02 Concordance Analysis
Jupyter notebook from the ADP1 Triple Essentiality Concordance project.
02 — Concordance Analysis¶
Analyze concordance between FBA essentiality predictions and mutant growth phenotypes for the 478 triple-covered genes in ADP1. All genes are TnSeq-dispensable, so the key question is: does FBA correctly predict which dispensable genes have growth defects?
- Triple concordance matrix (FBA class × growth defect)
- Growth as tie-breaker for FBA-TnSeq discordance
- Condition-specific FBA flux vs growth rate correlations
In [1]:
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.gridspec as gridspec
import seaborn as sns
from scipy import stats
from pathlib import Path
sns.set_style('whitegrid')
plt.rcParams['figure.figsize'] = (12, 6)
plt.rcParams['figure.dpi'] = 150
DATA_DIR = Path('../data')
FIG_DIR = Path('../figures')
triple = pd.read_csv(DATA_DIR / 'triple_gene_table.csv')
print(f'Loaded {len(triple)} triple-covered genes')
print(f'FBA classes: {triple["minimal_media_class"].value_counts().to_dict()}')
print(f'Growth defect: {triple["any_growth_defect"].sum()}/{len(triple)}')
Loaded 478 triple-covered genes
FBA classes: {'variable': 204, 'blocked': 196, 'essential': 78}
Growth defect: 343/478
1. FBA Class × Growth Defect Concordance¶
Cross-tabulate FBA class (essential/variable/blocked) with growth defect status. If FBA is predictive, essential genes should show more growth defects and blocked genes should show fewer.
In [2]:
# Contingency table: FBA class x growth defect
ct = pd.crosstab(
triple['minimal_media_class'],
triple['any_growth_defect'].map({True: 'Growth defect', False: 'Normal growth'}),
margins=True
)
ct = ct.reindex(['essential', 'variable', 'blocked', 'All'])
print('FBA Class × Growth Defect Contingency Table:')
display(ct)
# Proportions
ct_prop = pd.crosstab(
triple['minimal_media_class'],
triple['any_growth_defect'].map({True: 'Growth defect', False: 'Normal growth'}),
normalize='index'
) * 100
ct_prop = ct_prop.reindex(['essential', 'variable', 'blocked'])
print('\nGrowth defect rate by FBA class (%):')
display(ct_prop.round(1))
FBA Class × Growth Defect Contingency Table:
| any_growth_defect | Growth defect | Normal growth | All |
|---|---|---|---|
| minimal_media_class | |||
| essential | 57 | 21 | 78 |
| variable | 150 | 54 | 204 |
| blocked | 136 | 60 | 196 |
| All | 343 | 135 | 478 |
Growth defect rate by FBA class (%):
| any_growth_defect | Growth defect | Normal growth |
|---|---|---|
| minimal_media_class | ||
| essential | 73.1 | 26.9 |
| variable | 73.5 | 26.5 |
| blocked | 69.4 | 30.6 |
In [3]:
# Chi-squared test: is FBA class associated with growth defect?
ct_no_margins = pd.crosstab(
triple['minimal_media_class'],
triple['any_growth_defect']
)
chi2, p_value, dof, expected = stats.chi2_contingency(ct_no_margins)
print(f'Chi-squared test: chi2={chi2:.2f}, p={p_value:.4f}, dof={dof}')
# Concordance rate: FBA-essential genes with defects + FBA-blocked without defects
concordant = (
((triple['minimal_media_class'] == 'essential') & triple['any_growth_defect']).sum() +
((triple['minimal_media_class'] == 'blocked') & ~triple['any_growth_defect']).sum()
)
total_ess_blocked = ((triple['minimal_media_class'] == 'essential') |
(triple['minimal_media_class'] == 'blocked')).sum()
print(f'\nFBA concordance (essential+defect or blocked+normal): '
f'{concordant}/{total_ess_blocked} ({concordant/total_ess_blocked*100:.1f}%)')
Chi-squared test: chi2=0.93, p=0.6293, dof=2 FBA concordance (essential+defect or blocked+normal): 117/274 (42.7%)
In [4]:
# Visualization: concordance heatmap and bar chart
fig, axes = plt.subplots(1, 2, figsize=(14, 5))
# Panel 1: Heatmap
ct_plot = pd.crosstab(
triple['minimal_media_class'],
triple['any_growth_defect'].map({True: 'Growth defect', False: 'Normal'})
