Length dependency of conformational change

Introduction

In this notebook, we set out to determine if there was a correlation between conformational change and the length of CDR loops. We looked at both the correlation of bulk movements when loops where aligned on the framework regions and also the deformation effects when loops are aligned to one another.

import matplotlib.pyplot as plt
import pandas as pd
import scipy
import seaborn as sns

Loading data

results_fw_align = pd.read_csv('../data/processed/apo-holo-tcr-pmhc-class-I-comparisons/rmsd_cdr_fw_align_results.csv')
results_fw_align['alignment'] = 'framework'

results_loop_align = pd.read_csv('../data/processed/apo-holo-tcr-pmhc-class-I-comparisons/rmsd_cdr_loop_align_results.csv')
results_loop_align['alignment'] = 'loop'

results = pd.concat([results_fw_align, results_loop_align])
results

	complex_id	structure_x_name	structure_y_name	chain_type	cdr	rmsd	alignment
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	1.932806	framework
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	2	1.308598	framework
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	3	1.244062	framework
3	3qdg_D-E-C-A-B_tcr_pmhc	3qdg_D-E-C-A-B_tcr_pmhc.pdb	3qeu_A-B_tcr.pdb	beta_chain	1	0.809066	framework
4	3qdg_D-E-C-A-B_tcr_pmhc	3qdg_D-E-C-A-B_tcr_pmhc.pdb	3qeu_A-B_tcr.pdb	beta_chain	2	0.688597	framework
...	...	...	...	...	...	...	...
1581	7rtr_D-E-C-A-B_tcr_pmhc	7n1d_A-B_tcr.pdb	7rtr_D-E-C-A-B_tcr_pmhc.pdb	alpha_chain	2	0.206414	loop
1582	7rtr_D-E-C-A-B_tcr_pmhc	7n1d_A-B_tcr.pdb	7rtr_D-E-C-A-B_tcr_pmhc.pdb	alpha_chain	3	0.459090	loop
1583	7rtr_D-E-C-A-B_tcr_pmhc	7n1d_A-B_tcr.pdb	7rtr_D-E-C-A-B_tcr_pmhc.pdb	beta_chain	1	0.255668	loop
1584	7rtr_D-E-C-A-B_tcr_pmhc	7n1d_A-B_tcr.pdb	7rtr_D-E-C-A-B_tcr_pmhc.pdb	beta_chain	2	0.175123	loop
1585	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	0.223801	loop

3172 rows × 7 columns

Loading meta data

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

apo_holo_summary_df['id'] = apo_holo_summary_df['file_name'].str.replace('.pdb$', '', regex=True)

apo_holo_summary_df

	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
0	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	1ao7_D-E-C-A-B_tcr_pmhc
1	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	1bd2_D-E-C-A-B_tcr_pmhc
2	1bii_A-B-P_pmhc.pdb	1bii	pmhc	apo	NaN	NaN	P	A	B	NaN	RGPGRAFVTI	h2_dd	1bii_A-B-P_pmhc
3	1ddh_A-B-P_pmhc.pdb	1ddh	pmhc	apo	NaN	NaN	P	A	B	NaN	RGPGRAFVTI	h2_dd	1ddh_A-B-P_pmhc
4	1duz_A-B-C_pmhc.pdb	1duz	pmhc	apo	NaN	NaN	C	A	B	NaN	LLFGYPVYV	hla_a_02_01	1duz_A-B-C_pmhc
...	...	...	...	...	...	...	...	...	...	...	...	...	...
353	8gon_D-E-C-A-B_tcr_pmhc.pdb	8gon	tcr_pmhc	holo	D	E	C	A	B	TSESDYY-QEAYKQQN-ASSGNTPLV-SGHNS-FNNNVP-ASTWGR...	NaN	NaN	8gon_D-E-C-A-B_tcr_pmhc
354	8gop_A-B_tcr.pdb	8gop	tcr	apo	A	B	NaN	NaN	NaN	TSESDYY-QEAYKQQN-ASSGNTPLV-SGHNS-FNNNVP-ASTWGR...	NaN	NaN	8gop_A-B_tcr
355	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	8gvb_A-B-P-H-L_tcr_pmhc
356	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	8gvg_A-B-P-H-L_tcr_pmhc
357	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	8gvi_A-B-P-H-L_tcr_pmhc

358 rows × 13 columns

cdr_types = ['CDR-A1', 'CDR-A2', 'CDR-A3','CDR-B1', 'CDR-B2', 'CDR-B3']
apo_holo_summary_df[cdr_types] = apo_holo_summary_df['cdr_sequences_collated'].str.split('-').apply(pd.Series)

apo_holo_summary_df = apo_holo_summary_df.melt(
    id_vars=[col for col in apo_holo_summary_df.columns if col not in cdr_types],
    var_name='cdr_type',
    value_name='cdr_sequence',
    value_vars=cdr_types,
)

apo_holo_summary_df[['chain_type', 'cdr']] = apo_holo_summary_df['cdr_type'].map(
    lambda cdr_type: ('alpha_chain' if cdr_type[-2] == 'A' else 'beta_chain',
                      int(cdr_type[-1]))
).apply(pd.Series)

