Steered Molecular Dynamics (SMD)

The SMD feature is independent from the harmonic constraints, although it follows the same ideas. In both SMD and harmonic constraints, one specifies a PDB file which indicates which atoms are 'tagged' as constrained. The PDB file also gives initial coordinates for the constraint positions. One also specifies such parameters as the force constant(s) for the constraints, and the velocity with which the constraints move.

There are two major differences between SMD and harmonic constraints:

• In harmonic constraints, each tagged atom is harmonically constrained to a reference point which moves with constant velocity. In SMD, it is the center of mass of the tagged atoms which is constrained to move with constant velocity.

• In harmonic constraints, each tagged atom is constrained in all three spatial dimensions. In SMD, tagged atoms are constrained only along the constraint direction (unless the optional SMDk2 keyword is used.)

The center of mass of the SMD atoms will be harmonically constrained with force constant $k$ (SMDk) to move with velocity $v$ (SMDVel) in the direction $\vec n$ (SMDDir). SMD thus results in the following potential being applied to the system:

$$U(\vec r_1, \vec r_2, ..., t) \; = \; \frac{1}{2} k\left[vt - (\vec R(t) - \vec R_0)\cdot \vec n \right]^2.$$ (33)

Here, $t \equiv N_{ts} dt$ where $N_{ts}$ is the number of elapsed timesteps in the simulation and $dt$ is the size of the timestep in femtoseconds. Also, $\vec R(t)$ is the current center of mass of the SMD atoms and $R_0$ is the initial center of mass as defined by the coordinates in SMDFile. Vector $\vec n$ is normalized by NAMD before being used.

Optionally, one may also specify a transverse force constant $k_2$ (SMDk2). The potential then becomes

$$U(\vec r_1, \vec r_2, ..., t) \; = \; \frac{1}{2} k\left[vt - (\v... ... \vec R_0\right)^2 - \left((\vec R(t) - \vec R_0) \cdot \vec n\right)^2\right].$$ (34)

In this case, the force constant $k$ controls the potential parallel to the pulling direction $\vec n$ , while the transverse force constant $k_2$ controls the potential perpendicular to $\vec n$ .

Output

NAMD provides output of the current SMD data. The frequency of output is specified by the SMDOutputFreq parameter in the configuration file. Every SMDOutputFreq timesteps NAMD will print the current timestep, current position of the center of mass of the restrained atoms, and the current force applied to the center of mass (in piconewtons, pN). The output line starts with word SMD

Parameters

The following parameters describe the parameters for the SMD feature of NAMD.

• SMD $<$ Are SMD features active $>$
  Acceptable Values: on or off
  Default Value: off
  Description: Should SMD harmonic constraint be applied to the system. If set to on, then SMDk, SMDFile, SMDVel, and SMDDir must be defined. Specifying SMDOutputFreq is optional.

• SMDFile $<$ SMD constraint reference position $>$
  Acceptable Values: UNIX filename
  Description: File to use for the initial reference position for the SMD harmonic constraints. All atoms in this PDB file with a nonzero value in the occupancy column will be tagged as SMD atoms. The coordinates of the tagged SMD atoms will be used to calculate the initial center of mass. During the simulation, this center of mass will move with velocity SMDVel in the direction SMDDir. The actual atom order in this PDB file must match that in the structure or coordinate file, since the atom number field in this PDB file will be ignored.

• SMDk $<$ force constant to use in SMD simulation $>$
  Acceptable Values: positive real
  Description: SMD harmonic constraint force constant. Must be specified in kcal/mol/Å$^2$ . The conversion factor is 1 kcal/mol = 69.479 pN Å.

• SMDk2 $<$ force constant for transverse direction to use in SMD simulation $>$
  Acceptable Values: positive real
  Default Value: 0
  Description: SMD transverse harmonic constraint force constant. Must be specified in kcal/mol/Å$^2$ . The conversion factor is 1 kcal/mol = 69.479 pN Å.

• SMDVel $<$ Velocity of the SMD reference position movement $>$
  Acceptable Values: nonzero real, Å/timestep
  Description: The velocity of the SMD center of mass movement. Gives the absolute value.

• SMDDir $<$ Direction of the SMD center of mass movement $>$
  Acceptable Values: non-zero vector
  Description: The direction of the SMD reference position movement. The vector does not have to be normalized, it is normalized by NAMD before being used.

• SMDOutputFreq $<$ frequency of SMD output $>$
  Acceptable Values: positive integer
  Default Value: 1
  Description: The frequency in timesteps with which the current SMD data values are printed out.