Source code for MDAnalysis.analysis.nuclinfo

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# 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.
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# 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
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"""
Nucleic acid analysis --- :mod:`MDAnalysis.analysis.nuclinfo`
=============================================================

:Author: Elizabeth Denning
:Year: 2011
:Copyright: GNU Public License v3

The module provides functions to analyze nuclic acid structures, in
particular

- backbone dihedrals,
- chi dihedrals,
- AS or CP phase angles,
- Watson-Crick N1-N3 distances, C2-O2 distances, N6-O4 distances, O6-N4 distances.

For applications of this kind of analysis see [Denning2011]_ and [Denning2012]_.

All functions take a :class:`~MDAnalysis.core.universe.Universe` as an
argument together with further parameters that specify the base or bases in
question. Angles are in degrees. The functions use standard CHARMM names for
nucleic acids and atom names.


.. rubric:: References

.. [Denning2011] E.J. Denning, U.D. Priyakumar, L. Nilsson, and A.D. Mackerell, Jr. Impact of
              2'-hydroxyl sampling on the conformational properties of RNA: update of the
              CHARMM all-atom additive force field for RNA. *J. Comput. Chem.* 32 (2011),
              1929--1943. doi: `10.1002/jcc.21777`_

.. [Denning2012] E.J. Denning and A.D. MacKerell, Jr. Intrinsic Contribution of the 2'-Hydroxyl to
              RNA Conformational Heterogeneity. *J. Am. Chem. Soc.* 134 (2012), 2800--2806.
              doi: `10.1021/ja211328g`_


.. _`10.1002/jcc.21777`: http://dx.doi.org/10.1002/jcc.21777
.. _`10.1021/ja211328g`: http://dx.doi.org/10.1021/ja211328g


