02 Cross Resistance Matrices
Jupyter notebook from the Gene-Resolution Metal Cross-Resistance Across Diverse Bacteria project.
NB02: Per-Organism Cross-Resistance Matrices¶
Project: metal_cross_resistance
Purpose: For each organism with ≥3 metals, compute metal × metal Pearson correlation matrices from gene fitness profiles. Assess significance, compare across organisms, and test H1 (conservation of cross-resistance patterns).
Environment: Local (runs from NB01 cached data)
Outputs:
data/cross_resistance_matrices/{orgId}_metal_corr.csv— Per-organism correlation matricesdata/all_metal_pairs.csv— All pairwise metal correlations across all organismsdata/consensus_cross_resistance.csv— Consensus matrix (mean r across organisms per metal pair)figures/cross_resistance_panel.png— Multi-organism heatmap panelfigures/metal_pair_conservation.png— How consistent are metal pairs across organismsfigures/metal_clustering_dendrogram.png— Hierarchical clustering of consensus matrix
In [1]:
import pandas as pd
import numpy as np
from pathlib import Path
from scipy import stats
from scipy.cluster.hierarchy import linkage, dendrogram, fcluster
from scipy.spatial.distance import squareform
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
import seaborn as sns
import warnings
warnings.filterwarnings('ignore', category=FutureWarning)
DATA_DIR = Path('../data')
MATRIX_DIR = DATA_DIR / 'gene_metal_fitness'
CORR_DIR = DATA_DIR / 'cross_resistance_matrices'
CORR_DIR.mkdir(exist_ok=True)
FIG_DIR = Path('../figures')
# Load extraction summary
summary = pd.read_csv(DATA_DIR / 'extraction_summary.csv')
print(f'Organisms available: {len(summary)}')
print(f'Organisms with >=3 metals: {(summary.n_metals >= 3).sum()}')
print(f'Organisms with >=5 metals: {(summary.n_metals >= 5).sum()}')
Organisms available: 30 Organisms with >=3 metals: 28 Organisms with >=5 metals: 13
1. Compute Per-Organism Cross-Resistance Matrices¶
For each organism, compute pairwise Pearson correlation between metal fitness profiles (each metal is a column vector of gene fitness values). This measures how similar the genetic basis of tolerance is between two metals.
In [2]:
all_pairs = [] # Collect all pairwise correlations
org_corr_matrices = {} # Store full matrices
for _, row in summary.iterrows():
org = row['orgId']
infile = MATRIX_DIR / f'{org}_metal_fitness.csv'
if not infile.exists():
continue
mat = pd.read_csv(infile, index_col=0)
# Need at least 3 metals for a meaningful matrix
if mat.shape[1] < 3:
continue
# Compute pairwise Pearson correlations with p-values
metals = list(mat.columns)
corr_matrix = mat.corr(method='pearson')
# Save per-organism matrix
corr_matrix.to_csv(CORR_DIR / f'{org}_metal_corr.csv')
org_corr_matrices[org] = corr_matrix
# Extract all pairs with p-values
for i, m1 in enumerate(metals):
for j, m2 in enumerate(metals):
if i < j:
# Get complete cases for this pair
valid = mat[[m1, m2]].dropna()
n_genes = len(valid)
if n_genes < 30: # minimum for meaningful correlation
continue
r, p = stats.pearsonr(valid[m1], valid[m2])
all_pairs.append({
'orgId': org, 'metal1': m1, 'metal2': m2,
'r': r, 'p': p, 'n_genes': n_genes,
'n_metals_org': len(metals),
'pair': f'{min(m1,m2)}-{max(m1,m2)}'
})
pairs_df = pd.DataFrame(all_pairs)
pairs_df.to_csv(DATA_DIR / 'all_metal_pairs.csv', index=False)
print(f'Computed cross-resistance for {len(org_corr_matrices)} organisms')
print(f'Total metal pairs: {len(pairs_df)}')
print(f'Unique metal pairs: {pairs_df.pair.nunique()}')
print(f'Pairs with p < 0.001: {(pairs_df.p < 0.001).sum()} ({(pairs_df.p < 0.001).mean():.1%})')
print(f'Pairs with p < 0.05: {(pairs_df.p < 0.05).sum()} ({(pairs_df.p < 0.05).mean():.1%})')
Computed cross-resistance for 28 organisms Total metal pairs: 317 Unique metal pairs: 85 Pairs with p < 0.001: 309 (97.5%) Pairs with p < 0.05: 314 (99.1%)
2. Consensus Cross-Resistance Matrix¶
For each metal pair tested in ≥3 organisms, compute the mean Pearson r across organisms. This gives us the "consensus" cross-resistance pattern — the central tendency across phylogenetically diverse bacteria.
