Bio Systems Biology Gene Essentiality

Approach: Perform in silico single gene deletions across all model genes, compare post-deletion growth to wild-type, and classify genes as essential (lethal), growth-reducing, or non-essential based on growth ratio thresholds.

import cobra
from cobra.flux_analysis import single_gene_deletion

model = cobra.io.load_model('textbook')

# Perform all single gene deletions
# Returns growth rate with each gene knocked out
deletion_results = single_gene_deletion(model)

# deletion_results is a DataFrame with:
# - ids: gene IDs (frozenset)
# - growth: growth rate after deletion
# - status: solver status

# Find essential genes (no growth when deleted)
# Essential: growth < 0.01 (allowing for numerical tolerance)
essential = deletion_results[deletion_results['growth'] < 0.01]
print(f'Essential genes: {len(essential)}')

Classify Gene Essentiality

def classify_gene_essentiality(model, growth_threshold=0.1):
    '''Classify genes by their impact on growth

    Categories:
    - Essential: Growth < 1% of WT (lethal)
    - Growth-reducing: 1-50% of WT
    - Non-essential: >50% of WT
    '''
    from cobra.flux_analysis import single_gene_deletion

    # Get wild-type growth
    wt_growth = model.optimize().objective_value

    # Run deletions
    results = single_gene_deletion(model)
    results['relative_growth'] = results['growth'] / wt_growth

    # Classify
    results['classification'] = 'non-essential'
    results.loc[results['relative_growth'] < 0.5, 'classification'] = 'growth-reducing'
    results.loc[results['relative_growth'] < 0.01, 'classification'] = 'essential'

    classification_counts = results['classification'].value_counts()
    return results, classification_counts

Synthetic Lethality

from cobra.flux_analysis import double_gene_deletion

# Warning: O(n^2) complexity - can be slow for large models
# For full E. coli (~1500 genes), this is ~1M combinations

# Subset to genes of interest
genes_of_interest = [g.id for g in model.genes[:50]]

# Run double deletions
double_results = double_gene_deletion(
    model,
    gene_list1=genes_of_interest,
    gene_list2=genes_of_interest
)

# Find synthetic lethal pairs
# Synthetic lethal: double KO is lethal when singles are viable

# Get single deletion results first
single_results = single_gene_deletion(model, gene_list=genes_of_interest)
single_dict = {list(ids)[0]: growth for ids, growth in
               zip(single_results['ids'], single_results['growth'])}

Identify Synthetic Lethal Pairs

def find_synthetic_lethal_pairs(model, genes=None, growth_threshold=0.01):
    '''Find synthetic lethal gene pairs

    Synthetic lethality criteria:
    - Single KO of gene A: viable (growth > threshold)
    - Single KO of gene B: viable (growth > threshold)
    - Double KO of A+B: lethal (growth < threshold)

    Useful for:
    - Drug combination targets
    - Genetic interaction networks
    - Backup pathway identification
    '''
    from cobra.flux_analysis import single_gene_deletion, double_gene_deletion

    if genes is None:
        genes = [g.id for g in model.genes]

    # Single deletions
    single = single_gene_deletion(model, gene_list=genes)
    viable_singles = single[single['growth'] > growth_threshold]
    viable_genes = [list(ids)[0] for ids in viable_singles['ids']]

    # Double deletions (only for viable single KOs)
    double = double_gene_deletion(model, gene_list1=viable_genes,
                                  gene_list2=viable_genes)

    # Find synthetic lethal pairs
    sl_pairs = []
    for _, row in double.iterrows():
        genes_in_pair = list(row['ids'])
        if len(genes_in_pair) == 2 and row['growth'] < growth_threshold:
            sl_pairs.append({
                'gene1': genes_in_pair[0],
                'gene2': genes_in_pair[1],
                'double_ko_growth': row['growth']
            })

    return sl_pairs

Condition-Specific Essentiality

def compare_essentiality_conditions(model, conditions):
    '''Compare gene essentiality across conditions

    Args:
        conditions: dict mapping condition name to media setup function

    Example:
        conditions = {
            'aerobic': lambda m: m.reactions.EX_o2_e.lower_bound = -20,
            'anaerobic': lambda m: m.reactions.EX_o2_e.lower_bound = 0
        }
    '''
    from cobra.flux_analysis import single_gene_deletion

    essentiality_by_condition = {}

    for condition_name, setup_func in conditions.items():
        with model:
            setup_func(model)
            results = single_gene_deletion(model)
            essential = set(list(ids)[0] for ids in
                          results[results['growth'] < 0.01]['ids'])
            essentiality_by_condition[condition_name] = essential

    # Find condition-specific essential genes
    all_essential = set.union(*essentiality_by_condition.values())
    core_essential = set.intersection(*essentiality_by_condition.values())
    condition_specific = {cond: ess - core_essential
                         for cond, ess in essentiality_by_condition.items()}

    return {
        'core_essential': core_essential,
        'condition_specific': condition_specific,
        'total_essential': len(all_essential)
    }

Robustness Analysis

def gene_robustness_analysis(model, gene_id, flux_levels=10):
    '''Analyze growth as function of gene expression level

    Instead of complete knockout, simulate reduced expression
    by constraining reactions associated with the gene.
    '''
    from cobra.flux_analysis import flux_variability_analysis

    gene = model.genes.get_by_id(gene_id)

    # Get reactions associated with this gene
    rxns = list(gene.reactions)

    results = []
    for level in [i/flux_levels for i in range(flux_levels + 1)]:
        with model:
            for rxn in rxns:
                # Get FVA bounds at wild-type
                fva = flux_variability_analysis(model, reaction_list=[rxn])
                max_flux = fva.loc[rxn.id, 'maximum']
                min_flux = fva.loc[rxn.id, 'minimum']

                # Constrain to fraction of wild-type
                rxn.upper_bound = max_flux * level
                rxn.lower_bound = min_flux * level

            sol = model.optimize()
            results.append({
                'expression_level': level,
                'growth': sol.objective_value
            })

    return results

Related Skills

• systems-biology/flux-balance-analysis - Base FBA methods
• pathway-analysis/go-enrichment - Enrich essential gene sets
• clinical-databases/variant-prioritization - Link to disease genes