# -*- Mode: python; tab-width: 4; indent-tabs-mode:nil; coding:utf-8 -*-
# vim: tabstop=4 expandtab shiftwidth=4 softtabstop=4
#
# MDAnalysis --- https://www.mdanalysis.org
# Copyright (c) 2006-2017 The MDAnalysis Development Team and contributors
# (see the file AUTHORS for the full list of names)
#
# Released under the GNU Public Licence, v2 or any higher version
#
# Please cite your use of MDAnalysis in published work:
#
# 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
# simulations. In S. Benthall and S. Rostrup editors, Proceedings of the 15th
# Python in Science Conference, pages 102-109, Austin, TX, 2016. SciPy.
# doi: 10.25080/majora-629e541a-00e
#
# 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
#
"""Coordinate fitting and alignment --- :mod:`MDAnalysis.analysis.align`
=====================================================================
:Author: Oliver Beckstein, Joshua Adelman
:Year: 2010--2013
:Copyright: GNU Public License v3
The module contains functions to fit a target structure to a reference
structure. They use the fast QCP algorithm to calculate the root mean
square distance (RMSD) between two coordinate sets [Theobald2005]_ and
the rotation matrix *R* that minimizes the RMSD [Liu2010]_. (Please
cite these references when using this module.).
Typically, one selects a group of atoms (such as the C-alphas),
calculates the RMSD and transformation matrix, and applys the
transformation to the current frame of a trajectory to obtain the
rotated structure. The :func:`alignto` and :class:`AlignTraj`
functions can be used to do this for individual frames and
trajectories respectively.
The :ref:`RMS-fitting-tutorial` shows how to do the individual steps
manually and explains the intermediate steps.
See Also
--------
:mod:`MDAnalysis.analysis.rms`
contains functions to compute RMSD (when structural alignment is not
required)
:mod:`MDAnalysis.lib.qcprot`
implements the fast RMSD algorithm.
.. _RMS-fitting-tutorial:
RMS-fitting tutorial
--------------------
The example uses files provided as part of the MDAnalysis test suite
(in the variables :data:`~MDAnalysis.tests.datafiles.PSF`,
:data:`~MDAnalysis.tests.datafiles.DCD`, and
:data:`~MDAnalysis.tests.datafiles.PDB_small`). For all further
examples execute first ::
>>> import MDAnalysis as mda
>>> from MDAnalysis.analysis import align
>>> from MDAnalysis.analysis.rms import rmsd
>>> from MDAnalysis.tests.datafiles import PSF, DCD, PDB_small
In the simplest case, we can simply calculate the C-alpha RMSD between
two structures, using :func:`rmsd`::
>>> ref = mda.Universe(PDB_small)
>>> mobile = mda.Universe(PSF,DCD)
>>> rmsd(mobile.select_atoms('name CA').positions, ref.select_atoms('name CA').positions)
28.20178579474479
Note that in this example translations have not been removed. In order
to look at the pure rotation one needs to superimpose the centres of
mass (or geometry) first:
>>> rmsd(mobile.select_atoms('name CA').positions, ref.select_atoms('name CA').positions, center=True)
21.892591663632704
This has only done a translational superposition. If you want to also do a
rotational superposition use the superposition keyword. This will calculate a
minimized RMSD between the reference and mobile structure.
>>> rmsd(mobile.select_atoms('name CA').positions, ref.select_atoms('name CA').positions,
>>> superposition=True)
6.809396586471815
The rotation matrix that superimposes *mobile* on *ref* while
minimizing the CA-RMSD is obtained with the :func:`rotation_matrix`
function ::
>>> mobile0 = mobile.select_atoms('name CA').positions - mobile.select_atoms('name CA').center_of_mass()
>>> ref0 = ref.select_atoms('name CA').positions - ref.select_atoms('name CA').center_of_mass()
>>> R, rmsd = align.rotation_matrix(mobile0, ref0)
>>> print rmsd
6.809396586471805
>>> print R
[[ 0.14514539 -0.27259113 0.95111876]
[ 0.88652593 0.46267112 -0.00268642]
[-0.43932289 0.84358136 0.30881368]]
Putting all this together one can superimpose all of *mobile* onto *ref*::
>>> mobile.atoms.translate(-mobile.select_atoms('name CA').center_of_mass())
>>> mobile.atoms.rotate(R)
>>> mobile.atoms.translate(ref.select_atoms('name CA').center_of_mass())
>>> mobile.atoms.write("mobile_on_ref.pdb")
Common usage
------------
To **fit a single structure** with :func:`alignto`::
>>> ref = mda.Universe(PSF, PDB_small)
>>> mobile = mda.Universe(PSF, DCD) # we use the first frame
>>> align.alignto(mobile, ref, select="protein and name CA", weights="mass")
This will change *all* coordinates in *mobile* so that the protein
C-alpha atoms are optimally superimposed (translation and rotation).
To **fit a whole trajectory** to a reference structure with the
:class:`AlignTraj` class::
>>> ref = mda.Universe(PSF, PDB_small) # reference structure 1AKE
>>> trj = mda.Universe(PSF, DCD) # trajectory of change 1AKE->4AKE
>>> alignment = align.AlignTraj(trj, ref, filename='rmsfit.dcd')
>>> alignment.run()
It is also possible to align two arbitrary structures by providing a
mapping between atoms based on a sequence alignment. This allows
fitting of structural homologs or wild type and mutant.
If a alignment was provided as "sequences.aln" one would first produce
the appropriate MDAnalysis selections with the :func:`fasta2select`
function and then feed the resulting dictionary to :class:`AlignTraj`::
>>> seldict = align.fasta2select('sequences.aln')
>>> alignment = align.AlignTraj(trj, ref, filename='rmsfit.dcd', select=seldict)
>>> alignment.run()
(See the documentation of the functions for this advanced usage.)
Functions and Classes
---------------------
.. versionchanged:: 0.10.0
Function :func:`~MDAnalysis.analysis.rms.rmsd` was removed from
this module and is now exclusively accessible as
:func:`~MDAnalysis.analysis.rms.rmsd`.
.. versionchanged:: 0.16.0
Function :func:`~MDAnalysis.analysis.align.rms_fit_trj` deprecated
in favor of :class:`AlignTraj` class.
