Torsion

class cvpack.Torsion(atom1, atom2, atom3, atom4, pbc=False, name='torsion')

The torsion angle formed by four atoms:

\[\varphi({\bf r}) = {\rm atan2}\left(\frac{ ({\bf r}_{2,1} \times {\bf r}_{3,4}) \cdot {\bf u}_{2,3} }{ {\bf r}_{2,1} \cdot {\bf r}_{3,4} - ({\bf r}_{2,1} \cdot {\bf u}_{2,3}) ({\bf r}_{3,4} \cdot {\bf u}_{2,3}) }\right),\]

where \({\bf r}_{i,j} = {\bf r}_j - {\bf r}_i\), \({\bf u}_{2,3} = {\bf r}_{2,3}/\|{\bf r}_{2,3}\|\), and atan2 is the arctangent function that receives the numerator and denominator above as separate arguments.

Parameters:

• atom1 (int) – The index of the first atom.

• atom2 (int) – The index of the second atom.

• atom3 (int) – The index of the third atom.

• atom4 (int) – The index of the fourth atom.

• pbc (bool) – Whether to use periodic boundary conditions in distance calculations.

• name (str) – The name of the collective variable.

Example

>>> import cvpack
>>> import openmm
>>> system = openmm.System()
>>> [system.addParticle(1) for i in range(4)]
[0, 1, 2, 3]
>>> torsion = cvpack.Torsion(0, 1, 2, 3, pbc=False)
>>> system.addForce(torsion)
0
>>> integrator = openmm.VerletIntegrator(0)
>>> platform = openmm.Platform.getPlatformByName('Reference')
>>> context = openmm.Context(system, integrator, platform)
>>> positions = [[0, 0, 0], [1, 0, 0], [1, 1, 0], [1, 1, 1]]
>>> context.setPositions([openmm.Vec3(*pos) for pos in positions])
>>> torsion.getValue(context)
1.5707... rad

Methods

addToSystem(system, setUnusedForceGroup=True)

Add this collective variable to an openmm.System.

Parameters:

• system (System) – The system to which this collective variable should be added

• setUnusedForceGroup (bool) – If True, the force group of this collective variable will be set to the first available force group in the system

getEffectiveMass(context, allowReinitialization=False)

Compute the effective mass of this collective variable at a given openmm.Context.

The effective mass of a collective variable \(q({\bf r})\) is defined as [1]:

\[m_\mathrm{eff}({\bf r}) = \left( \sum_{i=1}^N \frac{1}{m_i} \left\| \frac{dq}{d{\bf r}_i} \right\|^2 \right)^{-1}\]

If this collective variable share the force group with other forces, then evaluating its effective mass requires reinitializing the openmm.Context twice at each call. This is inefficient and should be avoided. To allow this behavior, the allowReinitialization parameter must be set to True.

Note

By adding this collective variable to the system using the addToSystem() method, the force group of this collective variable is set to an available force group in the system by default.

Parameters:

• context (Context) – The context at which this collective variable’s effective mass should be evaluated.

• allowReinitialization (bool) – If True, the context will be reinitialized if necessary.

Returns:

The effective mass of this collective variable at the given context.

Return type:

Quantity

Example

In this example, we compute the effective masses of the backbone dihedral angles and the radius of gyration of an alanine dipeptide molecule in water:

>>> import cvpack
>>> import openmm
>>> from openmmtools import testsystems
>>> model = testsystems.AlanineDipeptideExplicit()
>>> top = model.mdtraj_topology
>>> backbone_atoms = top.select("name N C CA and resid 1 2")
>>> phi = cvpack.Torsion(*backbone_atoms[0:4])
>>> psi = cvpack.Torsion(*backbone_atoms[1:5])
>>> radius_of_gyration = cvpack.RadiusOfGyration(
...     top.select("not water")
... )
>>> for cv in [phi, psi, radius_of_gyration]:
...     cv.addToSystem(model.system)
>>> context = openmm.Context(
...     model.system, openmm.VerletIntegrator(0)
... )
>>> context.setPositions(model.positions)
>>> phi.getEffectiveMass(context)
0.05119... nm**2 Da/(rad**2)
>>> psi.getEffectiveMass(context)
0.05186... nm**2 Da/(rad**2)
>>> radius_of_gyration.getEffectiveMass(context)
30.946... Da

getMassUnit()

Get the unit of measurement of the effective mass of this collective variable.

Return type:

Unit

getName()

Get the name of this collective variable.

Return type:

str

getPeriodicBounds()

Get the periodic bounds of this collective variable.

Returns:

The periodic bounds of this collective variable or None if it is not periodic

Return type:

Union[Quantity, None]

getUnit()

Get the unit of measurement of this collective variable.

Return type:

Unit

getValue(context, allowReinitialization=False)

Evaluate this collective variable at a given openmm.Context.

If this collective variable share the force group with other forces, then its evaluation requires reinitializing the openmm.Context twice at each call. This is inefficient and should be avoided. To allow this behavior, the allowReinitialization parameter must be set to True.

Note

By adding this collective variable to the system using the addToSystem() method, the force group of this collective variable is set to an available force group in the system by default.

Parameters:

• context (Context) – The context at which this collective variable should be evaluated.

• allowReinitialization (bool) – If True, the context will be reinitialized if necessary.

Returns:

The value of this collective variable at the given context.

Return type:

Quantity

Example

In this example, we compute the values of the backbone dihedral angles and the radius of gyration of an alanine dipeptide molecule in water:

>>> import cvpack
>>> import openmm
>>> from openmmtools import testsystems
>>> model = testsystems.AlanineDipeptideExplicit()
>>> top = model.mdtraj_topology
>>> backbone_atoms = top.select("name N C CA and resid 1 2")
>>> phi = cvpack.Torsion(*backbone_atoms[0:4])
>>> psi = cvpack.Torsion(*backbone_atoms[1:5])
>>> radius_of_gyration = cvpack.RadiusOfGyration(
...     top.select("not water")
... )
>>> for cv in [phi, psi, radius_of_gyration]:
...     cv.addToSystem(model.system)
>>> context = openmm.Context(
...     model.system, openmm.VerletIntegrator(0)
... )
>>> context.setPositions(model.positions)
>>> phi.getValue(context)
3.1415... rad
>>> psi.getValue(context)
3.1415... rad
>>> radius_of_gyration.getValue(context)
0.29514... nm