# Module MMTK.Deformation

This module implements deformational energies for use in the analysis of motions and conformational changes in macromolecules. A description of the techniques can be found in [Hinsen1998] and [Hinsen1999].

## Class DeformationFunction: Infinite-displacement deformation function

Constructor: DeformationFunction(universe, range=0.7, cutoff=1.2, factor=46402.)

universe

  the universe for which the deformation function should be defined

range

  the range parameter r_0 in the pair interaction term

cutoff

  the cutoff used in the deformation calculation

factor

  a global scaling factor

The default values are appropriate for a C_alpha model of a protein with the global scaling described in the reference cited above.

A DeformationFunction object must be called with a single parameter, which is a ParticleVector object containing the infinitesimal displacements of the atoms for which the deformation is to be evaluated. The return value is a ParticleScalar object containing the deformation value for each atom.

## Class NormalizedDeformationFunction: Normalized infinite-displacement deformation function

Constructor: NormalizedDeformationFunction(universe, range=0.7, cutoff=1.2, factor=46402.)

universe

  the universe for which the deformation function should be defined

range

  the range parameter r_0 in the pair interaction term

cutoff

  the cutoff used in the deformation calculation

factor

  a global scaling factor

The default values are appropriate for a C_alpha model of a protein with the global scaling described in the reference cited above. The normalization is defined by equation 10 of reference 1.

A NormalizedDeformationFunction object must be called with a single parameter, which is a ParticleVector object containing the infinitesimal displacements of the atoms for which the deformation is to be evaluated. The return value is a ParticleScalar object containing the deformation value for each atom.

## Class FiniteDeformationFunction: Finite-displacement deformation function

Constructor: FiniteDeformationFunction(universe, range=0.7, cutoff=1.2, factor=46402.)

universe

  the universe for which the deformation function should be defined

range

  the range parameter r_0 in the pair interaction term

cutoff

  the cutoff used in the deformation calculation

factor

  a global scaling factor

The default values are appropriate for a C_alpha model of a protein with the global scaling described in the reference cited above.

A FiniteDeformationFunction object must be called with a single parameter, which is a Configuration or a ParticleVector object containing the alternate configuration of the universe for which the deformation is to be evaluated. The return value is a ParticleScalar object containing the deformation value for each atom.

## Class DeformationEnergyFunction: Infinite-displacement deformation energy function

The deformation energy is the sum of the deformation values over all atoms of a system.

Constructor: DeformationEnergyFunction(universe, range=0.7, cutoff=1.2, factor=46402.)

universe

  the universe for which the deformation energy should be defined

range

  the range parameter r_0 in the pair interaction term

cutoff

  the cutoff used in the deformation energy calculation

factor

  a global scaling factor

The default values are appropriate for a C_alpha model of a protein with the global scaling described in the reference cited above.

A DeformationEnergyFunction is called with one or two parameters. The first parameter is a ParticleVector object containing the infinitesimal displacements of the atoms for which the deformation energy is to be evaluated. The optional second argument can be set to a non-zero value to request the gradients of the energy in addition to the energy itself. In that case there are two return values (energy and the gradients in a ParticleVector object), otherwise only the energy is returned.

## Class NormalizedDeformationEnergyFunction: Normalized infinite-displacement deformation energy function

The normalized deformation energy is the sum of the normalized deformation values over all atoms of a system.

Constructor: NormalizedDeformationEnergyFunction(universe, range=0.7, cutoff=1.2, factor=46402.)

universe

  the universe for which the deformation energy should be defined

range

  the range parameter r_0 in the pair interaction term

cutoff

  the cutoff used in the deformation energy calculation

factor

  a global scaling factor

The default values are appropriate for a C_alpha model of a protein with the global scaling described in the reference cited above. The normalization is defined by equation 10 of reference 1.

A NormalizedDeformationEnergyFunction is called with one or two parameters. The first parameter is a ParticleVector object containing the infinitesimal displacements of the atoms for which the deformation energy is to be evaluated. The optional second argument can be set to a non-zero value to request the gradients of the energy in addition to the energy itself. In that case there are two return values (energy and the gradients in a ParticleVector object), otherwise only the energy is returned.

## Class FiniteDeformationEnergyFunction: Finite-displacement deformation energy function

The deformation energy is the sum of the deformation values over all atoms of a system.

Constructor: FiniteDeformationEnergyFunction(universe, range=0.7, cutoff=1.2, factor=46402.)

universe

  the universe for which the deformation energy should be defined

range

  the range parameter r_0 in the pair interaction term

cutoff

  the cutoff used in the deformation energy calculation

factor

  a global scaling factor

The default values are appropriate for a C_alpha model of a protein with the global scaling described in the reference cited above.

A FiniteDeformationEnergyFunction is called with one or two parameters. The first parameter is a ParticleVector object containing the alternate configuration of the universe for which the deformation energy is to be evaluated. The optional second argument can be set to a non-zero value to request the gradients of the energy in addition to the energy itself. In that case there are two return values (energy and the gradients in a ParticleVector object), otherwise only the energy is returned.

## Class DeformationReducer: Iterative reduction of the deformation energy

Constructor: DeformationReducer(universe, range=0.7, cutoff=1.2, factor=46402.)

universe

  the universe for which the deformation function should be defined

range

  the range parameter r_0 in the pair interaction term

cutoff

  the cutoff used in the deformation calculation

factor

  a global scaling factor

The default values are appropriate for a C_alpha model of a protein with the global scaling described in the reference cited above.

A DeformationReducer is called with two arguments. The first is a ParticleVector containing the initial infinitesimal displacements for all atoms. The second is an integer indicating the number of iterations. The result is a modification of the displacements by steepest-descent minimization of the deformation energy.

## Class FiniteDeformationReducer: Iterative reduction of the finite-displacement deformation energy

Constructor: FiniteDeformationReducer(universe, range=0.7, cutoff=1.2, factor=46402.)

universe

  the universe for which the deformation function should be defined

range

  the range parameter r_0 in the pair interaction term

cutoff

  the cutoff used in the deformation calculation

factor

  a global scaling factor

The default values are appropriate for a C_alpha model of a protein with the global scaling described in the reference cited above.

A FiniteDeformationReducer is called with two arguments. The first is a ParticleVector or Configuration containing the alternate configuration for which the deformation energy is evaluated. The second is the RMS distance that defines the termination condition. The return value a configuration that differs from the input configuration by approximately the specified RMS distance, and which is obtained by iterative steepest-descent minimization of the finite-displacement deformation energy.