Structure analysis

Superposition

Gemmi includes the QCP method (Liu P, Agrafiotis DK, & Theobald DL, 2010) for superposing two lists of points in 3D. The C++ function superpose_positions() takes two arrays of positions and an optional array of weights. Before applying this function to chains it is necessary to determine pairs of corresponding atoms. Here, as a minimal example, we superpose the backbone of the third residue:

>>> model = gemmi.read_structure('../tests/4oz7.pdb')[0]
>>> res1 = model['A'][2]
>>> res2 = model['B'][2]
>>> atoms = ['N', 'CA', 'C', 'O']
>>> gemmi.superpose_positions([res1.sole_atom(a).pos for a in atoms],
...                           [res2.sole_atom(a).pos for a in atoms])  
<gemmi.SupResult object at 0x...>
>>> _.rmsd
0.006558389527590043

To make it easier, we also have a higher-level function calculate_superposition() that operates on ResidueSpans. This function first performs the sequence alignment. Then the matching residues are superposed, using either all atoms in both residues, or only Cα atoms (for peptides) and P atoms (for nucleotides). Atoms without matching counterparts are ignored. The returned object (SupResult) contains the RMSD and the transformation (rotation matrix + translation vector) that superposes the second span onto the first one.

Note that the RMSD can be defined in two ways: the sum of squared deviations is divided either by 3N (as in PyMOL and QCP) or by N (as in SciPy). Gemmi returns the former. To get the latter, multiply it by √3.

Here is a usage example:

>>> model = gemmi.read_structure('../tests/4oz7.pdb')[0]
>>> polymer1 = model['A'].get_polymer()
>>> polymer2 = model['B'].get_polymer()
>>> ptype = polymer1.check_polymer_type()
>>> sup = gemmi.calculate_superposition(polymer1, polymer2, ptype, gemmi.SupSelect.CaP)
>>> sup.count  # number of atoms used
10
>>> sup.rmsd
0.1462689168993659
>>> sup.transform.mat
<gemmi.Mat33 [-0.0271652, 0.995789, 0.0875545]
             [0.996396, 0.034014, -0.0777057]
             [-0.0803566, 0.085128, -0.993124]>
>>> sup.transform.vec
<gemmi.Vec3(-17.764, 16.9915, -1.77262)>

The arguments to calculate_superposition() are:

  • two ResidueSpans,

  • polymer type (to avoid determining it when it’s already known). The information of whether it’s a protein or nucleic acid is used during sequence alignment (to detect gaps between residues in the polymer – it helps in rare cases when the sequence alignment alone is ambiguous), and it decides whether to use Cα or P atoms (see the next point),

  • atom selection: one of SupSelect.CaP (only Cα or P atoms), SupSelect.MainChain or SupSelect.All (all atoms),

  • (optionally) altloc – the conformer choice. By default, atoms with non-blank altloc are ignored. With altloc=’A’, only the A conformer is considered (atoms with altloc either blank or A). Etc.

  • (optionally) trim_cycles (default: 0) – maximum number of outlier rejection cycles. This option was inspired by the align command in PyMOL.

    >>> sr = gemmi.calculate_superposition(polymer1, polymer2, ptype,
...                                    gemmi.SupSelect.All, trim_cycles=5)
>>> sr.count
73
>>> sr.rmsd
0.18315488879658484

  • (optionally) trim_cutoff (default: 2.0) – outlier rejection cutoff in RMSD,

To calculate current RMSD between atoms (without superposition), call calculate_current_rmsd(). It takes the same arguments except the ones for trimming:

>>> gemmi.calculate_current_rmsd(polymer1, polymer2, ptype, gemmi.SupSelect.CaP).rmsd
19.660883858565462

The calculated superposition can be applied to a span of residues, changing the atomic positions in-place:

>>> polymer2[2].sole_atom('CB')  # before
<gemmi.Atom CB at (-30.3, -10.6, -11.6)>
>>> polymer2.transform_pos_and_adp(sup.transform)
>>> polymer2[2].sole_atom('CB')  # after
<gemmi.Atom CB at (-28.5, -12.6, 11.2)>
>>> # it is now nearby the corresponding atom in chain A:
>>> polymer1[2].sole_atom('CB')
<gemmi.Atom CB at (-28.6, -12.7, 11.3)>

Selections

Gemmi selection syntax is based on the selection syntax from MMDB, which is sometimes called CID (Coordinate ID). The MMDB syntax is described at the bottom of the pdbcur documentation.

