were assigned and dipole-dipole-Curie-spin cross-correlated relaxation rates measured. These cross-correlation rates originating from the dipolar (1)H-(15)N interaction and the dipolar interaction between the (1)H and the Curie spin of the paramagnetic center contain long-range angular information about the orientation of the (1)H-(15)N bond with respect to the iron-(1)H vector, with information measurable up to 11 A from the metal for the low-spin complex, and between 10 to 25 A for the high-spin complex. Comparison of the experimental data with predictions from crystal structure data showed that the anisotropy of the magnetic susceptibility tensor in low spin cyano-met-myoglobin significantly influences the cross-correlated dipole-dipole-Curie-spin relaxation rates.
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Affiliation(s)
- Guido Pintacuda
- Department of Medical Biochemistry and Biophysics, Karolinska Institute, S-171 77 Stockholm, Sweden
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417
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Boisbouvier J, Delaglio F, Bax A. Direct observation of dipolar couplings between distant protons in weakly aligned nucleic acids. Proc Natl Acad Sci U S A 2003; 100:11333-8. [PMID: 12972645 PMCID: PMC208757 DOI: 10.1073/pnas.1534664100] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Under conditions where macromolecules are aligned very weakly with respect to an external magnetic field, Brownian diffusion no longer averages internuclear dipole-dipole interactions to zero. The resulting residual dipolar coupling, although typically 3 orders of magnitude weaker than in a fully aligned sample, can readily be measured by solution NMR methods. To date, application of this idea has focused primarily on pairs of nuclei separated by one or two covalent bonds, where the internuclear separation is known and the measured dipolar coupling provides direct information on the orientation of the internuclear vector. A method is described that allows observation of dipolar interactions over much larger distances. By decoupling nearest-neighbor interactions, it is readily possible to observe direct dipolar interactions between protons separated by up to 12 A. The approach is demonstrated for the DNA dodecamer d(CGCGAATTCGCG)2, where direct interactions are observed between protons up to three base pairs apart.
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Affiliation(s)
- Jérôme Boisbouvier
- Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, MD 20892-0520, USA
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418
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Ding K, Gronenborn AM. Simultaneous and accurate determination of one-bond (15)N-(13)C' and two-bond (1)H(N)--(13)C' dipolar couplings. J Am Chem Soc 2003; 125:11504-5. [PMID: 13129346 DOI: 10.1021/ja035954e] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Using the echo-anti-echo manipulation, the 15N-1HN cross-peaks split in the E.COSY spectrum by the 13CO couplings are separated into different, distinct regions in the HSQC spectrum. From this novel E.COSY 15N-1HN HSQC spectrum, the small one-bond 15N-13C' and two-bond 1HN-13C' residual dipolar couplings can be extracted easily and accurately. These dipolar couplings provide a set of important long-range constraints for protein structure determination.
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Affiliation(s)
- Keyang Ding
- Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, Maryland 20892, USA
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419
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Wedemeyer WJ, Baker D. Efficient minimization of angle-dependent potentials for polypeptides in internal coordinates. Proteins 2003; 53:262-72. [PMID: 14517977 DOI: 10.1002/prot.10525] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Angular potentials play an important role in the refinement of protein structures through angle-dependent restraints (e.g., those determined by cross-correlated relaxations, residual dipolar couplings, and hydrogen bonds). Analytic derivatives of such angular potentials with respect to the dihedral angles of proteins would be useful for optimizing such restraints and other types of angular potentials (i.e., such as we are now introducing into protein structure prediction) but have not been described. In this article, analytic derivatives are calculated for four types of angular potentials and integrated with the efficient recursive derivative calculation methods of Gō and coworkers. The formulas are implemented in publicly available software and illustrated by refining a low-resolution protein structure with idealized vector-angle, dipolar-coupling, and hydrogen-bond restraints. The method is now being used routinely to optimize hydrogen-bonding potentials in ROSETTA.
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420
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Mascioni A, Veglia G. Theoretical Analysis of Residual Dipolar Coupling Patterns in Regular Secondary Structures of Proteins. J Am Chem Soc 2003; 125:12520-6. [PMID: 14531696 DOI: 10.1021/ja0354824] [Citation(s) in RCA: 37] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
A new approach to the interpretation of residual dipolar couplings for the regular secondary structures of proteins is presented. This paper deals with the analysis of the steric and chiral requirements of protein secondary structures and establishes a quantitative correlation between structure periodicity and the experimental values of the backbone residual dipolar couplings. Building on the recent interpretation of the periodicity of residual dipolar couplings in alpha-helices (i.e., "dipolar waves"), a general parametric equation for fitting the residual dipolar couplings of any regular secondary structure is derived. This equation interprets the modulation of the residual dipolar couplings' periodicity in terms of the secondary structure orientation with respect to an arbitrary reference frame, laying the groundwork for using backbone residual dipolar couplings as a fast tool for determining protein folding by NMR spectroscopy.
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Affiliation(s)
- Alessandro Mascioni
- Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455, USA
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421
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Zhang Q, Throolin R, Pitt SW, Serganov A, Al-Hashimi HM. Probing motions between equivalent RNA domains using magnetic field induced residual dipolar couplings: accounting for correlations between motions and alignment. J Am Chem Soc 2003; 125:10530-1. [PMID: 12940730 DOI: 10.1021/ja0363056] [Citation(s) in RCA: 50] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Approaches developed thus for extracting structural and dynamical information from RDCs have rested on the assumption that motions do not affect molecular alignment. However, it is well established that molecular alignment in ordered media is dependent on conformation, and slowly interconverting conformational substates may exhibit different alignment properties. Neglecting these correlation effects can lead to aberrations in the structural and dynamical analysis of RDCs and diminish the utility of RDCs in probing motions between domains having similar alignment propensities. Here, we introduce a new approach based on measurement of magnetic field induced residual dipolar couplings in nucleic acids which can explicitly take into account such correlations and demonstrate measurements of motions between two "magnetically equivalent" domains in the transactivation response element (TAR) RNA.