Distances
---------

.. autofunction:: wc_pair

.. autofunction:: minor_pair

.. autofunction:: major_pair


Phases
------

.. autofunction:: phase_cp

.. autofunction:: phase_as


Dihedral angles
---------------

.. autofunction:: tors

.. autofunction:: tors_alpha

.. autofunction:: tors_beta

.. autofunction:: tors_gamma

.. autofunction:: tors_delta

.. autofunction:: tors_eps

.. autofunction:: tors_zeta

.. autofunction:: tors_chi

.. autofunction:: hydroxyl

.. autofunction:: pseudo_dihe_baseflip

"""
import numpy as np
from math import pi, sin, cos, atan2, sqrt, pow

from MDAnalysis.lib import mdamath


[docs]def wc_pair(universe, i, bp, seg1="SYSTEM", seg2="SYSTEM"): """Watson-Crick basepair distance for residue `i` with residue `bp`. The distance of the nitrogen atoms in a Watson-Crick hydrogen bond is computed. Parameters ---------- universe : Universe :class:`~MDAnalysis.core.universe.Universe` containing the trajectory i : int resid of the first base bp : int resid of the second base seg1 : str (optional) segment id for first base ["SYSTEM"] seg2 : str (optional) segment id for second base ["SYSTEM"] Returns ------- float Watson-Crick base pair distance Notes ----- If failure occurs be sure to check the segment identification. .. versionadded:: 0.7.6 """ if universe.select_atoms(" resid {0!s} ".format(i)).resnames[0] in ["DC", "DT", "U", "C", "T", "CYT", "THY", "URA"]: a1, a2 = "N3", "N1" if universe.select_atoms(" resid {0!s} ".format(i)).resnames[0] in ["DG", "DA", "A", "G", "ADE", "GUA"]: a1, a2 = "N1", "N3" wc_dist = universe.select_atoms("(segid {0!s} and resid {1!s} and name {2!s}) " "or (segid {3!s} and resid {4!s} and name {5!s}) " .format(seg1, i, a1, seg2, bp, a2)) wc = mdamath.norm(wc_dist[0].position - wc_dist[1].position) return wc
[docs]def minor_pair(universe, i, bp, seg1="SYSTEM", seg2="SYSTEM"): """Minor-Groove basepair distance for residue `i` with residue `bp`. The distance of the nitrogen and oxygen atoms in a Minor-groove hydrogen bond is computed. Parameters ---------- universe : Universe :class:`~MDAnalysis.core.universe.Universe` containing the trajectory i : int resid of the first base bp : int resid of the second base seg1 : str (optional) segment id for first base ["SYSTEM"] seg2 : str (optional) segment id for second base ["SYSTEM"] Returns ------- float Minor groove base pair distance Notes ----- If failure occurs be sure to check the segment identification. .. versionadded:: 0.7.6 """ if universe.select_atoms(" resid {0!s} ".format(i)).resnames[0] in ["DC", "DT", "U", "C", "T", "CYT", "THY", "URA"]: a1, a2 = "O2", "C2" if universe.select_atoms(" resid {0!s} ".format(i)).resnames[0] in ["DG", "DA", "A", "G", "ADE", "GUA"]: a1, a2 = "C2", "O2" c2o2_dist = universe.select_atoms("(segid {0!s} and resid {1!s} and name {2!s}) " "or (segid {3!s} and resid {4!s} and name {5!s})" .format(seg1, i, a1, seg2, bp, a2)) c2o2 = mdamath.norm(c2o2_dist[0].position - c2o2_dist[1].position) return c2o2
[docs]def major_pair(universe, i, bp, seg1="SYSTEM", seg2="SYSTEM"): """Major-Groove basepair distance for residue `i` with residue `bp`. The distance of the nitrogen and oxygen atoms in a Major-groove hydrogen bond is computed. Parameters ---------- universe : Universe :class:`~MDAnalysis.core.universe.Universe` containing the trajectory i : int resid of the first base bp : int resid of the second base seg1 : str (optional) segment id for first base ["SYSTEM"] seg2 : str (optional) segment id for second base ["SYSTEM"] Returns ------- float Major groove base pair distance Notes ----- If failure occurs be sure to check the segment