The selection has a form of slash-separated parts: /models/chains/residues/atoms. Leading and trailing parts can be omitted when it’s not ambiguous. An empty field means that all items match, with two exceptions. The empty chain part (e.g. /1//) matches only a chain without an ID (blank chainID in the PDB format; not spec-conformant, but possible in working files). The empty altloc (examples will follow) matches atoms with a blank altLoc field. Gemmi (but not MMDB) can take additional properties added at the end after a semicolon (;).

Let us go through the individual filters first:

  • /1 – selects model 1 (if the PDB file doesn’t have MODEL records, it is assumed that the only model is model 1).

  • //D (or just D) – selects chain D.

  • //*/10-30 (or 10-30) – residues with sequence IDs from 10 to 30.

  • //*/10A-30A (or 10A-30A or ///10.A-30.A or 10.A-30.A) – sequence ID can include insertion code. The MMDB syntax has a dot between the sequence sequence number and the insertion code. In Gemmi, the dot is optional.

  • //*/(ALA) (or (ALA)) – selects residues with a given name.

  • //*//CB (or CB:* or CB[*]) – selects atoms with a given name.

  • //*//[P] (or just [P]) – selects phosphorus atoms.

  • //*//:B (or :B) – selects atoms with altloc B.

  • //*//: (or :) – selects atoms without altloc.

  • //*//;q<0.5 (or ;q<0.5) – selects atoms with occupancy below 0.5 (inspired by PyMOL, where it’d be q<0.5).

  • //*//;b>40 (or ;b>40) – selects atoms with isotropic B-factor above a given value.

  • ;polymer or ;solvent – selects polymer or solvent residues (if the PDB file doesn’t have TER records, call setup_entities() first).

  • * – selects all atoms.

The syntax supports also comma-separated lists and negations with !:

  • (!ALA) – all residues but alanine,

  • [C,N,O] – all C, N and O atoms,

  • [!C,N,O] – all atoms except C, N and O,

  • :,A – altloc either empty or A (which makes one conformation),

  • /1/A,B/20-40/CA[C]:,A – multiple selection criteria, all of them must be fulfilled.

  • (CYS);!polymer – select cysteine ligands

Incompatibility with MMDB. In MMDB, if the chemical element is specified (e.g. [C] or [*]), the alternative location indicator defaults to “” (no altloc), rather than to “*” (any altloc). This might be surprising. In Gemmi, if ‘:’ is absent the altloc is not checked (“*”).

Note: the selections in Gemmi are not widely used yet and the API may evolve.

A selection is a standalone object with a list of filters that can be applied to any Structure, Model or its part. Empty selection matches all atoms:

>>> sel = gemmi.Selection()  # empty - no filters

Selection initialized with a string:

>>> sel = gemmi.Selection('A/1-4/N9')

parses the string and creates filters corresponding to each part of the selection, which can then be used to iterate over the selected items in the hierarchy:

>>> st = gemmi.read_structure('../tests/1pfe.cif.gz')
>>> for model in sel.models(st):
...     print('Model', model.name)
...     for chain in sel.chains(model):
...         print('-', chain.name)
...         for residue in sel.residues(chain):
...             print('   -', str(residue))
...             for atom in sel.atoms(residue):
...                 print('          -', atom.name)
...
Model 1
- A
   - 1(DG)
          - N9
   - 2(DC)
   - 3(DG)
          - N9
   - 4(DT)

str() creates a CID string from the selection:

>>> sel.str()
'//A/1.-4./N9'

A helper function first() returns the first matching atom:

>>> # find the first Cl atom - returns model and CRA (chain, residue, atom)
>>> gemmi.Selection('[CL]').first(st)
(<gemmi.Model 1 with 2 chain(s)>, <gemmi.CRA A/CL 20/CL>)

Selection can be used to create a new structure (or model) with a copy of the selected parts. In this example, we copy alpha-carbon atoms:

>>> st = gemmi.read_structure('../tests/1orc.pdb')
>>> st[0].count_atom_sites()
559
>>> selection = gemmi.Selection('CA[C]')

>>> # create a new structure
>>> ca_st = selection.copy_structure_selection(st)
>>> ca_st[0].count_atom_sites()
64

>>> # create a new model
>>> ca_model = selection.copy_model_selection(st[0])
>>> ca_model.count_atom_sites()
64