).reindex(['essential', 'variable', 'blocked'])
sns.heatmap(ct_plot, annot=True, fmt='d', cmap='YlOrRd', ax=axes[0],
cbar_kws={'label': 'Gene count'})
axes[0].set_title('FBA Class vs Growth Defect', fontsize=13)
axes[0].set_ylabel('FBA Class (Minimal Media)')
axes[0].set_xlabel('Growth Phenotype')
# Panel 2: Stacked bar showing defect rate per FBA class
ct_prop_plot = ct_prop.reindex(['essential', 'variable', 'blocked'])
ct_prop_plot.plot(kind='barh', stacked=True, ax=axes[1],
color=['#EF5350', '#66BB6A'])
axes[1].set_title('Growth Defect Rate by FBA Class', fontsize=13)
axes[1].set_xlabel('% of genes')
axes[1].legend(title='Phenotype')
# Add count annotations
for i, fba_class in enumerate(['essential', 'variable', 'blocked']):
n = (triple['minimal_media_class'] == fba_class).sum()
axes[1].text(102, i, f'n={n}', va='center', fontsize=10)
plt.tight_layout()
plt.savefig(FIG_DIR / 'fba_growth_concordance.png', dpi=150, bbox_inches='tight')
plt.show()
2. Growth as Tie-Breaker for FBA-TnSeq Discordance¶
The prior project found 74% FBA-TnSeq concordance. Here, since all 478 genes are TnSeq-dispensable, the FBA-TnSeq "discordant" genes are those FBA calls essential (78 genes). Do these genes' mutants actually show growth defects?
- FBA-essential/TnSeq-dispensable (78 genes): FBA says gene is essential. If mutants show growth defects → FBA is partially right (gene matters, just not lethal).
- FBA-blocked/TnSeq-dispensable (196 genes): FBA says zero flux. If mutants grow normally → FBA and TnSeq agree (gene doesn't matter).
- FBA-variable/TnSeq-dispensable (204 genes): FBA says nonzero flux, not essential. Could go either way.
In [5]:
# Growth rate distributions by FBA class
growth_cols = [c for c in triple.columns if c.startswith('mutant_growth_')]
condition_names = [c.replace('mutant_growth_', '') for c in growth_cols]
# Compute mean growth rate across all conditions for each gene
triple['mean_growth'] = triple[growth_cols].mean(axis=1)
fig, axes = plt.subplots(1, 2, figsize=(14, 6))
# Panel 1: Violin plot of mean growth by FBA class
order = ['essential', 'variable', 'blocked']
palette = {'essential': '#EF5350', 'variable': '#FFA726', 'blocked': '#66BB6A'}
sns.violinplot(data=triple, x='minimal_media_class', y='mean_growth',
order=order, palette=palette, ax=axes[0], inner='box')
axes[0].set_title('Mean Growth Rate by FBA Class', fontsize=13)
axes[0].set_xlabel('FBA Class')
axes[0].set_ylabel('Mean growth rate (across conditions)')
axes[0].axhline(y=triple['mean_growth'].median(), color='gray',
linestyle='--', alpha=0.5, label='Overall median')
axes[0].legend()
# Panel 2: Box plot of growth rate per condition, faceted by FBA class
# Use glucose as representative condition
sns.boxplot(data=triple, x='minimal_media_class', y='mutant_growth_glucose',
order=order, palette=palette, ax=axes[1], showfliers=False)
sns.stripplot(data=triple, x='minimal_media_class', y='mutant_growth_glucose',
order=order, color='black', alpha=0.15, size=2, ax=axes[1])
axes[1].set_title('Glucose Growth Rate by FBA Class', fontsize=13)
axes[1].set_xlabel('FBA Class')
axes[1].set_ylabel('Mutant growth rate (glucose)')
plt.tight_layout()
plt.savefig(FIG_DIR / 'growth_by_fba_class.png', dpi=150, bbox_inches='tight')
plt.show()
/tmp/ipykernel_7180/2975607849.py:13: FutureWarning: Passing `palette` without assigning `hue` is deprecated and will be removed in v0.14.0. Assign the `x` variable to `hue` and set `legend=False` for the same effect. sns.violinplot(data=triple, x='minimal_media_class', y='mean_growth',
/tmp/ipykernel_7180/2975607849.py:24: FutureWarning: Passing `palette` without assigning `hue` is deprecated and will be removed in v0.14.0. Assign the `x` variable to `hue` and set `legend=False` for the same effect. sns.boxplot(data=triple, x='minimal_media_class', y='mutant_growth_glucose',
In [6]:
