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r"""Dihedral angles analysis --- :mod:`MDAnalysis.analysis.dihedrals`
=================================================================
:Author: Henry Mull
:Year: 2018
:Copyright: GNU Public License v2
.. versionadded:: 0.19.0
This module contains classes for calculating dihedral angles for a given set of
atoms or residues. This can be done for selected frames or whole trajectories.
A list of time steps that contain angles of interest is generated and can be
easily plotted if desired. For the :class:`~MDAnalysis.analysis.dihedrals.Ramachandran`
and :class:`~MDAnalysis.analysis.dihedrals.Janin` classes, basic plots can be
generated using the method :meth:`Ramachandran.plot` or :meth:`Janin.plot`.
These plots are best used as references, but they also allow for user customization.
See Also
--------
:func:`MDAnalysis.lib.distances.calc_dihedrals()`
function to calculate dihedral angles from atom positions
Example applications
--------------------
General dihedral analysis
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The :class:`~MDAnalysis.analysis.dihedrals.Dihedral` class is useful for calculating
angles for many dihedrals of interest. For example, we can find the phi angles
for residues 5-10 of adenylate kinase (AdK). The trajectory is included within
the test data files::
import MDAnalysis as mda
from MDAnalysisTests.datafiles import GRO, XTC
u = mda.Universe(GRO, XTC)
# selection of atomgroups
ags = [res.phi_selection() for res in u.residues[4:9]]
from MDAnalysis.analysis.dihedrals import Dihedral
R = Dihedral(ags).run()
The angles can then be accessed with :attr:`Dihedral.results.angles`.
Ramachandran analysis
~~~~~~~~~~~~~~~~~~~~~
The :class:`~MDAnalysis.analysis.dihedrals.Ramachandran` class allows for the
quick calculation of classical Ramachandran plots [Ramachandran1963]_ in the
backbone :math:`phi` and :math:`psi` angles. Unlike the
:class:`~MDanalysis.analysis.dihedrals.Dihedral` class which takes a list of
`atomgroups`, this class only needs a list of residues or atoms from those
residues. The previous example can repeated with::
u = mda.Universe(GRO, XTC)
r = u.select_atoms("resid 5-10")
R = Ramachandran(r).run()
Then it can be plotted using the built-in plotting method :meth:`Ramachandran.plot()`::
import matplotlib.pyplot as plt
fig, ax = plt.subplots(figsize=plt.figaspect(1))
R.plot(ax=ax, color='k', marker='o', ref=True)
fig.tight_layout()
as shown in the example :ref:`Ramachandran plot figure <figure-ramachandran>`.
.. _figure-ramachandran:
.. figure:: /images/rama_demo_plot.png
:scale: 50 %
:alt: Ramachandran plot
Ramachandran plot for residues 5 to 10 of AdK, sampled from the AdK test
trajectory (XTC). The contours in the background are the "allowed region"
and the "marginally allowed" regions.
To plot the data yourself, the angles can be accessed using
:attr:`Ramachandran.results.angles`.
.. Note::
The Ramachandran analysis is prone to errors if the topology contains
duplicate or missing atoms (e.g. atoms with `altloc` or incomplete
residues). If the topology has as an `altloc` attribute, you must specify
only one `altloc` for the atoms with more than one (``"protein and not
altloc B"``).
Janin analysis
~~~~~~~~~~~~~~
Janin plots [Janin1978]_ for side chain conformations (:math:`\chi_1` and
:math:`chi_2` angles) can be created with the
:class:`~MDAnalysis.analysis.dihedrals.Janin` class. It works in the same way,
only needing a list of residues; see the :ref:`Janin plot figure
<figure-janin>` as an example.
The data for the angles can be accessed in the attribute
:attr:`Janin.results.angles`.
.. _figure-janin:
.. figure:: /images/janin_demo_plot.png
:scale: 50 %
:alt: Janin plot
Janin plot for all residues of AdK, sampled from the AdK test trajectory
(XTC). The contours in the background are the "allowed region" and the
"marginally allowed" regions for all possible residues.
.. Note::
The Janin analysis is prone to errors if the topology contains duplicate or
missing atoms (e.g. atoms with `altloc` or incomplete residues). If the
topology has as an `altloc` attribute, you must specify only one `altloc`
for the atoms with more than one (``"protein and not altloc B"``).
Furthermore, many residues do not have a :math:`\chi_2` dihedral and if the
selections of residues is not carefully filtered to only include those
residues with *both* sidechain dihedrals then a :exc:`ValueError` with the
message *Too many or too few atoms selected* is raised.