Selection can also be used to remove atoms. Here, we remove atoms with a B-factor above 50:

>>> sel = gemmi.Selection(';b>50')
>>> sel.remove_selected(ca_st)
>>> ca_st[0].count_atom_sites()
61
>>> sel.remove_selected(ca_model)
>>> ca_model.count_atom_sites()
61

We can also do the opposite and remove atoms that are not selected:

>>> sel.remove_not_selected(ca_model)
>>> ca_model.count_atom_sites()
0

Previously, we introduced a couple functions that take selection as an argument. As an example, we can use one of them to count heavy atoms in polymers:

>>> st[0].count_occupancies(gemmi.Selection('[!H,D];polymer'))
496.0

Each residue and atom has a flag that can be set manually and used to create a selection. In the following example we select residues within a radius of 8Å from a selected point:

>>> selected_point = gemmi.Position(20, 40, 30)
>>> ns = gemmi.NeighborSearch(st[0], st.cell, 8.0).populate()
>>> # First, a flag is set for neighbouring residues.
>>> for mark in ns.find_atoms(selected_point):
...     mark.to_cra(st[0]).residue.flag = 's'
>>> # Then, we select residues with this flag.
>>> selection = gemmi.Selection().set_residue_flags('s')
>>> # Next, we can use this selection.
>>> selection.copy_model_selection(st[0]).count_atom_sites()
121

Note: NeighborSearch searches for atoms in all symmetry images. This is why it takes UnitCell as a parameter. To search only in atoms directly listed in the file, pass an empty cell (gemmi.UnitCell()).

Instead of selecting whole residues, we can select atoms. Here, we select atoms in the radius of 8Å from a selected point:

>>> # selected_point and ns are reused from the previous example
>>> # First, a flag is set for neighbouring atoms.
>>> for mark in ns.find_atoms(selected_point):
...     mark.to_cra(st[0]).atom.flag = 's'
>>> # Then, we select atoms with this flag.
>>> selection = gemmi.Selection().set_atom_flags('s')
>>> # Next, we can use this selection.
>>> selection.copy_model_selection(st[0]).count_atom_sites()
59

Graph analysis

This section shows how to analyze chemical molecules (gemmi.ChemComp) using external libraries dedicated to graph analysis. We don’t plan to implement graph algorithms within gemmi, except for the simplest ones, like breadth-first search, which is used in a couple of functions ( Restraints::find_shortest_path(), BondIndex::graph_distance()).

Here is how to set up a graph in the Boost Graph Library (BGL) in C++:

#include <boost/graph/graph_traits.hpp>
#include <boost/graph/adjacency_list.hpp>
#include <gemmi/cif.hpp>             // for cif::read_file
#include <gemmi/chemcomp.hpp>        // for ChemComp, make_chemcomp_from_block

struct AtomVertex {
  gemmi::Element el = gemmi::El::X;
  std::string name;
};

struct BondEdge {
  gemmi::BondType type;
};

using Graph = boost::adjacency_list<boost::vecS, boost::vecS,
                                    boost::undirectedS,
                                    AtomVertex, BondEdge>;

Graph make_graph(const gemmi::ChemComp& cc) {
  Graph g(cc.atoms.size());
  for (size_t i = 0; i != cc.atoms.size(); ++i) {
    g[i].el = cc.atoms[i].el;
    g[i].name = cc.atoms[i].id;
  }
  for (const gemmi::Restraints::Bond& bond : cc.rt.bonds) {
    int n1 = cc.get_atom_index(bond.id1.atom);
    int n2 = cc.get_atom_index(bond.id2.atom);
    boost::add_edge(n1, n2, BondEdge{bond.type}, g);
  }
  return g;
}

Here, we set up a NetworkX graph in Python:

>>> import networkx

>>> G = networkx.Graph()
>>> block = gemmi.cif.read('../tests/SO3.cif')[-1]
>>> so3 = gemmi.make_chemcomp_from_block(block)
>>> for atom in so3.atoms:
...     G.add_node(atom.id, Z=atom.el.atomic_number)
...
>>> for bond in so3.rt.bonds:
...     G.add_edge(bond.id1.atom, bond.id2.atom)  # ignoring bond type
...

