Source code for MDAnalysis.analysis.density

# -*- Mode: python; tab-width: 4; indent-tabs-mode:nil; coding:utf-8 -*-
# vim: tabstop=4 expandtab shiftwidth=4 softtabstop=4
# MDAnalysis ---
# 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

# MDAnalysis -- density analysis
# Copyright (c) 2007-2011 Oliver Beckstein <[email protected]>
# (based on code from Hop --- a framework to analyze solvation dynamics from MD simulations)

r"""Generating densities from trajectories --- :mod:`MDAnalysis.analysis.density`

:Author: Oliver Beckstein
:Year: 2011
:Copyright: GNU Public License v3

The module provides classes and functions to generate and represent
volumetric data, in particular densities.

Generating a density from a MD trajectory

A common use case is to analyze the solvent density around a protein of
interest. The density is calculated with :func:`density_from_Universe` in the
fixed coordinate system of the simulation unit cell. It is therefore necessary
to orient and fix the protein with respect to the box coordinate system. In
practice this means centering and superimposing the protein, frame by frame, on
a reference structure and translating and rotating all other components of the
simulation with the protein. In this way, the solvent will appear in the
reference frame of the protein.

An input trajectory must

1. have been centered on the protein of interest;
2. have all molecules made whole that have been broken across periodic
   boundaries [#pbc]_;
3. have the solvent molecules remapped so that they are closest to the
   solute (this is important when using triclinic unit cells such as
   a dodecahedron or a truncated octahedron) [#pbc]_.
4. have a fixed frame of reference; for instance, by superimposing a protein
   on a reference structure so that one can study the solvent density around
   it [#fit]_.

To generate the density of water molecules around a protein (assuming that the
trajectory is already appropriately treated for periodic boundary artifacts and
is suitably superimposed to provide a fixed reference frame) [#testraj]_ ::

  from MDAnalysis.analysis.density import density_from_Universe
  u = Universe(TPR, XTC)
  D = density_from_Universe(u, delta=1.0, atomselection="name OW")
  D.export("water.dx", type="double")

The positions of all water oxygens are histogrammed on a grid with spacing
*delta* = 1 Å. Initially the density is measured in :math:`\text{Å}^{-3}`. With
the :meth:`Density.convert_density` method, the units of measurement are
changed. In the example we are now measuring the density relative to the
literature value of the TIP4P water model at ambient conditions (see the values
in :data:`MDAnalysis.units.water` for details). Finally, the density is written
as an OpenDX_ compatible file that can be read in VMD_, Chimera_, or PyMOL_.

See :class:`Density` for details. In particular, the density is stored
as a NumPy array in :attr:`Density.grid`, which can be processed in
any manner.

Creating densities

The following functions take trajectory or coordinate data and generate a
:class:`Density` object.

.. autofunction:: density_from_Universe
.. autofunction:: density_from_PDB
.. autofunction:: Bfactor2RMSF

Supporting classes and functions

The main output of the density creation functions is a
:class:`Density` instance, which is derived from a
:class:`gridData.core.Grid`. A :class:`Density` is essentially, a 3D
array with origin and lengths together with associated metadata (which
can be used in downstream processing).

.. autoclass:: Density

.. autoclass:: BfactorDensityCreator

.. autofunction:: notwithin_coordinates_factory

.. rubric:: Footnotes

.. [#pbc] Making molecules whole can be accomplished with the
          :meth:`MDAnalysis.core.groups.AtomGroup.wrap` of
          :attr:`Universe.atoms` (use ``compound="fragments"``).

          When using, for instance, the Gromacs_ command `gmx trjconv`_

          .. code-block:: bash

             gmx trjconv -pbc mol -center -ur compact

          one can make the molecules whole ``-pbc whole``, center it on a group
          (``-center``), and also pack all molecules in a compact unitcell
          representation, which can be useful for density generation.

.. [#fit] Superposition can be performed with

          The Gromacs_ command `gmx trjconv`_

          .. code-block:: bash

             gmx trjconv -fit rot+trans

          will also accomplish such a superposition. Note that the fitting has
          to be done in a *separate* step from the treatment of the periodic
          boundaries [#pbc]_.

