def _compute_bounded_geometry(traj,
triplets,
distance_cutoff,
distance_indices,
angle_indices,
freq=0.0,
periodic=True):
"""
Returns a tuple include
(1) the mask for triplets that fulfill the distance criteria frequently enough,
(2) the actual distances calculated, and
(3) the angles between the triplets specified by angle_indices.
"""
# First we calculate the requested distances
distances = compute_distances(traj,
triplets[:, distance_indices],
periodic=periodic)
# Now we discover which triplets meet the distance cutoff often enough
prevalence = np.mean(distances < distance_cutoff, axis=0)
mask = prevalence > freq
# Update data structures to ignore anything that isn't possible anymore
triplets = triplets.compress(mask, axis=0)
distances = distances.compress(mask, axis=1)
'''
# Calculate angles using the law of cosines
If angle_indices = [0,1,2],
abc_pairs = [(0, 1), (1, 2), (2, 0)].
'''
abc_pairs = zip(angle_indices, angle_indices[1:] + angle_indices[:1])
abc_distances = []
# Calculate distances (if necessary)
for abc_pair in abc_pairs:
if set(abc_pair) == set(distance_indices):
abc_distances.append(distances)
else:
abc_distances.append(
compute_distances(traj,
triplets[:, abc_pair],
periodic=periodic))
# Law of cosines calculation
a, b, c = abc_distances
cosines = (a**2 + b**2 - c**2) / (2 * a * b)
np.clip(cosines, -1, 1, out=cosines) # avoid NaN error
angles = np.arccos(cosines)
return mask, distances, angles
def _compute_bounded_geometry(traj, triplets, distance_cutoff, distance_indices,
angle_indices, freq=0.0, periodic=True):
"""
Returns a tuple include (1) the mask for triplets that fulfill the distance
criteria frequently enough, (2) the actual distances calculated, and (3) the
angles between the triplets specified by angle_indices.
"""
# First we calculate the requested distances
distances = compute_distances(traj, triplets[:, distance_indices], periodic=periodic)
# Now we discover which triplets meet the distance cutoff often enough
prevalence = np.mean(distances < distance_cutoff, axis=0)
mask = prevalence > freq
# Update data structures to ignore anything that isn't possible anymore
triplets = triplets.compress(mask, axis=0)
distances = distances.compress(mask, axis=1)
# Calculate angles using the law of cosines
abc_pairs = zip(angle_indices, angle_indices[1:] + angle_indices[:1])
abc_distances = []
# Calculate distances (if necessary)
for abc_pair in abc_pairs:
if set(abc_pair) == set(distance_indices):
abc_distances.append(distances)
else:
abc_distances.append(compute_distances(traj, triplets[:, abc_pair],
periodic=periodic))
# Law of cosines calculation
a, b, c = abc_distances
cosines = (a ** 2 + b ** 2 - c ** 2) / (2 * a * b)
np.clip(cosines, -1, 1, out=cosines) # avoid NaN error
angles = np.arccos(cosines)
return mask, distances, angles
def optimized_baker_hubbard(f,
top,
angle_triplets,
distance_pairs,
beg_ind,
traj,
freq=0.1,
exclude_water=True,
periodic=True):
print("Start optimized_baker_hubbard()")
# Cutoff criteria: these could be exposed as function arguments, or
# modified if there are better definitions than the this one based only
# on distances and angles
# distance_cutoff = 0.25 # nanometers
# angle_cutoff = 2.0*np.pi/3.0 # radians
distance_cutoff = 0.30 # nanometers
angle_cutoff = 11.0 * np.pi / 18.0 # radians
if top is None:
raise ValueError('baker_hubbard requires that traj contain topology '
'information')
tic = time.clock()
angles = compute_angles(traj, angle_triplets, periodic=periodic)
print("angles", angles, "with nFrames: ", len(angles), " for numAngles ",
len(angles[0]))
distances = compute_distances(traj, distance_pairs, periodic=periodic)
print("distances", distances, "with nFrames: ", len(distances),
" for numDistances ", len(distances[0]))
mask = np.logical_and(distances < distance_cutoff, angles > angle_cutoff)
del angles
del distances
nChunkFrames = computeAndWriteHBondAllFrames(f, beg_ind, top, mask,
angle_triplets)
toc = time.clock()
chunkComputingTime = toc - tic
print("Time to extract and write all hbFramePairs for beg_ind " +
str(beg_ind) + " is: " + str(chunkComputingTime))
return nChunkFrames, chunkComputingTime
def wernet_nilsson(traj, exclude_water=True, periodic=True):
"""Identify hydrogen bonds based on cutoffs for the Donor-H...Acceptor
distance and angle according to the criterion outlined in [1].