Now, as a quick example, we can count automorphisms:

>>> import networkx.algorithms.isomorphism as iso
>>> GM = iso.GraphMatcher(G, G, node_match=iso.categorical_node_match('Z', 0))
>>> # expecting 3! automorphisms (permutations of the three oxygens)
>>> sum(1 for _ in GM.isomorphisms_iter())
6

The median number of automorphisms of molecules in the CCD is only 4. However, the highest number of isomorphisms as of 2023 (ignoring hydrogens, bond orders, chiralities) is a staggering 6879707136 for T8W. This value can be calculated almost instantly with nauty, which returns a set of generators of the automorphism group and the sets of equivalent vertices called orbits, rather than listing all automorphisms. Nauty is a software for “determining the automorphism group of a vertex-coloured graph, and for testing graphs for isomorphism”. We can use it in Python through the pynauty module.

Here we set up a pynauty graph from the so3 object prepared in the previous example:

>>> import pynauty

>>> n_vertices = len(so3.atoms)
>>> adjacency = {n: [] for n in range(n_vertices)}
>>> indices = {atom.id: n for n, atom in enumerate(so3.atoms)}
>>> elements = {atom.el.atomic_number for atom in so3.atoms}
>>> # The order in dict in Python 3.6+ is the insertion order.
>>> coloring = {elem: set() for elem in sorted(elements)}
>>> for n, atom in enumerate(so3.atoms):
...   coloring[atom.el.atomic_number].add(n)
...
>>> for bond in so3.rt.bonds:
...   n1 = indices[bond.id1.atom]
...   n2 = indices[bond.id2.atom]
...   adjacency[n1].append(n2)
...
>>> G = pynauty.Graph(n_vertices, adjacency_dict=adjacency, vertex_coloring=coloring.values())

The colors of vertices in this graph correspond to elements. Pynauty takes a list of sets of vertices with the same color, without knowing which color corresponds to which element. We sorted the elements to ensure that two graphs with the same atoms have the same coloring. However, SO3 and PO3 graphs would also have the same coloring and would be reported as isomorphic. So it is necessary to check if the elements in molecules are the same.

You may also want to encode other properties in the graph, such as bond orders, atom charges and chiralities, as described in this paper. Here, we only present a simplified, minimal example. Now, to finish this example, let’s get the order of the isomorphism group (which should be the same as in the NetworkX example, i.e. 6):

>>> (gen, grpsize1, grpsize2, orbits, numorb) = pynauty.autgrp(G)
>>> grpsize1 * 10**grpsize2
6.0

Graph isomorphism

In this example we use Python NetworkX to compare molecules from the Refmac monomer library with the PDB’s Chemical Component Dictionary (CCD). The same could be done with other graph analysis libraries, such as Boost Graph Library, igraph, etc.

The program below takes compares specified monomer cif files with corresponding CCD entries. Hydrogens and bond types are ignored. It takes less than half a minute to go through the 25,000 monomer files distributed with CCP4 (as of Oct 2018), so we do not try to optimize the program.

# Compares graphs of molecules from cif files (Refmac dictionary or similar)
# with CCD entries.

import sys
import networkx
from networkx.algorithms import isomorphism
import gemmi

CCD_PATH = 'components.cif.gz'

def graph_from_chemcomp(cc):
    G = networkx.Graph()
    for atom in cc.atoms:
        G.add_node(atom.id, Z=atom.el.atomic_number)
    for bond in cc.rt.bonds:
        G.add_edge(bond.id1.atom, bond.id2.atom)
    return G

def compare(cc1, cc2):
    s1 = {a.id for a in cc1.atoms}
    s2 = {a.id for a in cc2.atoms}
    b1 = {b.lexicographic_str() for b in cc1.rt.bonds}
    b2 = {b.lexicographic_str() for b in cc2.rt.bonds}
    if s1 == s2 and b1 == b2:
        #print(cc1.name, "the same")
        return
    G1 = graph_from_chemcomp(cc1)
    G2 = graph_from_chemcomp(cc2)
    node_match = isomorphism.categorical_node_match('Z', 0)
    GM = isomorphism.GraphMatcher(G1, G2, node_match=node_match)
    if GM.is_isomorphic():
        print(cc1.name, 'is isomorphic')
        # we could use GM.match(), but here we try to find the shortest diff
        short_diff = None
        for n, mapping in enumerate(GM.isomorphisms_iter()):
            diff = {k: v for k, v in mapping.items() if k != v}
            if short_diff is None or len(diff) < len(short_diff):
                short_diff = diff
            if n == 10000:  # don't spend too much here
                print(' (it may not be the simplest isomorphism)')
                break
        assert short_diff is not None
        for id1, id2 in short_diff.items():
            print('\t', id1, '->', id2)
    else:
        print(cc1.name, 'differs')
        if s2 - s1:
            print('\tmissing:', ' '.join(s2 - s1))
        if s1 - s2:
            print('\textra:  ', ' '.join(s1 - s2))

