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# MDAnalysis --- http://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.
#
# 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
#
"""
Calculating root mean square quantities --- :mod:`MDAnalysis.analysis.rms`
==========================================================================
:Author: Oliver Beckstein, David L. Dotson, John Detlefs
:Year: 2016
:Copyright: GNU Public License v2
.. versionadded:: 0.7.7
.. versionchanged:: 0.11.0
Added :class:`RMSF` analysis.
.. versionchanged:: 0.16.0
Refactored RMSD to fit AnalysisBase API
The module contains code to analyze root mean square quantities such
as the coordinat root mean square distance (:class:`RMSD`) or the
per-residue root mean square fluctuations (:class:`RMSF`).
This module uses the fast QCP algorithm [Theobald2005]_ to calculate
the root mean square distance (RMSD) between two coordinate sets (as
implemented in
:func:`MDAnalysis.lib.qcprot.CalcRMSDRotationalMatrix`).
When using this module in published work please cite [Theobald2005]_.
See Also
--------
:mod:`MDAnalysis.analysis.align`
aligning structures based on RMSD
:mod:`MDAnalysis.lib.qcprot`
implements the fast RMSD algorithm.
Example applications
--------------------
Calculating RMSD for multiple domains
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
In this example we will globally fit a protein to a reference
structure and investigate the relative movements of domains by
computing the RMSD of the domains to the reference. The example is a
DIMS trajectory of adenylate kinase, which samples a large
closed-to-open transition. The protein consists of the CORE, LID, and
NMP domain.
* superimpose on the closed structure (frame 0 of the trajectory),
using backbone atoms
* calculate the backbone RMSD and RMSD for CORE, LID, NMP (backbone atoms)
The trajectory is included with the test data files. The data in
:attr:`RMSD.rmsd` is plotted with :func:`matplotlib.pyplot.plot`::
import MDAnalysis
from MDAnalysis.tests.datafiles import PSF,DCD,CRD
u = MDAnalysis.Universe(PSF,DCD)
ref = MDAnalysis.Universe(PSF,DCD) # reference closed AdK (1AKE) (with the default ref_frame=0)
#ref = MDAnalysis.Universe(PSF,CRD) # reference open AdK (4AKE)
import MDAnalysis.analysis.rms
R = MDAnalysis.analysis.rms.RMSD(u, ref,
select="backbone", # superimpose on whole backbone of the whole protein
groupselections=["backbone and (resid 1-29 or resid 60-121 or resid 160-214)", # CORE
"backbone and resid 122-159", # LID
"backbone and resid 30-59"], # NMP
filename="rmsd_all_CORE_LID_NMP.dat")
R.run()
R.save()
import matplotlib.pyplot as plt
rmsd = R.rmsd.T # transpose makes it easier for plotting
time = rmsd[1]
fig = plt.figure(figsize=(4,4))
ax = fig.add_subplot(111)
ax.plot(time, rmsd[2], 'k-', label="all")
ax.plot(time, rmsd[3], 'k--', label="CORE")
ax.plot(time, rmsd[4], 'r--', label="LID")
ax.plot(time, rmsd[5], 'b--', label="NMP")
ax.legend(loc="best")
ax.set_xlabel("time (ps)")
ax.set_ylabel(r"RMSD ($\AA$)")
fig.savefig("rmsd_all_CORE_LID_NMP_ref1AKE.pdf")
Functions
---------
.. autofunction:: rmsd
Analysis classes
----------------
.. autoclass:: RMSD
:members:
:inherited-members:
.. attribute:: rmsd
Contains the time series of the RMSD as an N×3 :class:`numpy.ndarray`
array with content ``[[frame, time (ps), RMSD (A)], [...], ...]``.
.. autoclass:: RMSF
:members:
:inherited-members:
.. attribute:: rmsf
Results are stored in this N-length :class:`numpy.ndarray` array,
giving RMSFs for each of the given atoms.
"""
from __future__ import division, absolute_import
from six.moves import zip
import numpy as np
import logging
import warnings
import MDAnalysis.lib.qcprot as qcp
from MDAnalysis.analysis.base import AnalysisBase
from MDAnalysis.exceptions import SelectionError, NoDataError
from MDAnalysis.lib.log import ProgressMeter, _set_verbose
from MDAnalysis.lib.util import asiterable
logger = logging.getLogger('MDAnalysis.analysis.rmsd')
[docs]def rmsd(a, b, weights=None, center=False, superposition=False):
"""Returns RMSD between two coordinate sets `a` and `b`.
