Visualizing Torsional Angle Distribution

Problem

You want to generate an interactive image (in svg file format) that visualizes the distribution of dihedral angles of rotatable bond in a multi-conformer molecule. See example in Figure 1.

hover over any rotatable bond in the molecule (marked with a circle)

Figure 1. Example of visualizing torsional information

../_images/dihedral2img-acyclovi.svg

Ingredients

  • OEChem TK - cheminformatics toolkit (including OEBio TK)

  • OEDepict TK - molecule depiction toolkit

  • Grapheme TK - molecule and property visualization toolkit

Difficulty level

../_images/chilly.png ../_images/chilly.png ../_images/chilly.png

Download

Download code

dihedral2img.py

See also the Usage subsection.

Solution

The first step of generating the image is to identify the rotatable bonds in the input molecule using the IsRotatableOrMacroCycleBond bond predicate. The get_dihedrals function iterates over rotatable bonds and identifies their dihedral atoms. These dihedral atoms are stored on the molecule in a OEGroupBase object for further process.

 1class IsRotatableOrMacroCycleBond(oechem.OEUnaryBondPred):
 2    """
 3    Identifies rotatable bonds and single bonds in macro-cycles.
 4    """
 5    def __call__(self, bond):
 6        """
 7        :type mol: oechem.OEBondBase
 8        :rtype: boolean
 9        """
10        if bond.GetOrder() != 1:
11            return False
12        if bond.IsAromatic():
13            return False
14
15        isrotor = oechem.OEIsRotor()
16        if isrotor(bond):
17            return True
18
19        if oechem.OEBondGetSmallestRingSize(bond) >= 10:
20            return True
21
22        return False

 1def get_dihedrals(mol, itag):
 2    """
 3    Iterates over rotatable bonds and identifies their dihedral
 4    atoms. These atoms are added to the molecule in a group
 5    using the given tag.
 6
 7    :type mol: oechem.OEMol
 8    :type itag: int
 9    :return: Number of dihedral angles identified
10    :rtype: int
11    """
12    nrdihedrals = 0
13    for bond in mol.GetBonds(IsRotatableOrMacroCycleBond()):
14        atomB = bond.GetBgn()
15        atomE = bond.GetEnd()
16
17        neighB = None
18        neighE = None
19
20        for atom in atomB.GetAtoms(oechem.OEIsHeavy()):
21            if atom != atomE:
22                neighB = atom
23                break
24        for atom in atomE.GetAtoms(oechem.OEIsHeavy()):
25            if atom != atomB:
26                neighE = atom
27                break
28
29        if neighB is None or neighE is None:
30            continue
31
32        atomorder = [neighB, atomB, atomE, neighE]
33        bondorder = [mol.GetBond(neighB, atomB), bond, mol.GetBond(neighE, atomE)]
34
35        if neighB.GetIdx() < neighE.GetIdx():
36            atomorder.reverse()
37            bondorder.reverse()
38
39        atoms = oechem.OEAtomVector(atomorder)
40        bonds = oechem.OEBondVector(bondorder)
41
42        nrdihedrals += 1
43        mol.NewGroup(itag, atoms, bonds)
44
45    return nrdihedrals

After the dihedral atoms are identified, the set_dihedral_histograms function is used to iterate over the conformation of the molecule and calculate torsion angles using the OEGetTorsion function . These angles are binned to

 1def set_dihedral_histograms(mol, itag, nrbins):
 2    """
 3    Iterates over the dihedral groups and bins the torsional
 4    angles for each conformation. The histogram data is then
 5    attached to the groups with the given tag.
 6
 7    :type mol: oechem.OEMol
 8    :type itag: int
 9    :type nrbins: int
10    """
11
12    angleinc = 360.0 / float(nrbins)
13
14    for group in mol.GetGroups(oechem.OEHasGroupType(itag)):
15        atoms = oechem.OEAtomVector()
16        for atom in group.GetAtoms():
17            atoms.append(atom)
18        histogram = [0] * nrbins
19
20        for conf in mol.GetConfs():
21            rad = oechem.OEGetTorsion(conf, atoms[0], atoms[1], atoms[2], atoms[3])
22            deg = math.degrees(rad)
23            deg = (deg + 360.0) % 360.0
24            binidx = int(math.floor((deg / angleinc)))
25            histogram[binidx] += 1
26
27        group.SetData(itag, histogram)