In [3]:
# Aggregate by metal pair
pair_summary = pairs_df.groupby('pair').agg(
mean_r=('r', 'mean'),
median_r=('r', 'median'),
std_r=('r', 'std'),
min_r=('r', 'min'),
max_r=('r', 'max'),
n_orgs=('orgId', 'nunique'),
pct_positive=('r', lambda x: (x > 0).mean()),
pct_sig=('p', lambda x: (x < 0.05).mean()),
mean_n_genes=('n_genes', 'mean'),
).reset_index()
# Sign consistency: what fraction of organisms agree on the direction
pair_summary['sign_consistency'] = pair_summary['pct_positive'].apply(
lambda x: max(x, 1-x) # e.g., 90% positive → 90% consistent
)
pair_summary = pair_summary.sort_values('n_orgs', ascending=False)
print('=== Metal Pair Summary (sorted by number of organisms) ===')
print(f'Pairs tested in >=5 organisms: {(pair_summary.n_orgs >= 5).sum()}')
print(f'Pairs tested in >=10 organisms: {(pair_summary.n_orgs >= 10).sum()}')
print()
print(pair_summary[pair_summary.n_orgs >= 3].to_string(index=False, float_format='%.3f'))
=== Metal Pair Summary (sorted by number of organisms) === Pairs tested in >=5 organisms: 15 Pairs tested in >=10 organisms: 10 pair mean_r median_r std_r min_r max_r n_orgs pct_positive pct_sig mean_n_genes sign_consistency Co-Ni 0.559 0.580 0.188 0.204 0.915 28 1.000 1.000 3903.571 1.000 Cu-Ni 0.429 0.421 0.219 -0.080 0.897 24 0.958 1.000 3769.958 0.958 Co-Cu 0.433 0.404 0.224 -0.017 0.902 24 0.958 0.958 3769.958 0.958 Al-Ni 0.337 0.333 0.210 -0.053 0.679 20 0.950 0.950 3892.450 0.950 Al-Co 0.302 0.281 0.197 -0.064 0.737 20 0.950 1.000 3892.450 0.950 Ni-Zn 0.513 0.487 0.218 0.127 0.974 18 1.000 1.000 3593.389 1.000 Co-Zn 0.518 0.500 0.198 0.252 0.861 18 1.000 1.000 3593.389 1.000 Al-Cu 0.340 0.329 0.227 -0.060 0.801 17 0.941 1.000 3847.765 0.941 Cu-Zn 0.477 0.483 0.217 -0.070 0.787 16 0.938 1.000 3371.688 0.938 Al-Zn 0.441 0.438 0.166 0.120 0.711 13 1.000 1.000 3588.846 1.000 Fe-Ni 0.375 0.352 0.268 0.105 0.837 7 1.000 1.000 3538.429 1.000 Cu-Fe 0.455 0.473 0.195 0.181 0.777 7 1.000 1.000 3538.429 1.000 Co-Fe 0.453 0.562 0.283 0.020 0.791 7 1.000 0.857 3538.429 1.000 Fe-Zn 0.614 0.620 0.084 0.475 0.731 6 1.000 1.000 3496.667 1.000 Al-Fe 0.381 0.293 0.313 0.048 0.720 5 1.000 1.000 3517.400 1.000 Ni-U 0.464 0.446 0.137 0.337 0.610 3 1.000 1.000 3381.667 1.000 Al-U 0.193 0.102 0.173 0.085 0.394 3 1.000 1.000 3381.667 1.000 Co-U 0.422 0.434 0.179 0.238 0.595 3 1.000 1.000 3381.667 1.000 Cu-U 0.513 0.575 0.293 0.194 0.769 3 1.000 1.000 3381.667 1.000 U-Zn 0.356 0.248 0.306 0.120 0.702 3 1.000 1.000 3381.667 1.000
