Structural Bioinformatics Library
Template C++ / Python API for developping structural bioinformatics applications.
User Manual

Table of Contents

Protein_representation

Authors: F. Cazals and T. Dreyfus and T. O'Donnell and R. Tetley

Illustration of Proteus, a god of changing nature, by Andrea Alciato. Similarly to Proteus, proteins keep changing shape, which is of paramount importance for the regulation of their functions.

Introduction

Proteins: a mix of geometry, topology, biophysics, and biology. Biomolecules in general and polypeptide chains (PC in this package) in particular are complex objects. Their description indeed involves

  • geometric information i.e. the coordinates which may be Cartesian or internal – see also Molecular_coordinates ,
  • biophysical annotations inherently associated to the PCs: the hierarchical organization of PCs (atoms, amino-acids, whole chain), and also selected annotations (e.g. secondary structures). (See also ESBTL for data structures giving access to such pieces of information.)

It should be stressed that these three categories of information exist independently and may be used independently. For example:

  • The study of conformations, say in the context of the exploration of potential (and free) energy landscape requires geometric and topological information to compute energies See e.g. the packages Molecular_potential_energy and Landscape_explorer .

Functionalities offered. Because of these varying needs, this package provides functionalities to access all the information available at once. The main classes provided are:

  • Class SBL::IO::T_Protein_representation_loader : to create instances of the previous two classes. Recall that a PDB file may define several geometric models, typically if the PDB file comes from NMR. If so, the loader forces the choice of one model. For this model, a SBL::CSB::T_Protein_representation containing instances of SBl::CSB::T_Polypeptide_chain_representation is returned.

Using Polypeptide chain and protein representations

The following piece of code illustrates how to access protein representations and their chains. For the latter, one gets access to

  • topological information encoded in the covalent structure,
  • geometric information encoded in the conformation,
  • biological/chemical information.

Loading proteins and polypeptide chains

Consider a PDB file containing one or several chains. The loader creates one SBL::CSB::T_Polypeptide_chain_representation for each chain, and these are stored within a SBL::CSB::T_Protein_representation .

Note that one can specify the chains to be loaded. In that case, SBL::CSB::T_Protein_representation contains a map mapping a chain id to the corresponding SBL::CSB::T_Polypeptide_chain_representation .

Note also that if there are missing residues in the input PDB file, the chain will be constructed with the missing residues. As a result, the corresponding SBL::CSB::T_Polypeptide_chain_representation will have several connected components. See the package Molecular_covalent_structure for further details.


In the sequel, we show how to access the various pieces of information. The following point should be stressed:

Covalent Structure File Loader statistics:
Number of loaded covalent structures: 1
Details for each covalent structure :
-- structure 1:
-- -- Number of loaded atoms: 3408
-- -- Number of particles: 5406
-- -- Number of modeled particles: 3408
-- -- Number of loaded conformations: 1
-- -- Number of bonds: 5467
-- -- Number of modeled bonds: 3469
-- -- Number of built disulfide bonds: 4 / 4
A common difficulty with PDB files is the presence of non-standard molecules / residues. Since this package is concerned with protein chains only, upon facing a residue which is non standard for a protein, the loader issues a message and halts the construction of the molecule. In other words, for a file containing a mixture of molecules (proteins, nucleic acids, drugs, etc), the loader only returns the protein chains found.


Enumerating atoms, residues, and the associated information

In the sequel, we focus on SBL::CSB::T_Polypeptide_chain_representation , and show how to access information associated with atoms. As an illustration, the first part of the snippet shows how to count elements of each type via a map; the second one collects the temperature factors of all atoms.

In terms of data structures, dereferencing the iterator on atoms via (*it) gives access to the ESBTL::Molecular_atom, data structure.

