Structural alignment of lysozyme variants using ‘Protein Blocks’

In this example we perform a structural alignment of multiple lysozyme variants from different organisms. A feasible approach to perfrom such a multiple structure alignment is the usage of a structural alphabet: At first the structure is translated into a sequence that represents the structure. Then the sequences can be aligned with the standard sequence alignment techniques, using the substitution matrix of the structural alphabet.

In this example, the structural alphabet we will use is called protein blocks (PBs) 1 2: There are 16 different PBs, represented by the symbols a to p. Each one depicts a different set of the backbone dihedral angles of a peptide 5-mer. To assign a PB to an amino acid, the 5-mer centered on the respective residue is taken, its backbone dihedral angles are calculated and the PB with the least deviation to this set of angles is chosen.

1

AG de Brevern, C Etchebest and S Hazout, “Bayesian probabilistic approach for predicting backbone structures in terms of protein blocks.” Proteins, 41, 271-288 (2000).

2

J Barnoud, H Santuz, P Craveur, AP Joseph, V Jallu, AG de Brevern, P Poulain, “PBxplore: a tool to analyze local protein structure and deformability with Protein Blocks.” PeerJ, 5, (2017).

../../../_images/sphx_glr_pb_alignment_001.png
# Code source: Patrick Kunzmann
# License: BSD 3 clause

import numpy as np
import matplotlib.pyplot as plt
import biotite
import biotite.sequence as seq
import biotite.sequence.align as align
import biotite.sequence.graphics as graphics
import biotite.structure as struc
import biotite.structure.io.mmtf as mmtf
import biotite.database.rcsb as rcsb


# PB alphabet
pb_alphabet = seq.LetterAlphabet("abcdefghijklmnop")

# PB substitution matrix, adapted from PBxplore
matrix_str = """
    a     b     c     d     e     f     g     h     i     j     k     l     m     n     o     p
a  516   -59   113  -105  -411  -177   -27  -361    47  -103  -644  -259  -599  -372  -124   -83
b  -59   541  -146  -210  -155  -310   -97    90   182  -128   -30    29  -745  -242  -165    22
c  113  -146   360   -14  -333  -240    49  -438  -269  -282  -688  -682  -608  -455  -147     6
d -105  -210   -14   221     5  -131  -349  -278  -253  -173  -585  -670 -1573 -1048  -691  -497
e -411  -155  -333     5   520   185   186   138  -378   -70  -112  -514 -1136  -469  -617  -632
f -177  -310  -240  -131   185   459   -99   -45  -445    83  -214   -88  -547  -629  -406  -552
g  -27   -97    49  -349   186   -99   665   -99   -89  -118  -409  -138  -124   172   128   254
h -361    90  -438  -278   138   -45   -99   632  -205   316   192  -108  -712  -359    95  -399
i   47   182  -269  -253  -378  -445   -89  -205   696   186     8    15  -709  -269  -169   226
j -103  -128  -282  -173   -70    83  -118   316   186   768   196     5  -398  -340  -117  -104
k -644   -30  -688  -585  -112  -214  -409   192     8   196   568   -65  -270  -231  -471  -382
l -259    29  -682  -670  -514   -88  -138  -108    15     5   -65   533  -131     8   -11  -316
m -599  -745  -608 -1573 -1136  -547  -124  -712  -709  -398  -270  -131   241    -4  -190  -155
n -372  -242  -455 -1048  -469  -629   172  -359  -269  -340  -231     8    -4   703    88   146
o -124  -165  -147  -691  -617  -406   128    95  -169  -117  -471   -11  -190    88   716    58
p  -83    22     6  -497  -632  -552   254  -399   226  -104  -382  -316  -155   146    58   609
"""