`a` and `b` are arrays of the coordinates of N atoms of shape N*3
as generated by, e.g.,
:meth:`MDAnalysis.core.groups.AtomGroup.coordinates`.
.. note::
If you use trajectory data from simulations performed under **periodic
boundary conditions** then you *must make your molecules whole* before
performing RMSD calculations so that the centers of mass of the mobile
and reference structure are properly superimposed.
Parameters
----------
a, b : array_like
coordinates to align
weights : array_like (optional)
1D array with weights, use to compute weighted average
center : bool (optional)
subtract center of geometry before calculation. With weights given
compute weighted average as center.
superposition : bool (optional)
perform a rotational and translational superposition with the fast QCP
algorithm [Theobald2005]_ before calculating the RMSD
Returns
-------
rmsd : float
RMSD between a and b
Example
-------
>>> u = Universe(PSF,DCD)
>>> bb = u.select_atoms('backbone')
>>> A = bb.positions.copy() # coordinates of first frame
>>> u.trajectory[-1] # forward to last frame
>>> B = bb.positions.copy() # coordinates of last frame
>>> rmsd(A, B, center=True)
3.9482355416565049
.. versionchanged: 0.8.1
*center* keyword added
.. versionchanged: 0.14.0
*superposition* keyword added
"""
a = np.asarray(a, dtype=np.float64)
b = np.asarray(b, dtype=np.float64)
N = b.shape[0]
if a.shape != b.shape:
raise ValueError('a and b must have same shape')
# superposition only works if structures are centered
if center or superposition:
# make copies (do not change the user data!)
# weights=None is equivalent to all weights 1
a = a - np.average(a, axis=0, weights=weights)
b = b - np.average(b, axis=0, weights=weights)
if weights is not None:
if len(weights) != len(a):
raise ValueError('weights must have same length as a/b')
# weights are constructed as relative to the mean
weights = np.asarray(weights, dtype=np.float64) / np.mean(weights)
if superposition:
return qcp.CalcRMSDRotationalMatrix(a, b, N, None, weights)
else:
if weights is not None:
return np.sqrt(np.sum(weights[:, np.newaxis]
* ((a - b) ** 2)) / N)
else:
return np.sqrt(np.sum((a - b) ** 2) / N)
def process_selection(select):
"""Return a canonical selection dictionary.
Parameters
----------
select : str / tuple / dict
- `str` -> Any valid string selection
- `dict` -> ``{'mobile':sel1, 'reference':sel2}``
- `tuple` -> ``(sel1, sel2)``
Returns
-------
dict
selections for 'reference' and 'mobile'. Values are guarenteed to be
iterable (so that one can provide selections to retain order)
Notes
-----
The dictionary input for `select` can be generated by
:func:`fasta2select` based on a ClustalW_ or STAMP_ sequence alignment.
"""
if type(select) is str:
select = {'reference': select, 'mobile': select}
elif type(select) is tuple:
try:
select = {'mobile': select[0], 'reference': select[1]}
except IndexError:
raise IndexError("select must contain two selection strings "
"(reference, mobile)")
elif type(select) is dict:
# compatability hack to use new nomenclature
try:
select['mobile'] = select['target']
warnings.warn("use key 'mobile' instead of deprecated 'target'; "
"'target' will be removed in 0.8",
DeprecationWarning)
except KeyError:
pass
try:
select['mobile']
select['reference']
except KeyError:
raise KeyError("select dictionary must contain entries for keys "
"'mobile' and 'reference'.")
else:
raise TypeError("'select' must be either a string, 2-tuple, or dict")
select['mobile'] = asiterable(select['mobile'])
select['reference'] = asiterable(select['reference'])
return select
[docs]class RMSD(AnalysisBase):
r"""Class to perform RMSD analysis on a trajectory.
The RMSD will be computed between `select` and `reference` for
all frames in the trajectory belonging to `atomgroup`.
