%load_ext autoreload
%autoreload 2

import molsysmt as msm

Get dihedral quartets

MolSysMT includes a method to obtain the sets of atoms quartets defining all dihedral angles present in the system given their names. There is no need then to remember the atom names defining the angle \(\phi\), \(\psi\), \(\omega\), or any of the \(\chi\) angles. Lets see how this method works over one of the demo molecular systems:

molecular_system = msm.systems['TcTIM']['1tcd.mmtf']
molecular_system = msm.convert(molecular_system)

The quartets defining the angles \(\phi\), \(\psi\) or \(\omega\) over the whole system can be obtained as follows:

phi_chains = msm.topology.get_dihedral_quartets(molecular_system, phi=True)

phi_chains

array([[   2,    9,   10,   11],
       [  11,   16,   17,   18],
       [  18,   25,   26,   27],
       ...,
       [3789, 3796, 3797, 3798],
       [3798, 3801, 3802, 3803],
       [3803, 3808, 3809, 3810]])

The search of these quartets can be limited to a specific selection. Lets see how to get the quartes of the \(\psi\) angles in residues 10 to 15:

psi_chains = msm.topology.get_dihedral_quartets(molecular_system, selection='10<=group_index<=15', psi=True)

psi_chains

array([[ 77,  78,  79,  86],
       [ 86,  87,  88,  92],
       [ 92,  93,  94, 100],
       [100, 101, 102, 104],
       [104, 105, 106, 110]])

Atoms chains defining \(\chi\) angles can be also extracted. Lets get, for instance, all \(\chi_{5}\) in the system:

chi5_chains = msm.topology.get_dihedral_quartets(molecular_system, chi5=True)

There’s a high number of ARG residues in our system. ARG is the only amino-acide with a \(\chi_{5}\) dihedral angle.

print(chi5_chains.shape[0])

26

n_args = msm.get(molecular_system, element='group', selection='group_name=="ARG"', n_groups=True)
print(n_args)

26

phi, psi = msm.topology.get_dihedral_quartets(molecular_system, phi=True, psi=True)

phi

array([[   2,    9,   10,   11],
       [  11,   16,   17,   18],
       [  18,   25,   26,   27],
       ...,
       [3789, 3796, 3797, 3798],
       [3798, 3801, 3802, 3803],
       [3803, 3808, 3809, 3810]])

psi

array([[   0,    1,    2,    9],
       [   9,   10,   11,   16],
       [  16,   17,   18,   25],
       ...,
       [3787, 3788, 3789, 3796],
       [3796, 3797, 3798, 3801],
       [3801, 3802, 3803, 3808]])

msm.get(molecular_system, element='atom', selection=phi[0], name=True)

['C', 'N', 'CA', 'C']

In the following tables a summary of the dihedral angle definitions are included in this document for future reference. The corresponding string taken by the input argument dihedral_angle is written down between parentesis next to each greek letter naming the angle:

\(\phi\) (phi)

Residue	Atoms	Zero value	Range (degrees)
all but PRO	C-N-CA-C	C cis to C	[-180, 180)
PRO	C-N-CA-C	C cis to C	~-90

\(\psi\) (psi)

Residue	Atoms	Zero value	Range (degrees)
all	N-CA-C-N	N cis to N	[-180, 180)

\(\omega\) (omega)

Residue	Atoms	Zero value	Range (degrees)
all	CA-C-N-CA	CA cis to CA	~180
all	CH3-C-N-CA	CA cis to CA	~180
all	CA-C-N-CH3	CA cis to CA	~180

\(\chi_{1}\) (chi1)

Residue	Atoms	Zero value	Range (degrees)
ARG	N-CA-CB-CG	CG cis to N	[-180, 180)
ASN	N-CA-CB-CG	CG cis to N	[-180, 180)
ASP	N-CA-CB-CG	CG cis to N	[-180, 180)
CYS	N-CA-CB-SG	SG cis to N	[-180, 180)
GLN	N-CA-CB-CG	CG cis to N	[-180, 180)
GLU	N-CA-CB-CG	CG cis to N	[-180, 180)
HIS	N-CA-CB-CG	CG cis to N	[-180, 180)
ILE	N-CA-CB-CG1	CG1 cis to N	[-180°, 180)
LEU	N-CA-CB-CG	CG cis to N	[-180, 180)
LYS	N-CA-CB-CG	CG cis to N	[-180, 180)
MET	N-CA-CB-CG	CG cis to N	[-180, 180)
PHE	N-CA-CB-CG	CG cis to N	[-180, 180)
PRO	N-CA-CB-CG	CG cis to N	CA-CB is part of ring
SER	N-CA-CB-OG	OG cis to N	[-180, 180)
THR	N-CA-CB-OG1	OG1 cis to N	[-180, 180)
TRP	N-CA-CB-CG	CG cis to N	[-180, 180)
TYR	N-CA-CB-CG	CG cis to N	[-180, 180)
VAL	N-CA-CB-CG1	CG1 cis to N	[-180, 180)

