Per residue changes of TCR CDRs between apo and holo structures

Introduction

In this notebook, we look if there are certain residue positions that move more than others in the TCR CDR loops. We use these visualisations to further characterise the movement of CDR loops as either rigid-body, where the entire loop moves as one unit, or plastic, where the loop can mold to its target.

[1]:

import os

import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import seaborn as sns

[2]:

from matplotlib_inline.backend_inline import set_matplotlib_formats
set_matplotlib_formats('svg')

[3]:

DATA_DIR = '../data/processed/apo-holo-tcr-pmhc-class-I-comparisons'

Loading Data

[4]:

results = pd.read_csv(os.path.join(DATA_DIR, 'tcr_per_res_apo_holo_loop_align.csv'))
results

[4]:

	complex_id	structure_x_name	structure_y_name	chain_type	cdr	residue_name	residue_seq_id	residue_insert_code	rmsd	ca_distance	chi_angle_change	com_distance
0	3qdg_D-E-C-A-B_tcr_pmhc	3qdg_D-E-C-A-B_tcr_pmhc.pdb	3qeu_A-B_tcr.pdb	alpha_chain	1	ASP	27	NaN	4.922807	2.215234	-1.001709	3.836500
1	3qdg_D-E-C-A-B_tcr_pmhc	3qdg_D-E-C-A-B_tcr_pmhc.pdb	3qeu_A-B_tcr.pdb	alpha_chain	1	ARG	28	NaN	7.683418	2.322292	-1.010462	6.119157
2	3qdg_D-E-C-A-B_tcr_pmhc	3qdg_D-E-C-A-B_tcr_pmhc.pdb	3qeu_A-B_tcr.pdb	alpha_chain	1	GLY	29	NaN	0.657793	0.718576	NaN	0.452200
3	3qdg_D-E-C-A-B_tcr_pmhc	3qdg_D-E-C-A-B_tcr_pmhc.pdb	3qeu_A-B_tcr.pdb	alpha_chain	1	SER	36	NaN	1.224430	0.404912	-2.505061	0.866544
4	3qdg_D-E-C-A-B_tcr_pmhc	3qdg_D-E-C-A-B_tcr_pmhc.pdb	3qeu_A-B_tcr.pdb	alpha_chain	1	GLN	37	NaN	1.133408	0.467132	0.667185	0.798590
...	...	...	...	...	...	...	...	...	...	...	...	...
6228	7rtr_D-E-C-A-B_tcr_pmhc	7n1d_A-B_tcr.pdb	7rtr_D-E-C-A-B_tcr_pmhc.pdb	beta_chain	3	ASP	109	NaN	0.507077	0.180564	0.198956	0.208659
6229	7rtr_D-E-C-A-B_tcr_pmhc	7n1d_A-B_tcr.pdb	7rtr_D-E-C-A-B_tcr_pmhc.pdb	beta_chain	3	ILE	114	NaN	2.164965	0.158682	3.679442	0.829175
6230	7rtr_D-E-C-A-B_tcr_pmhc	7n1d_A-B_tcr.pdb	7rtr_D-E-C-A-B_tcr_pmhc.pdb	beta_chain	3	GLU	115	NaN	1.577728	0.195887	3.091039	0.995351
6231	7rtr_D-E-C-A-B_tcr_pmhc	7n1d_A-B_tcr.pdb	7rtr_D-E-C-A-B_tcr_pmhc.pdb	beta_chain	3	GLN	116	NaN	0.204783	0.197683	-0.014126	0.166472
6232	7rtr_D-E-C-A-B_tcr_pmhc	7n1d_A-B_tcr.pdb	7rtr_D-E-C-A-B_tcr_pmhc.pdb	beta_chain	3	TYR	117	NaN	0.180118	0.164981	-0.024244	0.170852