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Affiliation(s)
- Qi Zhang
- Department of Chemistry and Biophysics Research Division, University of Michigan, Ann Arbor, MI 48109, USA
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422
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Abstract
NMR-based ligand screening is now an established field in its own right. In recent years, advances in both methodology and hardware have broadened its range of applications and pushed back practical limitations, leading to the growing importance of NMR screening as a tool in industrial drug research. An overview of new screening methods and applications is presented here, and ways in which NMR-screening is being used in cooperation with other screening techniques are discussed.
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Affiliation(s)
- Murray Coles
- Institut für Organische Chemie und Biochemie, Technische Universität München Lichtenbergstrasse 4, 85747, Garching, Germany
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423
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Lipsitz RS, Tjandra N. 15N chemical shift anisotropy in protein structure refinement and comparison with NH residual dipolar couplings. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2003; 164:171-176. [PMID: 12932470 DOI: 10.1016/s1090-7807(03)00176-9] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Recent methods of aligning proteins which were developed in order to measure residual dipolar couplings (RDCs) in solution can also be used for additional applications such as measuring the 15N CSA in the form of chemical shift differences, Deltadelta. A new XPLOR-NIH module has been developed and implemented for NMR structure refinement using the 15N Deltadelta data as restraints. The results of this refinement are shown using the protein Bax. This method should be amenable to any protein which can be studied by NMR. An analysis comparing the structural information provided by NH RDCs and the 15N Deltadelta is included.
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Affiliation(s)
- Rebecca S Lipsitz
- Laboratory of Biophysical Chemistry, Building 50, Room 3503, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, MD 20892-8013, USA
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424
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Pervushin K, Vögeli B. Observation of individual transitions in magnetically equivalent spin systems. J Am Chem Soc 2003; 125:9566-7. [PMID: 12904004 DOI: 10.1021/ja035288h] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Individual transitions of magnetically equivalent spin systems such as methyl groups residing on isotropically tumbling molecules in solution usually cannot be observed as multiplet-split NMR lines. We propose a pair of NMR experiments, 2D [13C,1Halphaalpha]Methyl and [13C,1Hbetabeta]Methyl HSQC, to overcome this limitation and enable direct and selective observation of individual 1H transitions in 13C-labeled methyl spin systems. Immediate applications include quantitative measurements of 1H-1H residual dipolar couplings (RDC) and cross-correlated relaxation between 1H chemical shift anisotropy and 1H-1H dipole-dipole interactions. The use of the experiments for the measurement of RDCs is demonstrated with two proteins, one weakly aligned by means of Pf1 phages and the other using a naturally present paramagnetic heme group.
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Affiliation(s)
- Konstantin Pervushin
- Laboratory of Physical Chemistry, Swiss Federal Institute of Technology, ETH Hönggerberg, CH-8093 Zürich, Switzerland.
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425
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Kennedy MA, Montelione GT, Arrowsmith CH, Markley JL. Role for NMR in structural genomics. JOURNAL OF STRUCTURAL AND FUNCTIONAL GENOMICS 2003; 2:155-69. [PMID: 12836706 DOI: 10.1023/a:1021261026670] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
The 2nd EMSL Workshop on Structural Genomics was held on 28th and 29th July 2000 at the Environmental Molecular Sciences Laboratory at the Department of Energy's Pacific Northwest National Laboratory in Richland, WA. The workshop focused on four topics: 1. The role for NMR in structural and functional genomics; 2. The technical challenges NMR faces for structural and functional genomics; 3. The potential need for a national NMR center for structural and functional genomics in the United States; and 4. Organization of the NMR community. This report summarizes the workshop proceedings and conclusions reached regarding the role of NMR in the emerging fields of structural and functional genomics.
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Affiliation(s)
- Michael A Kennedy
- Pacific Northwest National Laboratory, Environmental Molecular Sciences Laboratory, Richland, WA 99352, USA.
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426
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Fehér K, Berger S, Kövér KE. Accurate determination of small one-bond heteronuclear residual dipolar couplings by F1 coupled HSQC modified with a G-BIRD(r) module. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2003; 163:340-346. [PMID: 12914850 DOI: 10.1016/s1090-7807(03)00113-7] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
We report a G-BIRD(r) modified coupled HSQC experiment for the accurate determination of one-bond heteronuclear residual dipolar couplings. The G-BIRD(r) module has been employed to refocus the long-range coupling evolution of the heteronucleus during the t1 frequency labeling period. As a result, the crosspeaks obtained are split by only the direct one-bond coupling that can be extracted by measuring simple frequency differences between singlet maxima. Additionally the decoupling of long-range multiple bond splittings leads to considerable sensitivity enhancement. The modification also has been applied in a TROSY sequence resulting in a significant sensitivity and resolution improvement.