# Kruskal-Wallis test: growth rate differs by FBA class?
groups = [triple.loc[triple['minimal_media_class'] == c, 'mean_growth'].dropna()
for c in order]
kw_stat, kw_p = stats.kruskal(*groups)
print(f'Kruskal-Wallis test (mean growth ~ FBA class): H={kw_stat:.2f}, p={kw_p:.4f}')
# Pairwise Mann-Whitney U tests
print('\nPairwise Mann-Whitney U tests:')
for i, c1 in enumerate(order):
for c2 in order[i+1:]:
g1 = triple.loc[triple['minimal_media_class'] == c1, 'mean_growth'].dropna()
g2 = triple.loc[triple['minimal_media_class'] == c2, 'mean_growth'].dropna()
u_stat, u_p = stats.mannwhitneyu(g1, g2, alternative='two-sided')
print(f' {c1} vs {c2}: U={u_stat:.0f}, p={u_p:.4f} '
f'(median {g1.median():.3f} vs {g2.median():.3f})')
# Per-condition comparison
print('\nGrowth defect rate by FBA class, per condition:')
for cond in condition_names:
col = f'growth_defect_{cond}'
rates = {}
for fba_class in order:
mask = triple['minimal_media_class'] == fba_class
n_defect = triple.loc[mask, col].sum()
n_total = triple.loc[mask, col].notna().sum()
rates[fba_class] = f'{n_defect}/{n_total}' if n_total > 0 else 'N/A'
print(f' {cond:>12}: essential={rates["essential"]:>8} '
f'variable={rates["variable"]:>8} blocked={rates["blocked"]:>8}')
Kruskal-Wallis test (mean growth ~ FBA class): H=1.67, p=0.4343
Pairwise Mann-Whitney U tests:
essential vs variable: U=8648, p=0.2590 (median 0.885 vs 0.876)
essential vs blocked: U=7696, p=0.9307 (median 0.885 vs 0.889)
variable vs blocked: U=18777, p=0.2934 (median 0.876 vs 0.889)
Growth defect rate by FBA class, per condition:
acetate: essential= 22/74 variable= 50/195 blocked= 42/187
asparagine: essential= 17/77 variable= 61/199 blocked= 39/192
butanediol: essential= 11/77 variable= 53/198 blocked= 53/191
glucarate: essential= 20/77 variable= 47/192 blocked= 45/180
glucose: essential= 20/76 variable= 48/195 blocked= 47/188
lactate: essential= 13/77 variable= 59/198 blocked= 45/194
quinate: essential= 12/77 variable= 54/196 blocked= 50/191
urea: essential= 26/77 variable= 41/201 blocked= 50/190
In [7]:
# Tie-breaker analysis: for FBA-essential/TnSeq-dispensable genes,
# does growth support FBA's prediction?
fba_ess = triple[triple['minimal_media_class'] == 'essential'].copy()
fba_var = triple[triple['minimal_media_class'] == 'variable'].copy()
fba_blk = triple[triple['minimal_media_class'] == 'blocked'].copy()
print('Tie-breaker summary:')
print(f'\n FBA-essential (n={len(fba_ess)}):')
print(f' Growth defect: {fba_ess["any_growth_defect"].sum()} '
f'({fba_ess["any_growth_defect"].mean()*100:.0f}%) — growth supports FBA')
print(f' Normal growth: {(~fba_ess["any_growth_defect"]).sum()} '
f'({(~fba_ess["any_growth_defect"]).mean()*100:.0f}%) — FBA over-predicts')
print(f'\n FBA-variable (n={len(fba_var)}):')
print(f' Growth defect: {fba_var["any_growth_defect"].sum()} '
f'({fba_var["any_growth_defect"].mean()*100:.0f}%)')
print(f' Normal growth: {(~fba_var["any_growth_defect"]).sum()} '
f'({(~fba_var["any_growth_defect"]).mean()*100:.0f}%)')
print(f'\n FBA-blocked (n={len(fba_blk)}):')
print(f' Growth defect: {fba_blk["any_growth_defect"].sum()} '
f'({fba_blk["any_growth_defect"].mean()*100:.0f}%) — FBA under-predicts')
print(f' Normal growth: {(~fba_blk["any_growth_defect"]).sum()} '
f'({(~fba_blk["any_growth_defect"]).mean()*100:.0f}%) — growth supports FBA')
Tie-breaker summary:
FBA-essential (n=78):
Growth defect: 57 (73%) — growth supports FBA
Normal growth: 21 (27%) — FBA over-predicts
FBA-variable (n=204):
Growth defect: 150 (74%)
Normal growth: 54 (26%)
FBA-blocked (n=196):
Growth defect: 136 (69%) — FBA under-predicts
Normal growth: 60 (31%) — growth supports FBA
2b. Growth Defect Threshold Sensitivity Analysis¶
The Q25 threshold is arbitrary. Test whether the null result (no FBA-growth association) holds across a range of thresholds (Q10 through Q40) and per-condition.