6233 rows × 12 columns

[5]:

summary_df = pd.read_csv('../data/processed/apo-holo-tcr-pmhc-class-I/apo_holo_summary.csv')

ids = summary_df['file_name'].str.replace('.pdb', '', regex=False)
ids.name = 'id'
summary_df = summary_df.set_index(ids)

summary_df

[5]:

	file_name	pdb_id	structure_type	state	alpha_chain	beta_chain	antigen_chain	mhc_chain1	mhc_chain2	cdr_sequences_collated	peptide_sequence	mhc_slug
id
1ao7_D-E-C-A-B_tcr_pmhc	1ao7_D-E-C-A-B_tcr_pmhc.pdb	1ao7	tcr_pmhc	holo	D	E	C	A	B	DRGSQS-IYSNGD-AVTTDSWGKLQ-MNHEY-SVGAGI-ASRPGLA...	LLFGYPVYV	hla_a_02_01
1b0g_C-A-B_pmhc	1b0g_C-A-B_pmhc.pdb	1b0g	pmhc	apo	NaN	NaN	C	A	B	NaN	ALWGFFPVL	hla_a_02_01
1b0g_F-D-E_pmhc	1b0g_F-D-E_pmhc.pdb	1b0g	pmhc	apo	NaN	NaN	F	D	E	NaN	ALWGFFPVL	hla_a_02_01
1bd2_D-E-C-A-B_tcr_pmhc	1bd2_D-E-C-A-B_tcr_pmhc.pdb	1bd2	tcr_pmhc	holo	D	E	C	A	B	NSMFDY-ISSIKDK-AAMEGAQKLV-MNHEY-SVGAGI-ASSYPGG...	LLFGYPVYV	hla_a_02_01
1bii_P-A-B_pmhc	1bii_P-A-B_pmhc.pdb	1bii	pmhc	apo	NaN	NaN	P	A	B	NaN	RGPGRAFVTI	h2_dd
...	...	...	...	...	...	...	...	...	...	...	...	...
7rtd_C-A-B_pmhc	7rtd_C-A-B_pmhc.pdb	7rtd	pmhc	apo	NaN	NaN	C	A	B	NaN	YLQPRTFLL	hla_a_02_01
7rtr_D-E-C-A-B_tcr_pmhc	7rtr_D-E-C-A-B_tcr_pmhc.pdb	7rtr	tcr_pmhc	holo	D	E	C	A	B	DRGSQS-IYSNGD-AVNRDDKII-SEHNR-FQNEAQ-ASSPDIEQY	YLQPRTFLL	hla_a_02_01
8gvb_A-B-P-H-L_tcr_pmhc	8gvb_A-B-P-H-L_tcr_pmhc.pdb	8gvb	tcr_pmhc	holo	A	B	P	H	L	YGATPY-YFSGDTLV-AVGFTGGGNKLT-SEHNR-FQNEAQ-ASSD...	RYPLTFGW	hla_a_24_02
8gvg_A-B-P-H-L_tcr_pmhc	8gvg_A-B-P-H-L_tcr_pmhc.pdb	8gvg	tcr_pmhc	holo	A	B	P	H	L	YGATPY-YFSGDTLV-AVGFTGGGNKLT-SEHNR-FQNEAQ-ASSD...	RFPLTFGW	hla_a_24_02
8gvi_A-B-P-H-L_tcr_pmhc	8gvi_A-B-P-H-L_tcr_pmhc.pdb	8gvi	tcr_pmhc	holo	A	B	P	H	L	YGATPY-YFSGDTLV-AVVFTGGGNKLT-SEHNR-FQNEAQ-ASSL...	RYPLTFGW	hla_a_24_02

391 rows × 12 columns

[6]:

results = results.merge(
    summary_df[['cdr_sequences_collated', 'peptide_sequence', 'mhc_slug']],
    how='left',
    left_on='complex_id',
    right_index=True,
)

[7]:

results = results.merge(
    summary_df[['file_name', 'pdb_id', 'structure_type', 'state', 'alpha_chain', 'beta_chain', 'antigen_chain', 'mhc_chain1', 'mhc_chain2']],
    how='left',
    left_on='structure_x_name',
    right_on='file_name',
).merge(
    summary_df[['file_name', 'pdb_id', 'structure_type', 'state', 'alpha_chain', 'beta_chain', 'antigen_chain', 'mhc_chain1', 'mhc_chain2']],
    how='left',
    left_on='structure_y_name',
    right_on='file_name',
    suffixes=('_x', '_y')
)

[8]:

results['comparison'] = results['state_x'] + '-' + results['state_y']
results['comparison'] = results['comparison'].map(lambda entry: 'apo-holo' if entry == 'holo-apo' else entry)

[9]:

results['structure_comparison'] = results.apply(
    lambda row: '-'.join(sorted([row.structure_x_name, row.structure_y_name])),
    axis='columns',
)
results = results.drop_duplicates(['structure_comparison',
                                   'chain_type',
                                   'cdr',
                                   'residue_name',
                                   'residue_seq_id',
                                   'residue_insert_code'])

