# -*- coding: utf-8 -*-
"""This module defines customized gamma functions for elastic network model
analysis."""
import numpy as np
from prody.atomic import Atomic
__all__ = ['Gamma', 'GammaStructureBased', 'GammaVariableCutoff']
[docs]class Gamma(object):
"""Base class for facilitating use of atom type, residue type, or residue
property dependent force constants (γ).
Derived classes:
* :class:`.GammaStructureBased`
* :class:`.GammaVariableCutoff`"""
def __init__(self):
pass
[docs] def gamma(self, dist2, i, j):
"""Returns force constant.
For efficiency purposes square of the distance between interacting
atom/residue (node) pairs is passed to this function. In addition,
node indices are passed."""
pass
[docs]class GammaStructureBased(Gamma):
"""Facilitate setting the spring constant based on the secondary structure
and connectivity of the residues.
A recent systematic study [LT10]_ of a large set of NMR-structures analyzed
using a method based on entropy maximization showed that taking into
consideration properties such as sequential separation between
contacting residues and the secondary structure types of the interacting
residues provides refinement in the ENM description of proteins.
This class determines pairs of connected residues or pairs of proximal
residues in a helix or a sheet, and assigns them a larger user defined
spring constant value.
DSSP single letter abbreviations are recognized:
* **H**: α-helix
* **G**: 3-10-helix
* **I**: π-helix
* **E**: extended part of a sheet
*helix*:
Applies to residue (or Cα atom) pairs that are in the same helical
segment, at most 7 Å apart, and separated by at most
3 (3-10-helix), 4 (α-helix), or 5 (π-helix) residues.
*sheet*:
Applies to Cα atom pairs that are in different β-strands and at most
6 Å apart.
*connected*:
Applies to Cα atoms that are at most 4 Å apart.
Note that this class does not take into account insertion codes.
.. [LT10] Lezon TR, Bahar I. Using entropy maximization to understand the
determinants of structural dynamics beyond native contact topology.
*PLoS Comput Biol* **2010** 6(6):e1000816.
**Example**:
Let's parse coordinates and header data from a PDB file, and then
assign secondary structure to the atoms.
.. ipython:: python
from prody import *
ubi, header = parsePDB('1aar', chain='A', subset='calpha', header=True)
assignSecstr(header, ubi)
In the above we parsed only the atoms needed for this calculation, i.e.
Cα atoms from chain A.
We build the Hessian matrix using structure based force constants as
follows;
.. ipython:: python
gamma = GammaStructureBased(ubi)
anm = ANM('')
anm.buildHessian(ubi, gamma=gamma)
We can obtain the force constants assigned to residue pairs from the
Kirchhoff matrix as follows:
.. ipython:: python
k = anm.getKirchhoff()
k[0,1] # a pair of connected residues
k[0,16] # a pair of residues from a sheet"""
def __init__(self, atoms, gamma=1.0, helix=6.0, sheet=6.0, connected=10.0):
"""Setup the parameters.
:arg atoms: A set of atoms with chain identifiers, residue numbers,
and secondary structure assignments are set.
:type atoms: :class:`.Atomic`
:arg gamma: Force constant in arbitrary units. Default is 1.0.
:type gamma: float
:arg helix: Force constant factor for residues hydrogen bonded in
α-helices, 3,10-helices, and π-helices. Default is 6.0, i.e.
``6.0`*gamma``.
:type helix: float
:arg sheet: Force constant factor for residue pairs forming a hydrogen
bond in a β-sheet. Default is 6.0, i.e. ``6.0`*gamma``.
:type sheet: float
:arg connected: Force constant factor for residue pairs that are
connected. Default is 10.0, i.e. ``10.0`*gamma``.
:type connected: float"""
if not isinstance(atoms, Atomic):
raise TypeError('atoms must be an Atomic instance')
n_atoms = atoms.numAtoms()
if n_atoms < 3:
raise ValueError('number of atoms must be larger than 2')
sstr = atoms.getSecstrs()
assert sstr is not None, 'secondary structure assignments must be set'
chid = atoms.getChids()
assert chid is not None, 'chain identifiers must be set'
rnum = atoms.getResindices()
assert rnum is not None, 'residue numbers must be set'
gamma = float(gamma)
assert gamma > 0, 'gamma must be greater than 0'
helix = float(helix)
assert helix > 0, 'helix must be greater than 0'
sheet = float(sheet)
assert sheet > 0, 'sheet must be greater than 0'
connected = float(connected)
assert connected > 0, 'connected must be greater than 0'
ssid = np.zeros(n_atoms)
for i in range(1, n_atoms):
if (sstr[i-1] == sstr[i] and chid[i-1] == chid[i] and
rnum[i]-rnum[i-1] == 1):
ssid[i] = ssid[i-1]
else:
ssid[i] = ssid[i-1] + 1
self._sstr = sstr
self._chid = chid
self._rnum = rnum
self._ssid = ssid
self._gamma = gamma
self._helix = gamma * helix
self._sheet = gamma * sheet
self._connected = gamma * connected
[docs] def getSecstrs(self):
"""Returns a copy of secondary structure assignments."""