As opposed to Baker-Hubbard, this is a "cone" criterion where the
distance cutoff depends on the angle.
The criterion employed is :math:`r_\\text{DA} < 3.3 A - 0.00044*\\delta_{HDA}*\\delta_{HDA}`,
where :math:`r_\\text{DA}` is the distance between donor and acceptor heavy atoms,
and :math:`\\delta_{HDA}` is the angle made by the hydrogen atom, donor, and acceptor atoms,
measured in degrees (zero in the case of a perfectly straight bond: D-H ... A).
When donor the donor is 'O' and the acceptor is 'O', this corresponds to
the definition established in [1]_. The donors considered by this method
are NH and OH, and the acceptors considered are O and N. In the paper the only
donor considered is OH.
Parameters
----------
traj : md.Trajectory
An mdtraj trajectory. It must contain topology information.
exclude_water : bool, default=True
Exclude solvent molecules from consideration.
periodic : bool, default=True
Set to True to calculate displacements and angles across periodic box boundaries.
Returns
-------
hbonds : list, len=n_frames
A list containing the atom indices involved in each of the identified
hydrogen bonds at each frame. Each element in the list is an array
where each row contains three integer indices, `(d_i, h_i, a_i)`,
such that `d_i` is the index of the donor atom, `h_i` the index
of the hydrogen atom, and `a_i` the index of the acceptor atom involved
in a hydrogen bond which occurs in that frame.
Notes
-----
Each hydrogen bond is distinguished for the purpose of this function by the
indices of the donor, hydrogen, and acceptor atoms. This means that, for
example, when an ARG sidechain makes a hydrogen bond with its NH2 group,
you might see what appear like double counting of the h-bonds, since the
hydrogen bond formed via the H_1 and H_2 are counted separately, despite
their "chemical indistinguishably"
Examples
--------
>>> md.wernet_nilsson(t)
array([[ 0, 10, 8],
[ 0, 11, 7],
[ 69, 73, 54],
[ 76, 82, 65],
[119, 131, 89],
[140, 148, 265],
[166, 177, 122],
[181, 188, 231]])
>>> label = lambda hbond : '%s -- %s' % (t.topology.atom(hbond[0]), t.topology.atom(hbond[2]))
>>> for hbond in hbonds:
>>> print label(hbond)
GLU1-N -- GLU1-OE2
GLU1-N -- GLU1-OE1
GLY6-N -- SER4-O
CYS7-N -- GLY5-O
TYR11-N -- VAL8-O
MET12-N -- LYS20-O
See Also
--------
baker_hubbard, kabsch_sander
References
----------
.. [1] Wernet, Ph., L.G.M. Pettersson, and A. Nilsson, et al.
"The Structure of the First Coordination Shell in Liquid Water." (2004)
Science 304, 995-999.