In [4]:
# Build consensus correlation matrix from pairs tested in >=3 organisms
well_tested = pair_summary[pair_summary.n_orgs >= 3].copy()
# Get all metals that appear in well-tested pairs
metals_in_pairs = set()
for pair in well_tested['pair']:
m1, m2 = pair.split('-')
metals_in_pairs.add(m1)
metals_in_pairs.add(m2)
metals_sorted = sorted(metals_in_pairs)
# Build symmetric matrix
consensus = pd.DataFrame(np.eye(len(metals_sorted)),
index=metals_sorted, columns=metals_sorted)
n_orgs_matrix = pd.DataFrame(0, index=metals_sorted, columns=metals_sorted, dtype=int)
for _, row in well_tested.iterrows():
m1, m2 = row['pair'].split('-')
consensus.loc[m1, m2] = row['mean_r']
consensus.loc[m2, m1] = row['mean_r']
n_orgs_matrix.loc[m1, m2] = row['n_orgs']
n_orgs_matrix.loc[m2, m1] = row['n_orgs']
consensus.to_csv(DATA_DIR / 'consensus_cross_resistance.csv')
n_orgs_matrix.to_csv(DATA_DIR / 'consensus_n_organisms.csv')
print('Consensus cross-resistance matrix (mean r across organisms):')
print(consensus.round(3).to_string())
print()
print('Number of organisms per pair:')
print(n_orgs_matrix.to_string())
Consensus cross-resistance matrix (mean r across organisms):
Al Co Cu Fe Ni U Zn
Al 1.000 0.302 0.340 0.381 0.337 0.193 0.441
Co 0.302 1.000 0.433 0.453 0.559 0.422 0.518
Cu 0.340 0.433 1.000 0.455 0.429 0.513 0.477
Fe 0.381 0.453 0.455 1.000 0.375 0.000 0.614
Ni 0.337 0.559 0.429 0.375 1.000 0.464 0.513
U 0.193 0.422 0.513 0.000 0.464 1.000 0.356
Zn 0.441 0.518 0.477 0.614 0.513 0.356 1.000
Number of organisms per pair:
Al Co Cu Fe Ni U Zn
Al 0 20 17 5 20 3 13
Co 20 0 24 7 28 3 18
Cu 17 24 0 7 24 3 16
Fe 5 7 7 0 7 0 6
Ni 20 28 24 7 0 3 18
U 3 3 3 0 3 0 3
Zn 13 18 16 6 18 3 0
3. Test H1: Is Cross-Resistance Conserved?¶
H1 predicts that the same metal pairs cluster together in >70% of species. We test this using sign consistency (do organisms agree on whether two metals are positively correlated?) and rank-order conservation (does the ranking of metal pair correlations stay the same across organisms?).
In [5]:
# H1 Test 1: Sign consistency
# For well-tested pairs (>=5 organisms), what fraction have >70% sign agreement?
robust_pairs = pair_summary[pair_summary.n_orgs >= 5].copy()
print('=== H1 Test: Sign Consistency ===')
print(f'Metal pairs tested in >=5 organisms: {len(robust_pairs)}')
print(f'Pairs with >70% sign consistency: {(robust_pairs.sign_consistency > 0.70).sum()} '
f'({(robust_pairs.sign_consistency > 0.70).mean():.1%})')
print(f'Pairs with >80% sign consistency: {(robust_pairs.sign_consistency > 0.80).sum()} '
f'({(robust_pairs.sign_consistency > 0.80).mean():.1%})')
print(f'Pairs with >90% sign consistency: {(robust_pairs.sign_consistency > 0.90).sum()} '
f'({(robust_pairs.sign_consistency > 0.90).mean():.1%})')
print(f'Pairs with 100% positive: {(robust_pairs.pct_positive == 1.0).sum()}')
print()
# All pairs are positive (cross-resistance, not cross-sensitivity)
print(f'Mean sign consistency: {robust_pairs.sign_consistency.mean():.3f}')
print(f'Mean pct_positive: {robust_pairs.pct_positive.mean():.3f}')
print()
# Binomial test: is 100% positive significant?
n_all_positive = (robust_pairs.pct_positive == 1.0).sum()
n_total = len(robust_pairs)
binom_result = stats.binomtest(n_all_positive, n_total, 0.5)
binom_p = binom_result.pvalue
print(f'Binomial test (all pairs positive vs 50% chance): '
f'{n_all_positive}/{n_total} = {n_all_positive/n_total:.1%}, p = {binom_p:.2e}')
=== H1 Test: Sign Consistency === Metal pairs tested in >=5 organisms: 15 Pairs with >70% sign consistency: 15 (100.0%) Pairs with >80% sign consistency: 15 (100.0%) Pairs with >90% sign consistency: 15 (100.0%) Pairs with 100% positive: 9 Mean sign consistency: 0.980 Mean pct_positive: 0.980 Binomial test (all pairs positive vs 50% chance): 9/15 = 60.0%, p = 6.07e-01
In [6]:
# H1 Test 2: Rank-order conservation
# For organisms with >=5 metals, do they agree on which metal pairs are most/least correlated?
# Use Kendall's W (coefficient of concordance) across organisms
# Get organisms with >=5 metals
rich_orgs = summary[summary.n_metals >= 5]['orgId'].tolist()
# Find metal pairs present in ALL rich organisms
# The common set is likely {Al, Co, Cu, Ni, Zn} tested in 12 organisms
common_metals = None
for org in rich_orgs:
if org in org_corr_matrices:
metals_org = set(org_corr_matrices[org].columns)
if common_metals is None:
common_metals = metals_org
else:
common_metals = common_metals & metals_org
common_metals = sorted(common_metals) if common_metals else []
print(f'Common metals across {len(rich_orgs)} rich organisms: {common_metals}')
# Extract the common-metal correlation values for each organism
if len(common_metals) >= 3:
# Build pairs from common metals
common_pairs = []
for i, m1 in enumerate(common_metals):
for j, m2 in enumerate(common_metals):
if i < j:
common_pairs.append((m1, m2))
# For each organism, get the correlation for each common pair
rank_data = []
for org in rich_orgs:
if org not in org_corr_matrices:
continue
corr_mat = org_corr_matrices[org]
org_corrs = []
for m1, m2 in common_pairs:
if m1 in corr_mat.columns and m2 in corr_mat.columns:
org_corrs.append(corr_mat.loc[m1, m2])
else:
org_corrs.append(np.nan)
rank_data.append(org_corrs)
rank_df = pd.DataFrame(rank_data, columns=[f'{m1}-{m2}' for m1, m2 in common_pairs])
rank_df.index = [org for org in rich_orgs if org in org_corr_matrices]
# Compute pairwise Spearman correlations between organisms
# (do they agree on the ranking of metal pairs?)
org_agreement = rank_df.T.corr(method='spearman')
# Mean inter-organism agreement
upper_tri = org_agreement.values[np.triu_indices_from(org_agreement.values, k=1)]
print(f'\nMean inter-organism Spearman rho (rank agreement): {upper_tri.mean():.3f}')
print(f'Median: {np.median(upper_tri):.3f}')
print(f'Range: [{upper_tri.min():.3f}, {upper_tri.max():.3f}]')
print(f'Fraction positive: {(upper_tri > 0).mean():.1%}')