.. [#testraj] Note that the trajectory in the example (`XTC`) is *not* properly
          made whole and fitted to a reference structure; these steps were
          omitted to clearly show the steps necessary for the actual density

.. Links
.. -----

.. _OpenDX:
.. _VMD:
.. _Chimera:
.. _PyMOL:
.. _Gromacs:
.. _`gmx trjconv`:


from __future__ import print_function, division, absolute_import
from six.moves import range, zip
from six import string_types

import numpy as np
import sys
import os
import os.path
import errno
import warnings

from gridData import Grid

import MDAnalysis
from MDAnalysis.core import groups
from MDAnalysis.lib.util import fixedwidth_bins, iterable, asiterable
from MDAnalysis.lib import NeighborSearch as NS
from MDAnalysis import NoDataError, MissingDataWarning
from .. import units
from ..lib import distances
from MDAnalysis.lib.log import ProgressMeter

import logging

logger = logging.getLogger("MDAnalysis.analysis.density")

[docs]class Density(Grid): r"""Class representing a density on a regular cartesian grid. Parameters ---------- grid : array_like histogram or density, typically a :class:`numpy.ndarray` edges : list list of arrays, the lower and upper bin edges along the axes parameters : dict dictionary of class parameters; saved with :meth:``. The following keys are meaningful to the class. Meaning of the values are listed: *isDensity* - ``False``: grid is a histogram with counts [default] - ``True``: a density Applying :meth:`Density.make_density`` sets it to ``True``. units : dict A dict with the keys - *length*: physical unit of grid edges (Angstrom or nm) [Angstrom] - *density*: unit of the density if ``isDensity=True`` or ``None`` otherwise; the default is "Angstrom^{-3}" for densities (meaning :math:`\text{Å}^{-3}`). (Actually, the default unit is the value of ``MDAnalysis.core.flags['length_unit']``; in most cases this is "Angstrom".) metadata : dict a user defined dictionary of arbitrary values associated with the density; the class does not touch :attr:`Density.metadata` but stores it with :meth:`` Attributes ---------- grid : array counts or density edges : list of 1d-arrays The boundaries of each cell in `grid` along all axes (equivalent to what :func:`numpy.histogramdd` returns). delta : array Cell size in each dimension. origin : array Coordinates of the *center* of the cell at index `grid[0, 0, 0, ..., 0]`, which is considered to be the front lower left corner. units : dict The units for lengths and density; change units with the method :meth:`~Density.convert_length` or :meth:`~Density.convert_density`. Notes ----- The data (:attr:`Density.grid`) can be manipulated as a standard numpy array. Changes can be saved to a file using the :meth:`` method. The grid can be restored using the :meth:`Density.load` method or by supplying the filename to the constructor. The attribute :attr:`Density.metadata` holds a user-defined dictionary that can be used to annotate the data. It is also saved with :meth:``. The :meth:`Density.export` method always exports a 3D object (written in such a way to be readable in VMD_, Chimera_, and PyMOL_), the rest should work for an array of any dimension. Note that PyMOL_ only understands DX files with the DX data type "double" in the "array" object (see `known issues when writing OpenDX files`_ and issue `MDAnalysis/GridDataFormats#35`_ for details). Using the keyword ``type="double"`` for the method :meth:`Density.export`, the user can ensure that the DX file is written in a format suitable for PyMOL_. If the input histogram consists of counts per cell then the :meth:`Density.make_density` method converts the grid to a physical density. For a probability density, divide it by :meth:`Density.grid.sum` or use ``normed=True`` right away in :func:`~numpy.histogramdd`. The user *should* set the *parameters* keyword (see docs for the constructor); in particular, if the data are already a density, one must set ``isDensity=True`` because there is no reliable way to detect if data represent counts or a density. As a special convenience, if data are read from a file and the user has not set ``isDensity`` then it is assumed that the data are in fact a density. .. _`MDAnalysis/GridDataFormats#35`: .. _`known issues when writing OpenDX files`: See Also -------- gridData.core.Grid : the base class of :class:`Density`. Examples -------- Typical use: 1. From a histogram (i.e. counts on a grid):: h,edges = numpy.histogramdd(...) D = Density(h, edges, parameters={'isDensity': False}, units={'length': 'A'}) D.make_density() 2. From a saved density file (e.g. in OpenDX format), where the lengths are in Angstrom and the density in 1/A**3:: D = Density("density.dx") 3. From a saved density file (e.g. in OpenDX format), where the lengths are in Angstrom and the density is measured relative to the density of water at ambient conditions:: D = Density("density.dx", units={'density': 'water'}) 