# Visualize protein deformability

Table of Contents

- Block occurences per position
- Protein Block entropy
- Display PB variability as a logo

Note

This page is initialy a jupyter notebook. You can see a notebook HTML render of it or download the notebook itself.

Protein Blocks are great tools to study protein deformability. Indeed, if the block assigned to a residue changes between two frames of a trajectory, it represents a local deformation of the protein rather than the displacement of the residue.

The API allows to visualize Protein Block variability throughout a molecular dynamics simulation trajectory.

    from __future__ import print_function, division
    from pprint import pprint
    from IPython.display import Image, display
    import matplotlib.pyplot as plt
    import os

    # The following line, in a jupyter notebook, allows to display
    # the figure directly in the notebook. See <https://jupyter.org/>
    %matplotlib inline

    import pbxplore as pbx

    ---------------------------------------------------------------------------

    ImportError                               Traceback (most recent call last)

    <ipython-input-2-853cbdb98b68> in <module>()
    ----> 1 import pbxplore as pbx

    ImportError: No module named pbxplore

Here we will look at a molecular dynamics simulation of the barstar. As we will analyse Protein Block sequences, we first need to assign these sequences for each frame of the trajectory.

    # Assign PB sequences for all frames of a trajectory
    trajectory = os.path.join(pbx.DEMO_DATA_PATH, 'barstar_md_traj.xtc')
    topology = os.path.join(pbx.DEMO_DATA_PATH, 'barstar_md_traj.gro')
    sequences = []
    for chain_name, chain in pbx.chains_from_trajectory(trajectory, topology):
        dihedrals = chain.get_phi_psi_angles()
        pb_seq = pbx.assign(dihedrals)
        sequences.append(pb_seq)

    ---------------------------------------------------------------------------

    NameError                                 Traceback (most recent call last)

    <ipython-input-3-495e579af03b> in <module>()
          1 # Assign PB sequences for all frames of a trajectory
    ----> 2 trajectory = os.path.join(pbx.DEMO_DATA_PATH, 'barstar_md_traj.xtc')
          3 topology = os.path.join(pbx.DEMO_DATA_PATH, 'barstar_md_traj.gro')
          4 sequences = []
          5 for chain_name, chain in pbx.chains_from_trajectory(trajectory, topology):

    NameError: name 'pbx' is not defined

## Block occurences per position

The basic information we need to analyse protein deformability is the count of occurences of each PB for each position throughout the trajectory. This occurence matrix can be calculated with the `pbxplore.analysis.count_matrix()` function.

    count_matrix = pbx.analysis.count_matrix(sequences)

    ---------------------------------------------------------------------------

    NameError                                 Traceback (most recent call last)

    <ipython-input-4-25d9f2aed9b5> in <module>()
    ----> 1 count_matrix = pbx.analysis.count_matrix(sequences)

    NameError: name 'pbx' is not defined

`count_matrix` is a numpy array with one row per PB and one column per position. In each cell is the number of time a position was assigned to a PB.

We can visualize `count_matrix` using Matplotlib as any 2D numpy array.

    im = plt.imshow(count_matrix, interpolation='none', aspect='auto')
    plt.colorbar(im)
    plt.xlabel('Position')
    plt.ylabel('Block')

    ---------------------------------------------------------------------------

    NameError                                 Traceback (most recent call last)

    <ipython-input-5-2544c1e550cd> in <module>()
    ----> 1 im = plt.imshow(count_matrix, interpolation='none', aspect='auto')
          2 plt.colorbar(im)
          3 plt.xlabel('Position')
          4 plt.ylabel('Block')

    NameError: name 'count_matrix' is not defined

PBxplore provides the `pbxplore.analysis.plot_map()` function to ease the visualization of the occurence matrix.

    pbx.analysis.plot_map('map.png', count_matrix)
    !rm map.png

    ---------------------------------------------------------------------------

    NameError                                 Traceback (most recent call last)

    <ipython-input-6-89cb23d2983b> in <module>()
    ----> 1 pbx.analysis.plot_map('map.png', count_matrix)
          2 get_ipython().system(u'rm map.png')

    NameError: name 'pbx' is not defined

The `pbxplore.analysis.plot_map()` helper has a `residue_min` and a `residue_max` optional arguments to display only part of the matrix. These two arguments can be pass to all PBxplore functions that produce a figure.

    pbx.analysis.plot_map('map.png', count_matrix,
                          residue_min=60, residue_max=70)
    !rm map.png

    ---------------------------------------------------------------------------

    NameError                                 Traceback (most recent call last)

