NMR Models

This example shows how to perform principal component analysis (PCA) of an ensemble of NMR models. The protein of interest is ubiquitin, and for illustration puposes, we will repeat the calculations for the ensemble of ubiquitin models that were analyzed in [AB09].

A PCA object that stores covariance matrix and principal modes that describe the dominant changes in the dataset will be obtained. PCA and principal modes (Mode) can be used as input to functions in dynamics module for further analysis.

Notes

Note that this example is slightly different from that in the ProDy Tutorial. This example uses Ensemble which has a method for performing iterative superposition.

Also, note that this example applies to any PDB file that contains multiple models.

Prepare ensemble

We start by importing everything from the ProDy package:

In [1]: from prody import *

In [2]: from pylab import *

In [3]: ion()

We parse only Cα atoms using parsePDB() (note that it is possible to repeat this calculation for all atoms):

In [4]: ubi = parsePDB('2k39', subset='calpha')

We use residues 1 to 70, as residues 71 to 76 are very mobile and including them skews the results.

In [5]: ubi = ubi.select('resnum < 71').copy()
In [6]: ensemble = Ensemble('Ubiquitin NMR ensemble')

In [7]: ensemble.setCoords( ubi.getCoords() )

Then, we add all of the coordinate sets to the ensemble, and perform an iterative superposition:

In [8]: ensemble.addCoordset( ubi.getCoordsets() )

In [9]: ensemble.iterpose()

PCA calculations

Performing PCA is only three lines of code:

In [10]: pca = PCA('Ubiquitin')

In [11]: pca.buildCovariance(ensemble)

In [12]: pca.calcModes()

In [13]: repr(pca)
Out[13]: '<PCA: Ubiquitin (20 modes; 70 atoms)>'

Faster method

Principal modes can be calculated faster using singular value decomposition:

In [14]: svd = PCA('Ubiquitin')

In [15]: svd.performSVD(ensemble)

For heterogeneous NMR datasets, both methods yields identical results:

In [16]: abs(svd.getEigvals()[:20] - pca.getEigvals()).max()
Out[16]: 1.2434497875801753e-14

In [17]: abs(calcOverlap(pca, svd).diagonal()[:20]).min()
Out[17]: 0.99999999999999956

Write NMD file

Write principal modes into an NMD Format file for NMWiz using writeNMD() function:

In [18]: writeNMD('ubi_pca.nmd', pca[:3], ubi)
Out[18]: 'ubi_pca.nmd'

Compare with ANM results

We set the active coordinate set to 79, which is the one that is closest to the mean structure (note that indices start from 0 in Python). Then, we perform ANM calculations using calcANM() for the active coordset:

In [20]: ubi.setACSIndex(78)

In [21]: anm, temp = calcANM(ubi)

In [22]: anm.setTitle('Ubiquitin')

We calculate overlaps between ANM and PCA modes (presented in Table 1). printOverlapTable() function is handy to print a formatted overlap table:

In [23]: printOverlapTable(pca[:4], anm[:4])
Overlap Table
                         ANM Ubiquitin
                     #1     #2     #3     #4
PCA Ubiquitin #1   -0.19  -0.30  +0.22  -0.62
PCA Ubiquitin #2   +0.09  -0.72  -0.16  +0.16
PCA Ubiquitin #3   +0.31  -0.06  -0.23   0.00
PCA Ubiquitin #4   +0.11  +0.02  +0.16  -0.31