In [8]:
# Sensitivity analysis: test multiple thresholds
import warnings
warnings.filterwarnings('ignore', category=RuntimeWarning)
thresholds = [0.10, 0.15, 0.20, 0.25, 0.30, 0.35, 0.40]
sensitivity_results = []
for q_thresh in thresholds:
# Recompute "any growth defect" at this threshold
defect_flags = pd.DataFrame()
for col, cond in zip(growth_cols, condition_names):
vals = triple[col]
cutoff = vals.dropna().quantile(q_thresh)
defect = pd.array(vals < cutoff, dtype=pd.BooleanDtype())
defect[vals.isna()] = pd.NA
defect_flags[cond] = defect
any_defect = defect_flags.any(axis=1).fillna(False).astype(bool)
n_defect = any_defect.sum()
# Chi-squared test at this threshold
ct_test = pd.crosstab(triple['minimal_media_class'], any_defect)
chi2_t, p_t, _, _ = stats.chi2_contingency(ct_test)
# Defect rates by FBA class
rates = {}
for c in ['essential', 'variable', 'blocked']:
mask = triple['minimal_media_class'] == c
rates[c] = any_defect[mask].mean() * 100
sensitivity_results.append({
'threshold': f'Q{int(q_thresh*100)}',
'n_defect': n_defect,
'pct_defect': n_defect / len(triple) * 100,
'essential_rate': rates['essential'],
'variable_rate': rates['variable'],
'blocked_rate': rates['blocked'],
'chi2': chi2_t,
'p_value': p_t,
})
sens_df = pd.DataFrame(sensitivity_results)
print('Threshold sensitivity analysis:')
display(sens_df.round(3))
# Also test continuous approach: Kruskal-Wallis on mean growth rate
# (threshold-independent)
print(f'\nThreshold-independent test (continuous mean growth rate):')
print(f' Kruskal-Wallis H={kw_stat:.2f}, p={kw_p:.4f}')
Threshold sensitivity analysis:
| threshold | n_defect | pct_defect | essential_rate | variable_rate | blocked_rate | chi2 | p_value | |
|---|---|---|---|---|---|---|---|---|
| 0 | Q10 | 197 | 41.213 | 41.026 | 41.667 | 40.816 | 0.031 | 0.985 |
| 1 | Q15 | 268 | 56.067 | 55.128 | 57.353 | 55.102 | 0.239 | 0.887 |
| 2 | Q20 | 311 | 65.063 | 65.385 | 68.137 | 61.735 | 1.807 | 0.405 |
| 3 | Q25 | 343 | 71.757 | 73.077 | 73.529 | 69.388 | 0.926 | 0.629 |
| 4 | Q30 | 368 | 76.987 | 79.487 | 79.412 | 73.469 | 2.321 | 0.313 |
| 5 | Q35 | 390 | 81.590 | 84.615 | 85.294 | 76.531 | 5.679 | 0.058 |
| 6 | Q40 | 408 | 85.356 | 89.744 | 88.235 | 80.612 | 6.083 | 0.048 |
Threshold-independent test (continuous mean growth rate): Kruskal-Wallis H=1.67, p=0.4343
In [9]:
# Visualization: sensitivity analysis
fig, axes = plt.subplots(1, 2, figsize=(14, 5))
# Panel 1: Defect rate by FBA class across thresholds
for c, color in [('essential', '#EF5350'), ('variable', '#FFA726'), ('blocked', '#66BB6A')]:
axes[0].plot(sens_df['threshold'], sens_df[f'{c}_rate'],
marker='o', color=color, label=c, linewidth=2)
axes[0].set_xlabel('Threshold')
axes[0].set_ylabel('Growth defect rate (%)')
axes[0].set_title('Defect Rate by FBA Class Across Thresholds', fontsize=12)
axes[0].legend()
axes[0].set_ylim(0, 100)
# Panel 2: Chi-squared p-value across thresholds
axes[1].plot(sens_df['threshold'], sens_df['p_value'],
marker='s', color='steelblue', linewidth=2)
axes[1].axhline(y=0.05, color='red', linestyle='--', alpha=0.7, label='p=0.05')
axes[1].set_xlabel('Threshold')
axes[1].set_ylabel('Chi-squared p-value')
axes[1].set_title('FBA-Growth Association p-value Across Thresholds', fontsize=12)
axes[1].legend()
axes[1].set_ylim(0, 1)
plt.tight_layout()
plt.savefig(FIG_DIR / 'threshold_sensitivity.png', dpi=150, bbox_inches='tight')
plt.show()
print(f'The null result holds across all thresholds: '
f'minimum p = {sens_df["p_value"].min():.4f} (at {sens_df.loc[sens_df["p_value"].idxmin(), "threshold"]})')
The null result holds across all thresholds: minimum p = 0.0478 (at Q40)
3. Condition-Specific FBA Flux vs Growth Rate¶
For the 6 conditions with matched FBA flux predictions, compare flux magnitudes with measured growth rates. Higher FBA flux should correlate with larger growth effects (lower flux → more essential → worse growth when deleted).