def main():
    ccd = gemmi.cif.read(CCD_PATH)
    absent = 0
    for f in sys.argv[1:]:
        block = gemmi.cif.read(f)[-1]
        cc1 = gemmi.make_chemcomp_from_block(block)
        try:
            block2 = ccd[cc1.name]
        except KeyError:
            absent += 1
            #print(cc1.name, 'not in CCD')
            continue
        cc2 = gemmi.make_chemcomp_from_block(block2)
        cc1.remove_hydrogens()
        cc2.remove_hydrogens()
        compare(cc1, cc2)
    if absent != 0:
        print(absent, 'of', len(sys.argv) - 1, 'monomers not found in CCD')

main()

If we run it on monomers that start with M we get:

$ examples/ccd_gi.py $CLIBD_MON/m/*.cif
M10 is isomorphic
       O9 -> O4
       O4 -> O9
MK8 is isomorphic
       O2 -> OXT
MMR differs
      missing: O12 O4
2 of 821 monomers not found in CCD

So in M10 the two atoms marked green are swapped:

_images/M10-isomorphism.png

(The image was generated in NGL and compressed with Compress-Or-Die.)

Substructure matching

Now, a little script to illustrate subgraph isomorphism. The script takes a (three-letter-)code of a molecule that is to be used as a pattern and finds CCD entries that contain such a substructure. As in the previous example, hydrogens and bond types are ignored.

# List CCD entries that contain the specified entry as a substructure.
# Ignoring hydrogens and bond types.

import sys
import networkx
from networkx.algorithms import isomorphism
import gemmi

CCD_PATH = 'components.cif.gz'

def graph_from_block(block):
    cc = gemmi.make_chemcomp_from_block(block)
    cc.remove_hydrogens()
    G = networkx.Graph()
    for atom in cc.atoms:
        G.add_node(atom.id, Z=atom.el.atomic_number)
    for bond in cc.rt.bonds:
        G.add_edge(bond.id1.atom, bond.id2.atom)
    return G

def main():
    assert len(sys.argv) == 2, "Usage: ccd_subgraph.py three-letter-code"
    ccd = gemmi.cif.read(CCD_PATH)
    entry = sys.argv[1]
    pattern = graph_from_block(ccd[entry])
    pattern_nodes = networkx.number_of_nodes(pattern)
    pattern_edges = networkx.number_of_edges(pattern)
    node_match = isomorphism.categorical_node_match('Z', 0)
    for block in ccd:
        G = graph_from_block(block)
        GM = isomorphism.GraphMatcher(G, pattern, node_match=node_match)
        if GM.subgraph_is_isomorphic():
            print(block.name, '\t +%d nodes, +%d edges' % (
                networkx.number_of_nodes(G) - pattern_nodes,
                networkx.number_of_edges(G) - pattern_edges))

main()

Let us check which entries have HEM as a substructure:

$ examples/ccd_subgraph.py HEM
1FH    +6 nodes, +7 edges
2FH    +6 nodes, +7 edges
4HE    +7 nodes, +8 edges
522    +2 nodes, +2 edges
6CO    +6 nodes, +7 edges
6CQ    +7 nodes, +8 edges
89R    +3 nodes, +3 edges
CLN    +1 nodes, +2 edges
DDH    +2 nodes, +2 edges
FEC    +6 nodes, +6 edges
HAS    +22 nodes, +22 edges
HCO    +1 nodes, +1 edges
HDM    +2 nodes, +2 edges
HEA    +17 nodes, +17 edges
HEB    +0 nodes, +0 edges
HEC    +0 nodes, +0 edges
HEM    +0 nodes, +0 edges
HEO    +16 nodes, +16 edges
HEV    +2 nodes, +2 edges
HP5    +2 nodes, +2 edges
ISW    +0 nodes, +0 edges
MH0    +0 nodes, +0 edges
MHM    +0 nodes, +0 edges
N7H    +3 nodes, +3 edges
NTE    +3 nodes, +3 edges
OBV    +14 nodes, +14 edges
SRM    +20 nodes, +20 edges
UFE    +18 nodes, +18 edges

Maximum common subgraph

In this example, we use McGregor’s algorithm, implemented in the Boost Graph Library, to identify the largest common induced subgraphs. To ensure connectivity, we set the option only_connected_subgraphs=true.