Reference plots
~~~~~~~~~~~~~~~
Reference plots can be added to the axes for both the Ramachandran and Janin
classes using the kwarg ``ref=True`` for the :meth:`Ramachandran.plot`
and :meth:`Janin.plot` methods. The Ramachandran reference data
(:data:`~MDAnalysis.analysis.data.filenames.Rama_ref`) and Janin reference data
(:data:`~MDAnalysis.analysis.data.filenames.Janin_ref`) were made using data
obtained from a large selection of 500 PDB files, and were analyzed using these
classes [Mull2018]_. The allowed and marginally allowed regions of the
Ramachandran reference plot have cutoffs set to include 90% and 99% of the data
points, and the Janin reference plot has cutoffs for 90% and 98% of the data
points. The list of PDB files used for the reference plots was taken from
[Lovell2003]_ and information about general Janin regions was taken from
[Janin1978]_.
Analysis Classes
----------------
.. autoclass:: Dihedral
:members:
:inherited-members:
.. attribute:: results.angles
Contains the time steps of the angles for each atomgroup in the list as
an ``n_frames×len(atomgroups)`` :class:`numpy.ndarray` with content
``[[angle 1, angle 2, ...], [time step 2], ...]``.
.. versionadded:: 2.0.0
.. attribute:: angles
Alias to the :attr:`results.angles` attribute.
.. deprecated:: 2.0.0
Will be removed in MDAnalysis 3.0.0. Please use
:attr:`results.angles` instead.
.. autoclass:: Ramachandran
:members:
:inherited-members:
.. attribute:: results.angles
Contains the time steps of the :math:`\phi` and :math:`\psi` angles for
each residue as an ``n_frames×n_residues×2`` :class:`numpy.ndarray` with
content ``[[[phi, psi], [residue 2], ...], [time step 2], ...]``.
.. versionadded:: 2.0.0
.. attribute:: angles
Alias to the :attr:`results.angles` attribute.
.. deprecated:: 2.0.0
Will be removed in MDAnalysis 3.0.0. Please use
:attr:`results.angles` instead.
.. autoclass:: Janin
:members:
:inherited-members:
.. attribute:: results.angles
Contains the time steps of the :math:`\chi_1` and :math:`\chi_2` angles
for each residue as an ``n_frames×n_residues×2`` :class:`numpy.ndarray`
with content ``[[[chi1, chi2], [residue 2], ...], [time step 2], ...]``.
.. versionadded:: 2.0.0
.. attribute:: angles
Alias to the :attr:`results.angles` attribute.
.. deprecated:: 2.0.0
Will be removed in MDAnalysis 3.0.0. Please use
:attr:`results.angles` instead.
References
----------
.. [Ramachandran1963] G. Ramachandran, C. Ramakrishnan, and
V. Sasisekharan. (1963) Stereochemistry of polypeptide chain
configurations. *Journal of Molecular Biology*, 7(1):95 – 99. doi:
`10.1016/S0022-2836(63)80023-6
<https://doi.org/10.1016/S0022-2836(63)80023-6>`_
.. [Janin1978] Joël Janin, Shoshanna Wodak, Michael Levitt, and Bernard
Maigret. (1978). "Conformation of amino acid side-chains in
proteins". *Journal of Molecular Biology* 125(3): 357-386. doi:
`10.1016/0022-2836(78)90408-4
<https://doi.org/10.1016/0022-2836(78)90408-4>`_
.. [Lovell2003] Simon C. Lovell, Ian W. Davis, W. Bryan Arendall III,
Paul I. W. de Bakker, J. Michael Word, Michael G. Prisant,
Jane S. Richardson, and David C. Richardson (2003). "Structure validation by
:math:`C_{\alpha}` geometry: :math:`\phi`, :math:`\psi`, and
:math:`C_{\beta}` deviation". *Proteins* 50(3): 437-450. doi:
`10.1002/prot.10286 <https://doi.org/10.1002/prot.10286>`_
.. [Mull2018] H. Mull and O. Beckstein. SPIDAL Summer REU 2018 Dihedral
Analysis in MDAnalysis. Technical report, Arizona State University, 8
2018. doi: `10.6084/m9.figshare.6957296
<https://doi.org/10.6084/m9.figshare.6957296>`_
"""
import numpy as np
import matplotlib.pyplot as plt
import warnings
import MDAnalysis as mda
from MDAnalysis.analysis.base import AnalysisBase
from MDAnalysis.lib.distances import calc_dihedrals
from MDAnalysis.analysis.data.filenames import Rama_ref, Janin_ref
[docs]class Dihedral(AnalysisBase):
"""Calculate dihedral angles for specified atomgroups.