Number of elements of each type :
C : 613
H : 264
N : 193
O : 185
S : 10

min / max / average of temperature factors : 0 84.09 28.3898
In a number of protein chains, residues are accompanied by insertion codes. Resid and insertion codes are accessed directly from the residue as follows : 
residue.residue_sequence_number(); residue.insertion_code();


If one or more residues are missing in a chain, that chain contains several connected components. Several methods apply both to the whole chain, and to connected components. These methods are parameterized by an integer: by default, this number is negative and the method applied to the whole chain irrespective of connected components. If there are say n connected components, the index in 0..n-1 indicates which c.c. should be processed.


Iterating on the backbone

In the following, an iterator on the backbone is used to store all backbone atoms into three containers, respectively for Calpha, C, N. As previously, backbone atoms are returned as ESBTL::Molecular_atom .

Found in the backbone : 129 CA, 129 C, 129 N.
We only iterate on those atoms which are provided in the PDB. That is, for a structure presenting gaps, backbone atoms in the gaps are skipped. Since the primary sequence information is easily accessed, users can identify gaps based on resids. It is also possible to iterate over the backbone for each connected component of the chain : the begin and end iterators are parameterized by the number of the connected component (if none is specified, the whole chain is considered). See the code snippet below for an illustration.


Counting residues by type

Molecular residues are accessed via the class ESBTL::Molecular_residue from ESBTL. Collecting residues of a given type is straightforward:

Number of residues of each type :
ALA : 12
ARG : 11
ASN : 14
ASP : 7
CYS : 8
GLN : 3
GLU : 2
GLY : 12
HIS : 1
ILE : 6
LEU : 8
LYS : 6
MET : 2
PHE : 3
PRO : 2
SER : 10
THR : 7
TRP : 6
TYR : 3
VAL : 6

Accessing the Cartesian atomic coordinates

In the following, we show how to compute the center of mass of Calpha carbons, in a pedestrian way.

The example also calls the function SBL::CSB::T_Polypeptide_chain_representation::compute_heavy_atoms_center_of_mass() , whose name is self-explanatory.

Center of mass of CA : (53.2452, -17.1442, 7.57498)

Center of mass of Heavy atoms: (53.1526, -17.1834, 7.31916)
(Advanced) Note that the functions get_x() get_y() get_z() retrieve cartesian coordinates from the conformation. As mentioned in Introduction, the Cartesian coordinates are available via two channels: the data structures for the information contained in the PDB file (the ESBTL data structures) and the data structure for the conformation. Both are coherent if the coordinates are not changed; nevertheless, functions get_x() get_y() get_z() use the conformation.


Changing the Cartesian atomic coordinates

The following example shows how to change Cartesian coordinates:

Distance between new and old center of mass: 2
(Advanced) Following the remark above, upon changing the coordinates, Cartesian coordinates must be accessed via the conformation and not the ESBTL data structures. This is naturally taken care of by the get_x() get_y() get_z() functions. (NB: to put it sharply, the user should not mine the data structures to access the hidden ESBTL data structures!)


Accessing internal coordinates

In the following, we show how to access internal coordinates, namely bond lengths, valence angles, and dihedral angles. Note in particular that the latter can be used to produce the so-called ramachandran plot. See also Fig. dihedral-angles-backbone.

This first snippet illustrates iterators returning all internal coordinates, which are accessed via dedicated iterators:

Mean bond length: 2.0449
Mean valence angle: 1.63797
Mean dihedral angle: 0.222753
Mean phi angle: -1.05698
Mean psi angle: 0.52554
Mean omega angle: 0.425752

This second snippet focuses on the dihedral angles associated with a given residue:

Residue 2 has Phi angle: -1.87983, Psi angle: 2.15193 and Omega angle: 3.11996
Residue 33 has Phi angle: -1.04222, Psi angle: -0.895227 and Omega angle: -3.08817

Dihedral angles along the backbone of a polypeptide chain. By convention, the three angles display, namely $\Phi, \Psi, \omega$, are associated with the i-th amino-acid.