To illustrate this example, we compare the ligands AUD and LSA:

_images/aud_lsa.png

The complete code is in examples/with_bgl.cpp. This file also contains examples of using the BGL’s VF2 implementation for checking graph and subgraph isomorphisms.

// We ignore hydrogens here.
// Example output:
//   $ time with_bgl -c monomers/a/AUD.cif monomers/l/LSA.cif
//   Searching largest subgraphs of AUD and LSA (10 and 12 vertices)...
//   Maximum connected common subgraph has 7 vertices:
//     SAA -> S10
//     OAG -> O12
//     OAH -> O11
//     NAF -> N9
//     CAE -> C7
//     OAI -> O8
//     CAD -> C1
//   Maximum connected common subgraph has 7 vertices:
//     SAA -> S10
//     OAG -> O11
//     OAH -> O12
//     NAF -> N9
//     CAE -> C7
//     OAI -> O8
//     CAD -> C1
//   
//   real	0m0.012s
//   user	0m0.008s
//   sys	0m0.004s

struct PrintCommonSubgraphCallback {
  Graph g1, g2;
  template <typename CorrespondenceMap1To2, typename CorrespondenceMap2To1>
  bool operator()(CorrespondenceMap1To2 map1, CorrespondenceMap2To1,
                  typename GraphTraits::vertices_size_type subgraph_size) {
    std::cout << "Maximum connected common subgraph has " << subgraph_size
              << " vertices:\n";
    for (auto vp = boost::vertices(g1); vp.first != vp.second; ++vp.first) {
      Vertex v1 = *vp.first;
      Vertex v2 = boost::get(map1, v1);
      if (v2 != GraphTraits::null_vertex())
        std::cout << "  " << g1[v1].name << " -> " << g2[v2].name << std::endl;
    }
    return true;
  }
};

void find_common_subgraph(const char* cif1, const char* cif2) {
  gemmi::ChemComp cc1 = make_chemcomp(cif1).remove_hydrogens();
  Graph graph1 = make_graph(cc1);
  gemmi::ChemComp cc2 = make_chemcomp(cif2).remove_hydrogens();
  Graph graph2 = make_graph(cc2);
  std::cout << "Searching largest subgraphs of " << cc1.name << " and "
      << cc2.name << " (" << cc1.atoms.size() << " and " << cc2.atoms.size()
      << " vertices)..." << std::endl;
  mcgregor_common_subgraphs_maximum_unique(
      graph1, graph2,
      get(boost::vertex_index, graph1), get(boost::vertex_index, graph2),
      [&](Edge a, Edge b) { return graph1[a].type == graph2[b].type; },
      [&](Vertex a, Vertex b) { return graph1[a].el == graph2[b].el; },
      /*only_connected_subgraphs=*/ true,
      PrintCommonSubgraphCallback{graph1, graph2});
}

Torsion angles

This section presents functions dedicated to the calculation of the dihedral angles φ (phi), ψ (psi), and ω (omega) of the protein backbone. These functions are built upon the more general calculate_dihedral function, introduced in the section about coordinates, which takes four points in space as arguments.

calculate_omega() calculates the ω angle, which is usually around 180°:

>>> from math import degrees
>>> chain = st_virus[0]['A']
>>> degrees(gemmi.calculate_omega(chain[0], chain[1]))
159.9092215006572
>>> for res in chain[:5]:
...     next_res = chain.next_residue(res)
...     if next_res:
...         omega = gemmi.calculate_omega(res, next_res)
...         print(res.name, degrees(omega))
...
ALA 159.9092215006572
ALA -165.26874513591127
ALA -165.85686681169696
THR -172.99968385093572
SER 176.74223937657652

The φ and ψ angles are often used together, so they are calculated in the same function calculate_phi_psi():

>>> for res in chain[:5]:
...     prev_res = chain.previous_residue(res)
...     next_res = chain.next_residue(res)
...     phi, psi = gemmi.calculate_phi_psi(prev_res, res, next_res)
...     print('%s %8.2f %8.2f' % (res.name, degrees(phi), degrees(psi)))
...
ALA      nan   106.94
ALA  -116.64    84.57
ALA   -45.57   127.40
THR   -62.01   147.45
SER   -92.85   161.53

In C++ these functions can be found in gemmi/calculate.hpp.

