Visualize protein deformability

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.



In [1]:

    
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



In [2]:

    
import pbxplore as pbx

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.



In [3]:

    
# 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)

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 :func:pbxplore.analysis.count_matrix function.



In [4]:

    
count_matrix = pbx.analysis.count_matrix(sequences)

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.



In [5]:

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









    Out[5]:





<matplotlib.text.Text at 0x10c5c8ad0>






    



/Users/jon/Envs/pbxtest/lib/python2.7/site-packages/matplotlib/collections.py:590: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison
  if self._edgecolors == str('face'):






    



---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call last)
/Users/jon/Envs/pbxtest/lib/python2.7/site-packages/IPython/core/formatters.pyc in __call__(self, obj)
    335                 pass
    336             else:
--> 337                 return printer(obj)
    338             # Finally look for special method names
    339             method = _safe_get_formatter_method(obj, self.print_method)

/Users/jon/Envs/pbxtest/lib/python2.7/site-packages/IPython/core/pylabtools.pyc in <lambda>(fig)
    205 
    206     if 'png' in formats:
--> 207         png_formatter.for_type(Figure, lambda fig: print_figure(fig, 'png', **kwargs))
    208     if 'retina' in formats or 'png2x' in formats:
    209         png_formatter.for_type(Figure, lambda fig: retina_figure(fig, **kwargs))

/Users/jon/Envs/pbxtest/lib/python2.7/site-packages/IPython/core/pylabtools.pyc in print_figure(fig, fmt, bbox_inches, **kwargs)
    115 
    116     bytes_io = BytesIO()
--> 117     fig.canvas.print_figure(bytes_io, **kw)
    118     data = bytes_io.getvalue()
    119     if fmt == 'svg':

/Users/jon/Envs/pbxtest/lib/python2.7/site-packages/matplotlib/backend_bases.pyc in print_figure(self, filename, dpi, facecolor, edgecolor, orientation, format, **kwargs)
   2156                     orientation=orientation,
   2157                     dryrun=True,
-> 2158                     **kwargs)
   2159                 renderer = self.figure._cachedRenderer
   2160                 bbox_inches = self.figure.get_tightbbox(renderer)

/Users/jon/Envs/pbxtest/lib/python2.7/site-packages/matplotlib/backends/backend_agg.pyc in print_png(self, filename_or_obj, *args, **kwargs)
    531             _png.write_png(renderer._renderer.buffer_rgba(),
    532                            renderer.width, renderer.height,
--> 533                            filename_or_obj, self.figure.dpi)
    534         finally:
    535             if close:

RuntimeError: Could not create write struct





    





<matplotlib.figure.Figure at 0x10ba96050>

PBxplore provides the :func:pbxplore.analysis.plot_map function to ease the visualization of the occurence matrix.



In [ ]:

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

The :func: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.



In [ ]:

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

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



In [ ]:

    
freq_matrix = pbx.analysis.compute_freq_matrix(count_matrix)



In [ ]:

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

Protein Block entropy

The $N_{eq}$ is a measure of variability based on the count matrix calculated above. It can be computed with the :func:pbxplore.analysis.compute_neq function.



In [ ]:

    
neq_by_position = pbx.analysis.compute_neq(count_matrix)

neq_by_position is a 1D numpy array with the $N_{eq}$ for each residue.



In [ ]:

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

The :func:pbxplore.analysis.plot_neq helper ease the plotting of the $N_{eq}$.



In [ ]:

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

The residue_min and residue_max arguments are available.



In [ ]:

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

Display PB variability as a logo



In [ ]:

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



In [ ]:

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