Implementation and functionalities

Data structures and classes

As mentioned in Introduction, PC come with topological, geometric, and biophysical information. This package provides three main classes:

Internally, the topological, geometric, and biophysical pieces of information are stored into the following DS:

Options offered by these classes

The loader SBL::IO::T_Protein_representation_loader has a number of options listed below, that can be set either from the command line using the Module_base framework, or directly using appropriate methods :

Example

The following example is the tutorial example presented in section Using Polypeptide chain and protein representations snippet by snippet :

Advanced: atoms, indices, and coordinates

Low level operations


Prerequisites. The manipulation of atoms involves three sets of indices:

  • Atomid: the index provided in the PDB file. May not be contiguous.
  • Linear position: atom position in the structure, once gaps have been removed. A plain linear ordering from 0 to n-1, if there are n atoms. This index is used to access the position i.e. the Cartesian coordinates of the atom in the conformation of the molecule – see below.
  • Particle representation, aka Vertex id: vertex id of the atom in the boost graph used to represent the molecular topology. This type is provided by the graph library used, boost graph in our case.

Finally, recall that an atom is term embeded if it has Cartesian coordinates. In particular, all missing atoms in a PDB files are stored in the graph representing the molecule, but are not embedded.


Particle info for proteins. The class SBL::CSB::T_Particle_info_for_proteins is a record providing the required information, namely: pointer to the atom itself, res_id, ins_code, res_name, atom_name, chain_id.

The particle info is used as a key in a map as follows:

    typename T_Molecular_covalent_structure<ParticleInfo>::Particle_rep
    T_Molecular_covalent_structure<ParticleInfo>::add_particle(const Particle_info& info)
    {
      Particle_rep p = boost::add_vertex(this->m_graph);
      this->m_graph[p] = info;

      // Particle_info to Particle_rep
      this->m_particleInfo_to_particleRep.insert(std::make_pair(this->m_graph[p], p));

      // ParticleRep to linearPosition
      this->m_particleRep_to_linearPosition.push_back(p);
            
      return p;
    }


Molecular_covalent_structure. The covalent structure is represented using the class SBL::CSB::T_Molecular_covalent_structure. It is effectively built by the class SBL::CSB::T_Molecular_covalent_structure_builder_for_proteins, which creates the individual amino acids and links them into the graph representing the molecule. This creation involves all atoms of all residues, be they present in the PDB file or not – see the notion of embedded atom below.

In the following, we use the following types, as defined above:

  • Particle_info : information record on the atom.
  • Particle_rep : index of the corresponding vertex in the boost graph.
  • ParticleInfo_to_particleRep_map_type: Particle_info to Particle_rep.

Key members of the class regarding indices: 

// The boost graph used to represent the structure
Covalent_structure_graph             m_graph;

// Mapping particleInfo to graph vertex/particleRep
ParticleInfo_to_particleRep_map_type                             m_particleInfo_to_particleRep; 

// Mapping the particleRep (an int, actually), to the linear position used in the conformation
std::vector<int>                     m_particleRep_to_linearPosition;

In the class SBL::CSB::T_Molecular_covalent_structure, the linear position is set/obtained as follows 

void  set_particle_linearPosition(Particle_rep p, int position){
        this->m_particleRep_to_linearPosition[p] = position;
}

int get_particle_linearPosition(Particle_rep p)const{
      assert(p < this->m_particleRep_to_linearPosition.size());
      return this->m_particleRep_to_linearPosition[p];
}

Then, the linear position is used to obtain the x/y/z coordinates from the conformation, as follows: 

   <ParticleInfo>::get_x(const Conformation& C, Particle_rep p)const{
      assert(this->is_embedded(p));
      return SBL::Models::T_Conformation_traits<Conformation>::at(C, 3*this->get_particle_linearPosition(p));
    }

The linear position is also used to know whether a particle has been assigned Cartesian coordinates: 

bool is_embedded(Particle_rep p)const{
      return this->get_particle_linearPosition(p) >= 0;
}
The covalent structure built by the class SBL::CSB::T_Molecular_covalent_structure_builder_for_proteins does
Note that the position is used in the conformation, not in the molecular covalent structure itself.



Conformations. The class SBL::Model::T_Conformation_traits proposes to store a conformation as a vector of float types representing coordinates.

