Accelerated Molecular Dynamics

Accelerated molecular dynamics (aMD) [38] is an enhanced-sampling method that improves the conformational space sampling by reducing energy barriers separating different states of a system. The method modifies the potential energy landscape by raising energy wells that are below a certain threshold level, while leaving those above this level unaffected. As a result, barriers separating adjacent energy basins are reduced, allowing the system to sample conformational space that cannot be easily accessed in a classical MD simulation.

Please include the following two references in your work using the NAMD implementation of aMD:

• Accelerated Molecular Dynamics: A Promising and Efficient Simulation Method for Biomolecules, D.Hamelberg, J.Mongan, and J.A. McCammon. J. Chem. Phys., 120:11919-11929, 2004.
• Implementation of Accelerated Molecular Dynamics in NAMD, Y.Wang, C.Harrison, K.Schulten, and J.A. McCammon, Comp. Sci. Discov., 4:015002, 2011.

Theoretical background

In the original form of aMD [38], when the system's potential energy falls below a threshold energy, $E$ , a boost potential is added, such that the modified potential, $V^*({\bf r})$ , is related to the original potential, $V({\bf r})$ , via

$$V^*({\bf r})= V({\bf r}) + \Delta V({\bf r}),$$ (70)

where $\Delta V({\bf r})$ is the boost potential,

$$\Delta V({\bf r})= \left \{ \begin{array}{l l} 0 & \quad \quad V(... ...r}))^2}{\alpha+E-V({\bf r})} & \quad \quad V({\bf r})<E. \\ \end{array} \right.$$ (71)

As shown in the following figure, the threshold energy $E$ controls the portion of the potential surface affected by the boost, while the acceleration factor $\alpha$ determines the shape of the modified potential. Note that $\alpha$ cannot be set to zero, otherwise the derivative of the modified potential is discontinuous.

Figure: Schematics of the aMD method. When the original potential (thick line) falls below a threshold energy $E$ (dashed line), a boost potential is added. The modified energy profiles (thin lines) have smaller barriers separating adjacent energy basins.

From an aMD simulation, the ensemble average, $\langle A \rangle$ , of an observable, $A({\bf r})$ , can be calculated using the following reweighting procedure:

$$\langle A \rangle =\frac{\langle A({\bf r})\,\text{exp} (\beta \D... ...{\bf r})) \rangle^* } {\langle \text{exp} (\beta \Delta V({\bf r})) \rangle^*},$$ (72)

in which $\beta$ =$1/k_BT$ , and $\langle ... \rangle$ and $\langle...\rangle^*$ represent the ensemble average in the original and the aMD ensembles, respectively.

Currently, aMD can be applied in three modes in NAMD: aMDd, aMDT, and aMDdual [104]. The boost energy is applied to the dihedral potential in the aMDd mode (the default mode), and to the total potential in the aMDT mode. In the dual boost mode (aMDdual) [37], two independent boost energies are applied, one on the dihedral potential and the other on the (Total - Dihedral) potential.

NAMD parameters

The following parameters are used to enable accelerated MD:

• accelMD $<$ Is accelerated molecular dynamics active? $>$
  Acceptable Values: on or off
  Default Value: off
  Description: Specifies if accelerated MD is active.

• accelMDdihe $<$ Apply boost to dihedrals? $>$
  Acceptable Values: on or off
  Default Value: on
  Description: Only applies boost to the dihedral potential. By default, accelMDdihe is turned on and the boost energy is applied to the dihedral potential of the simulated system. When accelMDdihe is turned off, aMD switches to the accelMDT mode, and the boost is applied to the total potential.

• accelMDE $<$ Threshold energy $E$ $>$
  Acceptable Values: Real number
  Description: Specifies the threshold energy $E$ in the aMD equations.

• accelMDalpha $<$ Acceleration factor $\alpha$ $>$
  Acceptable Values: Positive real number
  Description: Specifies the acceleration factor $\alpha$ in the aMD equations.

• accelMDdual $<$ Use dual boost mode? $>$
  Acceptable Values: on or off
  Default Value: off
  Description: When accelMDdual is on, aMD switches to the dual boost mode. Two independent boost potentials will be applied: one to the dihedral potential that is controlled by the parameters accelMDE and accelMDalpha, and a second to the (Total - Dihedral) potential that is controlled by the accelMDTE and accelMDTalpha parameters described below.

• accelMDTE $<$ Threshold energy $E$ in the dual boost mode $>$
  Acceptable Values: Real number
  Description: Specifies the threshold energy $E$ used in the calculation of boost energy for the (Total - Dihedral) potential. This option is only available when accelMDdual is turned on.

• accelMDTalpha $<$ Acceleration factor $\alpha$ in the dual boost mode $>$
  Acceptable Values: Positive real number
  Description: Specifies the acceleration factor $\alpha$ used in the calculation of boost energy for the (Total - Dihedral) potential. This option is only available when accelMDdual is turned on.

• accelMDFirstStep $<$ First accelerated MD step $>$
  Acceptable Values: Zero or positive integer
  Default Value: 0
  Description: Accelerated MD will only be performed when the current step is equal to or higher than accelMDFirstStep, and equal to or lower than accelMDLastStep. Otherwise regular MD will be performed.
• accelMDLastStep $<$ Last accelerated MD step $>$
  Acceptable Values: Zero or positive integer
  Default Value: 0
  Description: Accelerated MD will only be performed when the current step is equal to or higher than accelMDFirstStep, and equal to or lower than accelMDLastStep. Otherwise regular MD will be performed. Note that the accelMDLastStep parameter only has an effect when it is positive. When accelMDLastStep is set to zero (the default), aMD is `open-ended' and will be performed till the end of the simulation.

• accelMDOutFreq $<$ Frequency in steps of aMD output $>$
  Acceptable Values: Positive integer
  Default Value: 1
  Description: An aMD output line will be printed to the log file at the frequency specified by accelMDOutFreq. The aMD output will contain the boost potential ($dV$ ) at the current timestep, the average boost potential ($dVAVG$ ) since the last aMD output, and various potential energy values at the current timestep. The boost potential $dV$ can be used to reconstruct the ensemble average described earlier.