[10]:

results = results.groupby(['cdr_sequences_collated',
                           'comparison',
                           'chain_type',
                           'cdr',
                           'residue_name',
                           'residue_seq_id',
                           'residue_insert_code'], dropna=False)[['ca_distance', 'rmsd', 'chi_angle_change', 'com_distance']].mean().reset_index()

[11]:

results['resi'] = results['residue_seq_id'].apply(str) + results['residue_insert_code'].fillna('')

[12]:

results = results.query("comparison == 'apo-holo'")

[13]:

results

[13]:

	cdr_sequences_collated	comparison	chain_type	cdr	residue_name	residue_seq_id	residue_insert_code	ca_distance	rmsd	chi_angle_change	com_distance	resi
0	ATGYPS-ATKADDK-ALSDPVNDMR-SGHAT-FQNNGV-ASSLRGR...	apo-holo	alpha_chain	1	ALA	27	NaN	0.505979	0.727144	NaN	0.518151	27
1	ATGYPS-ATKADDK-ALSDPVNDMR-SGHAT-FQNNGV-ASSLRGR...	apo-holo	alpha_chain	1	GLY	29	NaN	0.914903	0.930089	NaN	0.854811	29
2	ATGYPS-ATKADDK-ALSDPVNDMR-SGHAT-FQNNGV-ASSLRGR...	apo-holo	alpha_chain	1	PRO	37	NaN	0.423195	0.503712	-0.025853	0.389174	37
3	ATGYPS-ATKADDK-ALSDPVNDMR-SGHAT-FQNNGV-ASSLRGR...	apo-holo	alpha_chain	1	SER	38	NaN	0.401867	0.469748	-0.121133	0.433753	38
4	ATGYPS-ATKADDK-ALSDPVNDMR-SGHAT-FQNNGV-ASSLRGR...	apo-holo	alpha_chain	1	THR	28	NaN	0.510473	1.928260	3.726374	0.564129	28
...	...	...	...	...	...	...	...	...	...	...	...	...
1442	YSGSPE-HISR-ALSGFNNAGNMLT-SGHAT-FQNNGV-ASSLGGA...	apo-holo	beta_chain	3	LEU	108	NaN	1.022477	1.809773	-1.412711	1.135954	108
1443	YSGSPE-HISR-ALSGFNNAGNMLT-SGHAT-FQNNGV-ASSLGGA...	apo-holo	beta_chain	3	SER	106	NaN	1.676174	1.573190	-0.192425	1.510255	106
1444	YSGSPE-HISR-ALSGFNNAGNMLT-SGHAT-FQNNGV-ASSLGGA...	apo-holo	beta_chain	3	SER	107	NaN	1.091206	1.232135	2.393467	0.895901	107
1445	YSGSPE-HISR-ALSGFNNAGNMLT-SGHAT-FQNNGV-ASSLGGA...	apo-holo	beta_chain	3	THR	115	NaN	1.236042	1.347615	-0.280349	1.218896	115
1446	YSGSPE-HISR-ALSGFNNAGNMLT-SGHAT-FQNNGV-ASSLGGA...	apo-holo	beta_chain	3	TYR	117	NaN	1.102913	1.209585	-0.137036	0.922437	117

992 rows × 12 columns

Visualising Results

Ca movement

[14]:

sns.catplot(results.sort_values(['resi', 'chain_type', 'cdr']),
            x='resi', y='ca_distance',
            row='chain_type', col='cdr',
            color='salmon',
            sharex=False,
            kind='bar')

[14]:

<seaborn.axisgrid.FacetGrid at 0x7f9a2a00b2b0>

../_images/source_Per_residue_changes_of_TCR_CDR_between_apo_and_holo_structures_18_1.svg

Residue RMSD difference

[15]:

sns.catplot(results.sort_values(['resi', 'chain_type', 'cdr']),
            x='resi', y='rmsd',
            row='chain_type', col='cdr',
            color='salmon',
            sharex=False,
            kind='bar')

[15]:

<seaborn.axisgrid.FacetGrid at 0x7f9a2a00af50>

../_images/source_Per_residue_changes_of_TCR_CDR_between_apo_and_holo_structures_20_1.svg

Centre of Mass Changes

[16]:

sns.catplot(results.sort_values(['resi', 'chain_type', 'cdr']),
            x='resi', y='com_distance',
            row='chain_type', col='cdr',
            color='salmon',
            sharex=False,
            kind='bar')

