Computational Structural Biology group focusing on dissecting, understanding and predicting biomolecular interactions at the molecular level.

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## Using Residual Dipolar Couplings

Residual dipolar couplings (RDCs) can provide useful information on the orientation of the molecules to be docked. They can be introduced in HADDOCK in two ways:

From our experience, both approaches give good results for docking. The use of intervector projection angle restraints ( Meiler et al. J. Biomol. NMR 17, 185 (2000)) avoids the burden of working with a tensor in the structure calculations. Another advantage is that one can distinguish between inter- and intra-molecular restraints. Considering that part of the system will typically be kept rigid during docking, the use of intra-molecular restraints might not make much sense anyway.

For both, the tensor components need first to be determined. In the case of complexes, this can be easily done by using the known structures of the single domains. The software Pales (Zweckstetter & Bax (2000). J. Am. Chem. Soc. 122, 3791-3792) can be used for this purpose.

You need for this to generate a Pales input file containing your residual dipolar couplings.

A csh script called ana_pdb_Q-factor.csh is provided in the haddock/tools directory that will calculate from the experimental dipolar coupling the tensor parameters for all PDB files present in the current directory by best-fitting the dipolar coupling tensor to the corresponding 3D structures.

Usage:

   $HADDOCK/tools/ana_pdb_Q-factor.csh pales.inp  The output will be written to files with extension PDBfilename.pales. The tensor parameters Axx, Ayy and Azz can then be extracted with the following command:  grep Axx *.pales | gawk '{print$4,$5,$6}' > xx-yy-zz.dat


The components from the structure giving the best fit to the experimental data can be used.
Alternatively, the average values can then be calculated with:

   cat xx-yy-zz.dat | awk '{print $1}' |$HADDOCKTOOLS/average.perl
cat xx-yy-zz.dat | awk '{print $2}' |$HADDOCKTOOLS/average.perl
cat xx-yy-zz.dat | awk '{print $3}' |$HADDOCKTOOLS/average.perl


Check the values in xx-yy-zz.dat to make sure they match (e.g. same sign) before averaging them.
Similarly, the axial (Da) and rhombic (Dr) components can be extracted from the Pales1.2 output files and averaged with the following command:

   grep Da *.pales | awk '{print $3}' |$HADDOCKTOOLS/average.perl
grep Dr *.pales | awk '{print $3}' |$HADDOCKTOOLS/average.perl


Note: For use in HADDOCK (and CNS), the tensor components should be expressed in Hertz and the Pales values should be scaled depending on the nuclei observed. For example, for N-H residual dipolar coupling the proper scaling factor is 21700. Also be careful in the conversion since different programs often use different conventions/notations/units.

Direct use of RDCs as restraints for docking

The proper format for RDC restraints is the following:

assi ( resid 999 and name OO )
( resid 999 and name Z  )
( resid 999 and name X  )
( resid 999 and name Y  )
( resid   20 and name N and segid A )
( resid   20 and name HN and segid A )   2.981   0.200


Given a file containing residue_number RDC_value and Segid a RDC restraint file in CNS format can be generated with the gawk script generate_sani provided in the HADDOCK/RDCtools directory:

    $HADDOCK/RDCtools/generate_sani rdc_data_file  The error on the RDCs is set by default to 0.2 Hz. This can be overruled by giving the error value as argument: $HADDOCK/RDCtools/generate_sani ERR=0.4 rdc_data_file


The 2.4 version of HADDOCK supports up to 5 different SANI restraints sets. Each can have a separate tensor. The tensor residue number should be in the range 999-995. You can edit and modify the generate_sani script to change the tensor number. To use RDC restraints in HADDOCK, use SANI in run.cns in the dipolar coupling section and define the proper Da and R parameters (R=Dr/Da). The RDC restraints are first used in the rigid body energy minimization step using as force constant the value defined for the hot phase. Keep this value small (the current default is 0.02) to keep a proper balance between the AIR and SANI energy terms.

Note 1: Only one set (corresponding to one alignment tensor) of dipolar couplings can be used as direct restraints (SANI) in HADDOCK since currently only one alignment tensor is supported. Multiple sets can however be used as intervector projection angle restraints (see below).

Note 2: For proper docking results, dipolar couplings restraints of the various molecules should be input as one set (and thus not split in separate sets for each molecule). The assumption here is that the RDCs of the various components share one common alignment tensor.

Intervector projection angle restraints for docking

Intervector projection angle restraints ( Meiler et al. J. Biomol. NMR 17, 185 (2000)) are obtained by taking pairs of residual dipolar couplings and generating intervector projection angle restraints (somewhat equivalent to dihedral angle restraints). These restraints have the advantage that they do no longer depend on the orientation of the dipole vector with respect to the alignment tensor. Instead they restrain the angle between two dipolar vectors, allowing for two minima. Two force constants must be therefore defined: one for the border potential function and one for the central part (e.g. between the two minima).

Thanks to Helen Mott and Wayne Boucher from Cambridge University we are providing in the HADDOCK/RDCtools a python script, dipole_segid.py that allows the generation of such restraints from RDC data. To use it, you need to have your RDC data in a tab separated file containing residue_number, RDC_value and Segid and provide the tensor components Dxx, Dyy and Dzz (in Hertz). For NH couplings, these components are equal to 21700 times the eigenvalues of the Saupe matrix given by Pales.

Usage:

    python $HADDOCK/RDCtools/dipolar_segid.py rdc_data_file vean_output_file Dxx Dyy Dzz  The resulting restraints file looks like:  assign (resid 19 and name N and segid B ) (resid 19 and name HN and segid B ) (resid 27 and name N and segid B ) (resid 27 and name HN and segid B ) 13.1 2.9 166.9 2.9 ! excluded 0.935 assign (resid 75 and name N and segid A ) (resid 75 and name HN and segid A ) (resid 27 and name N and segid B ) (resid 27 and name HN and segid B ) 13.1 2.9 166.9 2.9 ! excluded 0.935  The last column gives the fraction of angular space excluded by the restraint and can be used to select “significant” restraints, e.g. limiting more than 25% of the torsional space. Note that the number of restraints generated is very high since for N dipolar coupling there are N*(N-1) possible combinations. To select for example all inter- and intra-molecular restraint excluding more than 25% of the angular space type:  awk '{if ($27 == $9 &&$44 > 0.25) {print $0}}' vean_output_file >vean_intra_25.tbl awk '{if ($27 != $9 &&$44 > 0.25) {print \$0}}' vean_output_file >vean_inter_25.tbl


To use intervector projection angle restraints in HADDOCK, use VANGLE in run.cns in the dipolar coupling section. The VANGLE restraints are introduced in the rigid body energy minimization step using as initial force constants the value defined for the hot phase. The restraints are activated in the second rotational minimization phase (thus earlier than the SANI restraints!)