The torsion angles φ and ψ can be visualized on the Ramachandran plot. Let us plot angles from all PDB entries with a resolution higher than 1.5Å. Usually, glycine, proline and the residue preceding proline (pre-proline) are plotted separately. Here, we will exclude pre-proline and make a separate plot for each amino acid. So first, we calculate angles and save φ,ψ pairs in a set of files – one file per residue.

import sys
from math import degrees
import gemmi

ramas = {aa: [] for aa in [
    'LEU', 'ALA', 'GLY', 'VAL', 'GLU', 'SER', 'LYS', 'ASP', 'THR', 'ILE',
    'ARG', 'PRO', 'ASN', 'PHE', 'GLN', 'TYR', 'HIS', 'MET', 'CYS', 'TRP']}

for path in gemmi.CoorFileWalk(sys.argv[1]):
    st = gemmi.read_structure(path)
    if 0.1 < st.resolution < 1.5:
        model = st[0]
        for chain in model:
            for res in chain.get_polymer():
                # previous_residue() and next_residue() return previous/next
                # residue only if the residues are bonded. Otherwise -- None.
                prev_res = chain.previous_residue(res)
                next_res = chain.next_residue(res)
                if prev_res and next_res and next_res.name != 'PRO':
                    v = gemmi.calculate_phi_psi(prev_res, res, next_res)
                    try:
                        ramas[res.name].append(v)
                    except KeyError:
                        pass

# Write data to files
for aa, data in ramas.items():
    with open('ramas/' + aa + '.tsv', 'w') as f:
        for phi, psi in data:
            f.write(f'{degrees(phi):.4f}\t{degrees(psi):.4f}\n')

The script above works with coordinate files in any of the formats supported by gemmi (PDB, mmCIF, mmJSON). As of 2019, processing a local copy of the PDB archive in the PDB format takes about 20 minutes.

In the second step, we plot the data points with Matplotlib. We use a script that can be found in examples/rama_plot.py. Six of the resulting plots are shown here (click to enlarge):

_images/ramachandran-per-aa.png

Topology

In gemmi, topology contains restraints applied to a model, as well as information about the provenance of these restraints, and related utilities. (The restraints include bond-distance restraints and therefore also bonding information).

Applied restraints differ from template restraints in a monomer library, although both are referred to as restraints. The library (template) restraints specify, for instance, how to restrain the angle CD2-CE2-NE1 in any TRP residue. In contrast, topology (concrete, applied to a model) restraints specify how to restrain the angle between specific atoms in the model (say, atoms #721-#723-#722). The latter seems like a trivial application of the former, and it often is. But in general, if the aim is to support all atomic models present in the PDB, including those with unusual arrangements of alternative conformations, the process of determining the topology is quite convoluted.

The typical macromolecular refinement workflow begins by reading a coordinate file and a monomer library. The template monomer restraints from the library (for bond distances, angles, etc.) are applied to monomers, and link definitions are matched to explicit and implicit links between monomers. Link definitions contain additional restraints and modifications to restraints within the linked monomers.

Currently, our topology works only with the monomer library from CCP4. This library was introduced in the early 2000s. Monomer libraries distributed with other popular macromolecular refinement programs, PHENIX and BUSTER, are organized somewhat differently (geostd from PHENIX is actually quite similar).

The restraints that we use are also similar to what is used in molecular dynamics (bond, angle, dihedral and improper dihedral restraints). Although the MD potentials have been deemed inadequate for refinement, and the restraints in experimental structural biology have been improved independently of the restraints in MD, they haven’t diverged too much and with a little work one could be substituted for the other.

When preparing a topology, macromolecular programs (in particular, Refmac) may also add hydrogens or shift existing hydrogens to the riding positions. And reorder atoms. In Python, we have one function that does it all:

gemmi.prepare_topology(st: gemmi.Structure,
                       monlib: gemmi.MonLib,
                       model_index: int = 0,
                       h_change: gemmi.HydrogenChange = HydrogenChange.NoChange,
                       reorder: bool = False,
                       warnings: object = None,
                       ignore_unknown_links: bool = False) -> gemmi.Topo

where

  • monlib is an instance of an undocumented MonLib class. For now, here is an example of how to read the CCP4 monomer library (Refmac dictionary):

    monlib_path = os.environ['CCP4'] + '/lib/data/monomers'
resnames = st[0].get_all_residue_names()
monlib = gemmi.read_monomer_lib(monlib_path, resnames)