    <ipython-input-7-d2cdc6435a50> in <module>()
    ----> 1 pbx.analysis.plot_map('map.png', count_matrix,
          2                       residue_min=60, residue_max=70)
          3 get_ipython().system(u'rm map.png')

    NameError: name 'pbx' is not defined

Note that matrix in the the figure produced by `pbxplore.analysis.plot_map()` is normalized so as the sum of each column is 1. The matrix can be normalized with the `pbxplore.analysis.compute_freq_matrix()`.

    freq_matrix = pbx.analysis.compute_freq_matrix(count_matrix)

    ---------------------------------------------------------------------------

    NameError                                 Traceback (most recent call last)

    <ipython-input-8-65ead41a37b6> in <module>()
    ----> 1 freq_matrix = pbx.analysis.compute_freq_matrix(count_matrix)

    NameError: name 'pbx' is not defined

    im = plt.imshow(freq_matrix, interpolation='none', aspect='auto')
    plt.colorbar(im)
    plt.xlabel('Position')
    plt.ylabel('Block')

    ---------------------------------------------------------------------------

    NameError                                 Traceback (most recent call last)

    <ipython-input-9-81cb853faf4a> in <module>()
    ----> 1 im = plt.imshow(freq_matrix, interpolation='none', aspect='auto')
          2 plt.colorbar(im)
          3 plt.xlabel('Position')
          4 plt.ylabel('Block')

    NameError: name 'freq_matrix' is not defined

## Protein Block entropy

The \(N_{eq}\) is a measure of variability based on the count matrix calculated above. It can be computed with the `pbxplore.analysis.compute_neq()` function.

    neq_by_position = pbx.analysis.compute_neq(count_matrix)

    ---------------------------------------------------------------------------

    NameError                                 Traceback (most recent call last)

    <ipython-input-10-7eeb19d961f7> in <module>()
    ----> 1 neq_by_position = pbx.analysis.compute_neq(count_matrix)

    NameError: name 'pbx' is not defined

`neq_by_position` is a 1D numpy array with the \(N_{eq}\) for each residue.

    plt.plot(neq_by_position)
    plt.xlabel('Position')
    plt.ylabel('$N_{eq}$')

    ---------------------------------------------------------------------------

    NameError                                 Traceback (most recent call last)

    <ipython-input-11-b3b064739482> in <module>()
    ----> 1 plt.plot(neq_by_position)
          2 plt.xlabel('Position')
          3 plt.ylabel('$N_{eq}$')

    NameError: name 'neq_by_position' is not defined

The `pbxplore.analysis.plot_neq()` helper ease the plotting of the \(N_{eq}\).

    pbx.analysis.plot_neq('neq.png', neq_by_position)
    !rm neq.png

    ---------------------------------------------------------------------------

    NameError                                 Traceback (most recent call last)

    <ipython-input-12-f4134ffa3fff> in <module>()
    ----> 1 pbx.analysis.plot_neq('neq.png', neq_by_position)
          2 get_ipython().system(u'rm neq.png')

    NameError: name 'pbx' is not defined

The `residue_min` and `residue_max` arguments are available.

    pbx.analysis.plot_neq('neq.png', neq_by_position,
                          residue_min=60, residue_max=70)
    !rm neq.png

    ---------------------------------------------------------------------------

    NameError                                 Traceback (most recent call last)

    <ipython-input-13-d9fd90e1d17b> in <module>()
    ----> 1 pbx.analysis.plot_neq('neq.png', neq_by_position,
          2                       residue_min=60, residue_max=70)
          3 get_ipython().system(u'rm neq.png')

    NameError: name 'pbx' is not defined

## Display PB variability as a logo

    pbx.analysis.generate_weblogo('logo.png', count_matrix)
    display(Image('logo.png'))
    !rm logo.png

    ---------------------------------------------------------------------------

    NameError                                 Traceback (most recent call last)

    <ipython-input-14-a4d44c0d9f48> in <module>()
    ----> 1 pbx.analysis.generate_weblogo('logo.png', count_matrix)
          2 display(Image('logo.png'))
          3 get_ipython().system(u'rm logo.png')

    NameError: name 'pbx' is not defined

    pbx.analysis.generate_weblogo('logo.png', count_matrix,
                                  residue_min=60, residue_max=70)
    display(Image('logo.png'))
    !rm logo.png

    ---------------------------------------------------------------------------

    NameError                                 Traceback (most recent call last)

    <ipython-input-15-ae0b8a456c34> in <module>()
    ----> 1 pbx.analysis.generate_weblogo('logo.png', count_matrix,
          2                               residue_min=60, residue_max=70)
          3 display(Image('logo.png'))
          4 get_ipython().system(u'rm logo.png')

    NameError: name 'pbx' is not defined