4. From a saved *histogram* (less common, but in order to demonstrate the *parameters* keyword) where the lengths are in nm:: D = Density("counts.dx", parameters={'isDensity': False}, units={'length': 'nm'}) D.make_density() D.convert_length('Angstrom^{-3}') D.convert_density('water') After the final step, ``D`` will contain a density on a grid measured in Ångstrom, with the density values itself measured relative to the density of water. :class:`Density` objects can be algebraically manipulated (added, subtracted, multiplied, ...) but there are *no sanity checks* in place to make sure that units, metadata, etc are compatible! .. Note:: It is suggested to construct the Grid object from a histogram, to supply the appropriate length unit, and to use :meth:`Density.make_density` to obtain a density. This ensures that the length- and the density unit correspond to each other. """ def __init__(self, *args, **kwargs): length_unit = MDAnalysis.core.flags['length_unit'] parameters = kwargs.pop('parameters', {}) if len(args) > 0 and isinstance(args[0], string_types) or isinstance(kwargs.get('grid', None), string_types): # try to be smart: when reading from a file then it is likely that this # is a density parameters.setdefault('isDensity', True) else: parameters.setdefault('isDensity', False) units = kwargs.pop('units', {}) units.setdefault('length', length_unit) if parameters['isDensity']: units.setdefault('density', length_unit) else: units.setdefault('density', None) super(Density, self).__init__(*args, **kwargs) self.parameters = parameters # isDensity: set by make_density() self.units = units def _check_set_unit(self, u): """Check and set units. First check that all units and their values in the dict `u` are valid and then set the object's units attribute. Parameters ---------- u : dict ``{unit_type : value, ...}`` Raises ------ ValueError if unit types or unit values are not recognized or if required unit types are not in :attr:`units` """ # all this unit crap should be a class... try: for unit_type, value in u.items(): if value is None: # check here, too iffy to use dictionary[None]=None self.units[unit_type] = None continue try: units.conversion_factor[unit_type][value] self.units[unit_type] = value except KeyError: raise ValueError('Unit ' + str(value) + ' of type ' + str(unit_type) + ' is not recognized.') except AttributeError: errmsg = '"unit" must be a dictionary with keys "length" and "density.' logger.fatal(errmsg) raise ValueError(errmsg) # need at least length and density (can be None) if 'length' not in self.units: raise ValueError('"unit" must contain a unit for "length".') if 'density' not in self.units: self.units['density'] = None
[docs] def make_density(self): """Convert the grid (a histogram, counts in a cell) to a density (counts/volume). This method changes the grid irrevocably. For a probability density, manually divide by :meth:`grid.sum`. If this is already a density, then a warning is issued and nothing is done, so calling `make_density` multiple times does not do any harm. """ # Make it a density by dividing by the volume of each grid cell # (from numpy.histogramdd, which is for general n-D grids) if self.parameters['isDensity']: msg = "Running make_density() makes no sense: Grid is already a density. Nothing done." logger.warning(msg) warnings.warn(msg) return dedges = [np.diff(edge) for edge in self.edges] D = len(self.edges) for i in range(D): shape = np.ones(D, int) shape[i] = len(dedges[i]) self.grid /= dedges[i].reshape(shape) self.parameters['isDensity'] = True # see units.densityUnit_factor for units self.units['density'] = self.units['length'] + "^{-3}"
[docs] def convert_length(self, unit='Angstrom'): """Convert Grid object to the new `unit`. Parameters ---------- unit : str (optional) unit that the grid should be converted to: one of "Angstrom", "nm" Notes ----- This changes the edges but will not change the density; it is the user's responsibility to supply the appropriate unit if the Grid object is constructed from a density. It is suggested to start from a histogram and a length unit and use :meth:`make_density`. """ if unit == self.units['length']: return cvnfact = units.get_conversion_factor('length', self.units['length'], unit) self.edges = [x * cvnfact for x in self.edges] self.units['length'] = unit self._update() # needed to recalculate midpoints and origin
