b) NMR: prediction of molecular alignment from structure

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© 2008 Nature Publishing Group http: / / www. nature. com/ natureprotocols PROTOCOL To take into account electrostatic effects, each nonexcluded S matrix is weighted according to its Boltzmann probability, PB, after calculating the corresponding electrostatic potential of the solute (‘-elPales’ module in PALES). Continuum electrostatic theory43 is used for calculating the electrostatic interaction energy: the solute is embedded in a dielectric medium containing excess ions in addition to the counter ions neutralizing the solute and nematogen. The nonlinear Poisson–Boltzmann (PB) equation is used to derive the electrostatic potential44,45 . Even within the simplifications of a continuum description, calculations of the electrostatic potentials would require solving a full 3D electrostatics problem for each distance and orientation of the solute with respect to the surface of the charged liquid crystal particle. Instead, we further simplify the problem by treating the solute as a particle in the external field of the liquid crystal. Moreover, we assume that the nematogen carries a uniform charge density (‘-chSurf’ parameter in PALES) instead of discrete surface charges. The nonlinear 3D PB equation is then solved only once, in the absence of the solute, yielding an electrostatic potential j(r). The distance- and orientation-dependent electrostatic free energy of the protein comprising partial charges qi at positions ri are then approximated by DGelðr; OÞ ¼Si qi f½riðr; OÞŠ: The Boltzmann factor PB ¼ exp[ DGel(r,O)/kBT] provides relative electrostatic weights when averaging the individual alignment tensors, derived for each orientation and distance, to yield an overall solute alignment tensor: Z Z A mol ij ¼ AijPBðr; OÞ dr dO= PBðr; OÞ dr dO: ð5Þ MATERIALS EQUIPMENT .Hardware: Computer running Unix, Linux, Mac OS X or Windows operating system .Software: PALES is available to academic users for free download from http://www.mpibpc.mpg.de/groups/griesinger/zweckstetter/_links/ software_pales.htm .Input files (see also Supplementary Data): . 3D coordinate file; most standard PDB files are recognized, including multiple chain and segment molecules P B = exp[–∆G e1 (r,Ω)/k B T ] Figure 2 | Schematic outline of the PALES algorithm simulating weak ordering of molecules in charged alignment media. A protein is embedded in the external electrostatic field of the liquid crystal. Electrostatic interactions between the protein molecule and a liquid crystal particle cause the probabilities of sterically allowed solute orientations to depend strongly on this orientation and the distance from the liquid crystal particle. For details, see the section ‘Prediction of molecular alignment from the 3D charge distribution and shape of a molecule’. For a flat surface (‘-bic’ parameter in PALES), an analytical solution of the nonlinear PB equation exists 44,45 . For uniformly charged cylinders such as bacteriophage (‘-pf1’ parameter in PALES), the method of Stigter 46 is used assuming symmetric monovalent ions and vanishing potential at infinity. Input and output files used in the protocol can be found in the Supplementary Data online. In addition, a shell script is provided for running the PALES tasks outlined in the protocol. . RDC table (Table 1); required for best-fitting RDCs to a molecular structure (‘-bestFit’ module of PALES), but not essential for prediction of molecular alignment (‘-stPales’ and‘-elPales’ modules of PALES) . For prediction of molecular alignment induced by uniformly charged cylinders (‘-elPales -pf1’): . File containing the charges of the molecule (Table 2; see also Step 14). . File containing the electrostatic potential (Table 3). PROCEDURE Preparation of input 1| Prepare the coordinate file or download a 3D structure from the PDB (http://www.rcsb.org/pdb) (e.g.,‘pdb1ubq.ent’). When multiple models are present in the coordinate file, select one and remove the others by using your preferred editor. Remove unwanted parts of the structure (or use PALES selection flags (see Step 3)). If the PDB file does not contain protons, add protons to the structure using, for example, the program Reduce (http://kinemage.biochem.duke.edu/software/reduce.php) (e.g., ‘pdb1ubqH.ent’; see Supplementary Data to know how to add protons to a crystal structure using the program Reduce). If you are only interested in prediction of the molecular alignment tensor (and not RDCs), go to Step 9. m CRITICAL STEP For alignment prediction, all atoms in the PDB file will be used (including pseudo atoms such as ‘ANI’), when no appropriate selection command line arguments are specified. 2| Prepare the RDC input table (e.g., ‘dObs.tab’; Supplementary Data). The table must include a ‘VARS’ line and a ‘FORMAT’ line that label the corresponding columns of the table and define its data type, respectively (Table 1). Lines with a ‘#’ sign as first character as well as empty lines are ignored. The table must include columns for residue ID, three-character 682 | VOL.3 NO.4 | 2008 | NATURE PROTOCOLS