.. versionchanged:: 0.17.0
removed deprecated :func:`~MDAnalysis.analysis.align.rms_fit_trj`
.. autofunction:: alignto
.. autoclass:: AlignTraj
.. autoclass:: AverageStructure
.. autofunction:: rotation_matrix
Helper functions
----------------
The following functions are used by the other functions in this
module. They are probably of more interest to developers than to
normal users.
.. autofunction:: _fit_to
.. autofunction:: fasta2select
.. autofunction:: sequence_alignment
.. autofunction:: get_matching_atoms
"""
import os.path
import warnings
import logging
import numpy as np
import Bio.SeqIO
import Bio.AlignIO
import Bio.Align.Applications
import Bio.pairwise2
import MDAnalysis as mda
import MDAnalysis.lib.qcprot as qcp
from MDAnalysis.exceptions import SelectionError, SelectionWarning
import MDAnalysis.analysis.rms as rms
from MDAnalysis.coordinates.memory import MemoryReader
from MDAnalysis.lib.util import get_weights
from .base import AnalysisBase
logger = logging.getLogger('MDAnalysis.analysis.align')
[docs]def rotation_matrix(a, b, weights=None):
r"""Returns the 3x3 rotation matrix `R` for RMSD fitting coordinate
sets `a` and `b`.
The rotation matrix `R` transforms vector `a` to overlap with
vector `b` (i.e., `b` is the reference structure):
.. math::
\mathbf{b} = \mathsf{R} \cdot \mathbf{a}
Parameters
----------
a : array_like
coordinates that are to be rotated ("mobile set"); array of N atoms
of shape N*3 as generated by, e.g.,
:attr:`MDAnalysis.core.groups.AtomGroup.positions`.
b : array_like
reference coordinates; array of N atoms of shape N*3 as generated by,
e.g., :attr:`MDAnalysis.core.groups.AtomGroup.positions`.
weights : array_like (optional)
array of floats of size N for doing weighted RMSD fitting (e.g. the
masses of the atoms)
Returns
-------
R : ndarray
rotation matrix
rmsd : float
RMSD between `a` and `b` before rotation
``(R, rmsd)`` rmsd and rotation matrix *R*
Example
-------
`R` can be used as an argument for
:meth:`MDAnalysis.core.groups.AtomGroup.rotate` to generate a rotated
selection, e.g. ::
>>> R = rotation_matrix(A.select_atoms('backbone').positions,
>>> B.select_atoms('backbone').positions)[0]
>>> A.atoms.rotate(R)
>>> A.atoms.write("rotated.pdb")
Notes
-----
The function does *not* shift the centers of mass or geometry;
this needs to be done by the user.
See Also
--------
MDAnalysis.analysis.rms.rmsd: Calculates the RMSD between *a* and *b*.
alignto: A complete fit of two structures.
AlignTraj: Fit a whole trajectory.
"""
a = np.asarray(a, dtype=np.float64)
b = np.asarray(b, dtype=np.float64)
if a.shape != b.shape:
raise ValueError("'a' and 'b' must have same shape")
if np.allclose(a, b) and weights is None:
return np.eye(3, dtype=np.float64), 0.0
N = b.shape[0]
if weights is not None:
# qcp does NOT divide weights relative to the mean
weights = np.asarray(weights, dtype=np.float64) / np.mean(weights)
rot = np.zeros(9, dtype=np.float64)
# Need to transpose coordinates such that the coordinate array is
# 3xN instead of Nx3. Also qcp requires that the dtype be float64
# (I think we swapped the position of ref and traj in CalcRMSDRotationalMatrix
# so that R acts **to the left** and can be broadcasted; we're saving
# one transpose. [orbeckst])
rmsd = qcp.CalcRMSDRotationalMatrix(a, b, N, rot, weights)
return rot.reshape(3, 3), rmsd
[docs]def _fit_to(mobile_coordinates, ref_coordinates, mobile_atoms,
mobile_com, ref_com, weights=None):
r"""Perform an rmsd-fitting to determine rotation matrix and align atoms
Parameters
----------
mobile_coordinates : ndarray
Coordinates of atoms to be aligned
ref_coordinates : ndarray
Coordinates of atoms to be fit against
mobile_atoms : AtomGroup
Atoms to be translated
mobile_com: ndarray
array of xyz coordinate of mobile center of mass
ref_com : ndarray
array of xyz coordinate of reference center of mass
weights : array_like (optional)
choose weights. With ``None`` weigh each atom equally. If a float array
of the same length as `mobile_coordinates` is provided, use each element
of the `array_like` as a weight for the corresponding atom in
`mobile_coordinates`.
Returns
-------
mobile_atoms : AtomGroup
AtomGroup of translated and rotated atoms
min_rmsd : float
Minimum rmsd of coordinates
Notes
-----
This function assumes that `mobile_coordinates` and `ref_coordinates` have
already been shifted so that their centers of geometry (or centers of mass,
depending on `weights`) coincide at the origin. `mobile_com` and `ref_com`
are the centers *before* this shift.
1. The rotation matrix :math:`\mathsf{R}` is determined with
:func:`rotation_matrix` directly from `mobile_coordinates` and
`ref_coordinates`.
2. `mobile_atoms` :math:`X` is rotated according to the
rotation matrix and the centers according to
.. math::
X' = \mathsf{R}(X - \bar{X}) + \bar{X}_{\text{ref}}
where :math:`\bar{X}` is the center.
"""
R, min_rmsd = rotation_matrix(mobile_coordinates, ref_coordinates,
weights=weights)
mobile_atoms.translate(-mobile_com)
mobile_atoms.rotate(R)
mobile_atoms.translate(ref_com)
return mobile_atoms, min_rmsd
[docs]def alignto(mobile, reference, select=None, weights=None,
subselection=None, tol_mass=0.1, strict=False,
match_atoms=True):
"""Perform a spatial superposition by minimizing the RMSD.
Spatially align the group of atoms `mobile` to `reference` by
doing a RMSD fit on `select` atoms.
The superposition is done in the following way:
1. A rotation matrix is computed that minimizes the RMSD between
the coordinates of `mobile.select_atoms(sel1)` and
`reference.select_atoms(sel2)`; before the rotation, `mobile` is
translated so that its center of geometry (or center of mass)
coincides with the one of `reference`. (See below for explanation of
how *sel1* and *sel2* are derived from `select`.)
2. All atoms in :class:`~MDAnalysis.core.universe.Universe` that
contain `mobile` are shifted and rotated. (See below for how
to change this behavior through the `subselection` keyword.)