[docs] def convert_density(self, unit='Angstrom'): """Convert the density to the physical units given by `unit`. Parameters ---------- unit : str (optional) The target unit that the density should be converted to. `unit` can be one of the following: ============= =============================================================== name description of the unit ============= =============================================================== Angstrom^{-3} particles/A**3 nm^{-3} particles/nm**3 SPC density of SPC water at standard conditions TIP3P ... see :data:`MDAnalysis.units.water` TIP4P ... see :data:`MDAnalysis.units.water` water density of real water at standard conditions (0.997 g/cm**3) Molar mol/l ============= =============================================================== Raises ------ RuntimeError If the density does not have a unit associated with it to begin with (i.e., is not a density) then no conversion can take place. ValueError for unknown `unit`. Notes ----- (1) This method only works if there is already a length unit associated with the density; otherwise raises :exc:`RuntimeError` (2) Conversions always go back to unity so there can be rounding and floating point artifacts for multiple conversions. """ if not self.parameters['isDensity']: errmsg = 'The grid is not a density so converty_density() makes no sense.' logger.fatal(errmsg) raise RuntimeError(errmsg) if unit == self.units['density']: return try: self.grid *= units.get_conversion_factor('density', self.units['density'], unit) except KeyError: raise ValueError("The name of the unit ({0!r} supplied) must be one of:\n{1!r}".format(unit, units.conversion_factor['density'].keys())) self.units['density'] = unit
def __repr__(self): if self.parameters['isDensity']: grid_type = 'density' else: grid_type = 'histogram' return '<Density ' + grid_type + ' with ' + str(self.grid.shape) + ' bins>'
def _set_user_grid(gridcenter, xdim, ydim, zdim, smin, smax): """Helper function to set the grid dimensions to user defined values Parameters ---------- gridcenter : numpy ndarray, float32 3 element ndarray containing the x, y and z coordinates of the grid box center xdim : float Box edge length in the x dimension ydim : float Box edge length in the y dimension zdim : float Box edge length in the y dimension smin : numpy ndarray, float32 Minimum x,y,z coordinates for the input selection smax : numpy ndarray, float32 Maximum x,y,z coordinates for the input selection Returns ------- umin : numpy ndarray, float32 Minimum x,y,z coordinates of the user defined grid umax : numpy ndarray, float32 Maximum x,y,z coordinates of the user defined grid """ # Check user inputs try: gridcenter = np.asarray(gridcenter, dtype=np.float32) except ValueError: raise ValueError("Non-number values assigned to gridcenter") if gridcenter.shape != (3,): raise ValueError("gridcenter must be a 3D coordinate") try: xyzdim = np.array([xdim, ydim, zdim], dtype=np.float32) except ValueError: raise ValueError("xdim, ydim, and zdim must be numbers") # Set min/max by shifting by half the edge length of each dimension umin = gridcenter - xyzdim/2 umax = gridcenter + xyzdim/2 # Here we test if coords of selection fall outside of the defined grid # if this happens, we warn users they may want to resize their grids if any(smin < umin) or any(smax > umax): msg = ("Atom selection does not fit grid --- " "you may want to define a larger box") warnings.warn(msg) logger.warning(msg) return umin, umax
[docs]def density_from_Universe(universe, delta=1.0, atomselection='name OH2', start=None, stop=None, step=None, metadata=None, padding=2.0, cutoff=0, soluteselection=None, use_kdtree=True, update_selection=False, verbose=False, interval=1, quiet=None, parameters=None, gridcenter=None, xdim=None, ydim=None, zdim=None): """Create a density grid from a :class:`MDAnalysis.Universe` object. The trajectory is read, frame by frame, and the atoms selected with `atomselection` are histogrammed on a grid with spacing `delta`. Parameters ---------- universe : MDAnalysis.Universe :class:`MDAnalysis.Universe` object with a trajectory atomselection : str (optional) selection string (MDAnalysis syntax) for the species to be analyzed ["name OH2"] delta : float (optional) bin size for the density grid in Angstroem (same in x,y,z) [1.0] start : int (optional) stop : int (optional) step : int (optional) Slice the trajectory as ``trajectory[start:stop:step]``; default is to read the whole trajectory. metadata : dict. optional `dict` of additional data to be saved with the object; the meta data are passed through as they are. padding : float (optional) increase histogram dimensions by padding (on top of initial box size) in Angstroem. Padding is ignored when setting a user defined grid. [2.0] soluteselection : str (optional) MDAnalysis selection for the solute, e.g. "protein" [``None``] cutoff : float (optional) With `cutoff`, select "<atomsel> NOT WITHIN <cutoff> OF <soluteselection>" (Special routines that are faster than the standard ``AROUND`` selection); any value that evaluates to ``False`` (such as the default 0) disables this special selection. update_selection : bool (optional) Should the selection of atoms be updated for every step? [``False``] - ``True``: atom selection is updated for each frame, can be slow - ``False``: atoms are only selected at the beginning verbose : bool (optional) Print status update to the screen for every *interval* frame? [``True``] - ``False``: no status updates when a