Performing a quick distance comparison using PSA

In this example, the trajectories have been pre-aligned using the fitting scheme described in:

S.L. Seyler, A. Kumar, M.F. Thorpe, and O. Beckstein, Path Similarity Analysis: a Method for Quantifying Macromolecular Pathways. arXiv:1505.04807v1_ [q-bio.QM], 2015.

In [1]:
%matplotlib inline
%load_ext autoreload
%autoreload 2

# Suppress FutureWarning about element-wise comparison to None
# Occurs when calling PSA plotting functions
import warnings

1) Set up input data for PSA using MDAnalysis

In [2]:
from MDAnalysis import Universe
from MDAnalysis.analysis.psa import PSAnalysis
from pair_id import PairID

Initialize lists for the methods on which to perform PSA. PSA will be performed for four different simulations methods with three runs for each: DIMS, FRODA, rTMD-F, and rTMD-S. Also initialize a PSAIdentifier object to keep track of the data corresponding to comparisons between pairs of simulations.

In [3]:
method_names = ['DIMS', 'FRODA', 'GOdMD', 'MDdMD', 'rTMD-F', 'rTMD-S',
                'ANMP', 'iENM', 'MAP', 'MENM-SD', 'MENM-SP',
                'Morph', 'LinInt']
labels = [] # Heat map labels
simulations = [] # List of simulation topology/trajectory filename pairs
universes = [] # List of MDAnalysis Universes representing simulations

For each method, get the topology and each of three total trajectories (per method). Each simulation is represented as a (topology, trajectory) pair of file names, which is appended to a master list of simulations.

In [4]:
for method in method_names:
    # Note: DIMS uses the PSF topology format
    topname = 'top.psf' if 'DIMS' in method or 'TMD' in method else 'top.pdb'
    pathname = 'fitted_psa.dcd'
    method_dir = 'methods/{}'.format(method)
    if method is not 'LinInt':
        for run in xrange(1, 4): # 3 runs per method
            run_dir = '{}/{:03n}'.format(method_dir, run)
            topology = '{}/{}'.format(method_dir, topname)
            trajectory = '{}/{}'.format(run_dir, pathname)
            labels.append(method + '(' + str(run) + ')')
            simulations.append((topology, trajectory))
    else: # only one LinInt trajectory
        topology = '{}/{}'.format(method_dir, topname)
        trajectory = '{}/{}'.format(method_dir, pathname)
        simulations.append((topology, trajectory))

Generate a list of universes from the list of simulations.

In [5]:
for sim in simulations:

2) Compute and plot all-pairs distances using PSA

Initialize a PSA comparison from the universe list using a C$_\alpha$ trajectory representation, then generate PSA Paths from the universes.

In [6]:
psa_short = PSAnalysis(universes, path_select='name CA', labels=labels)

Computing mutual distances using Hausdorff and (discrete) Fréchet path metrics

Hausdorff: compute the Hausdorff distances between all unique pairs of Paths and store the distance matrix.

In [7]:'hausdorff')
hausdorff_distances = psa_short.get_pairwise_distances()

Plot clustered heat maps using Ward hierarchical clustering. The first heat map is plotted with the corresponding dendrogram and is fully labeled by the method names; the second heat map is annotated by the Hausdorff distances.

In [8]:
psa_short.plot(filename='dh_ward_psa-short.pdf', linkage='ward');
<matplotlib.figure.Figure at 0x7fa79411e550>
In [9]:
psa_short.plot_annotated_heatmap(filename='dh_ward_psa-short_annot.pdf', linkage='ward');
<matplotlib.figure.Figure at 0x7fa7615212d0>

Fréchet: compute the (discrete) Fréchet distances between all unique pairs of Paths and store the distance matrix.

In [10]:'discrete_frechet')
frechet_distances = psa_short.get_pairwise_distances()

As above, plot heat maps for (discrete) Fréchet distances.

In [11]:
psa_short.plot(filename='df_ward_psa-short.pdf', linkage='ward');
<matplotlib.figure.Figure at 0x7fa765e4bd10>
In [12]:
psa_short.plot_annotated_heatmap(filename='df_ward_psa-short_annot.pdf', linkage='ward');
<matplotlib.figure.Figure at 0x7fa75febc490>

3) Extract specific data from PSA

Get the Simulation IDs and PSA ID for the second DIMS simulation (DIMS 2) and third rTMD-F simulation (rTMD-F 3).

In [13]:
identifier = PairID()
for name in method_names:
    run_ids = [1] if 'LinInt' in name else [1,2,3]
    identifier.add_sim(name, run_ids)
In [14]:
sid1 = identifier.get_sim_id('DIMS 2')
sid2 = identifier.get_sim_id('rTMD-F 3')
pid = identifier.get_pair_id('DIMS 2', 'rTMD-F 3')

Use the Simulation IDs to locate Hausdorff and (discrete) Fréchet distances DIMS 2/rTMD-F 3 comparison:

In [15]:
print hausdorff_distances[sid1,sid2]
print frechet_distances[sid1,sid2]

Use the Pair ID when the distances are in the form of a distance vector (see scipy.spatial.distance.squareform)

In [16]:
from scipy.spatial.distance import squareform
hausdorff_vectorform = squareform(hausdorff_distances)
frechet_vectorform = squareform(frechet_distances)
In [17]:
print hausdorff_vectorform[pid]
print frechet_vectorform[pid]

Check that data obtained from the distance matrix is the same as that accessed from the distance vector

In [18]:
print hausdorff_distances[sid1,sid2] == hausdorff_vectorform[pid]
print frechet_distances[sid1,sid2] == frechet_vectorform[pid]