Source code for MDAnalysis.analysis.gnm
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# R. J. Gowers, M. Linke, J. Barnoud, T. J. E. Reddy, M. N. Melo, S. L. Seyler,
# D. L. Dotson, J. Domanski, S. Buchoux, I. M. Kenney, and O. Beckstein.
# MDAnalysis: A Python package for the rapid analysis of molecular dynamics
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# doi: 10.25080/majora-629e541a-00e
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# N. Michaud-Agrawal, E. J. Denning, T. B. Woolf, and O. Beckstein.
# MDAnalysis: A Toolkit for the Analysis of Molecular Dynamics Simulations.
# J. Comput. Chem. 32 (2011), 2319--2327, doi:10.1002/jcc.21787
#
#Analyse a trajectory using elastic network models, following the approach of Hall et al (JACS 2007)
#Ben Hall ([email protected]) is to blame
#Copyright 2011; Consider under GPL v2 or later
r"""
Elastic network analysis of MD trajectories --- :mod:`MDAnalysis.analysis.gnm`
==============================================================================
:Author: Benjamin Hall <[email protected]>
:Year: 2011
:Copyright: GNU Public License v2 or later
Analyse a trajectory using elastic network models, following the approach of
:footcite:p:`Hall2007`.
An example is provided in the MDAnalysis Cookbook_, listed as GNMExample_.
.. _GNMExample: https://github.com/MDAnalysis/MDAnalysisCookbook/blob/master/examples/GNMExample.py
.. _Cookbook: https://github.com/MDAnalysis/MDAnalysisCookbook
The basic approach is to pass a trajectory to :class:`GNMAnalysis` and then run
the analysis:
.. code-block:: python
u = MDAnalysis.Universe(PSF, DCD)
C = MDAnalysis.analysis.gnm.GNMAnalysis(u, ReportVector="output.txt")
C.run()
output = zip(*C.results)
with open("eigenvalues.dat", "w") as outputfile:
for item in output[1]:
outputfile.write(item + "\n")
The results are found in :attr:`GNMAnalysis.results`, which can be
used for further processing (see :footcite:p:`Hall2007`).
.. rubric:: References
.. footbibliography::
Analysis tasks
--------------
.. autoclass:: GNMAnalysis
:members:
.. autoclass:: closeContactGNMAnalysis
:members:
Utility functions
-----------------
The following functions are used internally and are typically not
directly needed to perform the analysis.
.. autofunction:: generate_grid
.. autofunction:: order_list
.. versionchanged:: 0.16.0
removed unused function :func:`backup_file`
"""
import itertools
import logging
import warnings
import numpy as np
from .base import AnalysisBase
from MDAnalysis.analysis.base import Results
logger = logging.getLogger('MDAnalysis.analysis.GNM')
def _dsq(a, b):
diff = (a - b)
return np.dot(diff, diff)
[docs]
def generate_grid(positions, cutoff):
"""Simple grid search.
An alternative to searching the entire list of each atom; divide the
structure into `cutoff` sized boxes This way, for each particle you only need
to search the neighbouring boxes to find the particles within the `cutoff`.
Observed a 6x speed up for a smallish protein with ~300 residues; this
should get better with bigger systems.
Parameters
----------
positions : array
coordinates of the atoms
cutoff : float
find particles with distance less than `cutoff` from each other; the
grid will consist of boxes with sides of at least length `cutoff`
"""
positions = np.asarray(positions)
x, y, z = positions.T
high_x = x.max()
high_y = y.max()
high_z = z.max()
low_x = x.min()
low_y = y.min()
low_z = z.min()
#Ok now generate a list with 3 dimensions representing boxes in x, y and z
grid = [[[[] for i in range(int((high_z - low_z) / cutoff) + 1)]
for j in range(int((high_y - low_y) / cutoff) + 1)]
for k in range(int((high_x - low_x) / cutoff) + 1)]
for i, pos in enumerate(positions):
x_pos = int((pos[0] - low_x) / cutoff)
y_pos = int((pos[1] - low_y) / cutoff)
z_pos = int((pos[2] - low_z) / cutoff)
grid[x_pos][y_pos][z_pos].append(i)
return grid
def neighbour_generator(positions, cutoff):
"""
return atom pairs that are in neighboring regions of space from a verlet-grid
Parameters
----------
positions : ndarray
atom positions
cutoff : float
size of grid box
Yields
------
i_atom, j_atom
indices of close atom pairs
"""
grid = generate_grid(positions, cutoff)
n_x = len(grid)
n_y = len(grid[0])
n_z = len(grid[0][0])
for cell_x, cell_y, cell_z in itertools.product(
range(n_x), range(n_y), range(n_z)):
atoms = grid[cell_x][cell_y][cell_z]
# collect all atoms in own cell and neighboring cell
all_atoms = []
nei_cells = (-1, 0, 1)
for x, y, z in itertools.product(nei_cells, nei_cells, nei_cells):
gx = cell_x + x
gy = cell_y + y
gz = cell_z + z
if 0 <= gx < n_x and 0 <= gy < n_y and 0 <= gz < n_z:
all_atoms += grid[gx][gy][gz]
# return all possible atom pairs in current cell
for i_atom in atoms:
for j_atom in all_atoms:
yield i_atom, j_atom
[docs]
def order_list(w):
"""Returns a dictionary showing the order of eigenvalues (which are reported scrambled normally)"""
ordered = list(w)
unordered = list(w)
ordered.sort()
list_map = {}
for i in range(len(w)):
list_map[i] = unordered.index(ordered[i])
return list_map
[docs]
class GNMAnalysis(AnalysisBase):
"""Basic tool for GNM analysis.