new frame is processed - ``True``: status update every frame (including number of atoms processed, which is interesting with ``update_selection=True``) interval : int (optional) Show status update every `interval` frame [1] parameters : dict (optional) `dict` with some special parameters for :class:`Density` (see docs) gridcenter : numpy ndarray, float32 (optional) 3 element numpy array detailing the x, y and z coordinates of the center of a user defined grid box in Angstroem [``None``] xdim : float (optional) User defined x dimension box edge in ångström; ignored if gridcenter is ``None`` ydim : float (optional) User defined y dimension box edge in ångström; ignored if gridcenter is ``None`` zdim : float (optional) User defined z dimension box edge in ångström; ignored if gridcenter is ``None`` Returns ------- :class:`Density` A :class:`Density` instance with the histogrammed data together with associated metadata. Notes ----- By default, the `atomselection` is static, i.e., atoms are only selected once at the beginning. If you want *dynamically changing selections* (such as "name OW and around 4.0 (protein and not name H*)", i.e., the water oxygen atoms that are within 4 Å of the protein heavy atoms) then set ``update_selection=True``. For the special case of calculating a density of the "bulk" solvent away from a solute use the optimized selections with keywords *cutoff* and *soluteselection* (see Examples below). Examples -------- Basic use for creating a water density (just using the water oxygen atoms "OW"):: density = density_from_Universe(universe, delta=1.0, atomselection='name OW') If you are only interested in water within a certain region, e.g., within a vicinity around a binding site, you can use a selection that updates every step by setting the `update_selection` keyword argument:: site_density = density_from_Universe(universe, delta=1.0, atomselection='name OW and around 5 (resid 156 157 305)', update_selection=True) A special case for an updating selection is to create the "bulk density", i.e., the water outside the immediate solvation shell of a protein: Select all water oxygen atoms that are *farther away* than a given cut-off (say, 4 Å) from the solute (here, heavy atoms of the protein):: bulk = density_from_Universe(universe, delta=1.0, atomselection='name OW', solute="protein and not name H*", cutoff=4) (Using the special case for the bulk with `soluteselection` and `cutoff` improves performance over the simple `update_selection` approach.) If you are interested in explicitly setting a grid box of a given edge size and origin, you can use the gridcenter and x/y/zdim arguments. For example to plot the density of waters within 5 Å of a ligand (in this case the ligand has been assigned the residue name "LIG") in a cubic grid with 20 Å edges which is centered on the centre of mass (COM) of the ligand:: # Create a selection based on the ligand ligand_selection = universe.select_atoms("resname LIG") # Extract the COM of the ligand ligand_COM = ligand_selection.center_of_mass() # Generate a density of waters on a cubic grid centered on the ligand COM # In this case, we update the atom selection as shown above. water_density = density_from_Universe(universe, delta=1.0, atomselection='name OW around 5 resname LIG', update_selection=True, gridcenter=ligand_COM, xdim=20.0, ydim=20.0, zdim=20.0) (It should be noted that the `padding` keyword is not used when a user defined grid is assigned). .. versionchanged:: 0.20.0 ProgressMeter now iterates over the number of frames analysed. .. versionchanged:: 0.19.0 *gridcenter*, *xdim*, *ydim* and *zdim* keywords added to allow for user defined boxes .. versionchanged:: 0.13.0 *update_selection* and *quiet* keywords added .. deprecated:: 0.16 The keyword argument *quiet* is deprecated in favor of *verbose*. """ u = universe if cutoff > 0 and soluteselection is not None: # special fast selection for '<atomsel> not within <cutoff> of <solutesel>' notwithin_coordinates = notwithin_coordinates_factory( u, atomselection, soluteselection, cutoff, use_kdtree=use_kdtree, updating_selection=update_selection) def current_coordinates(): return notwithin_coordinates() else: group = u.select_atoms(atomselection, updating=update_selection) def current_coordinates(): return group.positions coord = current_coordinates() "Selected {0:d} atoms out of {1:d} atoms ({2!s}) from {3:d} total." "".format(coord.shape[0], len(u.select_atoms(atomselection)), atomselection, len(u.atoms)) ) # mild warning; typically this is run on RMS-fitted trajectories and # so the box information is rather meaningless box, angles = u.trajectory.ts.dimensions[:3], u.trajectory.ts.dimensions[3:] if tuple(angles) != (90., 90., 90.): msg = "Non-orthorhombic unit-cell --- make sure that it has been remapped properly!" warnings.warn(msg) logger.warning(msg) if gridcenter is not None: # Generate a copy of smin/smax from coords to later