© 2008 Nature Publishing Group http: / / www. nature. com/ natureprotocols TABLE 1 | Example of a PALES RDC input table (selection of 1H-15N RDCs observed in the 76-residue protein ubiquitin weakly aligned in bicelles) 2 . VARS RESID_I RESNAME_I ATOMNAME_I RESID_J RESNAME_J ATOMNAME_J D DD W FORMAT %5d %6s %6s %5d %6s %6s %9.3f %9.3f %.2f 3 ILE N 3 ILE H 8.271 1.000 1.00 4 PHE N 4 PHE H 10.489 1.000 1.00 5 VAL N 5 VAL H 9.871 1.000 1.00 6 LYS N 6 LYS H 9.152 1.000 1.00 7 THR N 7 THR H 3.700 1.000 1.00 13 ILE N 13 ILE H 6.947 1.000 1.00 14 THR N 14 THR H 9.713 1.000 1.00 15 LEU N 15 LEU H 9.851 1.000 1.00 16 GLU N 16 GLU H 1.909 1.000 1.00 17 VAL N 17 VAL H 0.041 1.000 1.00 18 GLU N 18 GLU H 10.513 1.000 1.00 20 SER N 20 SER H 4.071 1.000 1.00 21 ASP N 21 ASP H 2.119 1.000 1.00 23 ILE N 23 ILE H 9.098 1.000 1.00 25 ASN N 25 ASN H 2.948 1.000 1.00 26 VAL N 26 VAL H 8.892 1.000 1.00 residue name and the atom name for both atoms that are involved in the dipolar coupling. Segment ID and Chain ID are optional. The ‘D’ column gives the RDC value in Hz. Hetero- and homonuclear RDCs involving C, N, H, P and F atoms can be used simultaneously. When no experimental RDCs are available, any nonzero dummy values can be entered (in this case, go directly to Step 9). The ‘DD’ column gives an indication of the experimental RDC error (relative to 1 D NH). The weight column ‘W’ is used for comparison of input and calculated RDCs (e.g., for calculation of root-mean-square deviations between input and calculated RDCs) and should be normalized to 1 D NH according to the gyromagnetic ratios of the involved nuclei and the internuclear distance, that is, W( 1 D NH) ¼ 1.000, W( 1 D CC) B 5.05, W( 1 D NC) B 8.33, W( 1 D CH) B 0.48, W( 2 D HnC) B 3.33. Note that values in column ‘W’ do not influence best-fitting or prediction of TABLE 2 | Example of a PALES charge file for the 76-residue protein ubiquitin. 1 Terminus Charge 0.711 6 Default Charge 0.989 11 Default Charge 0.989 16 Default Charge 0.924 18 Default Charge 0.924 21 Default Charge 0.924 24 Default Charge 0.924 27 Default Charge 0.989 29 Default Charge 0.989 32 Default Charge 0.924 33 Default Charge 0.989 34 Default Charge 0.924 39 Default Charge 0.924 42 Default Charge 0.993 48 Default Charge 0.989 51 Default Charge 0.924 52 Default Charge 0.924 54 Default Charge 0.993 58 Default Charge 0.924 59 Default Charge 0.039 63 Default Charge 0.989 64 Default Charge 0.924 68 Default Charge 0.231 72 Default Charge 0.993 74 Default Charge 0.993 76 O Charge 0.491 76 OXT Charge 0.491 PROTOCOL molecular alignment tensors and therefore also not RDCs back-calculated from calculated/predicted alignment tensors. For best-fitting or prediction of molecular alignment, input and calculated RDCs are scaled automatically by the dipolar interaction value for a specific internuclear vector. For one-bond backbone RDCs, optimized values of the internuclear distance are used for calculation of the dipolar interaction value. For all other RDCs, internuclear distances are taken from the3Dcoordinatefile. m CRITICAL STEP The atom notation in the RDC table must match that of the PDB file. Check, in particular, the notation of amide protons (i.e., ‘H’ or ‘HN’). TABLE 3 | Part of a PALES input file that contains the values for the electrostatic potential. 0.00 2.22 105 1.00E + 03 2.18 105 2.00E + 03 2.14 105 3.00E + 03 2.10 105 4.00E + 03 2.06 105 5.00E + 03 2.02 105 6.00E + 03 1.98 105 7.00E + 03 1.95 105 8.00E + 03 1.91 105 The first column specifies the distance from the surface of the alignment medium (in nm); the second column specifies the value of the electrostatic potential (in e kBT 1 ). Files containing the electrostatic potential of Pf1 phage at different salt concentrations can be downloaded from http://www.mpibpc. mpg.de/groups/griesinger/zweckstetter/_links/software_pales.htm. NATURE PROTOCOLS | VOL.3 NO.4 | 2008 | 683
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b) NMR: prediction of molecular alignment from structure

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