Such conformations are then stored by the PDB loader SBL::IO::T_Protein_representation_loader 

  std::vector<std::vector<Conformation_type> >        m_conformations_ensembles;

These conformations are then passed to the individual chains stored as instances of the class SBL::CSB::T_Polypeptide_chain_representation.


Summary. Summarizing, the construction of instances of the class SBL::CSB::T_Polypeptide_chain_representation involves the following steps:

High level operations


T_Polypeptide_chain_representation. The high level class SBL::CSB::T_Polypeptide_chain_representation proposes high level operations, in particular the ability to obtain internal coordinates from atomids – specified in the PDB file. Such operations use the internal representation of atoms via their particle representations. As an example, consider:

To provide these high level operations, we use the map: 

//! The covalent structure of the protein
Molecular_covalent_structure&               m_covalent_structure;

//! The conformation of the protein
Conformation_type                           m_conformation;

// mapping an ESBTL atom via its atom id to the corresponding Particle_rep ie Particle_vertex_descriptor
typedef typename std::map<unsigned, Particle_rep>  AtomId_to_particleRep_map_type;
AtomId_to_particleRep_map_type                     m_atomId_to_particleRep;

As an example, SBL::CSB::T_Polypeptide_chain_representation::Bond_angle proceeds as follows: 

      //! Return the value of this angle.
      FT get_valence_angle() const
      {
        //get the internal particle reps
        Particle_rep a = this->m_P->m_atomId_to_particleRep.at(boost::get<0>(this->m_bond_angle).atom_serial_number());
        Particle_rep b = this->m_P->m_atomId_to_particleRep.at(boost::get<1>(this->m_bond_angle).atom_serial_number());
        Particle_rep c = this->m_P->m_atomId_to_particleRep.at(boost::get<2>(this->m_bond_angle).atom_serial_number());

        //get the interal bond reps
        std::pair<bool, Bond_rep> bond1 = this->m_P->m_covalent_structure.get_bond_rep(a, b);
        std::pair<bool, Bond_rep> bond2 = this->m_P->m_covalent_structure.get_bond_rep(b, c);
        assert(bond1.first && bond2.first);

        //get the internal bond angle rep
        std::pair<bool, Bond_angle_rep> bond_angle = this->m_P->m_covalent_structure.get_bond_angle_rep(bond1.second, bond2.second);

        //return the valence angle
        return this->m_ic.get_valence_angle(this->m_P->m_conformation, this->m_P->m_covalent_structure, bond_angle.second);
      }


Coherence. For polypeptide chains represented by the class SBL::CSB::T_Protein_representation, the coherence between these maps is ensured by the following function

void  T_Polypeptide_chain_representation<ParticleTraits, MolecularCovalentStructure, ConformationType>::
    build_model_to_covalent_structure_mapping()
    {
      for(Particles_iterator it = this->particles_begin(); it != this->particles_end(); it++){
        this->m_atomId_to_particleRep[(*this)[*it]->atom_serial_number()] = *it;
        this->m_covalent_structure.set_particle_linearPosition((*it),m_atomId_to_particleRep.size()-1);
      }
    };

Due to the previous, the iterators of m_covalent_structure can now be used to extract particles and compute internal coordinate values using m_conformation as the coordinates of particles or for any other purpose requiring simultaneous use of m_covalent_structure and m_conformation.

Applications

This package also offers several useful programs to inspect properties of proteins / their conformations:

  • sbl-protein-info.exe: loads protein chain(s) form a PDB file, and parses it to deliver a variety of statistics (number of a.a. of each type, center of mass of the structure, calculation of internal coordinates and average statistics, etc. Note that the corresponding code of interest for developers that wish to use this package to develop novel applications.
  • sbl-protein-ramachandran.exe: computes the Ramachandran plot of a protein; alternatively, for conformations of the same protein, computes the Ramachandran plot of specified amino-acids.
  • sbl-protein-pdb-cleaner.py : a python script cleaning PDB files to make sure the contain the required information for ESBTL loaders (in particular chemical element names), and builders of the covalent structure (correct atom naming required to build the molecular topology).