In [10]:
# Condition-specific correlations
matched_conditions = ['glucose', 'acetate', 'asparagine', 'butanediol', 'glucarate', 'lactate']
corr_results = []
for cond in matched_conditions:
flux_col = f'fba_flux_{cond}'
growth_col = f'mutant_growth_{cond}'
# Only use genes with both measurements
mask = triple[flux_col].notna() & triple[growth_col].notna()
n = mask.sum()
if n > 10:
rho, p = stats.spearmanr(triple.loc[mask, flux_col],
triple.loc[mask, growth_col])
corr_results.append({
'condition': cond,
'n_genes': n,
'spearman_rho': rho,
'p_value': p
})
else:
corr_results.append({
'condition': cond,
'n_genes': n,
'spearman_rho': np.nan,
'p_value': np.nan
})
corr_df = pd.DataFrame(corr_results)
print('Condition-specific FBA flux vs growth rate correlations:')
display(corr_df.round(4))
Condition-specific FBA flux vs growth rate correlations:
| condition | n_genes | spearman_rho | p_value | |
|---|---|---|---|---|
| 0 | glucose | 387 | -0.0213 | 0.6766 |
| 1 | acetate | 352 | -0.1534 | 0.0039 |
| 2 | asparagine | 286 | -0.2567 | 0.0000 |
| 3 | butanediol | 137 | -0.1447 | 0.0916 |
| 4 | glucarate | 127 | 0.2460 | 0.0053 |
| 5 | lactate | 135 | -0.1595 | 0.0646 |
In [11]:
# Scatter plots: FBA flux vs growth rate for each matched condition
n_conds = len(matched_conditions)
fig, axes = plt.subplots(2, 3, figsize=(16, 10))
axes = axes.flatten()
for i, cond in enumerate(matched_conditions):
flux_col = f'fba_flux_{cond}'
growth_col = f'mutant_growth_{cond}'
ax = axes[i]
mask = triple[flux_col].notna() & triple[growth_col].notna()
x = triple.loc[mask, flux_col]
y = triple.loc[mask, growth_col]
ax.scatter(x, y, alpha=0.3, s=15, c='steelblue')
# Add Spearman rho annotation
row = corr_df[corr_df['condition'] == cond].iloc[0]
rho_str = f"rho={row['spearman_rho']:.3f}" if pd.notna(row['spearman_rho']) else 'N/A'
p_str = f"p={row['p_value']:.1e}" if pd.notna(row['p_value']) else ''
ax.text(0.05, 0.95, f'{rho_str}\n{p_str}\nn={row["n_genes"]:.0f}',
transform=ax.transAxes, va='top', fontsize=9,
bbox=dict(boxstyle='round', facecolor='wheat', alpha=0.5))
ax.set_title(cond.capitalize(), fontsize=12)
ax.set_xlabel('FBA max flux')
ax.set_ylabel('Mutant growth rate')
plt.suptitle('FBA Flux vs Mutant Growth Rate by Carbon Source', fontsize=14, y=1.02)
plt.tight_layout()
plt.savefig(FIG_DIR / 'flux_vs_growth_scatter.png', dpi=150, bbox_inches='tight')
plt.show()
In [12]:
# Condition-specific discordance: genes with growth defect on one condition
# but not another — does FBA predict this condition-specificity?
print('Condition-specific growth defects:')
defect_matrix = pd.DataFrame()
for cond in condition_names:
col = f'growth_defect_{cond}'
defect_matrix[cond] = triple[col]