"""
distance_cutoff = 0.33
angle_const = 0.000044
angle_cutoff = 45
if traj.topology is None:
raise ValueError('wernet_nilsson requires that traj contain topology '
'information')
def get_donors(e0, e1):
elems = set((e0, e1))
bonditer = traj.topology.bonds
atoms = [(b[0], b[1]) for b in bonditer
if set((b[0].element.symbol, b[1].element.symbol)) == elems]
indices = []
for a0, a1 in atoms:
if exclude_water and (a0.residue.name == 'HOH'
or a1.residue.name == 'HOH'):
continue
pair = (a0.index, a1.index)
# make sure to get the pair in the right order, so that the index
# for e0 comes before e1
if a0.element.symbol == e1:
pair = pair[::-1]
indices.append(pair)
return indices
nh_donors = get_donors('N', 'H')
oh_donors = get_donors('O', 'H')
xh_donors = np.array(nh_donors + oh_donors)
if len(xh_donors) == 0:
# if there are no hydrogens or protein in the trajectory, we get
# no possible pairs and return nothing
return [np.zeros((0, 3), dtype=int) for _ in range(traj.n_frames)]
if not exclude_water:
acceptors = [
a.index for a in traj.topology.atoms
if a.element.symbol == 'O' or a.element.symbol == 'N'
]
else:
acceptors = [
a.index for a in traj.topology.atoms
if (a.element.symbol == 'O' and a.residue.name != 'HOH')
or a.element.symbol == 'N'
]
# This is used to compute the angles
angle_triplets = np.array([(e[0][1], e[0][0], e[1])
for e in product(xh_donors, acceptors)
if e[0][0] != e[1]])
distance_pairs = angle_triplets[:, [0, 2]] # possible O..acceptor pairs
angles = compute_angles(traj, angle_triplets,
periodic=periodic) * 180.0 / np.pi # degrees
distances = compute_distances(traj,
distance_pairs,
periodic=periodic,
opt=True)
cutoffs = distance_cutoff - angle_const * angles**2
mask = np.logical_and(distances < cutoffs, angles < angle_cutoff)
# The triplets that are returned are O-H ... O, different
# from what's used to compute the angles.
angle_triplets2 = angle_triplets[:, [1, 0, 2]]
return [angle_triplets2[i] for i in mask]
def baker_hubbard(traj, freq=0.1, exclude_water=True, periodic=True):
"""Identify hydrogen bonds based on cutoffs for the Donor-H...Acceptor
distance and angle.
The criterion employed is :math:`\\theta > 120` and
:math:`r_\\text{H...Acceptor} < 2.5 A`.
When donor the donor is 'N' and the acceptor is 'O', this corresponds to
the definition established in [1]_. The donors considered by this method
are NH and OH, and the acceptors considered are O and N.
Parameters
----------
traj : md.Trajectory
An mdtraj trajectory. It must contain topology information.
freq : float, default=0.1
Return only hydrogen bonds that occur in greater this fraction of the
frames in the trajectory.
exclude_water : bool, default=True
Exclude solvent molecules from consideration
periodic : bool, default=True
Set to True to calculate displacements and angles across periodic box boundaries.
Returns
-------
hbonds : np.array, shape=[n_hbonds, 3], dtype=int
An array containing the indices atoms involved in each of the identified
hydrogen bonds. Each row contains three integer indices, `(d_i, h_i,
a_i)`, such that `d_i` is the index of the donor atom, `h_i` the index
of the hydrogen atom, and `a_i` the index of the acceptor atom involved
in a hydrogen bond which occurs (according to the definition above) in
proportion greater than `freq` of the trajectory.
Notes
-----
Each hydrogen bond is distinguished for the purpose of this function by the
indices of the donor, hydrogen, and acceptor atoms. This means that, for
example, when an ARG sidechain makes a hydrogen bond with its NH2 group,
you might see what appear like double counting of the h-bonds, since the
hydrogen bond formed via the H_1 and H_2 are counted separately, despite
their "chemical indistinguishably"
Examples
--------
>>> md.baker_hubbard(t)
array([[ 0, 10, 8],
[ 0, 11, 7],
[ 69, 73, 54],
[ 76, 82, 65],
[119, 131, 89],
[140, 148, 265],
[166, 177, 122],
[181, 188, 231]])
>>> label = lambda hbond : '%s -- %s' % (t.topology.atom(hbond[0]), t.topology.atom(hbond[2]))
>>> for hbond in hbonds:
>>> print label(hbond)
GLU1-N -- GLU1-OE2
GLU1-N -- GLU1-OE1
GLY6-N -- SER4-O
CYS7-N -- GLY5-O
TYR11-N -- VAL8-O
MET12-N -- LYS20-O
See Also
--------
kabsch_sander
References
----------
.. [1] Baker, E. N., and R. E. Hubbard. "Hydrogen bonding in globular
proteins." Progress in Biophysics and Molecular Biology
44.2 (1984): 97-179.