The `mobile` and `reference` atom groups can be constructed so that they
already match atom by atom. In this case, `select` should be set to "all"
(or ``None``) so that no further selections are applied to `mobile` and
`reference`, therefore preserving the exact atom ordering (see
:ref:`ordered-selections-label`).
.. Warning:: The atom order for `mobile` and `reference` is *only*
preserved when `select` is either "all" or ``None``. In any other case,
a new selection will be made that will sort the resulting AtomGroup by
index and therefore destroy the correspondence between the two groups.
**It is safest not to mix ordered AtomGroups with selection strings.**
Parameters
----------
mobile : Universe or AtomGroup
structure to be aligned, a
:class:`~MDAnalysis.core.groups.AtomGroup` or a whole
:class:`~MDAnalysis.core.universe.Universe`
reference : Universe or AtomGroup
reference structure, a :class:`~MDAnalysis.core.groups.AtomGroup`
or a whole :class:`~MDAnalysis.core.universe.Universe`
select : str or dict or tuple (optional)
The selection to operate on; can be one of:
1. any valid selection string for
:meth:`~MDAnalysis.core.groups.AtomGroup.select_atoms` that
produces identical selections in `mobile` and `reference`; or
2. a dictionary ``{'mobile': sel1, 'reference': sel2}`` where *sel1*
and *sel2* are valid selection strings that are applied to
`mobile` and `reference` respectively (the
:func:`MDAnalysis.analysis.align.fasta2select` function returns such
a dictionary based on a ClustalW_ or STAMP_ sequence alignment); or
3. a tuple ``(sel1, sel2)``
When using 2. or 3. with *sel1* and *sel2* then these selection strings
are applied to `atomgroup` and `reference` respectively and should
generate *groups of equivalent atoms*. *sel1* and *sel2* can each also
be a *list of selection strings* to generate a
:class:`~MDAnalysis.core.groups.AtomGroup` with defined atom order as
described under :ref:`ordered-selections-label`).
match_atoms : bool (optional)
Whether to match the mobile and reference atom-by-atom. Default ``True``.
weights : {"mass", ``None``} or array_like (optional)
choose weights. With ``"mass"`` uses masses as weights; with ``None``
weigh each atom equally. If a float array of the same length as
`mobile` is provided, use each element of the `array_like` as a
weight for the corresponding atom in `mobile`.
tol_mass: float (optional)
Reject match if the atomic masses for matched atoms differ by more than
`tol_mass`, default [0.1]
strict: bool (optional)
``True``
Will raise :exc:`SelectionError` if a single atom does not
match between the two selections.
``False`` [default]
Will try to prepare a matching selection by dropping
residues with non-matching atoms. See :func:`get_matching_atoms`
for details.
subselection : str or AtomGroup or None (optional)
Apply the transformation only to this selection.
``None`` [default]
Apply to ``mobile.universe.atoms`` (i.e., all atoms in the
context of the selection from `mobile` such as the rest of a
protein, ligands and the surrounding water)
*selection-string*
Apply to ``mobile.select_atoms(selection-string)``
:class:`~MDAnalysis.core.groups.AtomGroup`
Apply to the arbitrary group of atoms
Returns
-------
old_rmsd : float
RMSD before spatial alignment
new_rmsd : float
RMSD after spatial alignment
See Also
--------
AlignTraj: More efficient method for RMSD-fitting trajectories.
.. _ClustalW: http://www.clustal.org/
.. _STAMP: http://www.compbio.dundee.ac.uk/manuals/stamp.4.2/
.. versionchanged:: 1.0.0
Added *match_atoms* keyword to toggle atom matching.
.. versionchanged:: 0.8
Added check that the two groups describe the same atoms including
the new *tol_mass* keyword.
.. versionchanged:: 0.10.0
Uses :func:`get_matching_atoms` to work with incomplete selections
and new `strict` keyword. The new default is to be lenient whereas
the old behavior was the equivalent of ``strict = True``.
.. versionchanged:: 0.16.0
new general 'weights' kwarg replace `mass_weighted`, deprecated `mass_weighted`
.. deprecated:: 0.16.0
Instead of ``mass_weighted=True`` use new ``weights='mass'``
.. versionchanged:: 0.17.0
Deprecated keyword `mass_weighted` was removed.
"""
if select in ('all', None):
# keep the EXACT order in the input AtomGroups; select_atoms('all')
# orders them by index, which can lead to wrong results if the user
# has crafted mobile and reference to match atom by atom
mobile_atoms = mobile.atoms
ref_atoms = reference.atoms
else:
select = rms.process_selection(select)
mobile_atoms = mobile.select_atoms(*select['mobile'])
ref_atoms = reference.select_atoms(*select['reference'])
ref_atoms, mobile_atoms = get_matching_atoms(ref_atoms, mobile_atoms,
tol_mass=tol_mass,
strict=strict,
match_atoms=match_atoms)
weights = get_weights(ref_atoms, weights)
mobile_com = mobile_atoms.center(weights)
ref_com = ref_atoms.center(weights)
ref_coordinates = ref_atoms.positions - ref_com
mobile_coordinates = mobile_atoms.positions - mobile_com
old_rmsd = rms.rmsd(mobile_coordinates, ref_coordinates, weights)
if subselection is None:
# mobile_atoms is Universe
mobile_atoms = mobile.universe.atoms
elif isinstance(subselection, str):
# select mobile_atoms from string
mobile_atoms = mobile.select_atoms(subselection)
else:
try:
# treat subselection as AtomGroup
mobile_atoms = subselection.atoms
except AttributeError:
err = ("subselection must be a selection string, an"
" AtomGroup or Universe or None")
raise TypeError(err) from None
# _fit_to DOES subtract center of mass, will provide proper min_rmsd
mobile_atoms, new_rmsd = _fit_to(mobile_coordinates, ref_coordinates,
mobile_atoms, mobile_com, ref_com,
weights=weights)
return old_rmsd, new_rmsd
[docs]class AlignTraj(AnalysisBase):
"""RMS-align trajectory to a reference structure using a selection.
Both the reference `reference` and the trajectory `mobile` must be
:class:`MDAnalysis.Universe` instances. If they contain a trajectory then
it is used. The output file format is determined by the file extension of
`filename`. One can also use the same universe if one wants to fit to the
current frame.
