MDFF with Symmetry Restraints

This section will show you how to set up a MDFF run using symmetry restraints. Symmetry restraints use harmonic forces to maintain a symmetric structure during MDFF simulations for symmetric molecules. The symmetric structure is determined by transforming and overlapping the atomic coordinates of all symmetric units and calculating the average positions of the transformed atoms.

Preparing the initial structure

For this example we will be using a nitrilase structure with helical symmetry, found in helix.pdb. The structure is already rigid-body docked into an experimental map (EMDB 1313) with Situs. The map has been converted into the 3D potential for MDFF, named as helix-target.dx. Please refer to previous section for use of Situs for rigid-body docking and use of mdff griddx for map conversion.

1

Start a new VMD session.

2

Load the initial structure in VMD by typing:

mol new helix.pdb

3

Use the AutoPSF plugin as in Section 2.1. If you are working on the same VMD session from the beginning of the tutorial, make sure you click the Reset AutoPSF button and the choose the correct molecule in the AutoPSF plugin. Follow the same steps as before to make helix_autopsf.psf and helix_autopsf.pdb.

4

Generate a PDB file containing the per-atom scaling factors $w_j$ in Equation 1, as in previous section.

mdff gridpdb -psf helix_autopsf.psf -pdb helix_autopsf.pdb
-o helix-grid.pdb

5

Generate secondary structure restraints as in previous section:

package require ssrestraints
ssrestraints -psf helix_autopsf.psf -pdb helix_autopsf.pdb
-o helix-extrabonds.txt -hbonds

6

Generate restraints to prevent cis/trans peptide transitions and chirality errors:

mol new helix_autopsf.psf
mol addfile helix_autopsf.pdb
cispeptide restrain -o helix-extrabonds-cispeptide.txt
chirality restrain -o helix-extrabonds-chirality.txt

Setting up the Symmetry PDB file

We need to create a symmetry PDB file containing the designations of symmetric units, i.e. what the symmetric units are. In the symmetry PDB file, the occupancy column denotes the "symmetry group" atoms belong to, while the beta column denotes the symmetric units designation. In this example, we have a single symmetry relationship, the helical symmetry, so we only have one symmetry group and hence the occupancy column is set to 1. We have nine different symmetric unit within this helical symmetry group, so the beta column of the first symmetric unit is set to 1 and increases by 1 for the next symmetric until the last symmetric unit with beta column assigned to 9. For more information on symmetry restraint parameters, please read the documentation.

1

Load the pdb file we are using for the initial structure

mol new helix_autopsf.pdb

2

Assign beta and occupancy values for different symmetric units according to the rules described above. A tcl script has been provided to you for setting these values. Note that we are applying symmetric restraints to $C_{\alpha}$ atoms only.

source set_symmetry.tcl

Setting up the Transformation Matrix File

Next we have to create a matrix file which contains the transformation matrices needed to overlap the symmetric subunits based on their symmetry. If the matrix file is not given to NAMD, NAMD will attempt to generate these matrices automatically by guessing the symmetry information among the symmetric units. This file follows a specific format outlined below:

1

Matrices should be in order of symmetric units designation (beta column of the symmetry pdb file generated above) e.g. The first matrix is applied to symmetric unit 1, the second matrix to symmetric unit 2 and so on.

2

The matrices are defined as the transformation necessary to overlap the symmetric units onto the first symmetric unit. This means that the first matrix should be an identity matrix.

3

The file should not have any leading or trailing blank lines. Matrices should be separated by one and only one line. The matrix itself should be a 4x4 transformation matrix with one row per line and each column separated by one space only. For example, the identity matrix at the beginning of the file will look like the following:
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
Users can generate the 4x4 matrices for different transformations by using the measure fit command in VMD. Please refer to the documentation in the VMD user guide for more details. The matrix file for the helical nitrilase system has been provided: helix-matrices.txt

Running the MDFF simulation

NAMD configuration files for MDFF can be generated similarly to the previous example.  2.

mdff setup -o symmetry -psf helix_autopsf.psf
-pdb helix_autopsf.pdb
-griddx helix-target.dx
-gridpdb helix-grid.pdb
-extrab {helix-extrabonds.txt helix-extrabonds-cispeptide.txt
helix-extrabonds-chirality.txt} -gscale 1.0 -minsteps 2000 -numsteps 500000

1

Now we need to edit the configuration file symmetry-step1.namd that we just created by adding in the parameters necessary for symmetry restraints. Open the file in any text editor and add the following lines anywhere before the source mdff_template.namd line:

symmetryRestraints on
symmetryfile helix-symmetry.pdb
symmetryk 200
symmetryMatrixFile helix-matrices.txt
symmetryfirststep 2001
symmetryfirstfullstep 502000

These parameters turn symmetry restraints on and let NAMD know where to look for the symmetry information. The symmetryk entry is a constant which scales the harmonic force applied by the restraint. Thie value is scaled down by the number of atoms in a symmetric unit. Users can define a per-atom force constant which assign force constant to individual atoms instead of to the whole symmetric unit, which is discussed in the NAMD user guide. One can vary the forces over time by modifying the force constant. In this case, the force constant will be linearly increased over time, allowing more conformational freedom at the beginning, working up to more rigid restraints as the molecule is fitted to the density. This is accomplished by the symmetryfirstfullstep entry which control when the force constant become the full assigned value (i.e. the symmetryk value). Setting this value to last timestep will linearly increase the force constant from the first timestep to the last timestep. More information about these parameters can be found in the symmetry restraint documentation in the NAMD User's Guide.

2

Quit VMD.

3

Run NAMD using the configuration files generated by VMD, i.e., run the following commands in a terminal (or submit them to a cluster):

namd2 symmetry-step1.namd > symmetry-step1.log

This step should take about 8 hours on a modern quad core desktop. If you don't want to wait, you can proceed to the analyzing section with the provided trajectory files.

Analyzing the results

The resulting trajectories will be saved to files symmetry-step1.dcd. If you want to continue working through the tutorial before the simulations are complete, you can use the provided trajectory files symmetry-step1-result.dcd instead. First, you should load and view the trajectory file no-symmetry-step1-result.dcd provided. This trajectory is the result of running the above simulation with symmetry restraints turned off. You should notice that the last dimer is pulled away from the molecule, seen in Fig. 12. This is due to the extra density adjacent to these regions.

Figure 12: MDFF simulation of nitrilase without symmetry restraints. Red box indicates region of last dimer affected by adjacent density.

While it is possible to cut off extraneous portions of the map, this can introduce errors along the boundaries. Instead, we can use symmetry restraints to avoid these distortions. Load and view the trajectory obtained from your simulation using symmetry restraints symmetry-step1.dcd or use the trajectory file provided symmetry-step1-result.dcd. Compare the movements of the first and last dimers to those without symmetry restraints.