"""
# Cutoff criteria: these could be exposed as function arguments, or
# modified if there are better definitions than the this one based only
# on distances and angles
distance_cutoff = 0.25 # nanometers
angle_cutoff = 2.0 * np.pi / 3.0 # radians
if traj.topology is None:
raise ValueError('baker_hubbard requires that traj contain topology '
'information')
def get_donors(e0, e1):
elems = set((e0, e1))
bonditer = traj.topology.bonds
atoms = [(b[0], b[1]) for b in bonditer
if set((b[0].element.symbol, b[1].element.symbol)) == elems]
indices = []
for a0, a1 in atoms:
if exclude_water and (a0.residue.name == 'HOH'
or a1.residue.name == 'HOH'):
continue
pair = (a0.index, a1.index)
# make sure to get the pair in the right order, so that the index
# for e0 comes before e1
if a0.element.symbol == e1:
pair = pair[::-1]
indices.append(pair)
return indices
nh_donors = get_donors('N', 'H')
oh_donors = get_donors('O', 'H')
xh_donors = np.concatenate((nh_donors, oh_donors))
if len(xh_donors) == 0:
# if there are no hydrogens or protein in the trajectory, we get
# no possible pairs and return nothing
return np.zeros((0, 3), dtype=int)
if not exclude_water:
acceptors = [
a.index for a in traj.topology.atoms
if a.element.symbol == 'O' or a.element.symbol == 'N'
]
else:
acceptors = [
a.index for a in traj.topology.atoms
if (a.element.symbol == 'O' and a.residue.name != 'HOH')
or a.element.symbol == 'N'
]
angle_triplets = np.array([(e[0][0], e[0][1], e[1])
for e in product(xh_donors, acceptors)])
distance_pairs = angle_triplets[:, [1, 2]] # possible H..acceptor pairs
angles = compute_angles(traj, angle_triplets, periodic=periodic)
distances = compute_distances(traj, distance_pairs, periodic=periodic)
mask = np.logical_and(distances < distance_cutoff, angles > angle_cutoff)
# frequency of occurance of each hydrogen bond in the trajectory
occurance = np.sum(mask, axis=0).astype(np.double) / traj.n_frames
return angle_triplets[occurance > freq]
def baker_hubbard(traj, freq=0.1, exclude_water=True):
"""Identify hydrogen bonds based on cutoffs for the Donor-H...Acceptor
distance and angle.
The criterion employed is :math:`\\theta > 120` and
:math:`r_\\text{H...Acceptor} < 2.5 A`.
When donor the donor is 'N' and the acceptor is 'O', this corresponds to
the definition established in [1]_. The donors considered by this method
are NH and OH, and the acceptors considered are O.
Parameters
----------
traj : md.Trajectory
An mdtraj trajectory. It must contain topology information.
freq : float, default=0.1
Return only hydrogen bonds that occur in greater this fraction of the
frames in the trajectory.
exclude_water : bool, default=True
Exclude solvent molecules from consideration
Notes
-----
.. [1] Baker, E. N., and R. E. Hubbard. "Hydrogen bonding in globular proteins." Progress in Biophysics and Molecular Biology 44.2 (1984): 97-179.
Examples
--------
>>> md.baker_hubbard(t) # doctest: +SKIP
array([[ 0, 10, 8],
[ 0, 11, 7],
[ 69, 73, 54],
[ 76, 82, 65],
[119, 131, 89],
[140, 148, 265],
[166, 177, 122],
[181, 188, 231]])
>>> label = lambda hbond : '%s -- %s' % (t.topology.atom(hbond[0]), t.topology.atom(hbond[2])) # doctest: +SKIP
>>> for hbond in hbonds: # doctest: +SKIP
>>> print label(hbond) # doctest: +SKIP
GLU1-N -- GLU1-OE2
GLU1-N -- GLU1-OE1
GLY6-N -- SER4-O
CYS7-N -- GLY5-O
TYR11-N -- VAL8-O
MET12-N -- LYS20-O
See Also
--------
kabsch_sander
Returns
-------
hbonds : np.array, shape=[n_hbonds, 3], dtype=int
An array containing the indices atoms involved in each of the identified
hydrogen bonds. Each row contains three integer indices, `(d_i, h_i,
a_i)`, such that `d_i` is the index of the donor atom, `h_i` the index
of the hydrogen atom, and `a_i` the index of the acceptor atom involved
in a hydrogen bond which occurs (according to the definition above) in
proportion greater than `freq` of the trajectory.