# One-sample t-test: is mean rho > 0?
t, p = stats.ttest_1samp(upper_tri, 0)
print(f'One-sample t-test (rho > 0): t = {t:.2f}, p = {p:.2e}')
# Show the rank matrix
print(f'\nCorrelation values for common metals ({len(common_pairs)} pairs × {len(rank_df)} organisms):')
print(rank_df.round(3).to_string())
Common metals across 13 rich organisms: ['Co', 'Cu', 'Ni', 'Zn']
Mean inter-organism Spearman rho (rank agreement): -0.017
Median: 0.029
Range: [-0.886, 0.943]
Fraction positive: 51.3%
One-sample t-test (rho > 0): t = -0.29, p = 7.69e-01
Correlation values for common metals (6 pairs × 13 organisms):
Co-Cu Co-Ni Co-Zn Cu-Ni Cu-Zn Ni-Zn
DvH 0.659 0.323 0.502 0.341 0.355 0.358
psRCH2 0.417 0.577 0.381 0.449 0.129 0.387
Korea 0.548 0.513 0.635 0.491 0.526 0.565
Dino 0.570 0.431 0.498 0.165 0.455 0.127
Cola 0.506 0.716 0.826 0.405 0.495 0.680
Pedo557 0.790 0.866 0.711 0.622 0.472 0.784
acidovorax_3H11 0.337 0.505 0.709 0.437 0.541 0.499
SB2B 0.319 0.221 0.339 0.446 0.766 0.494
MR1 0.471 0.619 0.291 0.651 0.729 0.479
Marino 0.588 0.740 0.252 0.719 0.417 0.400
Phaeo 0.325 0.601 0.386 0.378 0.536 0.555
PV4 0.698 0.707 0.354 0.671 0.464 0.474
Btheta 0.902 0.915 0.606 0.897 0.592 0.627
4. Visualizations¶
In [7]:
# Figure 1: Panel of cross-resistance heatmaps for top organisms
top_orgs = summary.nlargest(9, 'n_metals')['orgId'].tolist()
top_orgs = [o for o in top_orgs if o in org_corr_matrices]
n_panels = min(len(top_orgs), 9)
ncols = 3
nrows = (n_panels + ncols - 1) // ncols
fig, axes = plt.subplots(nrows, ncols, figsize=(5*ncols, 4.5*nrows))
axes = axes.flatten() if n_panels > 1 else [axes]
for idx, org in enumerate(top_orgs[:n_panels]):
ax = axes[idx]
corr = org_corr_matrices[org]
n_metals = len(corr)
sns.heatmap(corr, annot=True, fmt='.2f', cmap='RdBu_r', center=0,
vmin=-0.2, vmax=1, square=True, ax=ax,
linewidths=0.5, linecolor='white',
annot_kws={'size': 7 if n_metals > 6 else 9})
ax.set_title(f'{org} ({n_metals} metals)', fontsize=10, fontweight='bold')
ax.tick_params(labelsize=7)
# Hide unused panels
for idx in range(n_panels, len(axes)):
axes[idx].set_visible(False)
fig.suptitle('Metal Cross-Resistance Matrices Across Organisms\n'
'(Gene-level Pearson correlation of fitness profiles)',
fontsize=14, y=1.02)
plt.tight_layout()
fig.savefig(FIG_DIR / 'cross_resistance_panel.png', dpi=150, bbox_inches='tight')
plt.show()
print('Saved to figures/cross_resistance_panel.png')
Saved to figures/cross_resistance_panel.png
In [8]:
# Figure 2: Metal pair conservation — distribution of r values across organisms
# For pairs tested in >=5 organisms, show boxplots
well_tested_pairs = pair_summary[pair_summary.n_orgs >= 5].sort_values('mean_r', ascending=False)
fig, ax = plt.subplots(figsize=(14, 6))
pair_order = well_tested_pairs['pair'].tolist()
plot_data = pairs_df[pairs_df['pair'].isin(pair_order)]
sns.boxplot(data=plot_data, x='pair', y='r', order=pair_order, ax=ax,
color='steelblue', width=0.6, fliersize=3)
sns.stripplot(data=plot_data, x='pair', y='r', order=pair_order, ax=ax,