Dihedral angles will be calculated for each atomgroup that is given for
each step in the trajectory. Each :class:`~MDAnalysis.core.groups.AtomGroup`
must contain 4 atoms.
Note
----
This class takes a list as an input and is most useful for a large
selection of atomgroups. If there is only one atomgroup of interest, then
it must be given as a list of one atomgroup.
.. versionchanged:: 2.0.0
:attr:`angles` results are now stored in a
:class:`MDAnalysis.analysis.base.Results` instance.
"""
def __init__(self, atomgroups, **kwargs):
"""Parameters
----------
atomgroups : list
a list of atomgroups for which the dihedral angles are calculated
Raises
------
ValueError
If any atomgroups do not contain 4 atoms
"""
super(Dihedral, self).__init__(
atomgroups[0].universe.trajectory, **kwargs)
self.atomgroups = atomgroups
if any([len(ag) != 4 for ag in atomgroups]):
raise ValueError("All AtomGroups must contain 4 atoms")
self.ag1 = mda.AtomGroup([ag[0] for ag in atomgroups])
self.ag2 = mda.AtomGroup([ag[1] for ag in atomgroups])
self.ag3 = mda.AtomGroup([ag[2] for ag in atomgroups])
self.ag4 = mda.AtomGroup([ag[3] for ag in atomgroups])
def _prepare(self):
self.results.angles = []
def _single_frame(self):
angle = calc_dihedrals(self.ag1.positions, self.ag2.positions,
self.ag3.positions, self.ag4.positions,
box=self.ag1.dimensions)
self.results.angles.append(angle)
def _conclude(self):
self.results.angles = np.rad2deg(np.array(self.results.angles))
@property
def angles(self):
wmsg = ("The `angle` attribute was deprecated in MDAnalysis 2.0.0 "
"and will be removed in MDAnalysis 3.0.0. Please use "
"`results.angles` instead")
warnings.warn(wmsg, DeprecationWarning)
return self.results.angles
[docs]class Ramachandran(AnalysisBase):
r"""Calculate :math:`\phi` and :math:`\psi` dihedral angles of selected
residues.
:math:`\phi` and :math:`\psi` angles will be calculated for each residue
corresponding to `atomgroup` for each time step in the trajectory. A
:class:`~MDAnalysis.ResidueGroup` is generated from `atomgroup` which is
compared to the protein to determine if it is a legitimate selection.
Parameters
----------
atomgroup : AtomGroup or ResidueGroup
atoms for residues for which :math:`\phi` and :math:`\psi` are
calculated
c_name : str (optional)
name for the backbone C atom
n_name : str (optional)
name for the backbone N atom
ca_name : str (optional)
name for the alpha-carbon atom
check_protein : bool (optional)
whether to raise an error if the provided atomgroup is not a
subset of protein atoms
Example
-------
For standard proteins, the default arguments will suffice to run a
Ramachandran analysis::
r = Ramachandran(u.select_atoms('protein')).run()
For proteins with non-standard residues, or for calculating dihedral
angles for other linear polymers, you can switch off the protein checking
and provide your own atom names in place of the typical peptide backbone
atoms::
r = Ramachandran(u.atoms, c_name='CX', n_name='NT', ca_name='S',
check_protein=False).run()
The above analysis will calculate angles from a "phi" selection of
CX'-NT-S-CX and "psi" selections of NT-S-CX-NT'.
Raises
------
ValueError
If the selection of residues is not contained within the protein
and ``check_protein`` is ``True``
Note
----
If ``check_protein`` is ``True`` and the residue selection is beyond
the scope of the protein and, then an error will be raised.
If the residue selection includes the first or last residue,
then a warning will be raised and they will be removed from the list of
residues, but the analysis will still run. If a :math:`\phi` or :math:`\psi`
selection cannot be made, that residue will be removed from the analysis.
.. versionchanged:: 1.0.0
added c_name, n_name, ca_name, and check_protein keyword arguments
.. versionchanged:: 2.0.0
:attr:`angles` results are now stored in a
:class:`MDAnalysis.analysis.base.Results` instance.