\(\chi_{2}\) (chi2)

Residue	Atoms	Zero value	Range (degrees)
ARG	CA-CB-CG-CD	CD cis to CA	[-180, 180)
ASN	CA-CB-CG-OD1	OD1 cis to CA	[-180, 180)
ASP	CA-CB-CG-OD	OD1 cis to CA	[-180, 180)
GLN	CA-CB-CG-CD	CD cis to CA	[-180, 180)
GLU	CA-CB-CG-CD	CD cis to CA	[-180, 180)
HIS	CA-CB-CG-ND1	ND1 cis to CA	[-180, 180)
ILE	CA-CB-CG1-CD	CD cis to CA	[-180, 180)
LEU	CA-CB-CG-CD1	CD1 cis to CA	[-180, 180)
LYS	CA-CB-CG-CD	CD cis to CA	[-180, 180)
MET	CA-CB-CG-SD	SD cis to CA	[-180, 180)
PHE	CA-CB-CG-CD	CD1 cis to CA	[-180, 180)
PRO	CA-CB-CG-CD	CD cis to CA	CB-CG is part of ring
TRP	CA-CB-CG-CD1	CD1 cis to CA	[-180, 180)
TYR	CA-CB-CG-CD1	CD1 cis to CA	[-180, 180)

\(\chi_{3}\) (chi3)

Residue	Atoms	Zero value	Range (degrees)
ARG	CB-CG-CD-NE	NE cis to CB	[-180, 180)
GLN	CB-CG-CD-OE1	OE1 cis to CB	[-180, 180)
GLU	CB-CG-CD-OE1	OE1 cis to CB	[-180, 180)
LYS	CB-CG-CD-CE	CE cis to CB	[-180, 180)
MET	CB-CG-SD-CE	CE cis to CB	[-180, 180)

\(\chi_{4}\) (chi4)

Residue	Atoms	Zero value	Range (degrees)
ARG	CG-CD-NE-CZ	CZ cis to CG	[-180, 180)
LYS	CG-CD-CE-NZ	NZ cis to CG	[-180, 180)

\(\chi_{5}\) (chi5)

Residue	Atoms	Zero value	Range (degrees)
ARG	CD-NE-CZ-NH1	NH1 cis to CD	[-180, 180)

Every dihedral angle is defined in a peptide by three vectors delimited by four consecutive covalently bonded atoms. The vector in the middle defines the orthogonal plane where rotations are defined by the projection of vectors first and third, this way two blocks of atoms change its relative positions: all atoms covalently bonded before and after the second vector in the polymer. Or explained in other words, removing the second vector two sets of covalently bonded atoms are defined. Each of these two atoms sets move in unison when the dihedral angle changes. MolSysMT includes the input argument with_blocks for the method molsysmt.covalent_dihedral_quartets to return these atoms sets together with the quartets. Lets see how it works with an example:

molecular_system = msm.convert(msm.systems['Met-enkephalin']['met_enkephalin.h5msm'], to_form='molsysmt.MolSys')

phi_chains, phi_blocks = msm.topology.get_dihedral_quartets(molecular_system, with_blocks=True, phi=True)

Lets for instance have a look to the quartet defining the 3-th \(\phi\) angle:

view = msm.view(molecular_system, viewer='NGLView')
selection_quartet = msm.select(molecular_system, selection=phi_chains[2], to_syntax='NGLView')
view.clear()
view.add_licorice(color='white')
view.add_ball_and_stick(selection_quartet, color='orange')
view

phi_chains[2]

array([33, 35, 37, 53])

phi_blocks[2]

array([{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36},
       {37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71}],
      dtype=object)

Lets show in blue and red the two blocks of atoms defined by this 4-th \(\phi\) dihedral angle.

view = msm.view(molecular_system, viewer='NGLView')
view.clear()
selection_quartet = msm.select(molecular_system, selection=phi_chains[2], to_syntax='NGLView')
selection_block_0 = msm.select(molecular_system, selection=list(phi_blocks[2][0]), to_syntax='NGLView')
selection_block_1 = msm.select(molecular_system, selection=list(phi_blocks[2][1]), to_syntax='NGLView')
view.add_licorice(color='white')
view.add_ball_and_stick(selection_quartet, color='orange')
view.add_ball_and_stick(selection_block_0, color='red')
view.add_ball_and_stick(selection_block_1, color='blue')
view