.. Note::
If you use trajectory data from simulations performed under **periodic
boundary conditions** then you *must make your molecules whole* before
performing RMSD calculations so that the centers of mass of the mobile
and reference structure are properly superimposed.
Run the analysis with :meth:`RMSD.run`, which stores the results
in the array :attr:`RMSD.rmsd`.
Parameters
----------
atomgroup : :class:`~MDAnalysis.core.groups.AtomGroup` or
:class:`~MDAnalysis.core.universe.Universe`
MDAnalysis `AtomGroup` or `Universe` with an associated trajectory
to be RMSD fit.
reference : :class:`~MDAnalysis.core.groups.AtomGroup` or
:class:`~MDAnalysis.core.universe.Universe`, optional
Reference coordinates, if ``None`` current frame of `atomgroup` is
used
select : str / dict / 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}`` (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 selections
can also each be a list of selection strings (to generate a
AtomGroup with defined atom order as described under
:ref:`ordered-selections-label`).
groupselections : list (optional)
A list of selections as described for `select` Each selection
describes additional RMSDs to be computed *after the structures
have be superpositioned* according to `select`. The output contains
one additional column for each selection. [``None``]
.. Note:: Experimental feature. Only limited error checking
implemented.
filename : str, optional
write RSMD into file file :meth:`RMSD.save`
mass_weighted : bool (deprecated)
do a mass-weighted RMSD fit
weights : str/array_like (optional)
choose weights. If 'str' uses masses as weights
tol_mass : float (optional)
Reject match if the atomic masses for matched atoms differ by more
than `tol_mass`
ref_frame : int (optional)
frame index to select frame from `reference`
Notes
-----
The root mean square deviation of a group of :math:`N` atoms relative to a
reference structure as a function of time is calculated as
.. math::
\rho(t) = \sqrt{\frac{1}{N} \sum_{i=1}^N \left(\mathbf{x}_i(t)
- \mathbf{x}_i^{\text{ref}}\right)^2}
This class uses Douglas Theobald's fast QCP algorithm [Theobald2005]_ to
calculate the RMSD (see :mod:`MDAnalysis.lib.qcprot` for implementation
details).
The class runs various checks on the input to ensure that the two atom
groups can be compared. This includes a comparison of atom masses (i.e.,
only the positions of atoms of the same mass will be considered to be
correct for comparison). If masses should not be checked, just set
`tol_mass` to a large value such as 1000.
.. _ClustalW: http://www.clustal.org/
.. _STAMP: http://www.compbio.dundee.ac.uk/manuals/stamp.4.2/
.. versionadded:: 0.7.7
.. versionchanged:: 0.8
`groupselections` added
.. versionchanged:: 0.16.0
Flexible weighting scheme with new `weights` keyword.
.. deprecated:: 0.16.0
Instead of ``mass_weighted=True`` use new ``weights='mass'``;
refactored to fit with AnalysisBase API
"""
def __init__(self, atomgroup, reference=None, select='all',
groupselections=None, filename="rmsd.dat",
mass_weighted=None,
weights=None, tol_mass=0.1, ref_frame=0, **kwargs):
super(RMSD, self).__init__(atomgroup.universe.trajectory,
**kwargs)
self.universe = atomgroup.universe
self.reference = reference if reference is not None else self.universe
select = process_selection(select)
self.groupselections = ([process_selection(s) for s in groupselections]
if groupselections is not None else [])
if mass_weighted is not None:
warnings.warn("mass weighted is deprecated argument. Please use "
" 'weights=\"mass\" instead. Will be removed in 0.17.0",
category=DeprecationWarning)
if mass_weighted:
weights = 'mass'
self.weights = weights
self.tol_mass = tol_mass
self.ref_frame = ref_frame
self.filename = filename