check if the # defined box might be too small for the selection smin = np.min(coord, axis=0) smax = np.max(coord, axis=0) # Overwrite smin/smax with user defined values smin, smax = _set_user_grid(gridcenter, xdim, ydim, zdim, smin, smax) else: # Make the box bigger to avoid as much as possible 'outlier'. This # is important if the sites are defined at a high density: in this # case the bulk regions don't have to be close to 1 * n0 but can # be less. It's much more difficult to deal with outliers. The # ideal solution would use images: implement 'looking across the # periodic boundaries' but that gets complicate when the box # rotates due to RMS fitting. smin = np.min(coord, axis=0) - padding smax = np.max(coord, axis=0) + padding BINS = fixedwidth_bins(delta, smin, smax) arange = np.vstack((BINS['min'], BINS['max'])) arange = np.transpose(arange) bins = BINS['Nbins'] # create empty grid with the right dimensions (and get the edges) grid, edges = np.histogramdd(np.zeros((1, 3)), bins=bins, range=arange, normed=False) grid *= 0.0 h = grid.copy() start, stop, step = u.trajectory.check_slice_indices(start, stop, step) n_frames = len(range(start, stop, step)) pm = ProgressMeter(n_frames, interval=interval, verbose=verbose, format="Histogramming %(n_atoms)6d atoms in frame " "%(step)5d/%(numsteps)d [%(percentage)5.1f%%]") for index, ts in enumerate(u.trajectory[start:stop:step]): coord = current_coordinates() pm.echo(index, n_atoms=len(coord)) if len(coord) == 0: continue h[:], edges[:] = np.histogramdd(coord, bins=bins, range=arange, normed=False) grid += h # accumulate average histogram grid /= float(n_frames) metadata = metadata if metadata is not None else {} metadata['psf'] = u.filename metadata['dcd'] = u.trajectory.filename metadata['atomselection'] = atomselection metadata['n_frames'] = n_frames metadata['totaltime'] = round(u.trajectory.n_frames * u.trajectory.dt, 3) metadata['dt'] = u.trajectory.dt metadata['time_unit'] = MDAnalysis.core.flags['time_unit'] try: metadata['trajectory_skip'] = u.trajectory.skip_timestep # frames except AttributeError: metadata['trajectory_skip'] = 1 # seems to not be used.. try: metadata['trajectory_delta'] = # in native units except AttributeError: metadata['trajectory_delta'] = 1 if cutoff > 0 and soluteselection is not None: metadata['soluteselection'] = soluteselection metadata['cutoff'] = cutoff # in Angstrom parameters = parameters if parameters is not None else {} parameters['isDensity'] = False # must override g = Density(grid=grid, edges=edges, units={'length': MDAnalysis.core.flags['length_unit']}, parameters=parameters, metadata=metadata) g.make_density()"Density completed (initial density in Angstrom**-3)") return g
[docs]def notwithin_coordinates_factory(universe, sel1, sel2, cutoff, not_within=True, use_kdtree=True, updating_selection=False): """Generate optimized selection for '*sel1* not within *cutoff* of *sel2*' Parameters ---------- universe : MDAnalysis.Universe Universe object on which to operate sel1 : str Selection string for the *solvent* selection (should be the group with the *larger number of atoms* to make the KD-Tree search more efficient) sel2 : str Selection string for the *solute* selection cutoff : float Distance cutoff not_within : bool - ``True``: selection behaves as "not within" (As described above) - ``False``: selection is a "<sel1> WITHIN <cutoff> OF <sel2>" use_kdtree : bool - ``True``: use fast KD-Tree based selections - ``False``: use distance matrix approach updating_selection : bool If ``True``, re-evaluate the selection string each frame. Notes ----- * Periodic boundary conditions are *not* taken into account: the naive minimum image convention employed in the distance check is currently not being applied to remap the coordinates themselves, and hence it would lead to counts in the wrong region. * With ``updating_selection=True``, the selection is evaluated every turn; do not use distance based selections (such as "AROUND") in your selection string because it will likely completely negate any gains from using this function factory in the first place. Examples -------- :func:`notwithin_coordinates_factory` creates an optimized function that, when called, returns the coordinates of the "solvent" selection that are *not within* a given cut-off distance of the "solute". Because it is KD-tree based, it is cheap to query the KD-tree with a different cut-off:: notwithin_coordinates = notwithin_coordinates_factory(universe, 'name OH2', 'protein and not name H*', 3.5) ... coord = notwithin_coordinates() # get coordinates outside cutoff 3.5 A coord = notwithin_coordinates(cutoff2) # can use different cut off For programmatic convenience, the function can also function as a factory for a simple *within cutoff* query if the keyword ``not_within=False`` is set:: within_coordinates = notwithin_coordinates_factory(universe, 'name OH2','protein and not name H*', 3.5, not_within=False) ... coord = within_coordinates() # get coordinates within cutoff 3.5 A coord = within_coordinates(cutoff2) # can use different cut off (Readability is enhanced by properly naming the generated function ``within_coordinates()``.) """ # Benchmark of FABP system (solvent 3400 OH2, protein 2100 atoms) on G4 powerbook, 500 frames # cpu/s relative speedup use_kdtree # distance matrix 633 1 1 False # AROUND + kdtree 420 0.66 1.5 n/a ('name OH2 around 4 protein') # manual + kdtree 182 0.29 3.5 True solvent = universe.select_atoms(sel1, updating=updating_selection) protein = universe.select_atoms(sel2, updating=updating_selection) if use_kdtree: # using faster hand-coded 'not within' selection with kd-tree if not_within is True: # default def notwithin_coordinates(cutoff=cutoff): # must update every time step ns_w = NS.AtomNeighborSearch(solvent) # build kd-tree on solvent (N_w > N_protein) solvation_shell =, cutoff) # solvent within CUTOFF of protein # Find indices in solvent NOT in solvation shell uniq_idx = np.setdiff1d(solvent.ix, solvation_shell.ix) # Then reselect these from Universe.atoms (as these indices are global) group = universe.atoms[uniq_idx] return group.positions else: def notwithin_coordinates(cutoff=cutoff): # acts as '<solvent> WITHIN <cutoff> OF <protein>' # must update every time step ns_w = NS.AtomNeighborSearch(solvent) # build kd-tree on solvent (N_w > N_protein) group =, cutoff) # solvent within CUTOFF of protein return group.positions else: # slower distance matrix based (calculate all with all distances first) dist = np.zeros((len(solvent), len(protein)), dtype=np.float64) box = None # as long as s_coor is not minimum-image remapped if not_within is True: # default compare = np.greater aggregatefunc = np.all else: compare = np.less_equal aggregatefunc = np.any def notwithin_coordinates(cutoff=cutoff): s_coor = solvent.positions p_coor = protein.positions # Does water i satisfy d[i,j] > r for ALL j? d = distances.distance_array(s_coor, p_coor, box=box, result=dist) return s_coor[aggregatefunc(compare(d, cutoff), axis=1)] return notwithin_coordinates
[docs]def Bfactor2RMSF(B): r"""Atomic root mean square fluctuation (in Angstrom) from the crystallographic B-factor RMSF and B-factor are related by [Willis1975]_ .. math:: B = \frac{8\pi^2}{3} \rm{RMSF}^2 and this function returns .. math:: \rm{RMSF} = \sqrt{\frac{3 B}{8\pi^2}} .. rubric:: References .. [Willis1975] BTM Willis and AW Pryor. *Thermal vibrations in crystallography*. Cambridge Univ. Press, 1975 """ return np.sqrt(3. * B / 8.) / np.pi
[docs]def density_from_PDB(pdb, **kwargs): """Create a density from a single frame PDB. Typical use is to make a density from the crystal water molecules. The density is created from isotropic gaussians centered at each selected atoms. If B-factors are present in the file then they are used to calculate the width of the gaussian. Using the *sigma* keyword, one can override this choice and prescribe a gaussian width for all atoms (in Angstrom), which is calculated as described for :func:`Bfactor2RMSF`. Parameters ---------- pdb : str PDB filename (should have the temperatureFactor set); ANISO records are currently *not* processed atomselection : str selection string (MDAnalysis syntax) for the species to be analyzed ['resname HOH and name O'] delta : float bin size for the density grid in Angstroem (same in x,y,z) [1.0] metadata : dict dictionary of additional data to be saved with the object [``None``] padding : float increase histogram dimensions by padding (on top of initial box size) [1.0] sigma : float width (in Angstrom) of the gaussians that are used to build up the density; if ``None`` then uses B-factors from *pdb* [``None``] Returns ------- :class:`Density` object with a density measured relative to the water density at standard conditions Notes ----- The current implementation is *painfully* slow. See Also -------- :func:`Bfactor2RMSF` and :class:`BfactorDensityCreator` """ return BfactorDensityCreator(pdb, **kwargs).Density()
[docs]class BfactorDensityCreator(object): """Create a density grid from a pdb file using MDAnalysis. The main purpose of this function is to convert crystal waters in an X-ray structure into a density so that one can compare the experimental density with the one from molecular dynamics trajectories. Because a pdb is a single snapshot, the density is estimated by placing Gaussians of width sigma at the position of all selected atoms. Sigma can be fixed or taken from the B-factor field, in which case sigma is taken as sqrt(3.*B/8.)