"""
def __init__(self, atomgroup, c_name='C', n_name='N', ca_name='CA',
check_protein=True, **kwargs):
super(Ramachandran, self).__init__(
atomgroup.universe.trajectory, **kwargs)
self.atomgroup = atomgroup
residues = self.atomgroup.residues
if check_protein:
protein = self.atomgroup.universe.select_atoms("protein").residues
if not residues.issubset(protein):
raise ValueError("Found atoms outside of protein. Only atoms "
"inside of a 'protein' selection can be used to "
"calculate dihedrals.")
elif not residues.isdisjoint(protein[[0, -1]]):
warnings.warn("Cannot determine phi and psi angles for the first "
"or last residues")
residues = residues.difference(protein[[0, -1]])
prev = residues._get_prev_residues_by_resid()
nxt = residues._get_next_residues_by_resid()
keep = np.array([r is not None for r in prev])
keep = keep & np.array([r is not None for r in nxt])
if not np.all(keep):
warnings.warn("Some residues in selection do not have "
"phi or psi selections")
prev = sum(prev[keep])
nxt = sum(nxt[keep])
residues = residues[keep]
# find n, c, ca
keep_prev = [sum(r.atoms.names==c_name)==1 for r in prev]
rnames = [n_name, c_name, ca_name]
keep_res = [all(sum(r.atoms.names == n) == 1 for n in rnames)
for r in residues]
keep_next = [sum(r.atoms.names == n_name) == 1 for r in nxt]
# alright we'll keep these
keep = np.array(keep_prev) & np.array(keep_res) & np.array(keep_next)
prev = prev[keep]
res = residues[keep]
nxt = nxt[keep]
rnames = res.atoms.names
self.ag1 = prev.atoms[prev.atoms.names == c_name]
self.ag2 = res.atoms[rnames == n_name]
self.ag3 = res.atoms[rnames == ca_name]
self.ag4 = res.atoms[rnames == c_name]
self.ag5 = nxt.atoms[nxt.atoms.names == n_name]
def _prepare(self):
self.results.angles = []
def _single_frame(self):
phi_angles = calc_dihedrals(self.ag1.positions, self.ag2.positions,
self.ag3.positions, self.ag4.positions,
box=self.ag1.dimensions)
psi_angles = calc_dihedrals(self.ag2.positions, self.ag3.positions,
self.ag4.positions, self.ag5.positions,
box=self.ag1.dimensions)
phi_psi = [(phi, psi) for phi, psi in zip(phi_angles, psi_angles)]
self.results.angles.append(phi_psi)
def _conclude(self):
self.results.angles = np.rad2deg(np.array(self.results.angles))
[docs] def plot(self, ax=None, ref=False, **kwargs):
"""Plots data into standard Ramachandran plot.
Each time step in :attr:`Ramachandran.results.angles` is plotted onto
the same graph.
Parameters
----------
ax : :class:`matplotlib.axes.Axes`
If no `ax` is supplied or set to ``None`` then the plot will
be added to the current active axes.
ref : bool, optional
Adds a general Ramachandran plot which shows allowed and
marginally allowed regions
kwargs : optional
All other kwargs are passed to :func:`matplotlib.pyplot.scatter`.
Returns
-------
ax : :class:`matplotlib.axes.Axes`
Axes with the plot, either `ax` or the current axes.
"""
if ax is None:
ax = plt.gca()
ax.axis([-180, 180, -180, 180])
ax.axhline(0, color='k', lw=1)
ax.axvline(0, color='k', lw=1)
ax.set(xticks=range(-180, 181, 60), yticks=range(-180, 181, 60),
xlabel=r"$\phi$", ylabel=r"$\psi$")
degree_formatter = plt.matplotlib.ticker.StrMethodFormatter(
r"{x:g}$\degree$")
ax.xaxis.set_major_formatter(degree_formatter)
ax.yaxis.set_major_formatter(degree_formatter)
if ref:
X, Y = np.meshgrid(np.arange(-180, 180, 4),
np.arange(-180, 180, 4))
levels = [1, 17, 15000]
colors = ['#A1D4FF', '#35A1FF']
ax.contourf(X, Y, np.load(Rama_ref), levels=levels, colors=colors)
a = self.results.angles.reshape(
np.prod(self.results.angles.shape[:2]), 2)
ax.scatter(a[:, 0], a[:, 1], **kwargs)
return ax
@property
def angles(self):
wmsg = ("The `angle` attribute was deprecated in MDAnalysis 2.0.0 "
"and will be removed in MDAnalysis 3.0.0. Please use "
"`results.angles` instead")
warnings.warn(wmsg, DeprecationWarning)
return self.results.angles
[docs]class Janin(Ramachandran):
r"""Calculate :math:`\chi_1` and :math:`\chi_2` dihedral angles of selected
residues.
:math:`\chi_1` and :math:`\chi_2` angles will be calculated for each residue
corresponding to `atomgroup` for each time step in the trajectory. A
:class:`~MDAnalysis.ResidueGroup` is generated from `atomgroup` which is
compared to the protein to determine if it is a legitimate selection.
