Solute Scaling and REST2

Solute scaling improves sampling efficiency by scaling the intramolecular potential energy of a protein to lower barriers separating different confirmations [83]. The potential is scaled based on a parameter $\beta$ ,

$$U^{\text{SS}}(\vec{r}) = \beta U_{\text{pp}}(\vec{r}) + \sqrt{\beta} U_{\text{pw}}(\vec{r}) + U_{\text{ww}}(\vec{r}),$$ (49)

with $U_{\text{pp}}$ denoting protein-protein interactions, $U_{\text{pw}}$ denoting protein-water interactions, and $U_{\text{ww}}$ denoting water-water interactions, effectively ``heating'' the protein's interatomic interactions whenever $\beta < 1$ . The NAMD implementation is made efficient by rescaling the force field parameters for the affected atoms [32]. In particular, this parameter scaling approach makes the calculation compatible with existing CUDA force kernels.

The NAMD implementation provides additional flexibility to solute scaling by allowing different scaling factors for electrostatics, van der Waals, and bonded interactions, as described in the following section. Solute scaling can be combined with replica exchange to produce a powerful sampling enhancement method that is highly transferable and provides higher efficiency than traditional temperature exchange methods. In the literature, this replica exchange solute scaling method is known as REST2, due to its improvement of the earlier REST (replica exchange solute tempering) method that directly scaled the temperature of the solute. Sample files are available in directory lib/replica/REST2, with script file lib/replica/REST2/rest2_remd.namd demonstrating use of solute scaling with multiple replicas.

NAMD parameters

The following parameters are used to control solute scaling:

• soluteScaling $<$ Is replica exchange solute tempering enabled? $>$
  Acceptable Values: on or off
  Default Value: off
  Description: Specifies whether or not REST2 is enabled. If set on, then soluteScaling must also be set.

• soluteScalingFactor $<$ Solute scaling factor $>$
  Acceptable Values: non-negative
  Default Value: 1.0
  Description: This option sets the scaling factor $\beta$ , and is typically set lower than 1 to reduce potential energy barriers for the solute. In a replica-exchange run, this option and the related options soluteScalingFactorCharge and soluteScalingFactorVdw serve also as Tcl scripting commands to update the corresponding parameters during a simulation. After using reinitatomsit is highly recommended that these commands are repeated even if the corresponding parameters are not being updated, to preserve their intended value.

• soluteScalingFactorCharge $<$ Solute scaling factor for electrostatics $>$
  Acceptable Values: non-negative
  Default Value: soluteScalingFactor
  Description: Scaling factor applied to just the electrostatics interactions. If not specified, this is set to soluteScalingFactor.

• soluteScalingFactorVdw $<$ Solute scaling factor for van der Waals $>$
  Acceptable Values: non-negative
  Default Value: soluteScalingFactor
  Description: Scaling factor applied to just the van der Waals interactions. If not specified, this is set to soluteScalingFactor.

• soluteScalingFile $<$ PDB file with scaling flags $>$
  Acceptable Values: UNIX filename
  Default Value: coordinates
  Description: PDB file used to flag solute atoms for scaling. If undefined, this defaults to the coordinate PDB file.

• soluteScalingCol $<$ Column of PDB file $>$
  Acceptable Values: X, Y, Z, O, or B
  Default Value: O
  Description: Column of the PDB file used to flag solute atoms for scaling. If undefined, this defaults to the O (occupancy) column. A value of 1.0 marks the atom for scaling.

• soluteScalingAll $<$ Apply scaling also to bond and angle interactions? $>$
  Acceptable Values: on or off
  Default Value: off
  Description: If set on, scalingFactor is applied also to bond and angle interactions. Otherwise, scalingFactor is applied only to dihedral, improper, and crossterm interactions.