def kabsch_sander(traj):
"""Compute the Kabsch-Sander hydrogen bond energy between each pair
of residues in every frame.
Hydrogen bonds are defined using an electrostatic definition, assuming
partial charges of -0.42 e and +0.20 e to the carbonyl oxygen and amide
hydrogen respectively, their opposites assigned to the carbonyl carbon
and amide nitrogen. A hydrogen bond is identified if E in the following
equation is less than -0.5 kcal/mol:
.. math::
E = 0.42 \cdot 0.2 \cdot 33.2 kcal/(mol \cdot nm) * \\
(1/r_{ON} + 1/r_{CH} - 1/r_{OH} - 1/r_{CN})
Parameters
----------
traj : md.Trajectory
An mdtraj trajectory. It must contain topology information.
Returns
-------
matrices : list of scipy.sparse.csr_matrix
The return value is a list of length equal to the number of frames
in the trajectory. Each element is an n_residues x n_residues sparse
matrix, where the existence of an entry at row `i`, column `j` with value
`x` means that there exists a hydrogen bond between a backbone CO
group at residue `i` with a backbone NH group at residue `j` whose
Kabsch-Sander energy is less than -0.5 kcal/mol (the threshold for
existence of the "bond"). The exact value of the energy is given by the
value `x`.
See Also
--------
wernet_nilsson, baker_hubbard
References
----------
.. [1] Kabsch W, Sander C (1983). "Dictionary of protein secondary structure: pattern recognition of hydrogen-bonded and geometrical features". Biopolymers 22 (12): 2577-637. dio:10.1002/bip.360221211
"""
if traj.topology is None:
raise ValueError('kabsch_sander requires topology')
import scipy.sparse
xyz, nco_indices, ca_indices, proline_indices = _prep_kabsch_sander_arrays(
traj)
n_residues = len(ca_indices)
hbonds = np.empty((xyz.shape[0], n_residues, 2), np.int32)
henergies = np.empty((xyz.shape[0], n_residues, 2), np.float32)
hbonds.fill(-1)
henergies.fill(np.nan)
_geometry._kabsch_sander(xyz, nco_indices, ca_indices, proline_indices,
hbonds, henergies)
# The C code returns its info in a pretty inconvenient format.
# Let's change it to a list of scipy CSR matrices.
matrices = []
hbonds_mask = (hbonds != -1)
for i in range(xyz.shape[0]):
# appologies for this cryptic code -- we need to deal with the low
# level aspects of the csr matrix format.
hbonds_frame = hbonds[i]
mask = hbonds_mask[i]
henergies_frame = henergies[i]
indptr = np.zeros(n_residues + 1, np.int32)
indptr[1:] = np.cumsum(mask.sum(axis=1))
indices = hbonds_frame[mask].flatten()
data = henergies_frame[mask].flatten()
matrices.append(
scipy.sparse.csr_matrix((data, indices, indptr),
shape=(n_residues, n_residues)).T)
return matrices
def kabsch_sander(traj):
"""Compute the Kabsch-Sander hydrogen bond energy between each pair
of residues in every frame.
Hydrogen bonds are defined using an electrostatic definition, assuming
partial charges of -0.42 e and +0.20 e to the carbonyl oxygen and amide
hydrogen respectively, their opposites assigned to the carbonyl carbon
and amide nitrogen. A hydrogen bond is identified if E in the following
equation is less than -0.5 kcal/mol:
.. math::
E = 0.42 \cdot 0.2 \cdot 33.2 kcal/(mol \cdot nm) * \\
(1/r_{ON} + 1/r_{CH} - 1/r_{OH} - 1/r_{CN})
Parameters
----------
traj : md.Trajectory
An mdtraj trajectory. It must contain topology information.
Returns
-------
matrices : list of scipy.sparse.csr_matrix
The return value is a list of length equal to the number of frames
in the trajectory. Each element is an n_residues x n_residues sparse
matrix, where the existence of an entry at row `i`, column `j` with value
`x` means that there exists a hydrogen bond between a backbone CO
group at residue `i` with a backbone NH group at residue `j` whose
Kabsch-Sander energy is less than -0.5 kcal/mol (the threshold for
existence of the "bond"). The exact value of the energy is given by the
value `x`.
See Also
--------
baker_hubbard
References
----------
.. [1] Kabsch W, Sander C (1983). "Dictionary of protein secondary structure: pattern recognition of hydrogen-bonded and geometrical features". Biopolymers 22 (12): 2577-637. dio:10.1002/bip.360221211
"""
if traj.topology is None:
raise ValueError('kabsch_sander requires topology')
import scipy.sparse
xyz = ensure_type(traj.xyz, dtype=np.float32, ndim=3, name='traj.xyz',
shape=(None, None, 3), warn_on_cast=False)
ca_indices, nco_indices = [], []
for residue in traj.topology.residues:
if residue.name == 'PRO':
ca_indices.append(-1)
else:
ca_indices.append([a.index for a in residue.atoms if a.name == 'CA'][0])
n = [a.index for a in residue.atoms if a.name == 'N'][0]
c = [a.index for a in residue.atoms if a.name == 'C'][0]
o = [a.index for a in residue.atoms if a.name == 'O'][0]
nco_indices.append([n, c, o])
nco_indices = np.array(nco_indices, np.int32)
ca_indices = np.array(ca_indices, np.int32)
n_residues = len(ca_indices)
hbonds = np.empty((xyz.shape[0], n_residues, 2), np.int32)
henergies = np.empty((xyz.shape[0], n_residues, 2), np.float32)
hbonds.fill(-1)
henergies.fill(np.nan)
_geometry._kabsch_sander(xyz, nco_indices, ca_indices, hbonds, henergies)
# The C code returns its info in a pretty inconvenient format.
# Let's change it to a list of scipy CSR matrices.
matrices = []
hbonds_mask = (hbonds != -1)
for i in range(xyz.shape[0]):
# appologies for this cryptic code -- we need to deal with the low
# level aspects of the csr matrix format.
hbonds_frame = hbonds[i]
mask = hbonds_mask[i]
henergies_frame = henergies[i]
indptr = np.zeros(n_residues + 1, np.int32)
indptr[1:] = np.cumsum(mask.sum(axis=1))
indices = hbonds_frame[mask].flatten()
data = henergies_frame[mask].flatten()
matrices.append(scipy.sparse.csr_matrix((data, indices, indptr), shape=(n_residues, n_residues)))
return matrices