  • h_change can be one of the following:

    • HydrogenChange.NoChange – no change,

    • HydrogenChange.Shift – shift existing hydrogens to their ideal (riding) positions,

    • HydrogenChange.Remove – remove all H and D atoms,

    • HydrogenChange.ReAdd – discard and re-create hydrogens in ideal positions (if the hydrogen position is not uniquely determined, its occupancy is set to zero),

    • HydrogenChange.ReAddButWater – the same as above, but doesn’t add H in waters,

    • HydrogenChange.ReAddKnown – the same as above, but doesn’t add any H atoms whose positions are not uniquely determined,

  • reorder – changes the order of atoms within each residue to match the order in the corresponding monomer cif file,

  • warnings – by default, an exception is raised when a chemical component is missing in the monomer library, or when a link is missing, or when the hydrogen adding procedure encounters an unexpected configuration. You can set warnings=sys.stderr to only print a warning to stderr and continue. sys.stderr can be replaced with any object that has the methods write(str) and flush().

TBC

Local copy of the PDB archive

Some of the examples in this documentation work with a local copy of the Protein Data Bank archive. This subsection describes the assumed setup.

Like in BioJava, we assume that the $PDB_DIR environment variable points to a directory that contains structures/divided/mmCIF – the same arrangement as on the PDB’s FTP server.

$ cd $PDB_DIR
$ du -sh structures/*/*  # as of Jun 2017
34G    structures/divided/mmCIF
25G    structures/divided/pdb
101G   structures/divided/structure_factors
2.6G   structures/obsolete/mmCIF

A traditional way to keep an up-to-date local archive is to rsync it once a week:

#!/bin/sh -x
set -u  # PDB_DIR must be defined
rsync_subdir() {
  mkdir -p "$PDB_DIR/$1"
  # Using PDBe (UK) here, can be replaced with RCSB (USA) or PDBj (Japan),
  # see https://www.wwpdb.org/download/downloads
  rsync -rlpt -v -z --delete \
      rsync.ebi.ac.uk::pub/databases/pdb/data/$1/ "$PDB_DIR/$1/"
}
rsync_subdir structures/divided/mmCIF
#rsync_subdir structures/obsolete/mmCIF
#rsync_subdir structures/divided/pdb
#rsync_subdir structures/divided/structure_factors

Gemmi has a helper function for using the local archive copy. It takes a PDB code (case insensitive) and a symbol denoting what file is requested: P for PDB, M for mmCIF, S for SF-mmCIF.

>>> os.environ['PDB_DIR'] = '/copy'
>>> gemmi.expand_if_pdb_code('1ABC', 'P') # PDB file
'/copy/structures/divided/pdb/ab/pdb1abc.ent.gz'
>>> gemmi.expand_if_pdb_code('1abc', 'M') # mmCIF file
'/copy/structures/divided/mmCIF/ab/1abc.cif.gz'
>>> gemmi.expand_if_pdb_code('1abc', 'S') # SF-mmCIF file
'/copy/structures/divided/structure_factors/ab/r1abcsf.ent.gz'

If the first argument is not in the PDB code format (4 characters for now) the function returns the first argument.

>>> arg = 'file.cif'
>>> gemmi.is_pdb_code(arg)
False
>>> gemmi.expand_if_pdb_code(arg, 'M')
'file.cif'

Multiprocessing

(Python-specific)

Most of the gemmi objects cannot be pickled. Therefore, they cannot be passed between processes when using the multiprocessing module. Currently, the only picklable classes (with protocol >= 2) are: UnitCell and SpaceGroup.

Usually, it is possible to organize multiprocessing in such a way that gemmi objects are not passed between processes. The example script below traverses subdirectories and asynchronously analyzes coordinate files, using 4 worker processes in parallel.

import multiprocessing
import sys
import gemmi

def f(path):
    st = gemmi.read_structure(path)
    weight = st[0].calculate_mass()
    return (st.name, weight)

def main(top_dir):
    with multiprocessing.Pool(processes=4) as pool:
        it = pool.imap_unordered(f, gemmi.CoorFileWalk(top_dir))
        for (name, weight) in it:
            print(f'{name} {weight / 1000:.1f} kDa')

if __name__ == '__main__':
    main(sys.argv[1])