.. versionchanged:: 1.0.0
``save()`` has now been removed, as an alternative use ``np.savetxt()``
on :attr:`results.rmsd`.
"""
def __init__(self, mobile, reference, select='all', filename=None,
prefix='rmsfit_', weights=None,
tol_mass=0.1, match_atoms=True, strict=False, force=True, in_memory=False,
**kwargs):
"""Parameters
----------
mobile : Universe
Universe containing trajectory to be fitted to reference
reference : Universe
Universe containing trajectory frame to be used as reference
select : str (optional)
Set as default to all, is used for Universe.select_atoms to choose
subdomain to be fitted against
filename : str (optional)
Provide a filename for results to be written to
prefix : str (optional)
Provide a string to prepend to filename for results to be written
to
weights : {"mass", ``None``} or array_like (optional)
choose weights. With ``"mass"`` uses masses of `reference` as
weights; with ``None`` weigh each atom equally. If a float array of
the same length as the selection is provided, use each element of
the `array_like` as a weight for the corresponding atom in the
selection.
tol_mass : float (optional)
Tolerance given to `get_matching_atoms` to find appropriate atoms
match_atoms : bool (optional)
Whether to match the mobile and reference atom-by-atom. Default ``True``.
strict : bool (optional)
Force `get_matching_atoms` to fail if atoms can't be found using
exact methods
force : bool (optional)
Force overwrite of filename for rmsd-fitting
in_memory : bool (optional)
*Permanently* switch `mobile` to an in-memory trajectory
so that alignment can be done in-place, which can improve
performance substantially in some cases. In this case, no file
is written out (`filename` and `prefix` are ignored) and only
the coordinates of `mobile` are *changed in memory*.
verbose : bool (optional)
Set logger to show more information and show detailed progress of
the calculation if set to ``True``; the default is ``False``.
Attributes
----------
reference_atoms : AtomGroup
Atoms of the reference structure to be aligned against
mobile_atoms : AtomGroup
Atoms inside each trajectory frame to be rmsd_aligned
results.rmsd : :class:`numpy.ndarray`
Array of the rmsd values of the least rmsd between the mobile_atoms
and reference_atoms after superposition and minimimization of rmsd
.. versionadded:: 2.0.0
rmsd : :class:`numpy.ndarray`
Alias to the :attr:`results.rmsd` attribute.
.. deprecated:: 2.0.0
Will be removed in MDAnalysis 3.0.0. Please use
:attr:`results.rmsd` instead.
filename : str
String reflecting the filename of the file where the aligned
positions will be written to upon running RMSD alignment
Notes
-----
- If set to ``verbose=False``, it is recommended to wrap the statement
in a ``try ... finally`` to guarantee restoring of the log level in
the case of an exception.
- The ``in_memory`` option changes the `mobile` universe to an
in-memory representation (see :mod:`MDAnalysis.coordinates.memory`)
for the remainder of the Python session. If ``mobile.trajectory`` is
already a :class:`MemoryReader` then it is *always* treated as if
``in_memory`` had been set to ``True``.
.. versionchanged:: 1.0.0
Default ``filename`` has now been changed to the current directory.
.. deprecated:: 0.19.1
Default ``filename`` directory will change in 1.0 to the current directory.
.. versionchanged:: 0.16.0
new general ``weights`` kwarg replace ``mass_weights``
.. deprecated:: 0.16.0
Instead of ``mass_weighted=True`` use new ``weights='mass'``
.. versionchanged:: 0.17.0
removed deprecated `mass_weighted` keyword
.. versionchanged:: 1.0.0
Support for the ``start``, ``stop``, and ``step`` keywords has been
removed. These should instead be passed to :meth:`AlignTraj.run`.
.. versionchanged:: 2.0.0
:attr:`rmsd` results are now stored in a
:class:`MDAnalysis.analysis.base.Results` instance.
"""
select = rms.process_selection(select)
self.ref_atoms = reference.select_atoms(*select['reference'])
self.mobile_atoms = mobile.select_atoms(*select['mobile'])
if in_memory or isinstance(mobile.trajectory, MemoryReader):
mobile.transfer_to_memory()
filename = None
logger.info("Moved mobile trajectory to in-memory representation")
else:
if filename is None:
fn = os.path.split(mobile.trajectory.filename)[1]
filename = prefix + fn
logger.info('filename of rms_align with no filename given'
': {0}'.format(filename))
if os.path.exists(filename) and not force:
raise IOError(
'Filename already exists in path and force is not set'
' to True')
# do this after setting the memory reader to have a reference to the
# right reader.
super(AlignTraj, self).__init__(mobile.trajectory, **kwargs)
if not self._verbose:
logging.disable(logging.WARN)
# store reference to mobile atoms
self.mobile = mobile.atoms
self.filename = filename
natoms = self.mobile.n_atoms
self.ref_atoms, self.mobile_atoms = get_matching_atoms(
self.ref_atoms, self.mobile_atoms, tol_mass=tol_mass,
strict=strict, match_atoms=match_atoms)
# with self.filename == None (in_memory), the NullWriter is chosen
# (which just ignores input) and so only the in_memory trajectory is
# retained
self._writer = mda.Writer(self.filename, natoms)
self._weights = get_weights(self.ref_atoms, weights)
logger.info("RMS-fitting on {0:d} atoms.".format(len(self.ref_atoms)))
def _prepare(self):
# reference centre of mass system
self._ref_com = self.ref_atoms.center(self._weights)
self._ref_coordinates = self.ref_atoms.positions - self._ref_com
# allocate the array for selection atom coords
self.results.rmsd = np.zeros((self.n_frames,))
def _single_frame(self):
index = self._frame_index
mobile_com = self.mobile_atoms.center(self._weights)
mobile_coordinates = self.mobile_atoms.positions - mobile_com
mobile_atoms, self.results.rmsd[index] = _fit_to(
mobile_coordinates,
self._ref_coordinates,
self.mobile,
mobile_com,
self._ref_com, self._weights)
# write whole aligned input trajectory system
self._writer.write(mobile_atoms)
def _conclude(self):
self._writer.close()
if not self._verbose:
logging.disable(logging.NOTSET)
@property
def rmsd(self):
wmsg = ("The `rmsd` attribute was deprecated in MDAnalysis 2.0.0 and "
"will be removed in MDAnalysis 3.0.0. Please use "
"`results.rmsd` instead.")
warnings.warn(wmsg, DeprecationWarning)
return self.results.rmsd
[docs]class AverageStructure(AnalysisBase):
"""RMS-align trajectory to a reference structure using a selection,
and calculate the average coordinates of the trajectory.
