Preparing coarse-grained runs

Preliminary note

The coarse-grained run requires the molecule topology on the one hand and suitable potentials on the other. In this chapter, the generation of coarse-grained runs is described next, followed by a post-processing of the potential.

If the potential is of such a form that it allows direct fitting of a functional form, the section on post-processing can be skipped. Instead, a program of choice should be used to fit a functional form to the potential. Nevertheless, special attention should be paid to units (angles, bond lengths). The resulting curve can then be specified in the MD package used for simulation. However, most potentials don’t allow an easy processing of this kind and tabulated potentials have to be used.

Generating a topology file for a coarse-grained run

WARNING: This section describes experimental features. The exact names and options of the program might change in the near future. The section is specific to GROMACS support though a generalization for other MD packages is planned.

The mapping definition is close to a topology needed for a coarse grained run. To avoid redundant work, csg_gmxtopol can be used to automatically generate a gromacs topology based on an atomistic reference system and a mapping file.

At the current state, csg_gmxtopol can only generate the topology for the first molecule in the system. If more molecule types are present, a special tpr file has to be prepared. The program can be executed by

csg_gmxtopol --top topol.tpr --cg map.xml --out cgtop

which will create a file cgtop.top. This file includes the topology for the first molecule including definitions for atoms, bonds, angles and dihedrals. It can directly be used as a topology in GROMACS, however the force field definitions (atom types, bond types, etc.) still have to be added manually.

Post-processing of the potential

The VOTCA package provides a collection of scripts to handle potentials. They can be modified, refined, integrated or inter- and extrapolated. These scripts are the same ones as those used for iterative methods in Iterative methods. Scripts are called by csg_call. A complete list of available scripts can be found in Scripts.

The post-processing roughly consists of the following steps (see further explanations below):

  • (manually) clipping poorly sampled (border) regions

  • resampling the potential in order to change the grid to the proper format ()

  • extrapolation of the potential at the borders ( table extrapolate)

  • exporting the table to xvg ( convert_potential gromacs)

Clipping of poorly sampled regions

Regions with an irregular distribution of samples should be deleted first. This is simply done by editing the .pot file and by deleting those values.

Alternatively, manually check the range where the potential still looks good and is not to noisy and set the flags in the potential file of the bad parts by hand to o (for out of range). Those values will later be extrapolated and overwritten.

Resampling

Use the command

csg_resample --in table.pot --out table_resample.pot \
             --grid min:step:max

to resample the potential given in file –table.pot from min to max with a grid spacing of step steps. The result is written to the file specified by out. Additionally, csg_resample allows the specification of spline interpolation (spfit), the calculation of derivatives (derivative) and comments (comment). Check the help (help) for further information.

It is important to note that the values min and max don’t correspond to the minimum and maximum value in the input file, but to the range of values the potential is desired to cover after extrapolation. Therefore, values in \([ \min,\max ]\) that are not covered in the file are automatically marked by a flag o (for out of range) for extrapolation in the next step.

The potential don’t have to start at 0, this is done by the export script (to xvg) automatically.

Extrapolation

The following line

csg_call table extrapolate [options] table_resample.pot \
         table_extrapolate.pot

calls the extrapolation procedure, which processes the range of values marked by csg_resample. The input file is table_resample.pot created in the last step.

After resampling, all values in the potential file that should be used as a basis for extrapolation are marked with an i, while all values that need extrapolation are marked by o. The command above now extrapolates all o values from the i values in the file. Available options include averaging over a certain number of points (avgpoints), changing the functional form (function, default is quadratic), extrapolating just the left or right region of the file (region) and setting the curvature (curvature).

The output table_extrapolate.pot of the extrapolation step can now be used for the coarse-grained run. If GROMACS is used as a molecule dynamics package, the potential has to be converted and exported to a suitable GROMACS format as described in the final step.

Exporting the table

Finally, the table is exported to xvg. The conversion procedure requires a small xml file table.xml as shown below:

<cg>
  <non-bonded>
    <name>XXX</name>
    <step>0.01</step>
  </non-bonded>
  <inverse>
    <gromacs>
      <pot_max>1e8</pot_max>
      <table_end>8.0</table_end>
      <table_bins>0.002</table_bins>
    </gromacs>
  </inverse>
</cg>

where <table_end> is the GROMACS rvdw+table_extension and <pot_max> is just a number slightly smaller than the upper value of single/ double precision. The value given in <table_bins> corresponds to the step value of csg_resample -grid min:step:max.

Using the xml file above, call

csg_call --options table.xml --ia-type non-bonded --ia-name XXX \
  convert_potential gromacs table_extrapolate.pot table.xvg

to convert the extrapolated values in table_extrapolate.pot to table.xvg (The file will contain the GROMACS C12 parts only which are stored in the sixth und seventh column, this can be changed by adding the –ia-type C6 option (for the fourth and fiveth column) or –ia-type CB option (for the second and third column) after csg_call. Ensure compatibility with the GROMACS topology. See the GROMACS manual for further information).

To obtain a bond table, run

csg_call --ia-type bond --ia-name XXX --options table.xml \
convert_potential gromacs table_extrapolate.pot table.xvg

It is also possible to use angle and dihedral as type as well, but make to sure to have a bonded section similar to the non-bonded section above with the corresponding interaction name.

Internally convert_potential gromacs will do the following steps:

  • Resampling of the potential from 0 (or -180 for dihedrals) to table_end (or 180 for angles and dihedrals) with step size table_bins. This is needed for gromacs the table must start with 0 or -180.

  • Extrapolate the left side (to 0 or -180) exponentially

  • Extrapolate the right side (to table_end or 180) exponentially (or constant for non-bonded interactions)

  • Shift it so that the potential is zero at table_end for non-bonded interactions or zero at the minimum for bonded interaction

  • Calculate the force (assume periodicity for dihedral potentials)

  • Write to the format needed by gromacs

An example on non-bonded interactions

csg_call pot shift_nonbonded table.pot table.pot.refined
csg_resample --grid 0.3:0.05:2 --in table.pot.refined \
         --out table.pot.refined
csg_call table extrapolate --function quadratic --region left \
         table.pot.refined table.pot.refined
csg_call table extrapolate --function constant --region right \
         table.pot.refined table.pot.refined

Alternatives

Additionally to the two methods described above, namely (a) providing the MD package directly with a functional form fitted with a program of choice or (b) using csg_resample, csg_call table extrapolate and csg_call convert_potential, another method would be suitable. This is integrating the force table as follows

# Integrate the table
csg_call table integrate force.d minus_pot.d
# multiply by -1
csg_call table linearop minus_pot.d pot.d -1 0