identification. .. versionadded:: 0.7.6 """ if universe.select_atoms(" resid {0!s} ".format(i)).resnames[0] in ["DC", "DG", "C", "G", "CYT", "GUA"]: if universe.select_atoms(" resid {0!s} ".format(i)).resnames[0] in ["DC", "C", "CYT"]: a1, a2 = "N4", "O6" else: a1, a2 = "O6", "N4" if universe.select_atoms(" resid {0!s} ".format(i)).resnames[0] in ["DT", "DA", "A", "T", "U", "ADE", "THY", "URA"]: if universe.select_atoms(" resid {0!s} ".format(i)).resnames[0] in ["DT", "T", "THY", "U", "URA"]: a1, a2 = "O4", "N6" else: a1, a2 = "N6", "O4" no_dist = universe.select_atoms("(segid {0!s} and resid {1!s} and name {2!s}) " "or (segid {3!s} and resid {4!s} and name {5!s}) " .format(seg1, i, a1, seg2, bp, a2)) major = mdamath.norm(no_dist[0].position - no_dist[1].position) return major
[docs]def phase_cp(universe, seg, i): """Pseudo-angle describing the phase of the ribose pucker for residue `i` using the CP method. The angle is computed by the positions of atoms in the ribose ring. Parameters ---------- universe : Universe :class:`~MDAnalysis.core.universe.Universe` containing the trajectory seg : str segment id for base i : int resid of the first base Returns ------- float phase angle in degrees .. versionadded:: 0.7.6 """ atom1 = universe.select_atoms(" atom {0!s} {1!s} O4\' ".format(seg, i)) atom2 = universe.select_atoms(" atom {0!s} {1!s} C1\' ".format(seg, i)) atom3 = universe.select_atoms(" atom {0!s} {1!s} C2\' ".format(seg, i)) atom4 = universe.select_atoms(" atom {0!s} {1!s} C3\' ".format(seg, i)) atom5 = universe.select_atoms(" atom {0!s} {1!s} C4\' ".format(seg, i)) data1 = atom1.positions data2 = atom2.positions data3 = atom3.positions data4 = atom4.positions data5 = atom5.positions r0 = (data1 + data2 + data3 + data4 + data5) * (1.0 / 5.0) r1 = data1 - r0 r2 = data2 - r0 r3 = data3 - r0 r4 = data4 - r0 r5 = data5 - r0 R1 = ((r1 * sin(2 * pi * 0.0 / 5.0)) + (r2 * sin(2 * pi * 1.0 / 5.0)) + (r3 * sin(2 * pi * 2.0 / 5.0)) + (r4 * sin(2 * pi * 3.0 / 5.0)) + (r5 * sin(2 * pi * 4.0 / 5.0))) R2 = ((r1 * cos(2 * pi * 0.0 / 5.0)) + (r2 * cos(2 * pi * 1.0 / 5.0)) + (r3 * cos(2 * pi * 2.0 / 5.0)) + (r4 * cos(2 * pi * 3.0 / 5.0)) + (r5 * cos(2 * pi * 4.0 / 5.0))) x = np.cross(R1[0], R2[0]) n = x / sqrt(pow(x[0], 2) + pow(x[1], 2) + pow(x[2], 2)) r1_d = np.dot(r1, n) r2_d = np.dot(r2, n) r3_d = np.dot(r3, n) r4_d = np.dot(r4, n) r5_d = np.dot(r5, n) D = ((r1_d * sin(4 * pi * 0.0 / 5.0)) + (r2_d * sin(4 * pi * 1.0 / 5.0)) + (r3_d * sin(4 * pi * 2.0 / 5.0)) + (r4_d * sin(4 * pi * 3.0 / 5.0)) + (r5_d * sin(4 * pi * 4.0 / 5.0))) * -1 * sqrt(2.0 / 5.0) C = ((r1_d * cos(4 * pi * 0.0 / 5.0)) + (r2_d * cos(4 * pi * 1.0 / 5.0)) + (r3_d * cos(4 * pi * 2.0 / 5.0)) + (r4_d * cos(4 * pi * 3.0 / 5.0)) + (r5_d * cos(4 * pi * 4.0 / 5.0))) * sqrt(2.0 / 5.0) phase_ang = (atan2(D, C) + (pi / 2.)) * 180. / pi return phase_ang % 360
[docs]def phase_as(universe, seg, i): """Pseudo-angle describing the phase of the ribose pucker for residue `i` using the AS method The angle is computed by the position vector of atoms in the ribose ring. Parameters ---------- universe : Universe :class:`~MDAnalysis.core.universe.Universe` containing the trajectory seg : str segment id for base i : int resid of the first base Returns ------- float phase angle in degrees .. versionadded:: 0.7.6 """ angle1 = universe.select_atoms(" atom {0!s} {1!s} C1\' ".format(seg, i), " atom {0!s} {1!s} C2\' ".format(seg, i), " atom {0!s} {1!s} C3\' ".format(seg, i), " atom {0!s} {1!s} C4\' ".format(seg, i)) angle2 = universe.select_atoms(" atom {0!s} {1!s} C2\' ".format(seg, i), " atom {0!s} {1!s} C3\' ".format(seg, i), " atom {0!s} {1!s} C4\' ".format(seg, i), " atom {0!s} {1!s} O4\' ".format(seg, i)) angle3 = universe.select_atoms(" atom {0!s} {1!s} C3\' ".format(seg, i), " atom {0!s} {1!s} C4\' ".format(seg, i), " atom {0!s} {1!s} O4\' ".format(seg, i), " atom {0!s} {1!s} C1\' ".format(seg, i)) angle4 = universe.select_atoms(" atom {0!s} {1!s} C4\' ".format(seg, i), " atom {0!s} {1!s} O4\' ".format(seg, i), " atom {0!s} {1!s} C1\' ".format(seg, i), " atom {0!s} {1!s} C2\' ".format(seg, i)) angle5 = universe.select_atoms(" atom {0!s} {1!s} O4\' ".format(seg, i), " atom {0!s} {1!s} C1\' ".format(seg, i), " atom {0!s} {1!s} C2\' ".format(seg, i), " atom {0!s} {1!s} C3\' ".format(seg, i)) data1 = angle1.dihedral.value() data2 = angle2.dihedral.value() data3 = angle3.dihedral.value() data4 = angle4.dihedral.value() data5 = angle5.dihedral.value() B = ((data1 * sin(2 * 2 * pi * (1 - 1.) / 5.)) + (data2 * sin(2 * 2 * pi * (2 - 1.) / 5.)) + (data3 * sin(2 * 2 * pi * (3 - 1.) / 5.)) + (data4 * sin(2 * 2 * pi * (4 - 1.) / 5.)) + (data5 * sin(2 * 2 * pi * (5 - 1.) / 5.))) * -2. / 5. A = ((data1 * cos(2 * 2 * pi * (1 - 1.) / 5.)) + (data2 * cos(2 * 2 * pi * (2 - 1.) / 5.)) + (data3 * cos(2 * 2 * pi * (3 - 1.) / 5.)) + (data4 * cos(2 * 2 * pi * (4 - 1.) / 5.)) + (data5 * cos(2 * 2 * pi * (5 - 1.) / 5.))) * 2. / 5. phase_ang = atan2(B, A) * 180. / pi return phase_ang % 360
[docs]def tors(universe, seg, i): """Calculation of nucleic backbone dihedral angles. The dihedral angles are alpha, beta, gamma, delta, epsilon, zeta, chi. The dihedral is computed based on position of atoms for resid `i`. Parameters ---------- universe : Universe :class:`~MDAnalysis.core.universe.Universe` containing the trajectory seg : str segment id for base i : int resid of the first base Returns ------- [alpha, beta, gamma, delta, epsilon, zeta, chi] : list of floats torsion angles in degrees Notes ----- If failure occurs be sure to check the segment identification. .. versionadded:: 0.7.6 """ a = universe.select_atoms(" atom {0!s} {1!s} O3\' ".format(seg, i - 1), " atom {0!s} {1!s} P ".format(seg, i), " atom {0!s} {1!s} O5\' ".format(seg, i), " atom {0!s} {1!s} C5\' ".format(seg, i)) b = universe.select_atoms(" atom {0!s} {1!s} P ".format(seg, i), " atom {0!s} {1!s} O5\' ".format(seg, i), " atom {0!s} {1!s} C5\' ".format(seg, i), " atom {0!s} {1!s} C4\' ".format(seg, i)) g = universe.select_atoms(" atom {0!s} {1!s} O5\' ".format(seg, i), " atom {0!s} {1!s} C5\' ".format(seg, i), " atom {0!s} {1!s} C4\' ".format(seg, i), " atom {0!s} {1!s} C3\' ".format(seg, i)) d = universe.select_atoms(" atom {0!s} {1!s} C5\' ".format(seg, i), " atom {0!s} {1!s} C4\' ".format(seg, i), " atom {0!s} {1!s} C3\' ".format(seg, i), " atom {0!s} {1!s} O3\' ".format(seg, i)) e = universe.select_atoms(" atom {0!s} {1!s} C4\' ".format(seg, i), " atom {0!s} {1!s} C3\' ".format(seg, i), " atom {0!s} {1!s} O3\' ".format(seg, i), " atom {0!s} {1!s} P ".format(seg, i + 1)) z = universe.select_atoms(" atom {0!s} {1!s} C3\' ".format(seg, i), " atom {0!s} {1!s} O3\' ".format(seg, i), " atom {0!s} {1!s} P ".format(seg, i + 1), " atom {0!s} {1!s} O5\' ".format(seg, i + 1)) c = universe.select_atoms(" atom {0!s} {1!s} O4\' ".format(seg, i), " atom {0!s} {1!s} C1\' ".format(seg, i), " atom {0!s} {1!s} N9 ".format(seg, i), " atom {0!s} {1!s} C4 ".format(seg, i)) if len(c) < 4: c = universe.select_atoms(" atom {0!s} {1!s} O4\' ".format(seg, i), " atom {0!s} {1!s} C1\' ".format(seg, i), " atom {0!s} {1!s} N1 ".format(seg, i), " atom {0!s} {1!s} C2 ".format(seg, i)) alpha = a.dihedral.value() % 360 beta = b.dihedral.value() % 360 gamma = g.dihedral.value() % 360 delta = d.dihedral.value() % 360 epsilon = e.dihedral.value() % 360 zeta = z.dihedral.value() % 360 chi = c.dihedral.value() % 360 return [alpha, beta, gamma, delta, epsilon, zeta, chi]