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Affiliation(s)
- Krisztina Fehér
- Institute for Analytical Chemistry, University of Leipzig, Johnnisallee 29, D-04103, Leipzig, Germany
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427
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Wu Z, Delaglio F, Tjandra N, Zhurkin VB, Bax A. Overall structure and sugar dynamics of a DNA dodecamer from homo- and heteronuclear dipolar couplings and 31P chemical shift anisotropy. JOURNAL OF BIOMOLECULAR NMR 2003; 26:297-315. [PMID: 12815257 DOI: 10.1023/a:1024047103398] [Citation(s) in RCA: 107] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
The solution structure of d(CGCGAATTCGCG)(2) has been determined on the basis of an exceptionally large set of residual dipolar couplings. In addition to the heteronuclear (13)C-(1)H and (15)N-(1)H and qualitative homonuclear (1)H-(1)H dipolar couplings, previously measured in bicelle medium, more than 300 quantitative (1)H-(1)H and 22 (31)P-(1)H dipolar restraints were obtained in liquid crystalline Pf1 medium, and 22 (31)P chemical shift anisotropy restraints. High quality DNA structures can be obtained solely on the basis of these new restraints, and these structures are in close agreement with those calculated previously on the basis of (13)C-(1)H and (15)N-(1)H dipolar couplings. In the newly calculated structures, (31)P-(1)H dipolar and (3)JsubH3(')Psub couplings and (31)P CSA data restrain the phosphodiester backbone torsion angles. The final structure represents a quite regular B-form helix with a modest bending of approximately 10 degrees, which is essentially independent of whether or not electrostatic terms are used in the calculation. Combined, the number of homo- and heteronuclear dipolar couplings significantly exceeds the number of degrees of freedom in the system. Results indicate that the dipolar coupling data cannot be fit by a single structure, but are compatible with the presence of rapid equilibria between C2(')-endo and C3(')-endo deoxyribose puckers (sugar switching). The C2(')-H2(')/H2(") dipolar couplings in B-form DNA are particularly sensitive to sugar pucker and yield the largest discrepancies when fit to a single structure. To resolve these discrepancies, we suggest a simplified dipolar coupling analysis that yields N/S equilibria for the ribose sugar puckers, which are in good agreement with previous analyses of NMR J(HH) couplings, with a population of the minor C3(')-endo form higher for pyrimidines than for purines.
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Affiliation(s)
- Zhengrong Wu
- Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, MD 20892, USA
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428
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Meiler J, Peti W, Griesinger C. Dipolar couplings in multiple alignments suggest alpha helical motion in ubiquitin. J Am Chem Soc 2003; 125:8072-3. [PMID: 12837055 DOI: 10.1021/ja029816l] [Citation(s) in RCA: 50] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Recently, residual dipolar couplings (RDCs) of backbone N-HN vectors measured in 11 different alignment media were analyzed with respect to structure and dynamics in a model-free way in terms of generalized order parameters and motional anisotropies. The anisotropies in the central alpha-helix were found to be strikingly uniformly distributed. In this communication, these parameters are further interpreted in terms of physically feasible cooperative reorientational motion of the helix with respect to the core of the protein. The RDCs are compatible with a model in which all N-HN vectors of the alpha-helix of ubiquitin exhibit correlated anisotropic excursions with amplitudes of 21 degrees and 12 degrees along two orthogonal directions x' ' and y' ' of a coordinate system C' ', if z' ' represents the helix axis. Such motion contradicts neither NOE data nor molecular force-field calculations.
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Affiliation(s)
- Jens Meiler
- Max Planck Insitute for Biophysical Chemistry, Göttingen, Germany
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429
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Luy B, Marino JP. JE-TROSY: combined J- and TROSY-spectroscopy for the measurement of one-bond couplings in macromolecules. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2003; 163:92-98. [PMID: 12852911 DOI: 10.1016/s1090-7807(03)00105-8] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
With the application of RDCs in high-resolution NMR studies of macromolecules, there has been an interest in the development of accurate, sensitive methods for measuring 15N-1H and 13C-1H one-bond coupling constants. Most methods for determining these couplings are based on the measurement of the displacement between cross-peak components in J-coupled spectra. However, for large macromolecules and macromolecular complexes, these methods are often unreliable since differential relaxation can significantly broaden one of the multiplet components (i.e., the anti-TROSY component) and thereby make accurate determination of its position difficult. To overcome this problem, a J-evolved transverse relaxation optimized (JE-TROSY) method is presented for the determination of one-bond couplings that involves J-evolution of the sharpest cross-peak multiplet component selected in a TROSY experiment. Couplings are measured from the displacement of the TROSY component in the additional J-evolution dimension relative to a zero frequency origin. The JE-TROSY method is demonstrated on uniformly labeled 15N, 13C-labeled RNA and peptide samples, as well as with an RNA-protein complex, in which the protein is uniformly 15N, 13C-labeled. In all cases, resolved, sensitive spectra are obtained from which heteronuclear one-bond J-couplings could be accurately and easily measured.
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Affiliation(s)
- Burkhard Luy
- Center for Advanced Research in Biotechnology of the University of Maryland Biotechnology Institute, 9600 Gudelsky Drive, Rockville, MD 20850, USA
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430
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Al-Hashimi HM, Pitt SW, Majumdar A, Xu W, Patel DJ. Mg2+-induced variations in the conformation and dynamics of HIV-1 TAR RNA probed using NMR residual dipolar couplings. J Mol Biol 2003; 329:867-73. [PMID: 12798678 PMCID: PMC4692374 DOI: 10.1016/s0022-2836(03)00517-5] [Citation(s) in RCA: 59] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
The effects of divalent Mg(2+) on the conformation and dynamics of the stem-loop transactivation response element (TAR) RNA from HIV-1 have been characterized using NMR residual dipolar couplings (RDCs). Order matrix analysis of one bond 13C-1H RDCs measured in TAR at [Mg(2+)]:[TAR] stoichiometric ratios of approximately 3:1 (TAR(3.0Mg)) and approximately 4.5:1 (TAR(4.5Mg)) revealed that Mg(2+) reduces the average inter-helical angle from 47(+/-5) degrees in TAR(free) to 5(+/-7) degrees in TAR(4.5Mg). In contrast to the TAR(free) state, the generalized degree of order for the two stems in TAR(4.5Mg) is found to be identical within experimental uncertainty, indicating that binding of Mg(2+) leads to an arrest of inter-helical motions in TAR(free). Results demonstrate that RDC-NMR methodology can provide new insight into the effects of Mg(2+) on both the conformation and dynamics of RNA.