"""
# Cutoff criteria: these could be exposed as function arguments, or
# modified if there are better definitions than the this one based only
# on distances and angles
distance_cutoff = 0.25 # nanometers
angle_cutoff = 2.0 * np.pi / 3.0 # radians
if traj.topology is None:
raise ValueError('baker_hubbard requires that traj contain topology '
'information')
def get_donors(e0, e1):
elems = set((e0, e1))
bonditer = traj.topology.bonds
atoms = [(b[0], b[1]) for b in bonditer if set((b[0].element.symbol, b[1].element.symbol)) == elems]
indices = []
for a0, a1 in atoms:
if exclude_water and (a0.residue.name == 'HOH' or a1.residue.name == 'HOH'):
continue
pair = (a0.index, a1.index)
# make sure to get the pair in the right order, so that the index
# for e0 comes before e1
if a0.element.symbol == e1:
pair = pair[::-1]
indices.append(pair)
return indices
nh_donors = get_donors('N', 'H')
oh_donors = get_donors('O', 'H')
xh_donors = np.concatenate((nh_donors, oh_donors))
if not exclude_water:
acceptors = [a.index for a in traj.topology.atoms if a.element.symbol == 'O']
else:
acceptors = [a.index for a in traj.topology.atoms if a.element.symbol == 'O' and a.residue.name != 'HOH']
angle_triplets = np.array([(e[0][0], e[0][1], e[1]) for e in product(xh_donors, acceptors)])
distance_pairs = angle_triplets[:, [1,2]] # possible H..acceptor pairs
angles = compute_angles(traj, angle_triplets)
distances = compute_distances(traj, distance_pairs, periodic=False)
mask = np.logical_and(distances < distance_cutoff, angles > angle_cutoff)
# frequency of occurance of each hydrogen bond in the trajectory
occurance = np.sum(mask, axis=0).astype(np.double) / traj.n_frames
return angle_triplets[occurance > freq]
def wernet_nilsson(traj, exclude_water=True, periodic=True):
"""Identify hydrogen bonds based on cutoffs for the Donor-H...Acceptor
distance and angle according to the criterion outlined in [1].
As opposed to Baker-Hubbard, this is a "cone" criterion where the
distance cutoff depends on the angle.
The criterion employed is :math:`r_\\text{DA} < 3.3 A - 0.00044*\\delta_{HDA}*\\delta_{HDA}`,
where :math:`r_\\text{DA}` is the distance between donor and acceptor heavy atoms,
and :math:`\\delta_{HDA}` is the angle made by the hydrogen atom, donor, and acceptor atoms,
measured in degrees (zero in the case of a perfectly straight bond: D-H ... A).
When donor the donor is 'O' and the acceptor is 'O', this corresponds to
the definition established in [1]_. The donors considered by this method
are NH and OH, and the acceptors considered are O and N. In the paper the only
donor considered is OH.
Parameters
----------
traj : md.Trajectory
An mdtraj trajectory. It must contain topology information.
exclude_water : bool, default=True
Exclude solvent molecules from consideration.
periodic : bool, default=True
Set to True to calculate displacements and angles across periodic box boundaries.
Returns
-------
hbonds : list, len=n_frames
A list containing the atom indices involved in each of the identified
hydrogen bonds at each frame. Each element in the list is an array
where each row contains three integer indices, `(d_i, h_i, a_i)`,
such that `d_i` is the index of the donor atom, `h_i` the index
of the hydrogen atom, and `a_i` the index of the acceptor atom involved
in a hydrogen bond which occurs in that frame.
Notes
-----
Each hydrogen bond is distinguished for the purpose of this function by the
indices of the donor, hydrogen, and acceptor atoms. This means that, for
example, when an ARG sidechain makes a hydrogen bond with its NH2 group,
you might see what appear like double counting of the h-bonds, since the
hydrogen bond formed via the H_1 and H_2 are counted separately, despite
their "chemical indistinguishably"
Examples
--------
>>> md.wernet_nilsson(t)
array([[ 0, 10, 8],
[ 0, 11, 7],
[ 69, 73, 54],
[ 76, 82, 65],
[119, 131, 89],
[140, 148, 265],
[166, 177, 122],
[181, 188, 231]])
>>> label = lambda hbond : '%s -- %s' % (t.topology.atom(hbond[0]), t.topology.atom(hbond[2]))
>>> for hbond in hbonds:
>>> print label(hbond)
GLU1-N -- GLU1-OE2
GLU1-N -- GLU1-OE1
GLY6-N -- SER4-O
CYS7-N -- GLY5-O
TYR11-N -- VAL8-O
MET12-N -- LYS20-O
See Also
--------
baker_hubbard, kabsch_sander
References
----------
.. [1] Wernet, Ph., L.G.M. Pettersson, and A. Nilsson, et al.