return self._sstr.copy()
[docs] def getChids(self):
"""Returns a copy of chain identifiers."""
return self._chid.socopypy()
[docs] def getResnums(self):
"""Returns a copy of residue numbers."""
return self._rnum.copy()
[docs] def gamma(self, dist2, i, j):
"""Returns force constant."""
if dist2 <= 16:
return self._connected
sstr = self._sstr
ssid = self._ssid
rnum = self._rnum
# if residues are in the same secondary structure element
if ssid[i] == ssid[j]:
i_j = abs(rnum[j] - rnum[i])
if ((i_j <= 4 and sstr[i] == 'H') or
(i_j <= 3 and sstr[i] == 'G') or
(i_j <= 5 and sstr[i] == 'I')) and dist2 <= 49:
return self._helix
elif sstr[i] == sstr[j] == 'E' and dist2 <= 36:
return self._sheet
return self._gamma
[docs]class GammaVariableCutoff(Gamma):
"""Facilitate setting the cutoff distance based on user defined
atom/residue (node) radii.
Half of the cutoff distance can be thought of as the radius of a node.
This class enables setting different radii for different node types.
**Example**:
Let's think of a protein-DNA complex for which we want to use different
radius for different residue types. Let's say, for protein Cα atoms we
want to set the radius to 7.5 Å, and for nucleic acid phosphate atoms to
10 Å. We use the HhaI-DNA complex structure :file:`1mht`.
.. ipython:: python
hhai = parsePDB('1mht')
ca_p = hhai.select('(protein and name CA) or (nucleic and name P)')
ca_p.getNames()
We set the radii of atoms:
.. ipython:: python
varcutoff = GammaVariableCutoff(ca_p.getNames(), gamma=1,
default_radius=7.5, debug=False, P=10)
varcutoff.getRadii()
The above shows that for phosphate atoms radii is set to 10 Å, because
we passed the ``P=10`` argument. As for Cα atoms, the default 7.5 Å
is set as the radius (``default_radius=7.5``). You can also try this with
``debug=True`` argument to print debugging information on the screen.
We build :class:`.ANM` Hessian matrix as follows:
.. ipython:: python
anm = ANM('HhaI-DNA')
anm.buildHessian(ca_p, gamma=varcutoff, cutoff=20)
Note that we passed ``cutoff=20.0`` to the :meth:`.ANM.buildHessian`
method. This is equal to the largest possible cutoff distance (between
two phosphate atoms) for this system, and ensures that all of the
potential interactions are evaluated.
For pairs of atoms for which the actual distance is larger than the
effective cutoff, the :meth:`.GammaVariableCutoff.gamma` method returns
``0``. This annuls the interaction between those atom pairs."""
def __init__(self, identifiers, gamma=1., default_radius=7.5, **kwargs):
"""Set the radii of atoms.
:arg identifiers: List of atom names or types, or residue names.
:type identifiers: list or :class:`numpy.ndarray`
:arg gamma: Uniform force constant value. Default is 1.0.
:type gamma: float
:arg default_radius: Default radius for atoms whose radii is not set
as a keyword argument. Default is 7.5
:type default_radius: float
Keywords in keyword arguments must match those in *atom_identifiers*.
Values of keyword arguments must be :class:`float`."""
self._identifiers = identifiers
radii = np.ones(len(identifiers)) * default_radius
for i, identifier in enumerate(identifiers):
radii[i] = kwargs.get(identifier, default_radius)
self._radii = radii
self._gamma = float(gamma)
self._debug = bool(kwargs.get('debug', False))
[docs] def getRadii(self):
"""Returns a copy of radii array."""
return self._radii.copy()
[docs] def getGamma(self):
"""Returns the uniform force constant value."""
return self._gamma
[docs] def gamma(self, dist2, i, j):
"""Returns force constant."""
cutoff = (self._radii[i] + self._radii[j])
cutoff2 = cutoff ** 2
if dist2 < cutoff2:
gamma = self._gamma
else:
gamma = 0
if self._debug:
print(' '.join([self._identifiers[i] + '_' + str(i), '--',
self._identifiers[j] + '_' + str(j),
'effective cutoff:', str(cutoff), 'distance:',
str(dist2**0.5), 'gamma:', str(gamma)])) # PY3K: OK
return gamma