Each frame is treated as a novel structure and the GNM
calculated. By default, this stores the dominant eigenvector
and its associated eigenvalue; either can be used to monitor
conformational change in a simulation.
Parameters
----------
universe : Universe
Analyze the full trajectory in the universe.
select : str (optional)
MDAnalysis selection string
cutoff : float (optional)
Consider selected atoms within the cutoff as neighbors for the
Gaussian network model.
ReportVector : str (optional)
filename to write eigenvectors to, by default no output is written
Bonus_groups : tuple
This is a tuple of selection strings that identify additional groups
(such as ligands). The center of mass of each group will be added as
a single point in the ENM (it is a popular way of treating small
ligands such as drugs). You need to ensure that none of the atoms in
`Bonus_groups` is contained in `selection` as this could lead to
double counting. No checks are applied.
Attributes
----------
results.times : numpy.ndarray
simulation times used in analysis
results.eigenvalues : numpy.ndarray
calculated eigenvalues
results.eigenvectors : numpy.ndarray
calculated eigenvectors
See Also
--------
:class:`closeContactGNMAnalysis`
.. versionchanged:: 0.16.0
Made :meth:`generate_output` a private method :meth:`_generate_output`.
.. versionchanged:: 1.0.0
Changed `selection` keyword to `select`
.. versionchanged:: 2.0.0
Use :class:`~MDAnalysis.analysis.AnalysisBase` as parent class and
store results as attributes ``times``, ``eigenvalues`` and
``eigenvectors`` of the ``results`` attribute.
"""
def __init__(self,
universe,
select='protein and name CA',
cutoff=7.0,
ReportVector=None,
Bonus_groups=None):
super(GNMAnalysis, self).__init__(universe.trajectory)
self.u = universe
self.select = select
self.cutoff = cutoff
self.results = Results()
self.results.eigenvalues = []
self.results.eigenvectors = []
self._timesteps = None # time for each frame
self.ReportVector = ReportVector
self.Bonus_groups = [self.u.select_atoms(item) for item in Bonus_groups] \
if Bonus_groups else []
self.ca = self.u.select_atoms(self.select)
def _generate_output(self, w, v, outputobject,
ReportVector=None, counter=0):
"""Appends time, eigenvalues and eigenvectors to results.
This generates the output by adding eigenvalue and
eigenvector data to an appendable object and optionally
printing some of the results to file. This is the function
to replace if you want to generate a more complex set of
outputs
"""
list_map = order_list(w)
if ReportVector:
with open(ReportVector, "a") as oup:
for item in enumerate(v[list_map[1]]):
print(
"",
counter,
item[0] + 1,
w[list_map[1]],
item[1],
file=oup)
outputobject.eigenvalues.append(w[list_map[1]])
outputobject.eigenvectors.append(v[list_map[1]])
[docs]
def generate_kirchoff(self):
"""Generate the Kirchhoff matrix of contacts.
This generates the neighbour matrix by generating a grid of
near-neighbours and then calculating which are are within
the cutoff.