/pi (see :func:`BFactor2RMSF`). .. TODO .. * Make Gaussian convolution more efficient (at least for same .. sigma) because right now it is *very* slow (which may be .. acceptable if one only runs this once) .. * Using a temporary Creator class with the .. :meth:`BfactorDensityCreator.Density` helper method is clumsy. """ def __init__(self, pdb, delta=1.0, atomselection='resname HOH and name O', metadata=None, padding=1.0, sigma=None): """Construct the density from psf and pdb and the atomselection. Parameters ---------- pdb : str PDB file or :class:`MDAnalysis.Universe`; atomselection : str selection string (MDAnalysis syntax) for the species to be analyzed delta : float bin size for the density grid in Angstroem (same in x,y,z) [1.0] metadata : dict dictionary of additional data to be saved with the object padding : float increase histogram dimensions by padding (on top of initial box size) sigma : float width (in Angstrom) of the gaussians that are used to build up the density; if ``None`` (the default) then uses B-factors from pdb Notes ----- For assigning X-ray waters to MD densities one might have to use a sigma of about 0.5 A to obtain a well-defined and resolved x-ray water density that can be easily matched to a broader density distribution. Examples -------- The following creates the density with the B-factors from the pdb file:: DC = BfactorDensityCreator(pdb, delta=1.0, atomselection="name HOH", padding=2, sigma=None) density = DC.Density() See Also -------- :func:`density_from_PDB` for a convenience function """ u = MDAnalysis.as_Universe(pdb) group = u.select_atoms(atomselection) coord = group.positions"Selected {0:d} atoms ({1!s}) out of {2:d} total.".format(coord.shape[0], atomselection, len(u.atoms))) smin = np.min(coord, axis=0) - padding smax = np.max(coord, axis=0) + padding BINS = fixedwidth_bins(delta, smin, smax) arange = list(zip(BINS['min'], BINS['max'])) bins = BINS['Nbins'] # get edges by doing a fake run grid, self.edges = np.histogramdd(np.zeros((1, 3)), bins=bins, range=arange, normed=False) = np.diag([(e[-1] - e[0]) / (len(e) - 1) for e in self.edges]) self.midpoints = [0.5 * (e[:-1] + e[1:]) for e in self.edges] self.origin = [m[0] for m in self.midpoints] n_frames = 1 if sigma is None: # histogram individually, and smear out at the same time # with the appropriate B-factor if np.any(group.bfactors == 0.0): wmsg = "Some B-factors are Zero (will be skipped)." logger.warning(wmsg) warnings.warn(wmsg, category=MissingDataWarning) rmsf = Bfactor2RMSF(group.bfactors) grid *= 0.0 # reset grid self.g = self._smear_rmsf(coord, grid, self.edges, rmsf) else: # histogram 'delta functions' grid, self.edges = np.histogramdd(coord, bins=bins, range=arange, normed=False)"Histogrammed {0:6d} atoms from pdb.".format(len(group.atoms))) # just a convolution of the density with a Gaussian self.g = self._smear_sigma(grid, sigma) try: metadata['pdb'] = pdb except TypeError: metadata = {'pdb': pdb} metadata['atomselection'] = atomselection metadata['n_frames'] = n_frames metadata['sigma'] = sigma self.metadata = metadata"Histogram completed (initial density in Angstrom**-3)") # Density automatically converts histogram to density for isDensity=False -- ??[OB]
[docs] def Density(self, threshold=None): """Returns a :class:`Density` object.""" d = Density(grid=self.g, edges=self.edges, units=dict(length='Angstrom'), parameters=dict(isDensity=False), metadata=self.metadata) d.make_density() d.convert_density('water') return d
def _smear_sigma(self, grid, sigma): # smear out points # (not optimized -- just to test the principle; faster approach could use # convolution of the whole density with a single Gaussian via FFTs: # rho_smeared = F^-1[ F[g]*F[rho] ] g = np.zeros(grid.shape) # holds the smeared out density pos = np.where(grid != 0) # position in histogram (as bin numbers) for iwat in range(len(pos[0])): # super-ugly loop p = tuple([wp[iwat] for wp in pos]) g += grid[p] * np.fromfunction(self._gaussian, grid.shape,, p=p, sigma=sigma) print("Smearing out atom position {0:4d}/{1:5d} with RMSF {2:4.2f} A\r".format(iwat + 1, len(pos[0]), sigma),) return g def _smear_rmsf(self, coordinates, grid, edges, rmsf): # smear out each water with its individual Gaussian # (slower than smear_sigma) g = np.zeros(grid.shape) # holds the smeared out density N, D = coordinates.shape for iwat, coord in enumerate(coordinates): if rmsf[iwat] == 0: continue g += np.fromfunction(self._gaussian_cartesian, grid.shape,, c=coord, sigma=rmsf[iwat]) print("Smearing out atom position {0:4d}/{1:5d} with RMSF {2:4.2f} A\r".format(iwat + 1, N, rmsf[iwat]),) return g def _gaussian(self, i, j, k, p, sigma): # i,j,k can be numpy arrays # p is center of gaussian as grid index, sigma its width (in A) x =[0, 0] * (i - p[0]) # in Angstrom y =[1, 1] * (j - p[1]) z =[2, 2] * (k - p[2]) return (2 * np.pi * sigma) ** (-1.5) * np.exp(-(x * x + y * y + z * z) / (2 * sigma * sigma)) def _gaussian_cartesian(self, i, j, k, c, sigma): # i,j,k can be numpy arrays # c is center of gaussian in cartesian coord (A), sigma its width (in A) x = self.origin[0] +[0, 0] * i - c[0] # in Angstrom y = self.origin[1] +[1, 1] * j - c[1] z = self.origin[2] +[2, 2] * k - c[2] return (2 * np.pi * sigma) ** (-1.5) * np.exp(-(x * x + y * y + z * z) / (2 * sigma * sigma))