Bio Systems Biology Flux Balance Analysis

Version Compatibility

Reference examples tested with: COBRApy 0.29+

Before using code patterns, verify installed versions match. If versions differ:

• Python: pip show <package> then help(module.function) to check signatures

If code throws ImportError, AttributeError, or TypeError, introspect the installed package and adapt the example to match the actual API rather than retrying.

Flux Balance Analysis

"Predict growth rate and metabolic fluxes for my organism" → Solve a linear program over a genome-scale metabolic model to find the optimal flux distribution that maximizes biomass (or a custom objective), and assess flux ranges with FVA.

• Python: model.optimize(), cobra.flux_analysis.flux_variability_analysis() (COBRApy)

Load Models

import cobra

# Load built-in test models
model = cobra.io.load_model('textbook')  # E. coli core (95 reactions)
model = cobra.io.load_model('iJO1366')   # Full E. coli (2583 reactions)

# Load from file
model = cobra.io.read_sbml_model('model.xml')
model = cobra.io.load_json_model('model.json')

# BiGG models available at: http://bigg.ucsd.edu/models

Basic FBA

Goal: Predict optimal metabolic flux distributions and growth rates for an organism under defined conditions.

Approach: Load a genome-scale metabolic model, solve the linear program to maximize the biomass objective function, then inspect flux values and solver status to interpret metabolic phenotype.

import cobra

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

# Run FBA (maximizes objective function, usually biomass)
solution = model.optimize()

# Growth rate interpretation:
# >0.8 h^-1: Fast growth (rich media)
# 0.3-0.8 h^-1: Moderate growth
# <0.3 h^-1: Slow growth or stress
# 0: No growth (lethal condition or missing nutrients)
print(f'Growth rate: {solution.objective_value:.4f} h^-1')
print(f'Status: {solution.status}')

# Access flux values
for rxn in model.reactions[:5]:
    print(f'{rxn.id}: {solution.fluxes[rxn.id]:.4f}')

Set Media Conditions

def set_minimal_media(model, carbon_source='EX_glc__D_e', carbon_uptake=10):
    '''Configure minimal media conditions

    Args:
        carbon_source: Exchange reaction ID for carbon source
        carbon_uptake: Maximum uptake rate (mmol/gDW/h)
                      Typical glucose uptake: 10-20 mmol/gDW/h
    '''
    # Close all exchange reactions
    for rxn in model.exchanges:
        rxn.lower_bound = 0  # No uptake

    # Open essential exchanges
    essential = ['EX_o2_e', 'EX_h2o_e', 'EX_h_e', 'EX_nh4_e',
                 'EX_pi_e', 'EX_so4_e', 'EX_k_e', 'EX_mg2_e']

    for ex_id in essential:
        if ex_id in model.reactions:
            model.reactions.get_by_id(ex_id).lower_bound = -1000

    # Set carbon source
    if carbon_source in model.reactions:
        model.reactions.get_by_id(carbon_source).lower_bound = -carbon_uptake

    return model


# Example: Compare growth on different carbon sources
carbon_sources = ['EX_glc__D_e', 'EX_ac_e', 'EX_succ_e']
for cs in carbon_sources:
    with model:
        set_minimal_media(model, carbon_source=cs)
        sol = model.optimize()
        print(f'{cs}: Growth = {sol.objective_value:.4f}')

Flux Variability Analysis (FVA)

from cobra.flux_analysis import flux_variability_analysis

# FVA finds the range of flux values for each reaction
# while maintaining optimal (or near-optimal) growth

# Standard FVA (at 100% optimum)
fva = flux_variability_analysis(model)

# FVA at 90% of optimal growth
# fraction_of_optimum=0.9: allows 10% suboptimal solutions
# This reveals alternative optimal flux distributions
fva = flux_variability_analysis(model, fraction_of_optimum=0.9)

# FVA for specific reactions
rxns_of_interest = ['PFK', 'PGI', 'GAPD']
fva = flux_variability_analysis(model, reaction_list=rxns_of_interest)

# Identify essential vs flexible reactions
fva['essential'] = (fva['minimum'] > 0) | (fva['maximum'] < 0)
fva['flexible'] = fva['maximum'] - fva['minimum'] > 0.01

print(fva[['minimum', 'maximum', 'essential', 'flexible']])

Production Envelope

from cobra.flux_analysis import production_envelope

# Analyze tradeoff between growth and product secretion
# Useful for metabolic engineering to find optimal conditions

prod_env = production_envelope(
    model,
    reactions=['EX_ac_e'],  # Product (acetate)
    objective='Biomass_Ecoli_core',
    points=20
)

# prod_env is a DataFrame with:
# - EX_ac_e: acetate production rate
# - Biomass_Ecoli_core: growth rate at that production level
print(prod_env)

Phenotype Phase Plane

from cobra.flux_analysis import phenotype_phase_plane

# Analyze growth across two varying conditions
# Typically oxygen and carbon uptake

ppp = phenotype_phase_plane(
    model,
    variables=['EX_glc__D_e', 'EX_o2_e'],  # X and Y axes
    points=10
)

# Returns growth rate as function of both uptake rates
# Useful for identifying metabolic modes (aerobic vs anaerobic)

Parsimonious FBA (pFBA)

from cobra.flux_analysis import pfba

# pFBA minimizes total flux while achieving optimal growth
# Produces more biologically realistic flux distributions

pfba_solution = pfba(model)

# Compare total flux
fba_total = sum(abs(model.optimize().fluxes))
pfba_total = sum(abs(pfba_solution.fluxes))
print(f'FBA total flux: {fba_total:.1f}')
print(f'pFBA total flux: {pfba_total:.1f}')

Loopless FBA

from cobra.flux_analysis import loopless_solution

# Remove thermodynamically infeasible loops
# Important for realistic flux predictions

solution = loopless_solution(model)

Related Skills

• systems-biology/gene-essentiality - In silico gene knockouts
• systems-biology/context-specific-models - Tissue-specific FBA
• metabolomics/pathway-mapping - Integrate metabolomics data