Both the reference `reference` and the trajectory `mobile` must be
:class:`MDAnalysis.Universe` instances. If they contain a trajectory, then
it is used. You can also use the same universe if you want to fit to the
current frame.
The output file format is determined by the file extension of
`filename`.
Example
-------
::
import MDAnalysis as mda
from MDAnalysis.tests.datafiles import PSF, DCD
from MDAnalysis.analysis import align
u = mda.Universe(PSF, DCD)
# align to the third frame and average structure
av = align.AverageStructure(u, ref_frame=3).run()
averaged_universe = av.results.universe
"""
def __init__(self, mobile, reference=None, select='all', filename=None,
weights=None,
tol_mass=0.1, match_atoms=True, strict=False, force=True, in_memory=False,
ref_frame=0, **kwargs):
"""Parameters
----------
mobile : Universe
Universe containing trajectory to be fitted to reference
reference : Universe (optional)
Universe containing trajectory frame to be used as reference
select : str (optional)
Set as default to all, is used for Universe.select_atoms to choose
subdomain to be fitted against
filename : str (optional)
Provide a filename for results to be written to
weights : {"mass", ``None``} or array_like (optional)
choose weights. With ``"mass"`` uses masses of `reference` as
weights; with ``None`` weigh each atom equally. If a float array of
the same length as the selection is provided, use each element of
the `array_like` as a weight for the corresponding atom in the
selection.
tol_mass : float (optional)
Tolerance given to `get_matching_atoms` to find appropriate atoms
match_atoms : bool (optional)
Whether to match the mobile and reference atom-by-atom. Default ``True``.
strict : bool (optional)
Force `get_matching_atoms` to fail if atoms can't be found using
exact methods
force : bool (optional)
Force overwrite of filename for rmsd-fitting
in_memory : bool (optional)
*Permanently* switch `mobile` to an in-memory trajectory
so that alignment can be done in-place, which can improve
performance substantially in some cases. In this case, no file
is written out (`filename` and `prefix` are ignored) and only
the coordinates of `mobile` are *changed in memory*.
ref_frame : int (optional)
frame index to select frame from `reference`
verbose : bool (optional)
Set logger to show more information and show detailed progress of
the calculation if set to ``True``; the default is ``False``.
Attributes
----------
reference_atoms : AtomGroup
Atoms of the reference structure to be aligned against
mobile_atoms : AtomGroup
Atoms inside each trajectory frame to be rmsd_aligned
results.universe : :class:`MDAnalysis.Universe`
New Universe with average positions
.. versionadded:: 2.0.0
universe : :class:`MDAnalysis.Universe`
Alias to the :attr:`results.universe` attribute.
.. deprecated:: 2.0.0
Will be removed in MDAnalysis 3.0.0. Please use
:attr:`results.universe` instead.
results.positions : np.ndarray(dtype=float)
Average positions
.. versionadded:: 2.0.0
positions : np.ndarray(dtype=float)
Alias to the :attr:`results.positions` attribute.
.. deprecated:: 2.0.0
Will be removed in MDAnalysis 3.0.0. Please use
:attr:`results.positions` instead.
results.rmsd : float
Average RMSD per frame
.. versionadded:: 2.0.0
rmsd : float
Alias to the :attr:`results.rmsd` attribute.
.. deprecated:: 2.0.0
Will be removed in MDAnalysis 3.0.0. Please use
:attr:`results.rmsd` instead.
filename : str
String reflecting the filename of the file where the average
structure is written
Notes
-----
- If set to ``verbose=False``, it is recommended to wrap the statement
in a ``try ... finally`` to guarantee restoring of the log level in
the case of an exception.
- The ``in_memory`` option changes the `mobile` universe to an
in-memory representation (see :mod:`MDAnalysis.coordinates.memory`)
for the remainder of the Python session. If ``mobile.trajectory`` is
already a :class:`MemoryReader` then it is *always* treated as if
``in_memory`` had been set to ``True``.
.. versionadded:: 1.0.0
.. versionchanged:: 2.0.0
:attr:`universe`, :attr:`positions`, and :attr:`rmsd` are now
stored in a :class:`MDAnalysis.analysis.base.Results` instance.
"""
if in_memory or isinstance(mobile.trajectory, MemoryReader):
mobile.transfer_to_memory()
filename = None
logger.info("Moved mobile trajectory to in-memory representation")
# do this after setting the memory reader to have a reference to the
# right reader.
super(AverageStructure, self).__init__(mobile.trajectory, **kwargs)
if not self._verbose:
logging.disable(logging.WARN)
self.reference = reference if reference is not None else mobile
select = rms.process_selection(select)
self.ref_atoms = self.reference.select_atoms(*select['reference'])
self.mobile_atoms = mobile.select_atoms(*select['mobile'])
if len(self.ref_atoms) != len(self.mobile_atoms):
err = ("Reference and trajectory atom selections do "
"not contain the same number of atoms: "
"N_ref={0:d}, N_traj={1:d}".format(self.ref_atoms.n_atoms,
self.mobile_atoms.n_atoms))
logger.exception(err)
raise SelectionError(err)
logger.info("RMS calculation "
"for {0:d} atoms.".format(len(self.ref_atoms)))
# store reference to mobile atoms
self.mobile = mobile.atoms
self.ref_frame = ref_frame
self.filename = filename
self.results.universe = mda.Merge(self.mobile_atoms)
natoms = len(self.results.universe.atoms)
self.ref_atoms, self.mobile_atoms = get_matching_atoms(
self.ref_atoms, self.mobile_atoms, tol_mass=tol_mass,
strict=strict, match_atoms=match_atoms)
# with self.filename == None (in_memory), the NullWriter is chosen
# (which just ignores input) and so only the in_memory trajectory is
# retained
self._writer = mda.Writer(self.filename, natoms)
self._weights = get_weights(self.ref_atoms, weights)
logger.info("RMS-fitting on {0:d} atoms.".format(len(self.ref_atoms)))
def _prepare(self):
current_frame = self.reference.universe.trajectory.ts.frame
try:
# Move to the ref_frame
# (coordinates MUST be stored in case the ref traj is advanced
# elsewhere or if ref == mobile universe)
self.reference.universe.trajectory[self.ref_frame]
self._ref_com = self.ref_atoms.center(self._weights)
# makes a copy
self._ref_coordinates = self.ref_atoms.positions - self._ref_com
self._ref_positions = self.ref_atoms.positions.copy()
finally:
# Move back to the original frame
self.reference.universe.trajectory[current_frame]
# allocate the array for selection atom coords
self.results.positions = np.zeros((len(self.mobile_atoms), 3))
self.results.rmsd = 0
def _single_frame(self):
mobile_com = self.mobile_atoms.center(self._weights)
mobile_coordinates = self.mobile_atoms.positions - mobile_com
self.results.rmsd += _fit_to(mobile_coordinates,
self._ref_coordinates,
self.mobile,
mobile_com,
self._ref_com, self._weights)[1]
self.results.positions += self.mobile_atoms.positions
def _conclude(self):
self.results.positions /= self.n_frames
self.results.rmsd /= self.n_frames
self.results.universe.load_new(
self.results.positions.reshape((1, -1, 3)))
self._writer.write(self.results.universe.atoms)
self._writer.close()
if not self._verbose:
logging.disable(logging.NOTSET)
@property
def universe(self):
wmsg = ("The `universe` attribute was deprecated in MDAnalysis 2.0.0 "
"and will be removed in MDAnalysis 3.0.0. Please use "
"`results.universe` instead.")