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Affiliation(s)
- Hashim M Al-Hashimi
- Cellular Biochemistry and Biophysics Program, Memorial Sloan-Kettering Cancer Center, New York, NY 10021, USA.
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431
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Assfalg M, Bertini I, Turano P, Mauk AG, Winkler JR, Gray HB. 15N-1H Residual dipolar coupling analysis of native and alkaline-K79A Saccharomyces cerevisiae cytochrome c. Biophys J 2003; 84:3917-23. [PMID: 12770897 PMCID: PMC1302973 DOI: 10.1016/s0006-3495(03)75119-4] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
Residual dipolar couplings (RDCs) and pseudocontact shifts are experimentally accessible properties in nuclear magnetic resonance that are related to structural parameters and to the magnetic susceptibility anisotropy. We have determined RDCs due to field-induced orientation of oxidized-K79A and reduced cytochrome c at pH 7.0 and oxidized-K79A cytochrome c at pH 11.1 through measurements of amide (15)N-(1)H (1)J couplings at 800 and 500 MHz. The pH 7.0 RDCs for Fe(III)- and Fe(II)-cytochrome c together with available nuclear Overhauser effects were used to recalculate solution structures that were consistent with both sets of constraints. Molecular magnetic susceptibility anisotropy values were calculated for both redox states of the protein. By subtracting the residual dipolar couplings (RDCs) of the reduced form from those of the oxidized form measured at the same magnetic field (800 MHz), we found the RDC contribution of the paramagnetic metal ion in the oxidized protein. The magnetic susceptibility anisotropy, which was calculated from the structure, was found to be the same as that of the paramagnetic metal ion obtained independently from pseudocontact shifts, thereby indicating that the elements of secondary structure either are rigid or display the same mobility in both oxidation states. The residual dipolar coupling values of the alkaline-K79A form are small with respect to those of oxidized native cytochrome, whereas the pseudocontact shifts are essentially of the same magnitude, indicating local mobility. Importantly, this is the first time that mobility has been found through comparison of RDCs with pseudocontact shifts.
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Affiliation(s)
- Michael Assfalg
- Magnetic Resonance Center (CERM), University of Florence, 50019 Sesto Fiorentino, Florence, Italy
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432
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Eletsky A, Moreira O, Kovacs H, Pervushin K. A novel strategy for the assignment of side-chain resonances in completely deuterated large proteins using 13C spectroscopy. JOURNAL OF BIOMOLECULAR NMR 2003; 26:167-179. [PMID: 12766412 DOI: 10.1023/a:1023572320699] [Citation(s) in RCA: 61] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
The assignment of the aliphatic (13)C resonances of trimeric Bacillus Subtilis chorismate mutase, a protein with a molecular mass of 44 kDa, consisting of three 127-residue monomers is presented by use of two-dimensional (2D) (13)C-start and (13)C-observe NMR experiments. These experiments start with (13)C excitation and end with (13)C observation while relying on the long transverse relaxation times of (13)C spins in uniformly deuterated and (13)C,(15)N-labeled large proteins. Gains in sensitivity are achieved by the use of a paramagnetic relaxation enhancement agent to reduce (13)C T(1) relaxation times with little effect on (13)C T(2) relaxation times. Such 2D (13)C-only NMR experiments circumvent problems associated with the application of conventional experiments for side-chain assignment to proteins of larger sizes, for instance, the absence or low concentration of the side-chain (1)H spins, the transfer of the side-chain spin polarization to the (1)H(N) spins for signal acquisition, or the necessity of a quantitative reprotonation of the methyl moieties in the otherwise fully deuterated side-chains. We demonstrate that having obtained a nearly complete assignment of the side-chain aliphatic (13)C resonances, the side-chain (1)H chemical shifts can be assigned in a semiautomatic fashion using 3D (15)N-resolved and (13)C-resolved NOESY experiments measured with a randomly partially protonated protein sample. We also discuss perspectives for structure determination of larger proteins by using novel strategies which are based on the (1)H,(1)H NOEs in combination with multiple residual dipolar couplings between adjacent (13)C spins determined with 2D (13)C-only experiments.
