Locally Enhanced Sampling

Locally enhanced sampling (LES) [16,17,18] increases sampling and transition rates for a portion of a molecule by the use of multiple non-interacting copies of the enhanced atoms. These enhanced atoms experience a nonbonded (electrostatics and van der Waals) potential that is divided by the number of copies present; the bonded potential is not affected. In this way the enhanced atoms can occupy the same space, while the multiple instances and reduces barriers imposed by the nonbonded interactions increase transition rates.

Structure Generation

To use LES, the structure and coordinate input files must be modified to contain multiple copies of the enhanced atoms. psfgen provides the multiply command for this purpose. NAMD supports a maximum of 15 copies, which should be sufficient. You may create more copies than you intend to use in a every simulation and NAMD will scale the nonbonded potential of these atoms to zero.

Begin by generating the complete molecular structure and guessing coordinates as described in Sec. 4. As the last operation in your script, prior to writing the psf and pdb files, add the multiply command, specifying the number of copies desired and listing segments, residues, or atoms to be multiplied. For example, multiply 4 BPTI:56 BPTI:57 will create four copies of the last two residues of segment BPTI. You must include all atoms to be enhanced in a single multiply command in order for the bonded terms in the psf file to be duplicated correctly. Calling multiply on connected sets of atoms multiple times will produce unpredictable results, as may running other commands after multiply.

The enhanced atoms are duplicated exactly in the structure--they have the same segment, residue, and atom names. They are distinguished only by the value of the B (beta) column in the pdb file, which is 0 for normal atoms and varies from 1 to the number of copies created for enhanced atoms. The enhanced atoms may be easily observed in VMD with the atom selection beta != 0.

Simulation

In practice, LES is a simple method used to increase sampling; no special output is generated. The following parameters are used to enable LES:

• les $<$ is locally enhanced sampling active? $>$
  Acceptable Values: on or off
  Default Value: off
  Description: Specifies whether or not LES is active.

• lesFactor $<$ number of LES images to use $>$
  Acceptable Values: positive integer equal to or less than the number of images present
  Description: This should generally be equal to the factor used in multiply when creating the structure. The nonbonded potential of images is divided by lesFactor. If atoms are present with an lesCol value in lesFile that is smaller than lesFactor, then the nonbonded potential of these atoms is set to zero.

• lesFile $<$ PDB file containing LES flags $>$
  Acceptable Values: UNIX filename
  Default Value: coordinates
  Description: PDB file to specify the LES image number of each atom. If this parameter is not specified, then the PDB file containing initial coordinates specified by coordinates is used.

• lesCol $<$ column of PDB file containing LES flags $>$
  Acceptable Values: X, Y, Z, O, or B
  Default Value: B
  Description: Column of the PDB file to specify the LES image number of each atom. This parameter may specify any of the floating point fields of the PDB file, either X, Y, Z, occupancy, or beta-coupling (temperature-coupling). A value of 0 in this column indicates that the atom is not enhanced. Any other value should be a positive integer less than 16.

The parameter lesFactor may be varied between simulations to interpolate between full enhancement and normal simulation (although multiple bonded images are present at all times). If lesFactor is decreased, the images with flags greater than lesFactor will be decoupled from nonbonded terms, sample based only on bonded terms, and should therefore be excluded from analysis. When increasing lesFactor the coordinates of these abandoned images should be reset to that of another image to avoid any bad initial contacts and the resulting instability in the simulation.