[docs]def tors_alpha(universe, seg, i): """alpha backbone dihedral The dihedral is computed based on position atoms for resid `i`. Parameters ---------- universe : Universe :class:`~MDAnalysis.core.universe.Universe` containing the trajectory seg : str segment id for base i : int resid of the first base Returns ------- alpha : float torsion angle in degrees .. versionadded:: 0.7.6 """ a = universe.select_atoms(" atom {0!s} {1!s} O3\' ".format(seg, i - 1), " atom {0!s} {1!s} P ".format(seg, i), " atom {0!s} {1!s} O5\' ".format(seg, i), " atom {0!s} {1!s} C5\' ".format(seg, i)) alpha = a.dihedral.value() % 360 return alpha
[docs]def tors_beta(universe, seg, i): """beta backbone dihedral The dihedral is computed based on position atoms for resid `i`. Parameters ---------- universe : Universe :class:`~MDAnalysis.core.universe.Universe` containing the trajectory seg : str segment id for base i : int resid of the first base Returns ------- beta : float torsion angle in degrees .. versionadded:: 0.7.6 """ b = universe.select_atoms(" atom {0!s} {1!s} P ".format(seg, i), " atom {0!s} {1!s} O5\' ".format(seg, i), " atom {0!s} {1!s} C5\' ".format(seg, i), " atom {0!s} {1!s} C4\' ".format(seg, i)) beta = b.dihedral.value() % 360 return beta
[docs]def tors_gamma(universe, seg, i): """ Gamma backbone dihedral The dihedral is computed based on position atoms for resid `i`. Parameters ---------- universe : Universe :class:`~MDAnalysis.core.universe.Universe` containing the trajectory seg : str segment id for base i : int resid of the first base Returns ------- gamma : float torsion angle in degrees .. versionadded:: 0.7.6 """ g = universe.select_atoms(" atom {0!s} {1!s} O5\' ".format(seg, i), " atom {0!s} {1!s} C5\' ".format(seg, i), " atom {0!s} {1!s} C4\' ".format(seg, i), " atom {0!s} {1!s} C3\' ".format(seg, i)) gamma = g.dihedral.value() % 360 return gamma
[docs]def tors_delta(universe, seg, i): """delta backbone dihedral The dihedral is computed based on position atoms for resid `i`. Parameters ---------- universe : Universe :class:`~MDAnalysis.core.universe.Universe` containing the trajectory seg : str segment id for base i : int resid of the first base Returns ------- delta : float torsion angle in degrees .. versionadded:: 0.7.6 """ d = universe.select_atoms(" atom {0!s} {1!s} C5\' ".format(seg, i), " atom {0!s} {1!s} C4\' ".format(seg, i), " atom {0!s} {1!s} C3\' ".format(seg, i), " atom {0!s} {1!s} O3\' ".format(seg, i)) delta = d.dihedral.value() % 360 return delta
[docs]def tors_eps(universe, seg, i): """Epsilon backbone dihedral The dihedral is computed based on position atoms for resid `i`. Parameters ---------- universe : Universe :class:`~MDAnalysis.core.universe.Universe` containing the trajectory seg : str segment id for base i : int resid of the first base Returns ------- epsilon : float torsion angle in degrees .. versionadded:: 0.7.6 """ e = universe.select_atoms(" atom {0!s} {1!s} C4\' ".format(seg, i), " atom {0!s} {1!s} C3\' ".format(seg, i), " atom {0!s} {1!s} O3\' ".format(seg, i), " atom {0!s} {1!s} P ".format(seg, i + 1)) epsilon = e.dihedral.value() % 360 return epsilon