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Affiliation(s)
- Alexander Eletsky
- Laboratory of Physical Chemistry, Swiss Federal Institute of Technology, ETH-Hönggerberg, CH-8093 Zürich, Switzerland
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433
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Zheng D, Huang YJ, Moseley HNB, Xiao R, Aramini J, Swapna GVT, Montelione GT. Automated protein fold determination using a minimal NMR constraint strategy. Protein Sci 2003; 12:1232-46. [PMID: 12761394 PMCID: PMC2323888 DOI: 10.1110/ps.0300203] [Citation(s) in RCA: 45] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/02/2003] [Revised: 03/11/2003] [Accepted: 03/12/2003] [Indexed: 10/27/2022]
Abstract
Determination of precise and accurate protein structures by NMR generally requires weeks or even months to acquire and interpret all the necessary NMR data. However, even medium-accuracy fold information can often provide key clues about protein evolution and biochemical function(s). In this article we describe a largely automatic strategy for rapid determination of medium-accuracy protein backbone structures. Our strategy derives from ideas originally introduced by other groups for determining medium-accuracy NMR structures of large proteins using deuterated, (13)C-, (15)N-enriched protein samples with selective protonation of side-chain methyl groups ((13)CH(3)). Data collection includes acquiring NMR spectra for automatically determining assignments of backbone and side-chain (15)N, H(N) resonances, and side-chain (13)CH(3) methyl resonances. These assignments are determined automatically by the program AutoAssign using backbone triple resonance NMR data, together with Spin System Type Assignment Constraints (STACs) derived from side-chain triple-resonance experiments. The program AutoStructure then derives conformational constraints using these chemical shifts, amide (1)H/(2)H exchange, nuclear Overhauser effect spectroscopy (NOESY), and residual dipolar coupling data. The total time required for collecting such NMR data can potentially be as short as a few days. Here we demonstrate an integrated set of NMR software which can process these NMR spectra, carry out resonance assignments, interpret NOESY data, and generate medium-accuracy structures within a few days. The feasibility of this combined data collection and analysis strategy starting from raw NMR time domain data was illustrated by automatic analysis of a medium accuracy structure of the Z domain of Staphylococcal protein A.
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Affiliation(s)
- Deyou Zheng
- Center for Advanced Biotechnology and Medicine (CABM), Northeast Structural Genomics Consortium, and Department of Molecular Biology and Biochemistry, Rutgers University, Piscataway, New Jersey 08854, USA
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434
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Tugarinov V, Kay LE. Quantitative NMR studies of high molecular weight proteins: application to domain orientation and ligand binding in the 723 residue enzyme malate synthase G. J Mol Biol 2003; 327:1121-33. [PMID: 12662935 DOI: 10.1016/s0022-2836(03)00238-9] [Citation(s) in RCA: 86] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
A high-resolution multidimensional NMR study of ligand-binding to Escherichia coli malate synthase G (MSG), a 723-residue monomeric enzyme (81.4 kDa), is presented. MSG catalyzes the condensation of glyoxylate with an acetyl group of acetyl-CoA, producing malate, an intermediate in the citric-acid cycle. We show that despite the size of the protein, important structural and dynamic information about the molecule can be obtained on a per-residue basis. 15N-1HN residual dipolar couplings and carbonyl chemical shift changes upon alignment in Pf1 phage establish that there are no significant domain reorientations in the molecule upon ligand binding, in contrast to what was anticipated on the basis of both the X-ray structure of the glyoxylate-bound form of the enzyme and structural studies of a related set of proteins. The chemical shift changes of 1HN, 15N and 13CO nuclei upon binding of pyruvate, a glyoxylate-mimicking inhibitor, and acetyl-CoA have been mapped onto the three-dimensional structure of the molecule. Binding constants of pyruvate, glyoxylate, and acetyl-CoA (in the presence of pyruvate) have been measured, along with the kinetic parameters for glyoxylate and pyruvate binding. The on-rates of pyruvate and glyoxalate binding, approximately 1.2 x 10(6)M(-1)s(-1) and approximately 2.7 x 10(6)M(-1)s(-1), respectively, are significantly lower than what is anticipated from a simple diffusion-controlled process. Some structural implications of the chemical shift perturbations upon binding and the estimated ligand on-rates are discussed.
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Affiliation(s)
- Vitali Tugarinov
- Protein Engineering Network Centres of Excellence and the Department of Medical Genetics, University of Toronto, 1 King's College Circle, M5S 1A8, Toronto, Ont., Canada
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435
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Sprangers R, Groves MR, Sinning I, Sattler M. High-resolution X-ray and NMR structures of the SMN Tudor domain: conformational variation in the binding site for symmetrically dimethylated arginine residues. J Mol Biol 2003; 327:507-20. [PMID: 12628254 DOI: 10.1016/s0022-2836(03)00148-7] [Citation(s) in RCA: 142] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
Abstract
The SMN protein, which is linked to spinal muscular atrophy (SMA), plays an important role in the assembly of the spliceosomal small nuclear ribonucleoprotein complexes. This function requires binding of SMN to the arginine-glycine (RG) rich C-terminal tails of the Sm proteins, which contain symmetrically dimethylated arginine residues (sDMA) in vivo. Using NMR titrations, we show that the SMN Tudor domain recognizes these sDMAs in the methylated RG repeats. Upon complex formation a cluster of conserved aromatic residues in the SMN Tudor domain interacts with the sDMA methyl groups. We present two high resolution structures of the uncomplexed SMN Tudor domain, a 1.8A crystal structure and an NMR structure that has been refined against a large number of backbone and side-chain residual dipolar couplings. The backbone conformation of both structures is very similar, however, differences are observed for the cluster of conserved aromatic side-chains in the sDMA binding pocket. In order to validate these variations we introduce a novel application of residual dipolar couplings for aromatic rings. We show that structural information can be derived from aromatic ring residual dipolar couplings, even in the presence of internal motions such as ring flipping. These residual dipolar couplings and ring current shifts independently confirm that the SMN Tudor domain adopts two different conformations in the sDMA binding pocket. The observed structural variations may play a role for the recognition of sDMAs.
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Affiliation(s)
- Remco Sprangers
- Structural and Computational Biology Programme, EMBL Heidelberg, Meyerhofstr. 1, Germany.