The last step is to highlight the dihedral atoms when hovered over and depict the corresponding dihedral angle histogram. In order to achieve the hover effect in the generated SVG image, SVG groups are utilized (OESVGGroup) in the depict_dihedrals function. For each dihedral two groups are created. These groups are associated by calling the OEAddSVGHover function: while hovering the mouse over objects drawn inside the torsion_area_<id> the objects drawn in the torsion_data_<id> will be displayed. The group id must be unique amongst all the ids in the SVG image. Everything that is rendered between the OEImageBase.PushGroup and the corresponding OEImageBase.PopGroup methods is considered “inside” the group.

It is important that the molecule is rendered into the image after the dihedral angles are highlighted (after the second loop). As a result the highlight will appear underneath the molecule rather than on top of.

In the last loop of the depict_dihedrals function transparent circles are drawn (using OESVGAreaPen) in the middle of the the dihedral angle representing the hover areas in the interactive SVG image.

 1def depict_dihedrals(image, dimage, mol, refmol, opts, itag, nrbins, colorg):
 2    """
 3    Highlights the dihedral atoms of a torsion and the depicts the
 4    corresponding dihedral angle histogram when hovering over
 5    the center of the torsion on the molecule display.
 6
 7    :type image: oedepict.OEImageBase
 8    :type dimage: oedepict.OEImageBase
 9    :type mol: oechem.OEMol
10    :type refmol: oechem.OEMol
11    :type opts: oedepict.OE2DMolDisplayOptions
12    :type itag: int
13    :type nrbins: int
14    :type oechem.OEColorGradientBase
15    """
16
17    nrconfs = mol.NumConfs()
18    center = oedepict.OEGetCenter(dimage)
19    radius = min(dimage.GetWidth(), dimage.GetHeight()) * 0.40
20
21    draw_dihedral_circle(dimage, center, radius, nrbins, nrconfs)
22
23    suppressH = True
24    oegrapheme.OEPrepareDepictionFrom3D(mol, suppressH)
25    if refmol is not None:
26        oegrapheme.OEPrepareDepictionFrom3D(refmol, suppressH)
27
28    disp = oedepict.OE2DMolDisplay(mol, opts)
29
30    dihedrals = []
31    ref_dihedrals = []
32    centers = []
33    agroups = []
34    dgroups = []
35
36    nrdihedrals = 0
37    for group in mol.GetGroups(oechem.OEHasGroupType(itag)):
38
39        uniqueid = uuid.uuid4().hex
40        agroup = image.NewSVGGroup("torsion_area_" + uniqueid)
41        dgroup = image.NewSVGGroup("torsion_data_" + uniqueid)
42        oedepict.OEAddSVGHover(agroup, dgroup)
43
44        dihedrals.append(group)
45        if refmol is not None:
46            ref_dihedrals.append(get_reference_dihedral(group, refmol, itag))
47
48        centers.append(get_center(disp, group))
49        agroups.append(agroup)
50        dgroups.append(dgroup)
51        nrdihedrals += 1
52
53    for didx in range(0, nrdihedrals):
54
55        image.PushGroup(dgroups[didx])
56
57        dihedral = dihedrals[didx]
58        abset = oechem.OEAtomBondSet(dihedral.GetAtoms(), dihedral.GetBonds())
59        draw_highlight(image, disp, abset)
60        dihedral_histogram = dihedral.GetData(itag)
61        draw_dihedral_histogram(dimage, dihedral_histogram, center, radius, nrbins, nrconfs)
62
63        if refmol is not None and ref_dihedrals[didx] is not None:
64            ref_dihedral = ref_dihedrals[didx]
65            draw_reference_dihedral(dimage, ref_dihedral, itag, center, radius)
66
67        image.PopGroup(dgroups[didx])
68
69    clearbackground = True
70    oedepict.OERenderMolecule(image, disp, not clearbackground)
71
72    markpen = oedepict.OEPen(oechem.OEBlack, oechem.OEWhite, oedepict.OEFill_On, 1.0)
73    farpen = oedepict.OEPen(oechem.OEBlack, oechem.OERed, oedepict.OEFill_Off, 2.0)
74
75    angleinc = 360.0 / float(nrbins)
76
77    for didx in range(0, nrdihedrals):
78
79        image.PushGroup(agroups[didx])
80
81        dihedral = dihedrals[didx]
82        dihedral_histogram = dihedral.GetData(itag)
83        flexibility = determine_flexibility(dihedral_histogram)
84        color = colorg.GetColorAt(flexibility)
85        markpen.SetBackColor(color)
86
87        markradius = disp.GetScale() / 8.0
88        image.DrawCircle(centers[didx], markradius, markpen)
89
90        if refmol is not None and ref_dihedrals[didx] is not None:
91            ref_dihedral = ref_dihedrals[didx]
92            if get_closest_dihedral_angle(mol, dihedral, ref_dihedral, itag) > angleinc:
93                image.DrawCircle(centers[didx], markradius, farpen)
94
95        radius = disp.GetScale() / 4.0
96        image.DrawCircle(centers[didx], radius, oedepict.OESVGAreaPen)
97
98        image.PopGroup(agroups[didx])

