Residual Dipolar Couplings in Structure Refinement

Introduction

Residual Dipolar Couplings (RDCs) originate from the anisotropic component of the dipolar interaction, which is dependent on the angle between an internuclear vector and the magnetic field. When a molecule sample orientations uniformly, as it does in normal solution NMR, RDCs average to zero and are not observable. However, if a molecule is dissolved in a dilute liquid crystalline medium it becomes partially aligned, and the dipolar couplings are not completely averaged to zero, leading to a small contribution to the splittings of NMR signals. The angular dependence of these contributions can provide valuable structural information. Protein structures can be validated using RDCs, and structures can be refined to improve quality.

Another application of RDCs is identification of the correct monomer orientations in homodimers. This application requires RDCs from two or more alignment media that give different orientations of principal alignment axes.

Below are protocols for the refinement of protein structures with RDCs using XPLOR-NIH (Ref. 1) and CNS (Ref. 2).

RDC Refinement Using XPLOR-NIH

Using XPLOR-NIH

X-PLOR can be downloaded from http://nmr.cit.nih.gov/xplor-nih/.

• Obtain a good estimate of the magnitude of Da and R from the alignment tensors. The alignment tensors can be obtained either from the extremes of distribution of RDCs (which forms a histogram) or from “REDCAT”. REDCAT gives values for Sxx, Syy and Szz. These values are relateive to the maxium RDC for that bond type. First, multiply these values from REDCAT by the associated maxium RDC value (for example 24350 for NH dipolar couplings). These absolute alignment tensors are related to Da and R as follows:

Da = Szz/2  
R=Dr/Da where Dr=0.5*(Sxx-Syy)

• Note that the sani constraint in XPLOR and or CNS requires three coefficients: DFS, Da and R. DFS is a fixed offset (for example a scalar coupling). For RDC data, DFS = 0.
• In XPLOR define the axis representing the alignment tensor coordinate system. The coordinate system is represented by four pseudo atoms: OO(origin), X ,Y and Z. The coordinate system has to be positioned far away to prevent any interaction with the protein. For more than one aligned media, define separate axes for each medium. These axes can either be defined at the end of the pdb file or as a separate .pdb file. Shown below is an example from the pdb:

ATOM    608  X   ANI   500      33.000  30.000  30.000  1.00  0.00
ATOM    609  Y   ANI   500      30.000  33.000  30.000  1.00  0.00
ATOM    610  Z   ANI   500      30.000  30.000  33.000  1.00  0.00
ATOM    611  OO  ANI   500      30.000  30.000  30.000  1.00  0.00
END

You can also create a separate, standalone pdb file ('axis.pdb') with only one residue starting with ATOM 1. This separate pdb file can then be read in XPLOR or CNS as an additional coordinate file using the coor command.

• Create an RDC constraint file. An example is shown below where -8.1 is the coupling value and 0.6 and 0.5 are the errors associated with it:

assign ( resid 500 and name OO )
         ( resid 500 and name Z )
         ( resid 500 and name X )
         ( resid 500 and name Y )
         ( resid 1 and name HN )
         ( resid 1 and name N ) -8.1 0.6 0.5

• The following perl script ('makeRdcAssign.pm') can be used to create RDC constraint file ('myprotRdc.tbl'). The input to the script is coupling values as one column text file (same as used in REDCAT to import rdcs). Usage for this script is makeRdcAssign.pm myprot.rdc myprotRdc.tbl startingResidue Err1 Err2. Same script can be used for CNS, the only change is to make a tbl file with only one error Err1.

#!/usr/bin/perl
if($ARGC < 3 ) {
    print "Usage: makeRDCAssign.pm infile outfile startingResidue# <err1> <err2> \n";
}
$fileIn = $ARGV[0];
$fileOut = $ARGV[1];
$startRes = $ARGV[2];
$rdcE1 = 0.6;
$rdcE2 = 0.5;
$useE2 = 0;

if ($ARGV[3] ){
   $rdcE1 = $ARGV[3];
}
if ($ARGV[4] ){
   $rdcE2 = $ARGV[4];
   $useE2 = 1;
}
unless( open(RDC_IN, $fileIn)) {
        die("could not open input file $fileIn \n");
}
unless( open(RDC_OUT, ">$fileOut")) {
        die("could not open outpu file $fileOut \n");
}

        $thisRes = $startRes;
while ($thisLine = <RDC_IN> ) {
        @parts = split(/\s+/,$thisLine );  # split by spaces
        $thisRDC = $parts[0];
        print("residue $thisRes, rdc $thisRDC \n");

        # if the rdc is  valid, write to the tbl file
        if ($thisRDC < 999 ) {
            print RDC_OUT "assign ( resid 500 and name OO ) \n";
            print RDC_OUT "           ( resid 500 and name Z ) \n";
            print RDC_OUT "           ( resid 500 and name X ) \n";
            print RDC_OUT "           ( resid 500 and name Y ) \n";
            print RDC_OUT "           ( resid $thisRes and name HN ) \n";
            print RDC_OUT "           ( resid $thisRes and name N )  ";
           if ($useE2 > 0 ) {
                print RDC_OUT " $thisRDC  $rdcE1  $rdcE2 \n\n";
            } else {
                print RDC_OUT " $thisRDC  $rdcE1  \n\n";
            }
        }
        $thisRes = $thisRes + 1;
}

• Do not include all the RDCs for refinement. Leave 15-20% of the RDCs for validation.

• Set the Xplor-NIH input file for dipolar coupling refinement. The RDC restraint is known as sani (susceptibility anisotropy). Define the force constant, ksani for each media and for each type of couplings.

• The refined structure can be validated with the RDCs that are not used in refinement. From the refined structure RDCs can be back calculated (using REDCAT) and plotted against the experimental RDCs.

References

1.  

2.   Brünger, A.T., Adams, P.D., Clore, G.M., DeLano, W.L., Gros, P., Grosse-Kunstleve, R.W., Jiang, J.-S., Kuszewski, J., Nilges, M., Pannu, N.S., Read, R.J., Rice, L.M., Simonson, T. and Warren,G.L. (1998) Crystallography & NMR system: a new software suite for macromolecular structure determination. Acta Crystallogr. D54, 905-921.