Targeted Molecular Dynamics (TMD)

In TMD, subset of atoms in the simulation is guided towards a final 'target' structure by means of steering forces. At each timestep, the RMS distance between the current coordinates and the target structure is computed (after first aligning the target structure to the current coordinates). The force on each atom is given by the gradient of the potential

$$U_{TMD} = \frac{1}{2} \frac{k}{N} \left[ RMS(t) - RMS^*(t) \right]^2$$ (31)

where $RMS(t)$ is the instantaneous best-fit RMS distance of the current coordinates from the target coordinates, and $RMS^*(t)$ evolves linearly from the initial RMSD at the first TMD step to the final RMSD at the last TMD step. The spring constant $k$ is scaled down by the number $N$ of targeted atoms.

Atoms can be separated into non-overlapping constraint domains by assigning integer values in the beta column of the TMDFile. Forces on the atoms will be calculated for each domain independently of the other domains.

Within each domain, the set of atoms used to fit the target structure can be different from the set of atoms that are biased towards the target structure. If the altloc field in the TMDFile is not ` ' or `0' then the atom is fitted. If the occupancy is non-zero then the atom is biased. If none of the atoms in a domain have altloc set then all biased atoms are fitted.

Note that using different atoms for fitting and biasing or not using the same spring constant for all target atoms within a domain will result in forces conserving neither energy nor momentum. In this case harmonic restraints and Langevin dynamics are likely needed.

• TMD $<$ Is TMD active $>$
  Acceptable Values: on or off
  Default Value: off
  Description: Should TMD steering forces be applied to the system. If TMD is enabled, TMDk, TMDFile, and TMDLastStep must be defined in the input file as well.

• TMDk $<$ Elastic constant for TMD forces $>$
  Acceptable Values: Positive value in $kcal/mol/$ Å$^2$ .
  Description: The value of $k$ in Eq. 31. A value of 200 seems to work well in many cases. If this setting is omitted, the value in the occupancy column of the pdb file specified by TMDFile will be used as the constant for that atom. This allows the user to specify the constant on a per-atom basis.

• TMDOutputFreq $<$ How often to print TMD output $>$
  Acceptable Values: Positive integer
  Default Value: 1
  Description: TMD output consists of lines of the form TMD ts targetRMS currentRMS where ts is the timestep, targetRMS is the target RMSD at that timestep, and currentRMS is the actual RMSD.

• TMDFile $<$ File for TMD information $>$
  Acceptable Values: Path to PDB file
  Description: Biased atoms are those whose occupancy (O) is nonzero in the TMD PDB file. Fitted atoms are those whose altloc field is not ` ' or `0', if present, otherwise all biased atoms are fitted. The file must contain no more atoms than the structure file and those atoms present must have the exact same index as the structure file (i.e., the file may contain a truncated atom selection ``index $< N$ '' but not an arbitrary selection). The coordinates for the target structure are also taken from the targeted atoms in this file. Non-targeted atoms are ignored. The beta column of targetted atoms is used to designate non-overlapping constraint domains. Forces will be calculated for atoms within a domain separately from atoms of other domains.

• TMDFirstStep $<$ first TMD timestep $>$
  Acceptable Values: Positive integer
  Default Value: 0
  Description:
• TMDLastStep $<$ last TMD timestep $>$
  Acceptable Values: Positive integer
  Description: TMD forces are applied only between TMDFirstStep and TMDLastStep. The target RMSD evolves linearly in time from the initial to the final target value.

• TMDInitialRMSD $<$ target RMSD at first TMD step $>$
  Acceptable Values: Non-negative value in Å
  Default Value: from coordinates
  Description: In order to perform TMD calculations that involve restarting a previous NAMD run, be sure to specify TMDInitialRMSD with the same value in each NAMD input file, and use the NAMD parameter firstTimestep in the continuation runs so that the target RMSD continues from where the last run left off.
• TMDFinalRMSD $<$ target RMSD at last TMD step $>$
  Acceptable Values: Non-negative value in Å
  Default Value: 0
  Description: If no TMDInitialRMSD is given, the initial RMSD will be calculated at the first TMD step. TMDFinalRMSD may be less than or greater than TMDInitialRMSD, depending on whether the system is to be steered towards or away from a target structure, respectively. Forces are applied only if $RMS(t)$ is betwween TMDInitialRMSD and $RMS*(t)$ ; in other words, only if the current RMSD fails to keep pace with the target value.

• TMDDiffRMSD $<$ Is double-sided TMD active? $>$
  Acceptable Values: on or off
  Default Value: off
  Description: Turns on the double-sided TMD feature which targets the transition between two structures. This is accomplished by modifying the TMD force such that the potential is based on the difference of RMSD's from the two structures:

  $$U_{TMD} = \frac{1}{2} \frac{k}{N} \left[ DRMS(t) - DRMS^*(t) \right]^2$$ (32)

  
  
  where $DRMS(t)$ is RMS1(t) - RMS2(2) (RMS1 being the RMSD from structure 1 and RMS2 the RMSD from structure 2). The first structure is specified as normal in TMDFile and the second structure should be specified in TMDFile2, preserving any domain designations found in TMDFile.

• TMDFile2 $<$ Second structure file for double-sided TMD $>$
  Acceptable Values: Path to PDB file
  Description: PDB file defining the second structure of a double sided TMD. This file should contain the same number of atoms as TMDFile along with the same domain designations if any are specified.