b) NMR: prediction of molecular alignment from structure

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© 2008 Nature Publishing Group http: / / www. nature. com/ natureprotocols PROTOCOL TABLE 4 | Parameters reported by PALES in RDC output files (see Supplementary Data). Parameter Definition DATA SAUPE Five independent values (S(zz), S(xx-yy), S(xy), S(xz), S(yz)) of the alignment tensor7 DATA IRREDUCIBLE Irreducible representation of the alignment tensor47 DATA IRREDUCIBLE GENERAL_MAGNITUDE General magnitude of the alignment tensor4,47 DATA MAPPING Sauson–Flamsteed coordinates (i.e., x and y coordinates for the x, y and z axis of the alignment tensor) DATA MAPPING INV Sauson–Flamsteed coordinates of the inverted axes of the alignment tensor (relative to DATA MAPPING) DATA EIGENVALUES Eigenvalues (Sxx_d,Syy_d,Szz_d) of the alignment tensor (i.e., the values of the alignment tensor in the principal axis frame) DATA EIGENVECTORS Eigenvectors for diagonalization of the alignment tensor DATA Q_EULER_ANGLES Euler angles for rotation of the alignment tensor into the principal axis frame, that is, for diagonalization of the alignment tensor. Values are specified according to the definition used in quantum mechanics, that is, for clockwise rotation about the three independent axes z (angle ALPHA), y ¢ (angle BETA) and z 00 (angle GAMMA). Four different Euler angles are reported due to the fourfold degeneracy of alignment tensors DATA EULER_ANGLES Euler angles for rotation into the principal axis frame using a rotation about three dependent axes x (angle psi), y (angle theta) and z (angle phi). Two solutions are provided DATA Da Da ¼ 1 / 2 S d zz DATA Dr Dr ¼ 1 / 3 (S xx d S yy d ) DATA Aa Axial component of the alignment tensor Aa ¼ S d zz . DATA Ar Rhombic component of the tensor Ar ¼ 2 / 3 (S d xx S d yy ) DATA Da_HN Axial component (in Hz) of the alignment tensor normalized to the dipolar interaction constant of the one-bond NH internuclear vector (Da_HN ¼ 1 /2 D NH max Aa ¼ 1 /2 21585.19 Aa) DATA rhombicity Rhombicity R ¼ Ar/Aa of the alignment tensor (range: [0, 2 /3]) DATA N Number of RDCs used in the calculation DATA RMS Root-mean-square deviation between input and calculated RDCs DATA Chi2 w2 value between input and calculated RDCs DATA CORR R Pearson’s linear correlation coefficient between input and calculated RDCs (range: [ 1, 1]) DATA Q SAUPE RDC Q-factor calculated according to Q ¼ {Si¼1,..,N [d norm i (exp) di norm (calc)] 2 /N} 1/2 /Dr.m.s. ,withNbeing the number of measured and normalized couplings, d norm i (exp). Dr.m.s. refers to the root-mean-square value of RDCs for randomly distributed internuclear vectors. It can be calculated directly from experimental dipolar couplings Dr.m.s. ¼ [Si¼1,..,N (di norm ) 2 ] 1/2 (‘-qRms’ flag) or from the axial and rhombic component of the alignment tensor Dr.m.s. ¼ [2 (Da norm ) 2 (4 + 3R2 )/5] 1/2 ,withDa norm being the normalized axial component (‘-qDa’flag;thisisthedefault selection) DATA REGRESSION OFFSET Vertical offset of straight line fit to a comparison of input and calculated RDCs DATA REGRESSION SLOPE Slope of straight line fit to a comparison of input and calculated RDCs DATA REGRESSION BAX SLOPE Average of slope obtained from straight line fits of y ¼ ax + b and x ¼ cy + d, thatis,BAXSLOPE¼0.5 (a + 1/c) Best-fitting experimental RDCs to 3D structure 3| Run PALES to best-fit experimental RDCs to the 3D structure by executing the following command on the command line: PALES -bestFit -pdb pdb1ubqH.ent -inD dObs.tab -outD dCalc.Svd.tab m CRITICAL STEP Include the ‘-bestFit’ flag. ? TROUBLESHOOTING 4| Check if the RDC table and PDB file were properly read in by PALES. PALES reports some information (including errors and warnings on the command line as stderr). The first two lines indicate which PDB file and RDC table were provided as input, how many residues and atoms were recognized in the PDB file and how many residues and couplings were there in the RDC table. The first line starting with ‘REMARK’ reports how many atom pairs (RDCs) in the input table could be matched to internuclear vectors in the PDB file (i.e., how many RDCs will be used for best-fitting). The second ‘REMARK’ line reports the selection criteria applied to the PDB file. ? TROUBLESHOOTING 684 | VOL.3 NO.4 | 2008 | NATURE PROTOCOLS