warnings.warn(wmsg, DeprecationWarning)
return self.results.universe
@property
def positions(self):
wmsg = ("The `positions` attribute was deprecated in MDAnalysis 2.0.0 "
"and will be removed in MDAnalyssi 3.0.0. Please use "
"`results.positions` instead.")
warnings.warn(wmsg, DeprecationWarning)
return self.results.positions
@property
def rmsd(self):
wmsg = ("The `rmsd` attribute was deprecated in MDAnalysis 2.0.0 "
"and will be removed in MDAnalysis 3.0.0. Please use "
"`results.rmsd` instead.")
warnings.warn(wmsg, DeprecationWarning)
return self.results.rmsd
[docs]def sequence_alignment(mobile, reference, match_score=2, mismatch_penalty=-1,
gap_penalty=-2, gapextension_penalty=-0.1):
"""Generate a global sequence alignment between two residue groups.
The residues in `reference` and `mobile` will be globally aligned.
The global alignment uses the Needleman-Wunsch algorithm as
implemented in :mod:`Bio.pairwise2`. The parameters of the dynamic
programming algorithm can be tuned with the keywords. The defaults
should be suitable for two similar sequences. For sequences with
low sequence identity, more specialized tools such as clustalw,
muscle, tcoffee, or similar should be used.
Parameters
----------
mobile : AtomGroup
Atom group to be aligned
reference : AtomGroup
Atom group to be aligned against
match_score : float (optional), default 2
score for matching residues, default 2
mismatch_penalty : float (optional), default -1
penalty for residues that do not match , default : -1
gap_penalty : float (optional), default -2
penalty for opening a gap; the high default value creates compact
alignments for highly identical sequences but might not be suitable
for sequences with low identity, default : -2
gapextension_penalty : float (optional), default -0.1
penalty for extending a gap, default: -0.1
Returns
-------
alignment : tuple
Tuple of top sequence matching output `('Sequence A', 'Sequence B', score,
begin, end)`
See Also
--------
BioPython documentation for `pairwise2`_. Alternatively, use
:func:`fasta2select` with :program:`clustalw2` and the option
``is_aligned=False``.
.. _`pairwise2`: http://biopython.org/DIST/docs/api/Bio.pairwise2-module.html
.. versionadded:: 0.10.0
"""
aln = Bio.pairwise2.align.globalms(
reference.residues.sequence(format="string"),
mobile.residues.sequence(format="string"),
match_score, mismatch_penalty, gap_penalty, gapextension_penalty)
# choose top alignment
return aln[0]
[docs]def fasta2select(fastafilename, is_aligned=False,
ref_resids=None, target_resids=None,
ref_offset=0, target_offset=0, verbosity=3,
alnfilename=None, treefilename=None, clustalw="clustalw2"):
"""Return selection strings that will select equivalent residues.
The function aligns two sequences provided in a FASTA file and
constructs MDAnalysis selection strings of the common atoms. When
these two strings are applied to the two different proteins they
will generate AtomGroups of the aligned residues.
`fastafilename` contains the two un-aligned sequences in FASTA
format. The reference is assumed to be the first sequence, the
target the second. ClustalW_ produces a pairwise
alignment (which is written to a file with suffix ``.aln``). The
output contains atom selection strings that select the same atoms
in the two structures.
Unless `ref_offset` and/or `target_offset` are specified, the resids
in the structure are assumed to correspond to the positions in the
un-aligned sequence, namely the first residue has resid == 1.
In more complicated cases (e.g., when the resid numbering in the
input structure has gaps due to missing parts), simply provide the
sequence of resids as they appear in the topology in `ref_resids` or
`target_resids`, e.g. ::
target_resids = [a.resid for a in trj.select_atoms('name CA')]
(This translation table *is* combined with any value for
`ref_offset` or `target_offset`!)
Parameters
----------
fastafilename : str, path to filename
FASTA file with first sequence as reference and
second the one to be aligned (ORDER IS IMPORTANT!)
is_aligned : bool (optional)
``False`` (default)
run clustalw for sequence alignment;
``True``
use the alignment in the file (e.g. from STAMP) [``False``]
ref_offset : int (optional)
add this number to the column number in the FASTA file
to get the original residue number, default: 0
target_offset : int (optional)
add this number to the column number in the FASTA file
to get the original residue number, default: 0
ref_resids : str (optional)
sequence of resids as they appear in the reference structure
target_resids : str (optional)
sequence of resids as they appear in the target
alnfilename : str (optional)
filename of ClustalW alignment (clustal format) that is
produced by *clustalw* when *is_aligned* = ``False``.
default ``None`` uses the name and path of *fastafilename* and
subsititutes the suffix with '.aln'.
treefilename: str (optional)
filename of ClustalW guide tree (Newick format);
if default ``None`` the the filename is generated from *alnfilename*
with the suffix '.dnd' instead of '.aln'
clustalw : str (optional)
path to the ClustalW (or ClustalW2) binary; only
needed for `is_aligned` = ``False``, default: "ClustalW2"
Returns
-------
select_dict : dict
dictionary with 'reference' and 'mobile' selection string
that can be used immediately in :class:`AlignTraj` as
``select=select_dict``.