[docs]def tors_zeta(universe, seg, i): """Zeta backbone dihedral The dihedral is computed based on position atoms for resid `i`. Parameters ---------- universe : Universe :class:`~MDAnalysis.core.universe.Universe` containing the trajectory seg : str segment id for base i : int resid of the first base Returns ------- zeta : float torsion angle in degrees .. versionadded:: 0.7.6 """ z = universe.select_atoms(" atom {0!s} {1!s} C3\' ".format(seg, i), " atom {0!s} {1!s} O3\' ".format(seg, i), " atom {0!s} {1!s} P ".format(seg, i + 1), " atom {0!s} {1!s} O5\' ".format(seg, i + 1)) zeta = z.dihedral.value() % 360 return zeta
[docs]def tors_chi(universe, seg, i): """chi nucleic acid dihedral The dihedral is computed based on position atoms for resid `i`. Parameters ---------- universe : Universe :class:`~MDAnalysis.core.universe.Universe` containing the trajectory seg : str segment id for base i : int resid of the first base Returns ------- chi : float torsion angle in degrees .. versionadded:: 0.7.6 """ c = universe.select_atoms(" atom {0!s} {1!s} O4\' ".format(seg, i), " atom {0!s} {1!s} C1\' ".format(seg, i), " atom {0!s} {1!s} N9 ".format(seg, i), " atom {0!s} {1!s} C4 ".format(seg, i)) if len(c) < 4: c = universe.select_atoms(" atom {0!s} {1!s} O4\' ".format(seg, i), " atom {0!s} {1!s} C1\' ".format(seg, i), " atom {0!s} {1!s} N1 ".format(seg, i), " atom {0!s} {1!s} C2 ".format(seg, i)) chi = c.dihedral.value() % 360 return chi
[docs]def hydroxyl(universe, seg, i): """2-hydroxyl dihedral. Useful only for RNA calculations. .. Note:: This dihedral calculation will only work if using atom names as documented by charmm force field parameters, namely "C1', C2', O2', H2'". Parameters ---------- universe : Universe :class:`~MDAnalysis.core.universe.Universe` containing the trajectory seg : str segment id for base i : int resid of the first base Returns ------- hydroxyl_angle : float torsion angle in degrees .. versionadded:: 0.7.6 """ h = universe.select_atoms("atom {0!s} {1!s} C1'".format(seg, i), "atom {0!s} {1!s} C2'".format(seg, i), "atom {0!s} {1!s} O2'".format(seg, i), "atom {0!s} {1!s} H2'".format(seg, i)) try: hydr = h.dihedral.value() % 360 except ValueError: errmsg = (f"Resid {i} does not contain atoms C1', C2', O2', H2' but " f"atoms {list(h.atoms)}") raise ValueError(errmsg) from None return hydr
[docs]def pseudo_dihe_baseflip(universe, bp1, bp2, i, seg1="SYSTEM", seg2="SYSTEM", seg3="SYSTEM"): """pseudo dihedral for flipped bases. Useful only for nucleic acid base flipping The dihedral is computed based on position atoms for resid `i` .. Note:: This dihedral calculation will only work if using atom names as documented by charmm force field parameters. Parameters ---------- universe : Universe :class:`~MDAnalysis.core.universe.Universe` containing the trajectory bp1 : int resid that base pairs with `bp2` bp2 : int resid below the base that flips i : int resid of the base that flips segid1 : str (optional) segid of resid base pairing with `bp2` segid2 : str (optional) segid, same as that of segid of flipping resid `i` segid3 : str (optional) segid of resid `i` that flips Returns ------- float pseudo dihedral angle in degrees .. versionadded:: 0.8.0 """ bf1 = universe.select_atoms( " ( segid {0!s} and resid {1!s} and nucleicbase ) " "or ( segid {2!s} and resid {3!s} and nucleicbase ) " .format( seg1, bp1, seg2, bp2)) bf4 = universe.select_atoms("(segid {0!s} and resid {1!s} and nucleicbase) ".format(seg3, i)) bf2 = universe.select_atoms("(segid {0!s} and resid {1!s} and nucleicsugar) ".format(seg2, bp2)) bf3 = universe.select_atoms("(segid {0!s} and resid {1!s} and nucleicsugar) ".format(seg3, i)) x = [bf1.center_of_mass(), bf2.center_of_mass(), bf3.center_of_mass(), bf4.center_of_mass()] pseudo = mdamath.dihedral(x[0] - x[1], x[1] - x[2], x[2] - x[3]) pseudo = np.rad2deg(pseudo) % 360 return pseudo