"The Structure of the First Coordination Shell in Liquid Water." (2004)
Science 304, 995-999.
"""
distance_cutoff = 0.33
angle_const = 0.000044
angle_cutoff = 45
if traj.topology is None:
raise ValueError('wernet_nilsson requires that traj contain topology '
'information')
def get_donors(e0, e1):
elems = set((e0, e1))
bonditer = traj.topology.bonds
atoms = [(b[0], b[1]) for b in bonditer if set((b[0].element.symbol, b[1].element.symbol)) == elems]
indices = []
for a0, a1 in atoms:
if exclude_water and (a0.residue.name == 'HOH' or a1.residue.name == 'HOH'):
continue
pair = (a0.index, a1.index)
# make sure to get the pair in the right order, so that the index
# for e0 comes before e1
if a0.element.symbol == e1:
pair = pair[::-1]
indices.append(pair)
return indices
nh_donors = get_donors('N', 'H')
oh_donors = get_donors('O', 'H')
xh_donors = np.array(nh_donors + oh_donors)
if len(xh_donors) == 0:
# if there are no hydrogens or protein in the trajectory, we get
# no possible pairs and return nothing
return [np.zeros((0, 3), dtype=int) for _ in range(traj.n_frames)]
if not exclude_water:
acceptors = [a.index for a in traj.topology.atoms if a.element.symbol == 'O' or a.element.symbol == 'N']
else:
acceptors = [a.index for a in traj.topology.atoms if (a.element.symbol == 'O' and a.residue.name != 'HOH') or a.element.symbol == 'N']
# This is used to compute the angles
angle_triplets = np.array([(e[0][1], e[0][0], e[1]) for e in product(xh_donors, acceptors) if e[0][0] != e[1]])
distance_pairs = angle_triplets[:, [0,2]] # possible O..acceptor pairs
angles = compute_angles(traj, angle_triplets, periodic=periodic) * 180.0 / np.pi # degrees
distances = compute_distances(traj, distance_pairs, periodic=periodic, opt=True)
cutoffs = distance_cutoff - angle_const * angles ** 2
mask = np.logical_and(distances < cutoffs, angles < angle_cutoff)
# The triplets that are returned are O-H ... O, different
# from what's used to compute the angles.
angle_triplets2 = angle_triplets[:, [1,0,2]]
return [angle_triplets2[i] for i in mask]
def baker_hubbard(traj, freq=0.1, exclude_water=True, periodic=True, get_list=False):
"""Identify hydrogen bonds based on cutoffs for the Donor-H...Acceptor
distance and angle.
The criterion employed is :math:`\\theta > 120` and
:math:`r_\\text{H...Acceptor} < 2.5 A`.
When donor the donor is 'N' and the acceptor is 'O', this corresponds to
the definition established in [1]_. The donors considered by this method
are NH and OH, and the acceptors considered are O and N.
Parameters
----------
traj : md.Trajectory
An mdtraj trajectory. It must contain topology information.
freq : float, default=0.1
Return only hydrogen bonds that occur in greater this fraction of the
frames in the trajectory.
exclude_water : bool, default=True
Exclude solvent molecules from consideration
periodic : bool, default=True
Set to True to calculate displacements and angles across periodic box boundaries.
get_list : bool, default=False
Set to True to obtain a list of hydrogen bonds that appear in each frame
(overrides the freq parameter).