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436
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Yan J, Kline AD, Mo H, Shapiro MJ, Zartler ER. A novel method for the determination of stereochemistry in six-membered chairlike rings using residual dipolar couplings. J Org Chem 2003; 68:1786-95. [PMID: 12608792 DOI: 10.1021/jo020670i] [Citation(s) in RCA: 67] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
A novel method for the determination of the relative stereochemistry of six-membered chairlike ring molecules by residual dipolar couplings is presented. C-H residual dipolar couplings were used to investigate the relative stereochemistry of 4,6-O-ethylidene-d-glucopyranose. For this and similar systems it is not necessary to acquire redundant dipolar couplings and to calculate the orientation order tensor. The presented methodology is a paradigmatic leap for the determination of the relative stereochemistry or remote stereochemistry in this kind of fused ring system. Residual dipolar coupling data were collected by 1D and 2D direct-measurement heteronuclear multiple quantum coherence (HMQC) spectroscopy. It was demonstrated that direct measurement of HMQC was quick and accurate for small molecules at natural abundance.
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Affiliation(s)
- Jiangli Yan
- Discovery Chemistry Research and Technologies, Lilly Research Labs, Lilly Corporate Center, Eli Lilly & Company, Indianapolis, Indiana 46285, USA
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437
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McCallum SA, Pardi A. Refined solution structure of the iron-responsive element RNA using residual dipolar couplings. J Mol Biol 2003; 326:1037-50. [PMID: 12589752 DOI: 10.1016/s0022-2836(02)01431-6] [Citation(s) in RCA: 56] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Abstract
The iron-responsive element (IRE) is a 30nt RNA motif located in the non-coding regions of mRNAs of proteins involved in iron regulation. In humans, the IRE plays a direct role in the control of iron levels by post-transcriptional regulation of the ferritin and transferrin receptor proteins through highly specific recognition by IRE-binding proteins. The IRE fold is representative of many RNA motifs that contain helical domains separated by a bulge or internal loop. The global structures of such extended multi-domain RNAs are not well defined by conventional NMR-distance and torsion angle structural restraints. Residual dipolar couplings (RDCs) are employed here to better define the global structure of the IRE RNA in solution. RDCs contain valuable long-range structural information that compliments the short-range structural data derived from standard NOE-distance and torsion angle restraints. Several approaches for estimating alignment tensor parameters and incorporating RDCs into RNA structure determinations are compared. Both the local and global structure of the IRE are improved significantly by refinement with RDCs. These RDC refinements provide insight on the conformational dynamics of the IRE. These studies highlight some issues that need to be addressed when incorporating RDCs in solution structure determinations of nucleic acids. The approach used here should prove valuable for structure determinations of various multi-domain systems.
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Affiliation(s)
- Scott A McCallum
- Department of Chemistry and Biochemistry, 215 UCB, University of Colorado, Boulder, CO 80309-0215, USA
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438
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McAteer K, Kennedy MA. Force field dependence of NMR-Based, restrained molecular dynamics DNA structure calculations including an analysis of the influence of residual dipolar coupling restraints. J Biomol Struct Dyn 2003; 20:487-506. [PMID: 12529149 DOI: 10.1080/07391102.2003.10506867] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
Abstract
Restrained molecular dynamics is widely used to calculate DNA structures from NMR data. Here, results of an in silico experiment show that the force field can be significant compared to the NMR restraints in driving the final structures to converge. Specifically, we observed that i) the influence of the force field leads to artificially tight convergence within final families of structures and ii) the precision and character of resulting structures depend on the choice of force field used in the calculations. A canonical B-DNA model was used as a target structure. Distances, dihedral angles, and simulated residual dipolar couplings were measured in the target structure and used as restraints. X-PLOR and Discover, which use force fields developed for CHARMM and AMBER programs, respectively, were tested and found to produce different final structures despite the use of identical distance and dihedral restraints. Incorporation of residual dipolar coupling restraints in X-PLOR improves convergence with the target structure and between families of structures indicating that the force field dependence can potentially be overcome if residual dipolar coupling restraints are employed.
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Affiliation(s)
- Kathleen McAteer
- Environmental Molecular Sciences Lab., Pacific Northwest National Laboratory, P.O. Box 999, K8-98, Richland, WA 99352, USA
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439
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440
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Abstract
Protein solution nuclear magnetic resonance (NMR) can be conducted in a slightly anisotropic environment, where the orientational distribution of the proteins is no longer random. In such an environment, the large one-bond internuclear dipolar interactions no longer average to zero and report on the average orientation of the corresponding vectors relative to the magnetic field. The desired very weak ordering, on the order of 10(-3), can be induced conveniently by the use of aqueous nematic liquid crystalline suspensions or by anisotropically compressed hydrogels. The resulting residual dipolar interactions are scaled down by three orders of magnitude relative to their static values, but nevertheless can be measured at high accuracy. They are very precise reporters on the average orientation of bonds relative to the molecular alignment frame, and they can be used in a variety of ways to enrich our understanding of protein structure and function. Applications to date have focused primarily on validation of structures, determined by NMR, X-ray crystallography, or homology modeling, and on refinement of structures determined by conventional NMR approaches. Although de novo structure determination on the basis of dipolar couplings suffers from a severe multiple minimum problem, related to the degeneracy of dipolar coupling relative to inversion of the internuclear vector, a number of approaches can address this problem and potentially can accelerate the NMR structure determination process considerably. In favorable cases, where large numbers of dipolar couplings can be measured, inconsistency between measured values can report on internal motions.
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Affiliation(s)
- Ad Bax
- Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, MD 20892-0520, USA.