color='black', size=3, alpha=0.5, jitter=0.15)
ax.axhline(0, color='red', linestyle='--', alpha=0.5, linewidth=0.8)
ax.set_xlabel('Metal Pair', fontsize=11)
ax.set_ylabel('Pearson r (gene fitness correlation)', fontsize=11)
ax.set_title('Cross-Resistance Conservation Across Organisms\n'
f'(pairs tested in ≥5 organisms; n={len(pair_order)} pairs)',
fontsize=12)
ax.tick_params(axis='x', rotation=45, labelsize=8)
# Add n_orgs annotation
for i, pair in enumerate(pair_order):
n = well_tested_pairs[well_tested_pairs.pair == pair]['n_orgs'].values[0]
ax.text(i, ax.get_ylim()[1] * 0.95, f'n={n}', ha='center', va='top', fontsize=6)
plt.tight_layout()
fig.savefig(FIG_DIR / 'metal_pair_conservation.png', dpi=150, bbox_inches='tight')
plt.show()
print('Saved to figures/metal_pair_conservation.png')
Saved to figures/metal_pair_conservation.png
In [9]:
# Figure 3: Hierarchical clustering of consensus matrix
# Only use metals with >=3 well-tested pairs
metals_with_data = [m for m in consensus.columns
if (consensus.loc[m] != 1.0).sum() >= 2] # at least 2 non-self entries
consensus_sub = consensus.loc[metals_with_data, metals_with_data]
# Convert correlation to distance: d = 1 - r
dist_matrix = 1 - consensus_sub.values
np.fill_diagonal(dist_matrix, 0)
# Ensure symmetry and non-negative
dist_matrix = (dist_matrix + dist_matrix.T) / 2
dist_matrix = np.clip(dist_matrix, 0, 2)
# Hierarchical clustering
condensed = squareform(dist_matrix)
Z = linkage(condensed, method='average')
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(16, 7),
gridspec_kw={'width_ratios': [1, 1.5]})
# Dendrogram
dend = dendrogram(Z, labels=metals_with_data, ax=ax1, leaf_rotation=0,
leaf_font_size=11, orientation='left', color_threshold=0.5)
ax1.set_xlabel('Distance (1 - mean r)', fontsize=11)
ax1.set_title('Metal Clustering\n(average linkage on consensus correlations)', fontsize=11)
# Reorder consensus matrix by dendrogram
order = dend['ivl'][::-1]
consensus_ordered = consensus_sub.loc[order, order]
sns.heatmap(consensus_ordered, annot=True, fmt='.2f', cmap='RdBu_r', center=0,
vmin=-0.2, vmax=1, square=True, ax=ax2,
linewidths=0.5, linecolor='white', annot_kws={'size': 10})
ax2.set_title('Consensus Cross-Resistance Matrix\n(mean Pearson r across organisms)', fontsize=11)
plt.tight_layout()
fig.savefig(FIG_DIR / 'metal_clustering_dendrogram.png', dpi=150, bbox_inches='tight')
plt.show()
print('Saved to figures/metal_clustering_dendrogram.png')
Saved to figures/metal_clustering_dendrogram.png
In [10]:
# Figure 4: Inter-organism agreement heatmap
if len(common_metals) >= 3:
fig, ax = plt.subplots(figsize=(10, 8))
sns.heatmap(org_agreement, annot=True, fmt='.2f', cmap='RdBu_r', center=0,
vmin=-1, vmax=1, square=True, ax=ax,
linewidths=0.5, linecolor='white', annot_kws={'size': 7})
ax.set_title(f'Inter-Organism Agreement on Metal Pair Rankings\n'
f'(Spearman rho on {len(common_pairs)} common metal pairs: {", ".join(common_metals)})',
fontsize=11)
ax.tick_params(labelsize=8)
plt.tight_layout()