Returns
-------
hbonds : np.array, shape=[n_hbonds, 3], dtype=int
(The default behavior if get_list == False)
An array containing the indices atoms involved in each of the identified
hydrogen bonds. Each row contains three integer indices, `(d_i, h_i,
a_i)`, such that `d_i` is the index of the donor atom, `h_i` the index
of the hydrogen atom, and `a_i` the index of the acceptor atom involved
in a hydrogen bond which occurs (according to the definition above) in
proportion greater than `freq` of the trajectory.
hbonds : list, len=n_frames
(The behavior if get_list = True)
A list containing the atom indices involved in each of the identified
hydrogen bonds at each frame. Each element in the list is an array
where each row contains three integer indices, `(d_i, h_i, a_i)`,
such that `d_i` is the index of the donor atom, `h_i` the index
of the hydrogen atom, and `a_i` the index of the acceptor atom involved
in a hydrogen bond which occurs in that frame.
Notes
-----
Each hydrogen bond is distinguished for the purpose of this function by the
indices of the donor, hydrogen, and acceptor atoms. This means that, for
example, when an ARG sidechain makes a hydrogen bond with its NH2 group,
you might see what appear like double counting of the h-bonds, since the
hydrogen bond formed via the H_1 and H_2 are counted separately, despite
their "chemical indistinguishably"
Examples
--------
>>> md.baker_hubbard(t)
array([[ 0, 10, 8],
[ 0, 11, 7],
[ 69, 73, 54],
[ 76, 82, 65],
[119, 131, 89],
[140, 148, 265],
[166, 177, 122],
[181, 188, 231]])
>>> label = lambda hbond : '%s -- %s' % (t.topology.atom(hbond[0]), t.topology.atom(hbond[2]))
>>> for hbond in hbonds:
>>> print label(hbond)
GLU1-N -- GLU1-OE2
GLU1-N -- GLU1-OE1
GLY6-N -- SER4-O
CYS7-N -- GLY5-O
TYR11-N -- VAL8-O
MET12-N -- LYS20-O
See Also
--------
kabsch_sander
References
----------
.. [1] Baker, E. N., and R. E. Hubbard. "Hydrogen bonding in globular
proteins." Progress in Biophysics and Molecular Biology
44.2 (1984): 97-179.
"""
# Cutoff criteria: these could be exposed as function arguments, or
# modified if there are better definitions than the this one based only
# on distances and angles
distance_cutoff = 0.25 # nanometers
angle_cutoff = 2.0 * np.pi / 3.0 # radians
if traj.topology is None:
raise ValueError('baker_hubbard requires that traj contain topology '
'information')
def get_donors(e0, e1):
elems = set((e0, e1))
bonditer = traj.topology.bonds
atoms = [(b[0], b[1]) for b in bonditer if set((b[0].element.symbol, b[1].element.symbol)) == elems]
indices = []
for a0, a1 in atoms:
if exclude_water and (a0.residue.name == 'HOH' or a1.residue.name == 'HOH'):
continue
pair = (a0.index, a1.index)
# make sure to get the pair in the right order, so that the index
# for e0 comes before e1
if a0.element.symbol == e1:
pair = pair[::-1]
indices.append(pair)
return indices
nh_donors = get_donors('N', 'H')
oh_donors = get_donors('O', 'H')
xh_donors = np.array(nh_donors + oh_donors)
if len(xh_donors) == 0:
# if there are no hydrogens or protein in the trajectory, we get
# no possible pairs and return nothing
return np.zeros((0, 3), dtype=int)
if not exclude_water:
acceptors = [a.index for a in traj.topology.atoms if a.element.symbol == 'O' or a.element.symbol == 'N']
else:
acceptors = [a.index for a in traj.topology.atoms if (a.element.symbol == 'O' and a.residue.name != 'HOH') or a.element.symbol == 'N']
angle_triplets = np.array([(e[0][0], e[0][1], e[1]) for e in product(xh_donors, acceptors)])
distance_pairs = angle_triplets[:, [1,2]] # possible H..acceptor pairs
angles = compute_angles(traj, angle_triplets, periodic=periodic)
distances = compute_distances(traj, distance_pairs, periodic=periodic)
mask = np.logical_and(distances < distance_cutoff, angles > angle_cutoff)
# frequency of occurance of each hydrogen bond in the trajectory
occurance = np.sum(mask, axis=0).astype(np.double) / traj.n_frames
if get_list:
return [angle_triplets[i] for i in mask]
else:
return angle_triplets[occurance > freq]