See Also
--------
:func:`sequence_alignment`, which does not require external
programs.
.. _ClustalW: http://www.clustal.org/
.. _STAMP: http://www.compbio.dundee.ac.uk/manuals/stamp.4.2/
.. versionchanged:: 1.0.0
Passing `alnfilename` or `treefilename` as `None` will create a file in
the current working directory.
"""
if is_aligned:
logger.info("Using provided alignment {}".format(fastafilename))
with open(fastafilename) as fasta:
alignment = Bio.AlignIO.read(
fasta, "fasta")
else:
if alnfilename is None:
filepath, ext = os.path.splitext(fastafilename)
alnfilename = os.path.basename(filepath) + '.aln'
if treefilename is None:
filepath, ext = os.path.splitext(alnfilename)
treefilename = os.path.basename(filepath) + '.dnd'
run_clustalw = Bio.Align.Applications.ClustalwCommandline(
clustalw,
infile=fastafilename,
type="protein",
align=True,
outfile=alnfilename,
newtree=treefilename)
logger.debug(
"Aligning sequences in %(fastafilename)r with %(clustalw)r.",
vars())
logger.debug("ClustalW commandline: %r", str(run_clustalw))
try:
stdout, stderr = run_clustalw()
except:
logger.exception("ClustalW %(clustalw)r failed", vars())
logger.info(
"(You can get clustalw2 from http://www.clustal.org/clustal2/)")
raise
with open(alnfilename) as aln:
alignment = Bio.AlignIO.read(
aln, "clustal")
logger.info(
"Using clustalw sequence alignment {0!r}".format(alnfilename))
logger.info(
"ClustalW Newick guide tree was also produced: {0!r}".format(treefilename))
nseq = len(alignment)
if nseq != 2:
raise ValueError(
"Only two sequences in the alignment can be processed.")
# implict assertion that we only have two sequences in the alignment
orig_resids = [ref_resids, target_resids]
offsets = [ref_offset, target_offset]
GAP = "-"
for iseq, a in enumerate(alignment):
# need iseq index to change orig_resids
if orig_resids[iseq] is None:
# build default: assume consecutive numbering of all
# residues in the alignment
length = len(a.seq) - a.seq.count(GAP)
orig_resids[iseq] = np.arange(1, length + 1)
else:
orig_resids[iseq] = np.asarray(orig_resids[iseq])
# add offsets to the sequence <--> resid translation table
seq2resids = [resids + offset for resids, offset in zip(
orig_resids, offsets)]
del orig_resids
del offsets
def resid_factory(alignment, seq2resids):
"""Return a function that gives the resid for a position ipos in
the nseq'th alignment.
resid = resid_factory(alignment,seq2resids)
r = resid(nseq,ipos)
It is based on a look up table that translates position in the
alignment to the residue number in the original
sequence/structure.
The first index of resid() is the alignmment number, the
second the position in the alignment.
seq2resids translates the residues in the sequence to resid
numbers in the psf. In the simplest case this is a linear map
but if whole parts such as loops are ommitted from the protein
the seq2resids may have big gaps.
Format: a tuple of two numpy arrays; the first array is for
the reference, the second for the target, The index in each
array gives the consecutive number of the amino acid in the
sequence, the value the resid in the structure/psf.
Note: assumes that alignments have same length and are padded if
necessary.
"""
# could maybe use Bio.PDB.StructureAlignment instead?
nseq = len(alignment)
t = np.zeros((nseq, alignment.get_alignment_length()), dtype=int)
for iseq, a in enumerate(alignment):
GAP = "-"
t[iseq, :] = seq2resids[iseq][np.cumsum(np.where(
np.array(list(a.seq)) == GAP, 0, 1)) - 1]
# -1 because seq2resid is index-1 based (resids start at 1)
def resid(nseq, ipos, t=t):
return t[nseq, ipos]
return resid
resid = resid_factory(alignment, seq2resids)
res_list = [] # collect individual selection string
# could collect just resid and type (with/without CB) and
# then post-process and use ranges for continuous stretches, eg
# ( resid 1:35 and ( backbone or name CB ) ) or ( resid 36 and backbone )
for ipos in range(alignment.get_alignment_length()):
aligned = list(alignment[:, ipos])
if GAP in aligned:
continue # skip residue
template = "resid %i"
if 'G' not in aligned:
# can use CB
template += " and ( backbone or name CB )"
else:
template += " and backbone"
template = "( " + template + " )"
res_list.append([template % resid(iseq, ipos) for iseq in range(nseq)])
sel = np.array(res_list).transpose()
ref_selection = " or ".join(sel[0])
target_selection = " or ".join(sel[1])
return {'reference': ref_selection, 'mobile': target_selection}
[docs]def get_matching_atoms(ag1, ag2, tol_mass=0.1, strict=False, match_atoms=True):
"""Return two atom groups with one-to-one matched atoms.
The function takes two :class:`~MDAnalysis.core.groups.AtomGroup`
instances `ag1` and `ag2` and returns two atom groups `g1` and `g2` that
consist of atoms so that the mass of atom ``g1[0]`` is the same as the mass
of atom ``g2[0]``, ``g1[1]`` and ``g2[1]`` etc.
The current implementation is very simplistic and works on a per-residue basis:
1. The two groups must contain the same number of residues.
2. Any residues in each group that have differing number of atoms are discarded.
3. The masses of corresponding atoms are compared. and if any masses differ
by more than `tol_mass` the test is considered failed and a
:exc:`SelectionError` is raised.
The log file (see :func:`MDAnalysis.start_logging`) will contain detailed
information about mismatches.
Parameters
----------
ag1 : AtomGroup
First :class:`~MDAnalysis.core.groups.AtomGroup` instance that is
compared
ag2 : AtomGroup
Second :class:`~MDAnalysis.core.groups.AtomGroup` instance that is
compared
tol_mass : float (optional)
Reject if the atomic masses for matched atoms differ by more than
`tol_mass` [0.1]
strict : bool (optional)
``True``
Will raise :exc:`SelectionError` if a single atom does not
match between the two selections.