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441
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Giesen AW, Homans SW, Brown JM. Determination of protein global folds using backbone residual dipolar coupling and long-range NOE restraints. JOURNAL OF BIOMOLECULAR NMR 2003; 25:63-71. [PMID: 12567000 DOI: 10.1023/a:1021954812977] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
We report the determination of the global fold of human ubiquitin using protein backbone NMR residual dipolar coupling and long-range nuclear Overhauser effect (NOE) data as conformational restraints. Specifically, by use of a maximum of three backbone residual dipolar couplings per residue (Ni-H N i, Ni-C'(i-1), H N i - C'(i-1)) in two tensor frames and only backbone H N -H N NOEs, a global fold of ubiquitin can be derived with a backbone root-mean-square deviation of 1.4 A with respect to the crystal structure. This degree of accuracy is more than adequate for use in databases of structural motifs, and suggests a general approach for the determination of protein global folds using conformational restraints derived only from backbone atoms.
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Affiliation(s)
- Alexander W Giesen
- Astbury Centre for Structural Molecular Biology, School of Biochemistry and Molecular Biology University of Leeds, LS2 9JT UK
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442
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Bryce DL, Wasylishen RE. Evaluation of the influence of anisotropic indirect nuclear spin-spin coupling tensors on effective residual dipolar couplings for model peptides. JOURNAL OF BIOMOLECULAR NMR 2003; 25:73-78. [PMID: 12567001 DOI: 10.1023/a:1021903427920] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Residual dipolar couplings (RDCs) observed between nuclear spins in molecules in partially oriented media have become a valuable source of information for NMR spectroscopists seeking to structurally characterize biological macromolecules. Examination of the form of the direct (D) and indirect (J) nuclear spin-spin coupling Hamiltonians indicates that all observed RDCs contain an unknown contribution from the anisotropic part of J (Delta J) in addition to the direct dipolar contribution, DPQ. Here, we evaluate the influence of DeltaJ on RDCs through a series of DFT calculations on model peptides. Very small corrections to one-bond RDCs measured between heavy atoms in peptides and proteins are recommended: +0.51% for N-C' spin pairs, and +0.45% for C alpha-C' spin pairs. The corrections to RDCs involving at least one proton are negligible. This latter point is likely to be equally applicable to nucleic acids and oligosaccharides in addition to peptides and proteins. Finally, the orientations of the J(N, C') and J(C alpha, C') tensors in the molecular framework are reported for glycylglycine.
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Affiliation(s)
- David L Bryce
- Department of Chemistry, University of Alberta, Edmonton, Alberta, Canada T6G 2G2
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443
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Wiesner S, Stier G, Sattler M, Macias MJ. Solution structure and ligand recognition of the WW domain pair of the yeast splicing factor Prp40. J Mol Biol 2002; 324:807-22. [PMID: 12460579 DOI: 10.1016/s0022-2836(02)01145-2] [Citation(s) in RCA: 68] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
Abstract
The yeast splicing factor pre-mRNA processing protein 40 (Prp40) comprises two N-terminal WW domains, separated by a ten-residue linker, and six consecutive FF domains. In the spliceosome, the Prp40 WW domains participate in cross-intron bridging by interacting with proline-rich regions present in the branch-point binding protein (BBP) and the U5 small nuclear ribonucleoprotein component Prp8. Furthermore, binding of Prp40 to the phosphorylated C-terminal domain (CTD) of the largest subunit of RNA polymerase II is thought to link splicing to transcription. To gain insight into this complex interaction network we have determined the solution structure of the tandem Prp40 WW domains by NMR spectroscopy and performed chemical shift mapping experiments with different proline-rich peptides. The WW domains each adopt the characteristic triple-stranded beta-sheet structure and are connected by a stable alpha-helical linker. On the basis of a detailed analysis of residual dipolar couplings (RDC) and 15N relaxation data we show that the tandem Prp40 WW domains behave in solution as a single folded unit with unique alignment and diffusion tensor, respectively. Using [1H-15N]-RDCs, we were able to accurately define the relative orientation of the WW domains revealing that the binding pockets of each domain face opposite sides of the structure. Furthermore, we found that both Prp40 WW domains interact with PPxY motifs (where x is any residue) present in peptides derived from the splicing factors BBP and Prp8. Moreover, the Prp40 WW domains are shown to bind proline-rich peptides devoid of aromatic residues, which are also recognised by the Abl-SH3 domain and the WW domain of the mammalian Prp40 orthologue formin binding protein 11. In contrast, no interaction was observed between the Prp40 WW domains and the CTD repeats used in this work.
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Affiliation(s)
- Silke Wiesner
- Structural Biology Programme, EMBL Heidelberg, Meyerhofstr. 1, 69117 Heidelberg, Germany.
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444
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Meier S, Häussinger D, Grzesiek S. Charged acrylamide copolymer gels as media for weak alignment. JOURNAL OF BIOMOLECULAR NMR 2002; 24:351-356. [PMID: 12522299 DOI: 10.1023/a:1021609207024] [Citation(s) in RCA: 39] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
The use of mechanically strained acrylamide/acrylate copolymers is reported as a new alignment medium for biomacromolecules. Compared to uncharged, strained polyacrylamide gels, the negative charges of the acrylamide/acrylate copolymer strongly alter the alignment tensor and lead to pronounced electroosmotic swelling. The swelling itself can be used to achieve anisotropic, mechanical strain. The method is demonstrated for the alignment of TipAS, a 17 kDa antibiotic resistance protein, as well as for human ubiquitin, where alignment tensors with an A(ZZ,NH) of up to 60 Hz are achieved at a gel concentration of 2% (w/v). The alignment can be modulated by the variation of pH, ionic strength, and gel concentration. The high mechanical stability of the swollen gels makes it possible to obtain alignment at polymer concentrations of less than 1% (w/v).