Returns
-------
array
the resulting Kirchhoff matrix
"""
positions = self.ca.positions
#add the com from each bonus group to the ca_positions list
for item in self.Bonus_groups:
#bonus = self.u.select_atoms(item)
positions = np.vstack((positions, item.center_of_mass()))
natoms = len(positions)
matrix = np.zeros((natoms, natoms), np.float64)
cutoffsq = self.cutoff**2
for i_atom, j_atom in neighbour_generator(positions, self.cutoff):
if j_atom > i_atom and _dsq(positions[i_atom],
positions[j_atom]) < cutoffsq:
matrix[i_atom][j_atom] = -1.0
matrix[j_atom][i_atom] = -1.0
matrix[i_atom][i_atom] = matrix[i_atom][i_atom] + 1
matrix[j_atom][j_atom] = matrix[j_atom][j_atom] + 1
return matrix
def _single_frame(self):
matrix = self.generate_kirchoff()
try:
_, w, v = np.linalg.svd(matrix)
except np.linalg.LinAlgError:
msg = f"SVD with cutoff {self.cutoff} failed to converge. "
msg += f"Skip frame at {self._ts.time}."
warnings.warn(msg)
logger.warning(msg)
return
# Save the results somewhere useful in some useful format. Usefully.
self._generate_output(
w,
v,
self.results,
ReportVector=self.ReportVector,
counter=self._ts.frame)
def _conclude(self):
self.results.times = self.times
self.results.eigenvalues = np.asarray(self.results.eigenvalues)
self.results.eigenvectors = np.asarray(self.results.eigenvectors)
[docs]
class closeContactGNMAnalysis(GNMAnalysis):
r"""GNMAnalysis only using close contacts.
This is a version of the GNM where the Kirchoff matrix is
constructed from the close contacts between individual atoms
in different residues.
Parameters
----------
universe : Universe
Analyze the full trajectory in the universe.
select : str (optional)
MDAnalysis selection string
cutoff : float (optional)
Consider selected atoms within the cutoff as neighbors for the
Gaussian network model.
ReportVector : str (optional)
filename to write eigenvectors to, by default no output is written
weights : {"size", None} (optional)
If set to "size" (the default) then weight the contact by
:math:`1/\sqrt{N_i N_j}` where :math:`N_i` and :math:`N_j` are the
number of atoms in the residues :math:`i` and :math:`j` that contain
the atoms that form a contact.
Attributes
----------
results.times : numpy.ndarray
simulation times used in analysis
results.eigenvalues : numpy.ndarray
calculated eigenvalues
results.eigenvectors : numpy.ndarray
calculated eigenvectors
Notes
-----
The `MassWeight` option has now been removed.
See Also
--------
:class:`GNMAnalysis`
.. versionchanged:: 0.16.0
Made :meth:`generate_output` a private method :meth:`_generate_output`.
.. deprecated:: 0.16.0
Instead of ``MassWeight=True`` use ``weights="size"``.
.. versionchanged:: 1.0.0
MassWeight option (see above deprecation entry).
Changed `selection` keyword to `select`
.. versionchanged:: 2.0.0
Use :class:`~MDAnalysis.analysis.AnalysisBase` as parent class and
store results as attributes ``times``, ``eigenvalues`` and
``eigenvectors`` of the `results` attribute.
"""
def __init__(self,
universe,
select='protein',
cutoff=4.5,
ReportVector=None,
weights="size"):
super(closeContactGNMAnalysis, self).__init__(universe,
select,
cutoff,
ReportVector)
self.weights = weights
[docs]
def generate_kirchoff(self):
nresidues = self.ca.n_residues
positions = self.ca.positions
residue_index_map = [
resnum
for [resnum, residue] in enumerate(self.ca.residues)
for atom in residue.atoms
]
matrix = np.zeros((nresidues, nresidues), dtype=np.float64)
cutoffsq = self.cutoff**2
# cache sqrt of residue sizes (slow) so that sr[i]*sr[j] == sqrt(r[i]*r[j])
inv_sqrt_res_sizes = np.ones(len(self.ca.residues))
if self.weights == 'size':
inv_sqrt_res_sizes = 1 / np.sqrt(
[r.atoms.n_atoms for r in self.ca.residues])
for i_atom, j_atom in neighbour_generator(positions, self.cutoff):
if j_atom > i_atom and _dsq(positions[i_atom],
positions[j_atom]) < cutoffsq:
iresidue = residue_index_map[i_atom]
jresidue = residue_index_map[j_atom]
contact = (inv_sqrt_res_sizes[iresidue] *
inv_sqrt_res_sizes[jresidue])
matrix[iresidue][jresidue] -= contact
matrix[jresidue][iresidue] -= contact
matrix[iresidue][iresidue] += contact
matrix[jresidue][jresidue] += contact
return matrix