``False`` [default]
Will try to prepare a matching selection by dropping
residues with non-matching atoms. See :func:`get_matching_atoms`
for details.
match_atoms : bool (optional)
``True``
Will attempt to match atoms based on mass
``False``
Will not attempt to match atoms based on mass
Returns
-------
(g1, g2) : tuple
Tuple with :class:`~MDAnalysis.core.groups.AtomGroup`
instances that match, atom by atom. The groups are either the
original groups if all matched or slices of the original
groups.
Raises
------
:exc:`SelectionError`
Error raised if the number of residues does not match or if in the final
matching masses differ by more than *tol*.
Notes
-----
The algorithm could be improved by using e.g. the Needleman-Wunsch
algorithm in :mod:`Bio.profile2` to align atoms in each residue (doing a
global alignment is too expensive).
.. versionadded:: 0.8
.. versionchanged:: 0.10.0
Renamed from :func:`check_same_atoms` to
:func:`get_matching_atoms` and now returns matching atomgroups
(possibly with residues removed)
"""
if ag1.n_atoms != ag2.n_atoms:
if not match_atoms:
errmsg = ("Mobile and reference atom selections do not "
"contain the same number of atoms and atom "
"matching is turned off. To match atoms based "
"on residue and mass, try match_atoms=True")
logger.error(errmsg)
raise SelectionError(errmsg)
if ag1.n_residues != ag2.n_residues:
errmsg = ("Reference and trajectory atom selections do not contain "
"the same number of atoms: \n"
"atoms: N_ref={0}, N_traj={1}\n"
"and also not the same number of residues:\n"
"residues: N_ref={2}, N_traj={3}").format(
ag1.n_atoms, ag2.n_atoms,
ag1.n_residues, ag2.n_residues)
logger.error(errmsg)
raise SelectionError(errmsg)
else:
msg = ("Reference and trajectory atom selections do not contain "
"the same number of atoms: \n"
"atoms: N_ref={0}, N_traj={1}").format(
ag1.n_atoms, ag2.n_atoms)
if strict:
logger.error(msg)
raise SelectionError(msg)
# continue with trying to create a valid selection
msg += ("\nbut we attempt to create a valid selection " +
"(use strict=True to disable this heuristic).")
logger.info(msg)
warnings.warn(msg, category=SelectionWarning)
# continue with trying to salvage the selection:
# - number of atoms is different
# - number of residues is the same
# We will remove residues with mismatching number of atoms (e.g. not resolved
# in an X-ray structure)
assert ag1.n_residues == ag2.n_residues
# Alternatively, we could align all atoms but Needleman-Wunsch
# pairwise2 consumes too much memory for thousands of characters in
# each sequence. Perhaps a solution would be pairwise alignment per residue.
#
# aln_elem = Bio.pairwise2.align.globalms("".join([MDAnalysis.topology.
# core.guess_atom_element(n) for n in gref.atoms.names]),
# "".join([MDAnalysis.topology.core.guess_atom_element(n)
# for n in models[0].atoms.names]),
# 2, -1, -1, -0.1,
# one_alignment_only=True)
# For now, just remove the residues that don't have matching numbers
# NOTE: This can create empty selections, e.g., when comparing a structure
# with hydrogens to a PDB structure without hydrogens.
rsize1 = np.array([r.atoms.n_atoms for r in ag1.residues])
rsize2 = np.array([r.atoms.n_atoms for r in ag2.residues])
rsize_mismatches = np.absolute(rsize1 - rsize2)
mismatch_mask = (rsize_mismatches > 0)
if np.any(mismatch_mask):
def get_atoms_byres(g, match_mask=np.logical_not(mismatch_mask)):
# not pretty... but need to do things on a per-atom basis in
# order to preserve original selection
ag = g.atoms
good = ag.residues.resids[match_mask] # resid for each residue
resids = ag.resids # resid for each atom
# boolean array for all matching atoms
ix_good = np.in1d(resids, good)
return ag[ix_good]
_ag1 = get_atoms_byres(ag1)
_ag2 = get_atoms_byres(ag2)
assert _ag1.atoms.n_atoms == _ag2.atoms.n_atoms
# diagnostics
mismatch_resindex = np.arange(ag1.n_residues)[mismatch_mask]
logger.warning("Removed {0} residues with non-matching numbers of atoms"
.format(mismatch_mask.sum()))
logger.debug("Removed residue ids: group 1: {0}"
.format(ag1.residues.resids[mismatch_resindex]))
logger.debug("Removed residue ids: group 2: {0}"
.format(ag2.residues.resids[mismatch_resindex]))
# replace after logging (still need old ag1 and ag2 for
# diagnostics)
ag1 = _ag1
ag2 = _ag2
del _ag1, _ag2
# stop if we created empty selections (by removing ALL residues...)
if ag1.n_atoms == 0 or ag2.n_atoms == 0:
errmsg = ("Failed to automatically find matching atoms: created empty selections. "
"Try to improve your selections for mobile and reference.")
logger.error(errmsg)
raise SelectionError(errmsg)
if match_atoms:
# check again because the residue matching heuristic is not very
# good and can easily be misled (e.g., when one of the selections
# had fewer atoms but the residues in mobile and reference have
# each the same number)
if (not hasattr(ag1, 'masses') or not hasattr(ag2, 'masses')):
msg = "Atoms could not be matched since they don't contain masses."
logger.info(msg)
warnings.warn(msg, category=SelectionWarning)
else:
try:
mass_mismatches = (np.absolute(ag1.masses - ag2.masses) > tol_mass)
except ValueError:
errmsg = ("Failed to find matching atoms: len(reference) = {}, len(mobile) = {} "
"Try to improve your selections for mobile and reference.").format(
ag1.n_atoms, ag2.n_atoms)
logger.error(errmsg)
raise SelectionError(errmsg) from None
if np.any(mass_mismatches):
# Test 2 failed.
# diagnostic output:
logger.error("Atoms: reference | trajectory")
for ar, at in zip(ag1[mass_mismatches], ag2[mass_mismatches]):
logger.error(
"{0!s:>4} {1:3d} {2!s:>3} {3!s:>3} {4:6.3f} | {5!s:>4} {6:3d} {7!s:>3} {8!s:>3} {9:6.3f}".format(
ar.segid,
ar.resid,
ar.resname,
ar.name,
ar.mass,
at.segid,
at.resid,
at.resname,
at.name,
at.mass))
errmsg = ("Inconsistent selections, masses differ by more than {0}; "
"mis-matching atoms are shown above.").format(tol_mass)
logger.error(errmsg)
raise SelectionError(errmsg)
return ag1, ag2