self.ref_atoms = self.reference.select_atoms(*select['reference'])
self.mobile_atoms = self.universe.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)))
mass_mismatches = (np.absolute((self.ref_atoms.masses -
self.mobile_atoms.masses)) >
self.tol_mass)
if np.any(mass_mismatches):
# diagnostic output:
logger.error("Atoms: reference | mobile")
for ar, at in zip(self.ref_atoms, self.mobile_atoms):
if ar.name != at.name:
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:f}; mis-matching atoms"
"are shown above.".format(self.tol_mass))
logger.error(errmsg)
raise SelectionError(errmsg)
del mass_mismatches
# TODO:
# - make a group comparison a class that contains the checks above
# - use this class for the *select* group and the additional
# *groupselections* groups each a dict with reference/mobile
self._groupselections_atoms = [
{
'reference': self.reference.select_atoms(*s['reference']),
'mobile': self.universe.select_atoms(*s['mobile']),
}
for s in self.groupselections]
# sanity check
for igroup, (sel, atoms) in enumerate(zip(self.groupselections,
self._groupselections_atoms)):
if len(atoms['mobile']) != len(atoms['reference']):
logger.exception('SelectionError: Group Selection')
raise SelectionError(
"Group selection {0}: {1} | {2}: Reference and trajectory "
"atom selections do not contain the same number of atoms: "
"N_ref={3}, N_traj={4}".format(
igroup, sel['reference'], sel['mobile'],
len(atoms['reference']), len(atoms['mobile'])))
# initialized to note for testing the save function
self.rmsd = None
def _prepare(self):
self._n_atoms = self.mobile_atoms.n_atoms
if not isinstance(self.weights, (list, tuple, np.ndarray)) and self.weights == 'mass':
self.weights = self.ref_atoms.masses
if self.weights is not None:
self.weights = (self.weights / self.weights.mean()).astype(np.float64)
current_frame = self.reference.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.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
if self._groupselections_atoms:
self._groupselections_ref_coords_64 = [(self.reference.
select_atoms(*s['reference']).
positions.astype(np.float64)) for s in
self.groupselections]
finally:
# Move back to the original frame
self.reference.trajectory[current_frame]
self._ref_coordinates_64 = self._ref_coordinates.astype(np.float64)
if self._groupselections_atoms:
# Only carry out a rotation if we want to calculate secondary
# RMSDs.
# R: rotation matrix that aligns r-r_com, x~-x~com
# (x~: selected coordinates, x: all coordinates)
# Final transformed traj coordinates: x' = (x-x~_com)*R + ref_com
self._rot = np.zeros(9, dtype=np.float64) # allocate space
self._R = np.matrix(self._rot.reshape(3, 3))
else:
self._rot = None
self.rmsd = np.zeros((self.n_frames,
3 + len(self._groupselections_atoms)))
self._pm.format = ("RMSD {rmsd:5.2f} A at frame "
"{step:5d}/{numsteps} [{percentage:5.1f}%]\r")
self._mobile_coordinates64 = self.mobile_atoms.positions.copy().astype(np.float64)
def _single_frame(self):
mobile_com = self.mobile_atoms.center(self.weights).astype(np.float64)
self._mobile_coordinates64[:] = self.mobile_atoms.positions
self._mobile_coordinates64 -= mobile_com
self.rmsd[self._frame_index, :2] = self._ts.frame, self._trajectory.time
if self._groupselections_atoms:
# superimpose structures: MDAnalysis qcprot needs Nx3 coordinate
# array with float64 datatype (float32 leads to errors up to 1e-3 in
# RMSD). Note that R is defined in such a way that it acts **to the
# left** so that we can easily use broadcasting and save one
# expensive numpy transposition.
self.rmsd[self._frame_index, 2] = qcp.CalcRMSDRotationalMatrix(
self._ref_coordinates_64, self._mobile_coordinates64,
self._n_atoms, self._rot, self.weights)
self._R[:, :] = self._rot.reshape(3, 3)