Note
----
If the residue selection is beyond the scope of the protein, then an error
will be raised. If the residue selection includes the residues ALA, CYS*,
GLY, PRO, SER, THR, or VAL (the default of the `select_remove` keyword
argument) then a warning will be raised and they will be removed from the
list of residues, but the analysis will still run. Some topologies have
altloc attribues which can add duplicate atoms to the selection and must be
removed.
"""
def __init__(self, atomgroup,
select_remove="resname ALA CYS* GLY PRO SER THR VAL",
select_protein="protein",
**kwargs):
r"""Parameters
----------
atomgroup : AtomGroup or ResidueGroup
atoms for residues for which :math:`\chi_1` and :math:`\chi_2` are
calculated
select_remove : str
selection string to remove residues that do not have :math:`chi_2`
angles
select_protein : str
selection string to subselect protein-only residues from
`atomgroup` to check that only amino acids are selected; if you
have non-standard amino acids then adjust this selection to include
them
Raises
------
ValueError
if the final selection of residues is not contained within the
protein (as determined by
``atomgroup.select_atoms(select_protein)``)
ValueError
if not enough or too many atoms are found for a residue in the
selection, usually due to missing atoms or alternative locations,
or due to non-standard residues
.. versionchanged:: 2.0.0
`select_remove` and `select_protein` keywords were added.
:attr:`angles` results are now stored in a
:class:`MDAnalysis.analysis.base.Results` instance.
"""
super(Ramachandran, self).__init__(
atomgroup.universe.trajectory, **kwargs)
self.atomgroup = atomgroup
residues = atomgroup.residues
protein = atomgroup.select_atoms(select_protein).residues
remove = residues.atoms.select_atoms(select_remove).residues
if not residues.issubset(protein):
raise ValueError("Found atoms outside of protein. Only atoms "
"inside of a protein "
f"(select_protein='{select_protein}') can be "
"used to calculate dihedrals.")
elif len(remove) != 0:
warnings.warn(f"All residues selected with '{select_remove}' "
"have been removed from the selection.")
residues = residues.difference(remove)
self.ag1 = residues.atoms.select_atoms("name N")
self.ag2 = residues.atoms.select_atoms("name CA")
self.ag3 = residues.atoms.select_atoms("name CB")
self.ag4 = residues.atoms.select_atoms("name CG CG1")
self.ag5 = residues.atoms.select_atoms("name CD CD1 OD1 ND1 SD")
# if there is an altloc attribute, too many atoms will be selected which
# must be removed before using the class, or the file is missing atoms
# for some residues which must also be removed
if any(len(self.ag1) != len(ag) for ag in [self.ag2, self.ag3,
self.ag4, self.ag5]):
raise ValueError("Too many or too few atoms selected. Check for "
"missing or duplicate atoms in topology.")
def _conclude(self):
self.results.angles = (np.rad2deg(np.array(
self.results.angles)) + 360) % 360
[docs] def plot(self, ax=None, ref=False, **kwargs):
"""Plots data into standard Janin plot.
Each time step in :attr:`Janin.results.angles` is plotted onto the
same graph.
Parameters
----------
ax : :class:`matplotlib.axes.Axes`
If no `ax` is supplied or set to ``None`` then the plot will
be added to the current active axes.
ref : bool, optional
Adds a general Janin plot which shows allowed and marginally
allowed regions
kwargs : optional
All other kwargs are passed to :func:`matplotlib.pyplot.scatter`.
Returns
-------
ax : :class:`matplotlib.axes.Axes`
Axes with the plot, either `ax` or the current axes.
"""
if ax is None:
ax = plt.gca()
ax.axis([0, 360, 0, 360])
ax.axhline(180, color='k', lw=1)
ax.axvline(180, color='k', lw=1)
ax.set(xticks=range(0, 361, 60), yticks=range(0, 361, 60),
xlabel=r"$\chi_1$", ylabel=r"$\chi_2$")
degree_formatter = plt.matplotlib.ticker.StrMethodFormatter(
r"{x:g}$\degree$")
ax.xaxis.set_major_formatter(degree_formatter)
ax.yaxis.set_major_formatter(degree_formatter)
if ref:
X, Y = np.meshgrid(np.arange(0, 360, 6), np.arange(0, 360, 6))
levels = [1, 6, 600]
colors = ['#A1D4FF', '#35A1FF']
ax.contourf(X, Y, np.load(Janin_ref), levels=levels, colors=colors)
a = self.results.angles.reshape(np.prod(
self.results.angles.shape[:2]), 2)
ax.scatter(a[:, 0], a[:, 1], **kwargs)
return ax