# PB reference angles, adapted from PBxplore
ref_angles = np.array([
    [ 41.14,   75.53,  13.92,  -99.80,  131.88,  -96.27, 122.08,  -99.68],
    [108.24,  -90.12, 119.54,  -92.21,  -18.06, -128.93, 147.04,  -99.90],
    [-11.61, -105.66,  94.81, -106.09,  133.56, -106.93, 135.97, -100.63],
    [141.98, -112.79, 132.20, -114.79,  140.11, -111.05, 139.54, -103.16],
    [133.25, -112.37, 137.64, -108.13,  133.00,  -87.30, 120.54,   77.40],
    [116.40, -105.53, 129.32,  -96.68,  140.72,  -74.19, -26.65,  -94.51],
    [  0.40,  -81.83,   4.91, -100.59,   85.50,  -71.65, 130.78,   84.98],
    [119.14, -102.58, 130.83,  -67.91,  121.55,   76.25,  -2.95,  -90.88],
    [130.68,  -56.92, 119.26,   77.85,   10.42,  -99.43, 141.40,  -98.01],
    [114.32, -121.47, 118.14,   82.88, -150.05,  -83.81,  23.35,  -85.82],
    [117.16,  -95.41, 140.40,  -59.35,  -29.23,  -72.39, -25.08,  -76.16],
    [139.20,  -55.96, -32.70,  -68.51,  -26.09,  -74.44, -22.60,  -71.74],
    [-39.62,  -64.73, -39.52,  -65.54,  -38.88,  -66.89, -37.76,  -70.19],
    [-35.34,  -65.03, -38.12,  -66.34,  -29.51,  -89.10,  -2.91,   77.90],
    [-45.29,  -67.44, -27.72,  -87.27,    5.13,   77.49,  30.71,  -93.23],
    [-27.09,  -86.14,   0.30,   59.85,   21.51,  -96.30, 132.67,  -92.91],
])


# Fetch animal lysoyzme structures
lyso_files = rcsb.fetch(
    ["1REX", "1AKI", "1DKJ", "1GD6"],
    format="mmtf", target_path=biotite.temp_dir()
)
organisms = ["H. sapiens", "G. gallus", "C. viginianus", "B. mori"]

# Create a PB sequence from each structure
pb_seqs = []
for file_name in lyso_files:
    file = mmtf.MMTFFile()
    file.read(file_name)
    # Take only the first model into account
    array = mmtf.get_structure(file, model=1)
    # Remove everything but the first protein chain
    array = array[struc.filter_amino_acids(array)]
    array = array[array.chain_id == array.chain_id[0]]

    # Calculate backbone dihedral angles,
    # as the PBs are determined from them
    phi, psi, omega = struc.dihedral_backbone(array)
    # A PB requires the 8 phi/psi angles of 5 amino acids,
    # centered on the amino acid to calculate the PB for
    # Hence, the PBs are not defined for the two amino acids
    # at each terminus
    pb_angles = np.full((len(phi)-4, 8), np.nan)
    pb_angles[:, 0] = psi[  : -4]
    pb_angles[:, 1] = phi[1 : -3]
    pb_angles[:, 2] = psi[1 : -3]
    pb_angles[:, 3] = phi[2 : -2]
    pb_angles[:, 4] = psi[2 : -2]
    pb_angles[:, 5] = phi[3 : -1]
    pb_angles[:, 6] = psi[3 : -1]
    pb_angles[:, 7] = phi[4 :   ]
    pb_angles = np.rad2deg(pb_angles)

    # Angle RMSD of all reference angles with all actual angles
    rmsda = np.sum(
        (
            (
                ref_angles[:, np.newaxis] - pb_angles[np.newaxis, :] + 180
            ) % 360 - 180
        )**2,
        axis=-1
    )
    # Chose PB, where the RMSDA to the reference angle is lowest
    # Due to the definition of Biotite symbol codes
    # the index of the chosen PB is directly the symbol code
    pb_seq_code = np.argmin(rmsda, axis=0)
    # Put the array of symbol codes into actual sequence objects
    pb_sequence = seq.GeneralSequence(pb_alphabet)
    pb_sequence.code = pb_seq_code
    pb_seqs.append(pb_sequence)

# Perfrom a multiple sequence alignment of the PB sequences
matrix_dict = align.SubstitutionMatrix.dict_from_str(matrix_str)
matrix = align.SubstitutionMatrix(pb_alphabet, pb_alphabet, matrix_dict)
alignment, order, _, _ = align.align_multiple(
    pb_seqs, matrix, gap_penalty=(-500,-100), terminal_penalty=False
)

# Visualize the alignment
# Order alignment according to guide tree
alignment = alignment[:, order.tolist()]
labels = [organisms[i] for i in order]
fig = plt.figure(figsize=(8.0, 4.0))
ax = fig.add_subplot(111)
# The color scheme was generated with the 'Gecos' software
graphics.plot_alignment_type_based(
    ax, alignment, labels=labels, symbols_per_line=45, spacing=2,
    show_numbers=True, color_scheme="flower"
)
# Organism names in italic
ax.set_yticklabels(ax.get_yticklabels(), fontdict={"fontstyle":"italic"})
fig.tight_layout()
plt.show()

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