[16]:

<seaborn.axisgrid.FacetGrid at 0x7f9a2996ae30>

../_images/source_Per_residue_changes_of_TCR_CDR_between_apo_and_holo_structures_22_1.svg

Comparing Residue Identity to movment

[17]:

results['aa_type'] = results['residue_name'].map({
    'ARG': 'Charged',
    'HIS': 'Charged',
    'LYS': 'Charged',
    'ASP': 'Charged',
    'GLU': 'Charged',
    'SER': 'Polar',
    'THR': 'Polar',
    'ASN': 'Polar',
    'GLN': 'Polar',
    'CYS': 'Special',
    'GLY': 'Special',
    'PRO': 'Special',
    'ALA': 'Hydrophobic',
    'VAL': 'Hydrophobic',
    'ILE': 'Hydrophobic',
    'LEU': 'Hydrophobic',
    'MET': 'Hydrophobic',
    'PHE': 'Hydrophobic',
    'TYR': 'Hydrophobic',
    'TRP': 'Hydrophobic',
})

[18]:

aa_means = results.groupby('residue_name')['rmsd'].mean().to_dict()
results['aa_mean'] = results['residue_name'].map(aa_means)

[19]:

sns.barplot(results.sort_values('aa_mean', ascending=False), y='rmsd', x='residue_name', hue='aa_type')
plt.xticks(rotation=-45)
print()

../_images/source_Per_residue_changes_of_TCR_CDR_between_apo_and_holo_structures_26_1.svg

[20]:

num_side_chain_heavy_atoms = results['residue_name'].map({
    'ARG': 7,
    'HIS': 7,
    'LYS': 5,
    'ASP': 4,
    'GLU': 5,
    'SER': 2,
    'THR': 3,
    'ASN': 4,
    'GLN': 5,
    'CYS': 2,
    'GLY': 0,
    'PRO': 3,
    'ALA': 1,
    'VAL': 3,
    'ILE': 4,
    'LEU': 4,
    'MET': 4,
    'PHE': 7,
    'TYR': 8,
    'TRP': 10,
})

[21]:

sns.scatterplot(x=num_side_chain_heavy_atoms, y=results['rmsd'], hue=results['aa_type'])
plt.xlabel('number of heavy atoms in side chain')
plt.show()

../_images/source_Per_residue_changes_of_TCR_CDR_between_apo_and_holo_structures_28_0.svg

Measuring differences in \(\chi\)-angles

Do the side chains change conformation as well?

[22]:

results['chi_angle_change_mag'] = results['chi_angle_change'].apply(np.abs)
results['chi_angle_change_deg_mag'] = results['chi_angle_change_mag'].apply(np.degrees)

[23]:

sns.catplot(results.sort_values(['resi', 'chain_type', 'cdr']),
            x='resi', y='chi_angle_change',
            row='chain_type', col='cdr',
            color='salmon',
            sharex=False,
            kind='bar')

[23]:

<seaborn.axisgrid.FacetGrid at 0x7f9a2a20bf70>

../_images/source_Per_residue_changes_of_TCR_CDR_between_apo_and_holo_structures_31_1.svg

[24]:

sns.catplot(results.sort_values(['resi', 'chain_type', 'cdr']),
            x='resi', y='chi_angle_change_mag',
            row='chain_type', col='cdr',
            color='salmon',
            sharex=False,
            kind='bar')

[24]:

<seaborn.axisgrid.FacetGrid at 0x7f9a29bfeb90>

../_images/source_Per_residue_changes_of_TCR_CDR_between_apo_and_holo_structures_32_1.svg

[25]:

sns.catplot(results.sort_values(['resi', 'chain_type', 'cdr']),
            x='resi', y='chi_angle_change_deg_mag',
            row='chain_type', col='cdr',
            color='salmon',
            sharex=False,
            kind='bar')

[25]:

<seaborn.axisgrid.FacetGrid at 0x7f9a23a0b910>

../_images/source_Per_residue_changes_of_TCR_CDR_between_apo_and_holo_structures_33_1.svg

Conclusion

From these results, it seems that the CDR-3 loops undergo plastic deformation but the CDR-1 and CDR-2 loops act as rigid bodies when contacting MHC molecules. This was determined by the flat profiles of the CDR-1 and -2 loops and the peaked, normal-like, distributions of CDR-3 loops (both CDR-A3 and CDR-B3).