apo_holo_summary_df['cdr_length'] = apo_holo_summary_df['cdr_sequence'].str.len()

apo_holo_summary_df

	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	cdr_type	cdr_sequence	chain_type	cdr	cdr_length
0	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	1ao7_D-E-C-A-B_tcr_pmhc	CDR-A1	DRGSQS	alpha_chain	1	6.0
1	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	1bd2_D-E-C-A-B_tcr_pmhc	CDR-A1	NSMFDY	alpha_chain	1	6.0
2	1bii_A-B-P_pmhc.pdb	1bii	pmhc	apo	NaN	NaN	P	A	B	NaN	RGPGRAFVTI	h2_dd	1bii_A-B-P_pmhc	CDR-A1	NaN	alpha_chain	1	NaN
3	1ddh_A-B-P_pmhc.pdb	1ddh	pmhc	apo	NaN	NaN	P	A	B	NaN	RGPGRAFVTI	h2_dd	1ddh_A-B-P_pmhc	CDR-A1	NaN	alpha_chain	1	NaN
4	1duz_A-B-C_pmhc.pdb	1duz	pmhc	apo	NaN	NaN	C	A	B	NaN	LLFGYPVYV	hla_a_02_01	1duz_A-B-C_pmhc	CDR-A1	NaN	alpha_chain	1	NaN
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
2143	8gon_D-E-C-A-B_tcr_pmhc.pdb	8gon	tcr_pmhc	holo	D	E	C	A	B	TSESDYY-QEAYKQQN-ASSGNTPLV-SGHNS-FNNNVP-ASTWGR...	NaN	NaN	8gon_D-E-C-A-B_tcr_pmhc	CDR-B3	ASTWGRASTDTQY	beta_chain	3	13.0
2144	8gop_A-B_tcr.pdb	8gop	tcr	apo	A	B	NaN	NaN	NaN	TSESDYY-QEAYKQQN-ASSGNTPLV-SGHNS-FNNNVP-ASTWGR...	NaN	NaN	8gop_A-B_tcr	CDR-B3	ASTWGRASTDTQY	beta_chain	3	13.0
2145	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	8gvb_A-B-P-H-L_tcr_pmhc	CDR-B3	ASSDRDRVPETQY	beta_chain	3	13.0
2146	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	8gvg_A-B-P-H-L_tcr_pmhc	CDR-B3	ASSDRDRVPETQY	beta_chain	3	13.0
2147	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	8gvi_A-B-P-H-L_tcr_pmhc	CDR-B3	ASSLRDRVPETQY	beta_chain	3	13.0

2148 rows × 18 columns

Merging data and metadata

results = results.merge(
    apo_holo_summary_df[['file_name', 'pdb_id', 'structure_type', 'state']],
    how='left',
    left_on='structure_x_name',
    right_on='file_name',
).merge(
    apo_holo_summary_df[['file_name', 'pdb_id', 'structure_type', 'state']],
    how='left',
    left_on='structure_y_name',
    right_on='file_name',
).merge(
    apo_holo_summary_df[['id',
                         'cdr_sequences_collated',
                         'peptide_sequence',
                         'mhc_slug',
                         'cdr_sequence',
                         'cdr_length',
                         'cdr_type',
                         'chain_type',
                         'cdr']],
    how='left',
    left_on=['complex_id', 'chain_type', 'cdr'],
    right_on=['id', 'chain_type', 'cdr'],
)

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

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', 'alignment'])

results = results.groupby(['cdr_sequences_collated',
                           'alignment',
                           'comparison',
                           'cdr_length',
                           'cdr_sequence',
                           'cdr_type',
                           'chain_type',
                           'cdr'])['rmsd'].mean().reset_index()

Visualising results

Alignment on Framework region

data = results.query("alignment == 'framework'")

r, p_val = scipy.stats.pearsonr(data['cdr_length'], data['rmsd'])

sns.lmplot(data.sort_values('cdr_type'), x='cdr_length', y='rmsd', scatter=False)
sns.scatterplot(data.sort_values('cdr_type'), x='cdr_length', y='rmsd', hue='cdr_type')

plt.text(4, 8, f'$r^2$ = {r**2: .2f}, p-value = {p_val: .2e}')

plt.show()

Alignment on loops

data = results.query("alignment == 'loop'")

r, p_val = scipy.stats.pearsonr(data['cdr_length'], data['rmsd'])

sns.lmplot(data.sort_values('cdr_type'), x='cdr_length', y='rmsd', scatter=False)
sns.scatterplot(data.sort_values('cdr_type'), x='cdr_length', y='rmsd', hue='cdr_type')

plt.text(7, 2.5, f'$r^2$ = {r**2: .2f}, p-value = {p_val: .2e}')

plt.show()

Conclusion

There is a correlation in both paradigms, framework alignment and loop alignment, but the correlation is much stronger looking at the loop alignments. The increased correlation for loop alignments make sense since the conformational changes from the framework regions can be driven by other parts of the protein, but when the loops are aligned together, the only differences can be driven by changes in the loops themselves, implying the loop length has more of an effect.