.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/gallery/structure/normal_modes.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_examples_gallery_structure_normal_modes.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_examples_gallery_structure_normal_modes.py:


Visualization of normal modes from an elastic network model
===========================================================

The *elastic network model* (ENM) is a fast method to estimate movements
in a protein structure, without the need to run time-consuming MD
simulations.
A protein is modelled as *mass-and-spring* model, with the masses being
the :math:`C_\alpha` atoms and the springs being the non-covalent bonds
between adjacent residues.
Via *normal mode analysis* distinct movements/oscillations can be
extracted from the model.

An *anisotropic network model* (ANM), is an ENM that includes
directional information.
Hence, the normal mode analysis yields eigenvectors, where each atom is
represented by three vector components (*x*, *y*, *z*).
Thus these vectors can be used for 3D representation.

In the case of this example a normal mode analysis on an ANM was already
conducted.
This script merely takes the structure and obtained eigenvectors
to add a smooth oscillation of the chosen normal mode to the structure.
The newly created structure has multiple models, where each model
depicts a different time in the oscillation period.
Then the multi-model structure can be used to create a video of the
oscillation using a molecular visualization program.

The file containing the eigenvectors can be downloaded via this
:download:`link </examples/download/glycosylase_anm_vectors.csv>`.

.. GENERATED FROM PYTHON SOURCE LINES 32-114



.. image-sg:: /examples/gallery/structure/images/sphx_glr_normal_modes_001.gif
   :alt: normal modes
   :srcset: /examples/gallery/structure/images/sphx_glr_normal_modes_001.gif
   :class: sphx-glr-single-img





.. code-block:: Python


    # Code source: Patrick Kunzmann
    # License: BSD 3 clause

    from tempfile import NamedTemporaryFile
    import numpy as np
    from numpy import newaxis
    import biotite.structure as struc
    import biotite.structure.io as strucio
    import biotite.structure.io.pdbx as pdbx
    import biotite.database.rcsb as rcsb


    # A CSV file containing the eigenvectors for the CA atoms
    VECTOR_FILE = "../../download/glycosylase_anm_vectors.csv"
    # The corresponding structure
    PDB_ID = "1MUG"
    # The normal mode to be visualized
    # '-1' is the last (and most significant) one
    MODE = -1
    # The amount of frames (models) per oscillation
    FRAMES = 60
    # The maximum oscillation amplitude for an atom
    # (The length of the ANM's eigenvectors make only sense when compared
    # relative to each other, the absolute values have no significance)
    MAX_AMPLITUDE = 5


    # Load structure
    pdbx_file = pdbx.BinaryCIFFile.read(rcsb.fetch(PDB_ID, "bcif"))
    structure = pdbx.get_structure(pdbx_file, model=1)


    # Filter first peptide chain
    protein_chain = structure[
        struc.filter_amino_acids(structure)
        & (structure.chain_id == structure.chain_id[0])
    ]
    # Filter CA atoms
    ca = protein_chain[protein_chain.atom_name == "CA"]


    # Load eigenvectors for CA atoms
    # The first axis indicates the mode,
    # the second axis indicates the vector component
    vectors = np.loadtxt(VECTOR_FILE, delimiter=",").transpose()
    # Discard the last 6 modes, as these are movements of the entire system:
    # A system with N atoms has only 3N - 6 degrees of freedom
    #                                   ^^^
    vectors = vectors[:-6]
    # Extract vectors for given mode and reshape to (n,3) array
    mode_vectors = vectors[MODE].reshape((-1, 3))
    # Rescale, so that the largest vector has the length 'MAX_AMPLITUDE'
    vector_lenghts = np.sqrt(np.sum(mode_vectors**2, axis=-1))
    scale = MAX_AMPLITUDE / np.max(vector_lenghts)
    mode_vectors *= scale


    # Stepwise application of eigenvectors as smooth sine oscillation
    time = np.linspace(0, 2*np.pi, FRAMES, endpoint=False)
    deviation = np.sin(time)[:, newaxis, newaxis] * mode_vectors

    # Apply oscillation of CA atom to all atoms in the corresponding residue
    oscillation = np.zeros((FRAMES, len(protein_chain), 3))
    residue_starts = struc.get_residue_starts(
        protein_chain,
        # The last array element will be the length of the atom array,
        # i.e. no valid index
        add_exclusive_stop=True
    )
    for i in range(len(residue_starts) -1):
        res_start = residue_starts[i]
        res_stop = residue_starts[i+1]
        oscillation[:, res_start:res_stop, :] \
            = protein_chain.coord[res_start:res_stop, :] + deviation[:, i:i+1, :]

    # An atom array stack containing all frames
    oscillating_structure = struc.from_template(protein_chain, oscillation)
    # Save as PDB for rendering a video with PyMOL
    temp = NamedTemporaryFile(suffix=".pdb")
    strucio.save_structure(temp.name, oscillating_structure)

    temp.close()

.. _sphx_glr_download_examples_gallery_structure_normal_modes.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: normal_modes.ipynb <normal_modes.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: normal_modes.py <normal_modes.py>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_