# Transform each atom in the trajectory (use inplace ops to
# avoid copying arrays) (Marginally (~3%) faster than
# "ts.positions[:] = (ts.positions - x_com) * R + ref_com".)
self._ts.positions[:] -= mobile_com
# R acts to the left & is broadcasted N times.
self._ts.positions[:,:] = (self._mobile_coordinates64[:] *
self._R)
self._ts.positions[:] += self._ref_com
# 2) calculate secondary RMSDs
for igroup, (refpos, atoms) in enumerate(
zip(self._groupselections_ref_coords_64,
self._groupselections_atoms), 3):
self.rmsd[self._frame_index, igroup] = qcp.CalcRMSDRotationalMatrix(
refpos, atoms['mobile'].positions.astype(np.float64),
atoms['mobile'].n_atoms, None, self.weights)
else:
# only calculate RMSD by setting the Rmatrix to None (no need
# to carry out the rotation as we already get the optimum RMSD)
self.rmsd[self._frame_index, 2] = qcp.CalcRMSDRotationalMatrix(
self._ref_coordinates_64, self._mobile_coordinates64,
self._n_atoms, None, self.weights)
self._pm.rmsd = self.rmsd[self._frame_index, 2]
[docs] def save(self, filename=None):
"""Save RMSD from :attr:`RMSD.rmsd` to text file *filename*.
Parameters
----------
filename : str (optional)
if no filename is given the default provided to the constructor is
used.
"""
filename = filename or self.filename
if filename is not None:
if self.rmsd is None:
raise NoDataError("rmsd has not been calculated yet")
np.savetxt(filename, self.rmsd)
logger.info("Wrote RMSD timeseries to file %r", filename)
return filename
[docs]class RMSF(AnalysisBase):
r"""Calculate RMSF of given atoms across a trajectory.
Parameters
----------
atomgroup : AtomGroup
Atoms for which RMSF is calculated
start : int (optional)
starting frame, default None becomes 0.
stop : int (optional)
Frame index to stop analysis. Default: None becomes
n_frames. Iteration stops *before* this frame number,
which means that the trajectory would be read until the end.
step : int (optional)
step between frames, default None becomes 1.
weights : str / array_like (optional)
used weights. If ``'mass'`` use masses of atomgroup, it ``None``
use uniform weights.
verbose : bool (optional)
if ``False``, suppress all output
Note
----
No RMSD-superposition is performed; it is assumed that the user is
providing a trajectory where the protein of interest has been structurally
aligned to a reference structure.
Notes
-----
The root mean square fluctuation of an atom :math:`i` is computed as the
time average
.. math::
\rho_i = \sqrt{\left\langle (\mathbf{x}_i - \langle\mathbf{x}_i\rangle)^2 \right\rangle}
This method implements an algorithm for computing sums of squares while
avoiding overflows and underflows [Welford1962]_.
References
----------
.. [Welford1962] B. P. Welford (1962). "Note on a Method for
Calculating Corrected Sums of Squares and Products." Technometrics
4(3):419-420.
.. versionadded:: 0.11.0
.. versionchanged:: 0.16.0
Flexible weighting scheme with new `weights` keyword.
.. deprecated:: 0.16.0
Instead of ``mass_weighted=True`` use new ``weights='mass'``;
refactored to fit with AnalysisBase API;
the keyword argument `quiet` is deprecated in favor of `verbose`.
"""
def __init__(self, atomgroup, weights=None, **kwargs):
super(RMSF, self).__init__(atomgroup.universe.trajectory, **kwargs)
self.atomgroup = atomgroup
if not isinstance(weights, (list, tuple, np.ndarray)) and weights == 'mass':
weights = self.atomgroup.masses
self.weights = weights
def run(self, start=None, stop=None, step=None, progout=None,
verbose=None, quiet=None):
if any([el is not None for el in (start, stop, step, progout, quiet)]):
warnings.warn("run arguments are deprecated. Please pass them at "
"class construction. These options will be removed in 0.17.0",
category=DeprecationWarning)
verbose = _set_verbose(verbose, quiet, default=False)
# regenerate class with correct args
super(RMSF, self).__init__(self.atomgroup.universe.trajectory,
start=start, stop=stop, step=step,
verbose=verbose)
return super(RMSF, self).run()
def _prepare(self):
self.sumsquares = np.zeros((self.atomgroup.n_atoms, 3))
self.mean = self.sumsquares.copy()
def _single_frame(self):
k = self._frame_index
self.sumsquares += (k / (k+1.0)) * (self.atomgroup.positions - self.mean) ** 2
self.mean = (k * self.mean + self.atomgroup.positions) / (k + 1)
def _conclude(self):
k = self._frame_index
self.rmsf = np.sqrt(self.sumsquares.sum(axis=1) / (k + 1))
if not (self.rmsf >= 0).all():
raise ValueError("Some RMSF values negative; overflow " +
"or underflow occurred")