#!/usr/bin/env python
##############################################################################
# MDTraj: A Python Library for Loading, Saving, and Manipulating
# Molecular Dynamics Trajectories.
# Copyright 2012-2014 Stanford University and the Authors
#
# Authors: Kyle A. Beauchamp
# Contributors: Robert McGibbon, TJ Lane, Osama El-Gabalawy
#
# MDTraj is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as
# published by the Free Software Foundation, either version 2.1
# of the License, or (at your option) any later version.
#
# This library is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public
# License along with MDTraj. If not, see <http://www.gnu.org/licenses/>.
#############################################################################
"""
This file contains scripts for calculating scalar (J) Couplings from backbone dihedrals.
"""
import numpy as np
from mdtraj.geometry import compute_phi
J3_HN_CB_coefficients = { # See full citations below in docstring references.
"Bax2007": dict(
phi0=+60 * np.pi / 180.0,
A=3.71,
B=-0.59,
C=0.08,
), # From Table 1. in paper
}
J3_HN_CB_uncertainties = {
# Values in [Hz]
"Bax2007": 0.22,
}
J3_HN_C_coefficients = { # See full citations below in docstring references.
"Bax2007": dict(
phi0=+180 * np.pi / 180.0,
A=4.36,
B=-1.08,
C=-0.01,
), # From Table 1. in paper
}
J3_HN_C_uncertainties = {
# Values in [Hz]
"Bax2007": 0.30,
}
J3_HN_HA_coefficients = { # See full citations below in docstring references.
"Ruterjans1999": dict(
phi0=-60 * np.pi / 180.0,
A=7.90,
B=-1.05,
C=0.65,
), # From Table 1. in paper.
"Bax2007": dict(
phi0=-60 * np.pi / 180.0,
A=8.4,
B=-1.36,
C=0.33,
), # From Table 1. in paper
"Bax1997": dict(
phi0=-60 * np.pi / 180.0,
A=7.09,
B=-1.42,
C=1.55,
), # From Table 2. in paper
}
J3_HN_HA_uncertainties = {
# Values in [Hz]
"Ruterjans1999": 0.25,
"Bax2007": 0.36,
"Bax1997": 0.39,
}
def _J3_function(phi, A, B, C, phi0):
"""Return a scalar couplings with a given choice of karplus coefficients. USES RADIANS!"""
return A * np.cos(phi + phi0) ** 2.0 + B * np.cos(phi + phi0) + C
[docs]
def compute_J3_HN_HA(traj, model="Bax2007"):
"""Calculate the scalar coupling between HN and H_alpha.
This function does not take into account periodic boundary conditions (it
will give spurious results if the three atoms which make up any angle jump
across a PBC (are not "wholed"))
Parameters
----------
traj : mdtraj.Trajectory
Trajectory to compute J3_HN_HA for
model : string, optional, default="Bax2007"
Which scalar coupling model to use. Must be one of Bax2007, Bax1999,
or Ruterjans1999
Returns
-------
indices : np.ndarray, shape=(n_phi, 4), dtype=int
Atom indices (zero-based) of the phi dihedrals
J : np.ndarray, shape=(n_frames, n_phi)
Scalar couplings (J3_HN_HA, in [Hz]) of this trajectory.
`J[k]` corresponds to the phi dihedral associated with
atoms `indices[k]`
Notes
-----
The coefficients are taken from the references below--please cite them.
References
----------
.. [1] Schmidt, J. M., Blümel, M., Löhr, F., & Rüterjans, H.
"Self-consistent 3J coupling analysis for the joint calibration
of Karplus coefficients and evaluation of torsion angles."
J. Biomol. NMR, 14, 1 1-12 (1999)
.. [2] Vögeli, B., Ying, J., Grishaev, A., & Bax, A.
"Limits on variations in protein backbone dynamics from precise
measurements of scalar couplings."
J. Am. Chem. Soc., 129(30), 9377-9385 (2007)
.. [3] Hu, J. S., & Bax, A.
"Determination of ϕ and ξ1 Angles in Proteins from 13C-13C
Three-Bond J Couplings Measured by Three-Dimensional Heteronuclear NMR.
How Planar Is the Peptide Bond?."
J. Am. Chem. Soc., 119(27), 6360-6368 (1997)
"""
indices, phi = compute_phi(traj)
if model not in J3_HN_HA_coefficients:
raise (KeyError("model must be one of %s" % J3_HN_HA_coefficients.keys()))
J = _J3_function(phi, **J3_HN_HA_coefficients[model])
return indices, J
[docs]
def compute_J3_HN_C(traj, model="Bax2007"):
"""Calculate the scalar coupling between HN and C_prime.
This function does not take into account periodic boundary conditions (it
will give spurious results if the three atoms which make up any angle jump
across a PBC (are not "wholed"))
Parameters
----------
traj : mdtraj.Trajectory
Trajectory to compute J3_HN_C for
model : string, optional, default="Bax2007"
Which scalar coupling model to use. Must be one of Bax2007
Returns
-------
indices : np.ndarray, shape=(n_phi, 4), dtype=int
Atom indices (zero-based) of the phi dihedrals
J : np.ndarray, shape=(n_frames, n_phi)
Scalar couplings (J3_HN_C, in [Hz]) of this trajectory.
`J[k]` corresponds to the phi dihedral associated with
atoms `indices[k]`
Notes
-----
The coefficients are taken from the references below--please cite them.
References
----------
.. [1] Hu, J. S., & Bax, A.
"Determination of ϕ and ξ1 Angles in Proteins from 13C-13C
Three-Bond J Couplings Measured by Three-Dimensional Heteronuclear NMR.
How Planar Is the Peptide Bond?."
J. Am. Chem. Soc., 119(27), 6360-6368 (1997)
"""
indices, phi = compute_phi(traj)
if model not in J3_HN_C_coefficients:
raise (KeyError("model must be one of %s" % J3_HN_C_coefficients.keys()))
J = _J3_function(phi, **J3_HN_C_coefficients[model])
return indices, J
[docs]
def compute_J3_HN_CB(traj, model="Bax2007"):
"""Calculate the scalar coupling between HN and C_beta.
This function does not take into account periodic boundary conditions (it
will give spurious results if the three atoms which make up any angle jump
across a PBC (are not "wholed"))
Parameters
----------
traj : mdtraj.Trajectory
Trajectory to compute J3_HN_CB for
model : string, optional, default="Bax2007"
Which scalar coupling model to use. Must be one of Bax2007
Returns
-------
indices : np.ndarray, shape=(n_phi, 4), dtype=int
Atom indices (zero-based) of the phi dihedrals
J : np.ndarray, shape=(n_frames, n_phi)
Scalar couplings (J3_HN_CB, in [Hz]) of this trajectory.
`J[k]` corresponds to the phi dihedral associated with
atoms `indices[k]`
Notes
-----
The coefficients are taken from the references below--please cite them.
References
----------
.. [1] Hu, J. S., & Bax, A.
"Determination of ϕ and ξ1 Angles in Proteins from 13C-13C
Three-Bond J Couplings Measured by Three-Dimensional Heteronuclear NMR.
How Planar Is the Peptide Bond?."
J. Am. Chem. Soc., 119(27), 6360-6368 (1997)
"""
indices, phi = compute_phi(traj)
if model not in J3_HN_CB_coefficients:
raise (KeyError("model must be one of %s" % J3_HN_CB_coefficients.keys()))
J = _J3_function(phi, **J3_HN_CB_coefficients[model])
return indices, J