fig.savefig(FIG_DIR / 'organism_agreement_heatmap.png', dpi=150, bbox_inches='tight')
plt.show()
print('Saved to figures/organism_agreement_heatmap.png')
Saved to figures/organism_agreement_heatmap.png
5. Strongest and Weakest Cross-Resistance Pairs¶
In [11]:
# Most and least cross-resistant pairs
well_tested = pair_summary[pair_summary.n_orgs >= 5].copy()
print('=== Strongest Cross-Resistance (highest mean r) ===')
top10 = well_tested.nlargest(10, 'mean_r')
for _, row in top10.iterrows():
print(f" {row['pair']:>6s}: r = {row['mean_r']:.3f} ± {row['std_r']:.3f} "
f"(n={row['n_orgs']} orgs, {row['pct_positive']:.0%} positive, "
f"{row['pct_sig']:.0%} significant)")
print()
print('=== Weakest Cross-Resistance (lowest mean r) ===')
bottom10 = well_tested.nsmallest(10, 'mean_r')
for _, row in bottom10.iterrows():
print(f" {row['pair']:>6s}: r = {row['mean_r']:.3f} ± {row['std_r']:.3f} "
f"(n={row['n_orgs']} orgs, {row['pct_positive']:.0%} positive, "
f"{row['pct_sig']:.0%} significant)")
print()
print('=== Overall Statistics ===')
print(f'Mean r across all well-tested pairs: {well_tested.mean_r.mean():.3f}')
print(f'All pairs positive: {(well_tested.pct_positive == 1.0).all()}')
print(f'Mean sign consistency: {well_tested.sign_consistency.mean():.3f}')
=== Strongest Cross-Resistance (highest mean r) === Fe-Zn: r = 0.614 ± 0.084 (n=6 orgs, 100% positive, 100% significant) Co-Ni: r = 0.559 ± 0.188 (n=28 orgs, 100% positive, 100% significant) Co-Zn: r = 0.518 ± 0.198 (n=18 orgs, 100% positive, 100% significant) Ni-Zn: r = 0.513 ± 0.218 (n=18 orgs, 100% positive, 100% significant) Cu-Zn: r = 0.477 ± 0.217 (n=16 orgs, 94% positive, 100% significant) Cu-Fe: r = 0.455 ± 0.195 (n=7 orgs, 100% positive, 100% significant) Co-Fe: r = 0.453 ± 0.283 (n=7 orgs, 100% positive, 86% significant) Al-Zn: r = 0.441 ± 0.166 (n=13 orgs, 100% positive, 100% significant) Co-Cu: r = 0.433 ± 0.224 (n=24 orgs, 96% positive, 96% significant) Cu-Ni: r = 0.429 ± 0.219 (n=24 orgs, 96% positive, 100% significant) === Weakest Cross-Resistance (lowest mean r) === Al-Co: r = 0.302 ± 0.197 (n=20 orgs, 95% positive, 100% significant) Al-Ni: r = 0.337 ± 0.210 (n=20 orgs, 95% positive, 95% significant) Al-Cu: r = 0.340 ± 0.227 (n=17 orgs, 94% positive, 100% significant) Fe-Ni: r = 0.375 ± 0.268 (n=7 orgs, 100% positive, 100% significant) Al-Fe: r = 0.381 ± 0.313 (n=5 orgs, 100% positive, 100% significant) Cu-Ni: r = 0.429 ± 0.219 (n=24 orgs, 96% positive, 100% significant) Co-Cu: r = 0.433 ± 0.224 (n=24 orgs, 96% positive, 96% significant) Al-Zn: r = 0.441 ± 0.166 (n=13 orgs, 100% positive, 100% significant) Co-Fe: r = 0.453 ± 0.283 (n=7 orgs, 100% positive, 86% significant) Cu-Fe: r = 0.455 ± 0.195 (n=7 orgs, 100% positive, 100% significant) === Overall Statistics === Mean r across all well-tested pairs: 0.442 All pairs positive: False Mean sign consistency: 0.980
6. Chemical Grouping Validation¶
Do metals cluster according to known chemical properties? Expected groups:
- Divalent cation displacers: Co, Ni, Zn, Mn, Cu — should cluster tightly
- Pathway-specific: Mo, W (molybdopterin), Se (selenoprotein), Fe (iron-sulfur) — should be distinct
- Heavy/toxic: Hg, U, Cr, Cd, Al — variable
In [12]:
# Define expected chemical groups
chem_groups = {
'Co': 'divalent', 'Ni': 'divalent', 'Zn': 'divalent',
'Mn': 'divalent', 'Cu': 'divalent',
'Mo': 'oxyanion', 'W': 'oxyanion', 'Se': 'oxyanion', 'Cr': 'oxyanion',
'Fe': 'essential',
'Al': 'trivalent',
'Hg': 'heavy', 'U': 'heavy', 'Cd': 'heavy',
}
# For well-tested pairs, check if within-group correlations > between-group
well_tested_with_groups = well_tested.copy()
well_tested_with_groups['m1'] = well_tested_with_groups['pair'].str.split('-').str[0]
well_tested_with_groups['m2'] = well_tested_with_groups['pair'].str.split('-').str[1]
well_tested_with_groups['g1'] = well_tested_with_groups['m1'].map(chem_groups)
well_tested_with_groups['g2'] = well_tested_with_groups['m2'].map(chem_groups)
well_tested_with_groups['same_group'] = well_tested_with_groups['g1'] == well_tested_with_groups['g2']
within = well_tested_with_groups[well_tested_with_groups.same_group]
between = well_tested_with_groups[~well_tested_with_groups.same_group]
print('=== Chemical Group Validation ===')
print(f'Within-group pairs: n={len(within)}, mean r = {within.mean_r.mean():.3f}')
print(f'Between-group pairs: n={len(between)}, mean r = {between.mean_r.mean():.3f}')
if len(within) > 0 and len(between) > 0:
t, p = stats.mannwhitneyu(within.mean_r, between.mean_r, alternative='greater')
effect = within.mean_r.mean() - between.mean_r.mean()
print(f'Mann-Whitney U (within > between): p = {p:.4f}, delta = {effect:+.3f}')
print()
print('Within-group pairs:')
for _, row in within.sort_values('mean_r', ascending=False).iterrows():
print(f" {row['pair']} ({row['g1']}): r = {row['mean_r']:.3f}")
print()
print('Highest between-group pairs (unexpected cross-resistance):')
for _, row in between.nlargest(5, 'mean_r').iterrows():
print(f" {row['pair']} ({row['g1']}/{row['g2']}): r = {row['mean_r']:.3f}")
=== Chemical Group Validation === Within-group pairs: n=6, mean r = 0.488 Between-group pairs: n=9, mean r = 0.411 Mann-Whitney U (within > between): p = 0.0440, delta = +0.077 Within-group pairs: Co-Ni (divalent): r = 0.559 Co-Zn (divalent): r = 0.518 Ni-Zn (divalent): r = 0.513 Cu-Zn (divalent): r = 0.477 Co-Cu (divalent): r = 0.433 Cu-Ni (divalent): r = 0.429 Highest between-group pairs (unexpected cross-resistance): Fe-Zn (essential/divalent): r = 0.614 Cu-Fe (divalent/essential): r = 0.455 Co-Fe (divalent/essential): r = 0.453 Al-Zn (trivalent/divalent): r = 0.441 Al-Fe (trivalent/essential): r = 0.381
Summary¶
This notebook computed per-organism cross-resistance matrices for all 30 organisms, built a consensus matrix, tested H1 (conservation), and validated against chemical groupings.
Next: NB03 will perform the conservation analysis in more depth (Mantel tests, phylogenetic controls) and NB04 will classify genes into shared vs specific tiers.