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Affiliation(s)
- Sebastian Meier
- Department of Structural Biology, Biozentrum, University of Basel, CH-4056 Basel, Switzerland
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445
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Abstract
Nuclear magnetic resonance (NMR) spectroscopy is the only experimental technique that can determine the structures and dynamics of biological macromolecules and their complexes in solution and with atomic resolution. The award of the 2002 Nobel Prize in Chemistry to Kurt Wüthrich of the Swiss Federal Institute of Technology and The Scripps Research Institute honors his pioneering efforts in developing and applying this technique. Wüthrich shared the prize with John B. Fenn and Koichi Tanaka, who were recognized for the development of ionization methods for the analysis of proteins using mass spectrometry.
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Affiliation(s)
- Arthur G Palmer
- Department of Biochemistry and Molecular Biophysics, Columbia University, 630 West 168th Street, New York, NY 10025, USA
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446
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Béraud S, Bersch B, Brutscher B, Gans P, Barras F, Blackledge M. Direct structure determination using residual dipolar couplings: reaction-site conformation of methionine sulfoxide reductase in solution. J Am Chem Soc 2002; 124:13709-15. [PMID: 12431100 DOI: 10.1021/ja0268783] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Residual dipolar couplings (RDC) from partially aligned molecules provide long-range structural data and are thus particularly well adapted to rapid structure validation or protein fold recognition. Extensive measurements in two alignment media can also provide precise de novo structure from RDC alone. We have applied a novel combination of these approaches to the study of methionine sulfoxide reductase (MsrA) from Erwinia chrysanthemi, a 27 kDa enzyme essential for repairing oxidative stress damage. The tertiary fold was initially validated by comparing backbone RDC to expected values from the crystal structure of the homologous MsrA from Escherichia coli. Good agreement was found throughout the chain, verifying the overall topology of the molecule, with the exception of the catalytically important peptide P196-L202, where strong and systematic RDC violation was observed. No evidence for local differential mobility in this region was detected, implying that the structure of the strand differs in the two molecules. We have therefore applied the de novo approach meccano to determine the conformation of this peptide using only RDC. A single conformation is found that is in agreement with all measured data. The aligned peptide can be docked onto the expected covalence of the rest of the template molecule while respecting its strictly defined relative orientation. In contrast to the structure of MsrA from E. coli, the reactive side chain of Cys200 is oriented toward the interior of the molecule and therefore closer to the catalytic Cys53, obviating the need for previously proposed conformational reorganization prior to formation of this disulfide intermediate. This analysis requires only backbone assignment and uses unambiguously assigned and readily measurable structural data, thereby greatly economizing investigation time compared to established nuclear Overhauser effect- (nOe-) based structure calculation methods.
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Affiliation(s)
- Sabine Béraud
- Institut de Biologie Structurale, Jean-Pierre Ebel, Centre National de la Recherche Scientifique-Commissariat à l'Energie Atomique UJF, 41 rue Jules Horowitz, 38027 Grenoble Cedex, France
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447
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Dvoretsky A, Gaponenko V, Rosevear PR. Derivation of structural restraints using a thiol-reactive chelator. FEBS Lett 2002; 528:189-92. [PMID: 12297302 DOI: 10.1016/s0014-5793(02)03297-0] [Citation(s) in RCA: 61] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
Recognition and identification of protein folds is a prerequisite for high-throughput structural genomics. Here we demonstrate a simple protocol for covalent attachment of a short and more rigid metal-chelating tag, thiol-reactive EDTA, by chemical modification of the single cysteine residue in barnase(H102C). Conjugation of the metal-chelating tag provides the advantage of allowing a greater range of paramagnetic metal substitutions. Substitution of Yb(3+), Mn(2+), and Co(2+) permitted measurement of metal-amide proton distances, dipolar shifts, and residual dipolar couplings. Paramagnetic-derived restraints are advantageous in the NMR structure elucidation of large protein complexes and are shown sufficient for validation of homology-based fold predictions.
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Affiliation(s)
- Alex Dvoretsky
- Department of Molecular Genetics, Biochemistry, and Microbiology, University of Cincinnati, College of Medicine, OH 45267, USA
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448
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High Resolution NMR of Biomolecules. ACTA ACUST UNITED AC 2002. [DOI: 10.1007/3-540-45649-x_18] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/03/2023]
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449
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Gaponenko V, Altieri AS, Li J, Byrd RA. Breaking symmetry in the structure determination of (large) symmetric protein dimers. JOURNAL OF BIOMOLECULAR NMR 2002; 24:143-8. [PMID: 12495030 DOI: 10.1023/a:1020948529076] [Citation(s) in RCA: 50] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/19/2023]
Abstract
We demonstrate a novel methodology to disrupt the symmetry in the NMR spectra of homodimers. A paramagnetic probe is introduced sub-stoichiometrically to create an asymmetric system with the paramagnetic probe residing on only one monomer within the dimer. This creates sufficient magnetic anisotropy for resolution of symmetry-related overlapped resonances and, consequently, detection of pseudocontact shifts and residual dipolar couplings specific to each monomeric component. These pseudocontact shifts can be readily incorporated into existing structure refinement calculations and enable determination of monomer orientation within the dimeric protein. This methodology can be widely used for solution structure determination of symmetric dimers.
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Affiliation(s)
- Vadim Gaponenko
- Structural Biophysics Laboratory, National Cancer Institute, PO Box B, Frederick, MD 21702-1201, USA
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450
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Longinetti M, Parigi G, Sgheri L. Uniqueness and degeneracy in the localization of rigid structural elements in paramagnetic proteins. ACTA ACUST UNITED AC 2002. [DOI: 10.1088/0305-4470/35/39/302] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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