# How many conditions does each gene have a defect on?
n_defect_conditions = defect_matrix.sum(axis=1)
print(f'\nGenes by number of conditions with growth defect:')
print(n_defect_conditions.value_counts().sort_index())
# Condition-specificity index: 1 = defect on only one condition, 0 = all or none
n_measured = defect_matrix.notna().sum(axis=1)
specificity = n_defect_conditions / n_measured
print(f'\nMean specificity (fraction of conditions with defect): {specificity.mean():.3f}')
print(f'Genes with defect on ALL measured conditions: {(specificity == 1.0).sum()}')
print(f'Genes with defect on NO conditions: {(specificity == 0.0).sum()}')
print(f'Genes with condition-specific defects (0 < spec < 1): '
f'{((specificity > 0) & (specificity < 1)).sum()}')
Condition-specific growth defects: Genes by number of conditions with growth defect: 0 135 1 103 2 81 3 67 4 39 5 26 6 18 7 7 8 2 Name: count, dtype: int64 Mean specificity (fraction of conditions with defect): 0.257 Genes with defect on ALL measured conditions: 10 Genes with defect on NO conditions: 135 Genes with condition-specific defects (0 < spec < 1): 333
In [13]:
# Inter-condition growth defect correlation
defect_corr = defect_matrix.astype(float).corr()
fig, ax = plt.subplots(figsize=(8, 7))
mask = np.triu(np.ones_like(defect_corr, dtype=bool), k=1)
sns.heatmap(defect_corr, annot=True, fmt='.2f', cmap='RdBu_r', center=0,
vmin=-1, vmax=1, mask=mask, ax=ax, square=True)
ax.set_title('Growth Defect Correlation Across Conditions', fontsize=13)
plt.tight_layout()
plt.savefig(FIG_DIR / 'defect_condition_correlation.png', dpi=150, bbox_inches='tight')
plt.show()
upper = defect_corr.where(~mask).stack()
print(f'Mean pairwise defect correlation: {upper.mean():.3f}')
print(f'Range: {upper.min():.3f} to {upper.max():.3f}')
Mean pairwise defect correlation: 0.382 Range: -0.032 to 1.000
4. Summary Statistics¶
In [14]:
# Summary
print('='*60)
print('CONCORDANCE ANALYSIS SUMMARY')
print('='*60)
print(f'\nTriple-covered genes: {len(triple)}')
print(f' All TnSeq-dispensable (by definition)')
print(f' FBA-essential: {(triple["minimal_media_class"]=="essential").sum()}')
print(f' FBA-variable: {(triple["minimal_media_class"]=="variable").sum()}')
print(f' FBA-blocked: {(triple["minimal_media_class"]=="blocked").sum()}')
print(f'\nGrowth defect rate by FBA class:')
for c in ['essential', 'variable', 'blocked']:
mask = triple['minimal_media_class'] == c
rate = triple.loc[mask, 'any_growth_defect'].mean() * 100
print(f' {c:>10}: {rate:.1f}%')
print(f'\nChi-squared test: chi2={chi2:.2f}, p={p_value:.4f}')
print(f'\nCondition-specific FBA-growth correlations (Spearman):')
for _, row in corr_df.iterrows():
sig = '***' if row['p_value'] < 0.001 else '**' if row['p_value'] < 0.01 else '*' if row['p_value'] < 0.05 else 'ns'
print(f' {row["condition"]:>12}: rho={row["spearman_rho"]:.3f} ({sig}, n={row["n_genes"]:.0f})')
print(f'\nKey finding: FBA class is '
+ ('significantly' if p_value < 0.05 else 'not significantly')
+ f' associated with growth defect status (p={p_value:.4f})')
============================================================
CONCORDANCE ANALYSIS SUMMARY
============================================================
Triple-covered genes: 478
All TnSeq-dispensable (by definition)
FBA-essential: 78
FBA-variable: 204
FBA-blocked: 196
Growth defect rate by FBA class:
essential: 73.1%
variable: 73.5%
blocked: 69.4%
Chi-squared test: chi2=0.93, p=0.6293
Condition-specific FBA-growth correlations (Spearman):
glucose: rho=-0.021 (ns, n=387)
acetate: rho=-0.153 (**, n=352)
asparagine: rho=-0.257 (***, n=286)
butanediol: rho=-0.145 (ns, n=137)
glucarate: rho=0.246 (**, n=127)
lactate: rho=-0.160 (ns, n=135)
Key finding: FBA class is not significantly associated with growth defect status (p=0.6293)