Usage

Usage

dihedral2img.py and acyclovi.sdf multi-conformer molecule file

The following command will generate the image shown in Figure 1:

prompt > python3 dihedral2img.py -in acyclovi.sdf  -out acyclovi.svg

Command Line Parameters

Simple parameter list
    input/output options
      -in : Input filename of a multi conformer molecule
      -out : Output filename of the generated image
      -ref : Input filename of reference molecule

    visualization options
      -flexibility : Visualize dihedral angle flexibility
      -nrbins : Number of bins in the dihedral angle histogram

Discussion

OpenEye’s Omega TK can be used to generate diverse sets of low-energy conformations.

Usage

omega.py

The following commands will generate a multi-conformer file for molecule acyclovi:

prompt > echo "c1nc2c(=O)[nH]c(nc2n1COCCO)N acyclovi" > acyclovi.ism
prompt > python3 omega.py acyclovi.ism acyclovi.sdf

Visualizing Torsion Flexibility

By using the -flexibility parameter, the flexibility of the torsions angles can be visualized using a color gradient. Torsions with high flexibility are colored red, while black color indicates restrained torsion angles.

The flexibility of the torsion is determined with the following rudimentary method:

 1def determine_flexibility(histogram):
 2    """
 3    Returns the simple estimation of torsion flexibility by counting the
 4    number of non-zero bins in the torsional histogram.
 5
 6    :type histogram: list(int)
 7    """
 8
 9    nr_non_zero_bins = sum([1 for x in histogram if x > 0]) * 2
10    return nr_non_zero_bins

Usage

dihedral2img.py and penicillin.sdf multi-conformer molecule file

The following command will generate the image shown in Figure 2:

prompt > python3 dihedral2img.py -in penicillin.sdf -out penicillin.svg -flexibility

The Figure 2 shows that the preferred angle of the amide bond in the molecule is around 180° coloring the corresponding bond circle black, while the other bonds have more flexibility. The utilized color gradient can revealed by hovering over the “Legend” label.

hover over any rotatable bond in the molecule (marked with a circle)

Figure 2. Example of visualizing torsion flexibility

../_images/dihedral2img-penicilling.svg

Visualizing Torsional Angle Distribution with Reference

By using the -ref parameter, the torsion angle of a reference molecule (such as experimental conformation) can visualized in the generated image.

Usage

dihedral2img.py and 0QI.sdf multi-conformer molecule file with corresponding 0QI.pdb reference molecule file

The following command will generate the image shown in Figure 3:

prompt > python3 dihedral2img.py -in 0QI.sdf -ref 0QI.pdb -out 0QI.svg

When hovering over a rotatable bond in Figure 3 the corresponding torsional angle of the reference molecule is depicted in the middle of the radial histogram. Red circle is depicted around the bond marker when the reference angle is not close to any generated torsional angles. This allows to make instant judgment whether the generated conformations can reproduce an experimentally determined conformation.

hover over any rotatable bond in the molecule (marked with a circle)

Figure 3. Example of visualizing torsion flexibility with reference molecule

../_images/dihedral2img-0QI.svg

See also in OEChem TK manual

API

See also in OEDepict TK manual

Theory

API

See also in GraphemeTM TK manual

API