Analysis Functions

This module defines functions for calculating physical properties from normal modes.

calcCollectivity(mode, masses=None)[source]

Returns collectivity of the mode. This function implements collectivity as defined in equation 5 of [BR95]. If masses are provided, they will be incorporated in the calculation. Otherwise, atoms are assumed to have uniform masses.

[BR95]Bruschweiler R. Collective protein dynamics and nuclear spin relaxation. J Chem Phys 1995 102:3396-3403.

Returns covariance matrix calculated for given modes.

calcCrossCorr(modes, n_cpu=1, norm=True)[source]

Returns cross-correlations matrix. For a 3-d model, cross-correlations matrix is an NxN matrix, where N is the number of atoms. Each element of this matrix is the trace of the submatrix corresponding to a pair of atoms. Covariance matrix may be calculated using all modes or a subset of modes of an NMA instance. For large systems, calculation of cross-correlations matrix may be time consuming. Optionally, multiple processors may be employed to perform calculations by passing n_cpu=2 or more.


Returns fraction of variance explained by the mode. Fraction of variance is the ratio of the variance along a mode to the trace of the covariance matrix of the model.


Returns sum of square-fluctuations for given set of normal modes. Square fluctuations for a single mode is obtained by multiplying the square of the mode array with the variance (Mode.getVariance()) along the mode. For PCA and EDA models built using coordinate data in Å, unit of square-fluctuations is Å2, for ANM and GNM, on the other hand, it is arbitrary or relative units.

calcTempFactors(modes, atoms)[source]

Returns temperature (β) factors calculated using modes from a ANM or GNM instance scaled according to the experimental B-factors from atoms.

calcProjection(ensemble, modes, rmsd=True, norm=True)[source]

Returns projection of conformational deviations onto given modes. ensemble coordinates are used to calculate the deviations that are projected onto modes. For K conformations and M modes, a (K,M) matrix is returned.


By default root-mean-square deviation (RMSD) along the normal mode is calculated. To calculate the projection pass rmsd=True. Vector instances are accepted as ensemble argument to allow for projecting a deformation vector onto normal modes.

calcCrossProjection(ensemble, mode1, mode2, scale=None, **kwargs)[source]

Returns projection of conformational deviations onto modes from different models.

  • ensemble (Ensemble) – ensemble for which deviations will be projected
  • mode1 (Mode, Vector) – normal mode to project conformations onto
  • mode2 (Mode, Vector) – normal mode to project conformations onto
  • scale – scale width of the projection onto mode1 (x) or mode2(y), an optimized scaling factor (scalar) will be calculated by default or a value of scalar can be passed.
Parameters:mode (Mode or Vector) – mode or vector
calcPairDeformationDist(model, coords, ind1, ind2, kbt=1.0)[source]

Returns distribution of the deformations in the distance contributed by each mode for selected pair of residues ind1 ind2 using model from a ANM. Method described in [EB08] equation (10) and figure (2).

[EB08]Eyal E., Bahar I. Toward a Molecular Understanding of the Anisotropic Response of Proteins to External Forces: Insights from Elastic Network Models. Biophys J 2008 94:3424-34355.
  • model (ANM) – this is an 3-dimensional NMA instance from a ANM calculations.
  • coords (ndarray.) – a coordinate set or an object with getCoords() method. Recommended: coords = parsePDB('pdbfile').select('protein and name CA').
  • ind1 (int) – first residue number.
  • ind2 (int) – secound residue number.
calcDistFlucts(modes, n_cpu=1, norm=True)[source]

Returns the matrix of distance fluctuations (i.e. an NxN matrix where N is the number of residues, of MSFs in the inter-residue distances) computed from the cross-correlation matrix (see Eq. 12.E.1 in [IB18]). The arguments are the same as in calcCrossCorr().

[IB18]Dill K, Jernigan RL, Bahar I. Protein Actions: Principles and Modeling. Garland Science 2017.