© 2008 Nature Publishing Group http: / / www. nature. com/ natureprotocols PROTOCOL 5| Inspect the output file (e.g., ‘dCalc.Svd.tab’). Determine the degree of alignment from the norm of the irreducible representation of the alignment tensor (‘DATA IRREDUCIBLE GENERAL_MAGNITUDE’) or the magnitude of its largest eigenvalue (‘Szz_d’). ‘Szz_d’ normalized to 1DNH can be found in the ‘DATA Da_HN’ parameter. ‘DATA Da_HN’ is generally in the range B5–20 Hz. Using ‘DATA Da_HN’ or ‘Szz_d’ can be misleading in the case of high rhombicity. Evaluate the orientation of the alignment tensor that is described by three Euler angles ‘ALPHA’(clockwiserotationaroundz,leadingtonewsystemx¢,y¢,z¢), ‘BETA’ (clockwise rotation around y’, leading to new system x00 ,y00 ,z00 ) and ‘GAMMA’ (clockwise rotation around z00 ). Four equivalent Euler orientations are reported due to the sign ambiguity of the eigenvectors. Check the RDC statistics, that is, did PALES use the number of RDCs you supplied (parameter ‘DATA N’), what is Pearson’s correlation coefficient between experimental and back-calculated RDCs (‘DATA CORR R’), is the dipolar coupling Q value sufficiently low (‘DATA Q SAUPE’; Q values for high-resolution structures range from 17% when comparing experimental ubiquitin dipolar couplings with its 1.8-A˚ X-ray structure to 11% when comparing dipolar couplings for the third IgG-binding domain of streptococcal protein G with its 1.1-A˚ X-ray structure), are there systematic errors in the experimental RDCs that cause an offset (‘DATA REGRESSION OFFSET’) between experimental and back-calculated RDCs or a slope (‘DATA REGRESSION SLOPE’) deviating from one (further details can be found in Table 4). m CRITICAL STEP For high-resolution X-ray structures (solved at a resolution of 2.5 A˚ or better), Pearson’s correlation coefficient between experimental and calculated couplings (‘DATA CORR R’) is expected to be above 0.9. ? TROUBLESHOOTING 6| Refine the RDC input table. Search the column ‘D_DIFF’, which lists the difference between experimental and calculated RDCs, for values that significantly exceed the values obtained for most of the other residues. Check the NMR spectra and determine, if signal overlap or low signal-to-noise ratio is responsible for the large deviations. Under these circumstances, remove the corresponding RDC values from the input table (e.g., by marking them out with a ‘#’ sign in the beginning of the line) and repeat Steps 3–6. 7| Visualize the orientation of the alignment tensor (optional). Rerun PALES by including the ‘-pdbRot’ flag, that is, ‘PALES -bestFit -pdb pdb1ubqH.ent -inD dObs.tab -outD dCalc.Svd.tab -pdbRot rot.pdb -nosurf –H’. In the PDB output file (e.g., ‘rot.pdb’), the molecule will be rotated such that the alignment tensor is parallel to the laboratory frame. Load the PDB output file into any molecular visualization program and activate the axes of the laboratory frame. ? TROUBLESHOOTING 8| Determine the uncertainty in the alignment tensor parameters. Execute PALES with the command line flag ‘-mcStruc’ and set the number of Monte Carlo steps to B1,000 (‘-map 1000’): PALES -bestFit -pdb pdb1ubqH.ent -inD dObs.tab -outD dCalc.McStruc.tab -mcStruc -map 1000 -outDa tMag.tab -outMap tCoor.tab -outAng tAng.tab -outA tSaupe.tab Alignment tensor parameters for each Monte Carlo step are written to files by specifying the ‘-outDa’, ‘-outMap’, ‘-outAng’ and ‘-outA’ flags. Extract the uncertainty in the alignment tensor parameters from the ‘DATA STATISTICS MAPPING’ fields in the output file (e.g., ‘dCalc.McStruc.tab’). m CRITICAL STEP The RDC weight factors (in the column ‘W’ of the RDC input table) must have the correct values (see Step 2). Prediction of molecular alignment from the 3D shape of a biomolecule 9| Perform the alignment prediction using the steric interaction model. When no RDCs are available (either experimental RDCs or dummy values), execute one of the following commands on the command line. PALES -pdb pdb1ubqH.ent -H If you have prepared an RDC input table (e.g., ‘dObs.tab’), execute PALES -pdb pdb1ubqH.ent -H -inD dObs.tab If you want to store the output into a file (e.g.,‘dCalc.Steric.tab’), execute PALES -pdb pdb1ubqH.ent -H -inD dObs.tab –outD dCalc.Steric.tab This is identical to executing PALES -stPales -bic -wv 0.05 -pdb pdb1ubqH.ent -inD dObs.tab -outD dCalc.Steric.tab -H The ‘-bic’ flag selects the infinite wall model (e.g., when using bicelles). For the infinite cylinder model, ‘-bic’ should be replaced by ‘-pf1’. The orientation of the bilayer/cylinder relative to the magnetic field cannot be changed. Specify the concentration of the liquid crystalline phase (‘-wv 0.05’ in g ml 1 ). m CRITICAL STEP Inclusion of protons (‘-H’ flag) can significantly influence the predicted alignment tensor. ? TROUBLESHOOTING 10| Evaluate the results of alignment prediction in the output file (e.g., ‘dCalc.Steric.tab’). Control the simulation parameters (lines starting with ‘DATA PALES’). The default value of the order parameter of the liquid crystal is 0.8 (‘DATA PALES LC_ORDER’). The magnitude of alignment (‘DATA Da_HN’) scales linearly with the concentration of the dilute liquid crystalline medium. Inspect the various quality measures of calculated RDCs such as root-mean-square deviation (‘DATA RMS’), Pearson’s linear correlation coefficient (‘DATA CORR R’) and RDC quality factor (‘DATA Q SAUPE’). ? TROUBLESHOOTING NATURE PROTOCOLS | VOL.3 NO.4 | 2008 | 685
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