Modeling the evolutionary trade-offs of antibiotic resistance using coalition-based equilibrium concepts will identify conditions where coordinated gene mutations enable multi-drug resistance with reduced fitness penalties.

Modeling the evolutionary dynamics of bacterial populations exposed to multiple antibiotics using coalition-based equilibrium concepts (e.g., cooperative game-theoretic models) will reveal specific conditions—quantifiable in terms of gene mutation rates, fitness penalties, and antibiotic concentrations—under which coordinated gene mutations result in multi-drug resistance with lower combined fitness costs than would result from independent acquisition of resistance.

1. Select two model bacterial strains (e.g., E. coli K-12) and two antibiotics with non-overlapping targets (e.g., ciprofloxacin and tetracycline).
2. Engineer single and double mutants with known resistance-conferring alleles, both independently and in combination.
3. Conduct competitive fitness assays in controlled media with various antibiotic concentrations.
4. Use whole-genome sequencing to confirm mutations and monitor population dynamics over 100 generations.
5. Build and fit coalition-based game-theoretic models (e.g., Shapley value or core stability analysis) to the experimental fitness and prevalence data.
6. Compare model predictions to empirical outcomes to identify conditions matching the hypothesis.
7. Run control experiments with models that do not incorporate coalition concepts for benchmarking.

Architecture Overview:

• Modular pipeline:
  1. Experimental Data Generation
  2. Data Ingestion & Preprocessing
  3. Model Construction
  4. Model Fitting & Simulation
  5. Analysis & Output Visualization

1. Experimental Data Generation:

• Lab automation scripts for culturing, plating, and sampling (Python + robotic interface).
• Sequencing pipeline (Illumina base-calling, QC).

2. Data Ingestion & Preprocessing:

# Pseudocode for data pipeline
def ingest_data(seq_files, fitness_files):
    seq_data = load_fastq(seq_files)
    fitness_data = load_csv(fitness_files)
    seq_data_qc = quality_filter(seq_data, threshold=30)
    fitness_data = normalize(fitness_data)
    return seq_data_qc, fitness_data

3. Model Construction:

• Represent each resistance gene as a "player" in a coalition game.
• Define payoff matrix where payoffs = measured fitness under each antibiotic condition.
• Incorporate epistatic interaction terms (e.g., fitness_penalty(A+B) ≠ penalty(A) + penalty(B)).

class CoalitionGame:
    def __init__(self, genes, fitness_matrix):
        self.genes = genes
        self.fitness_matrix = fitness_matrix
        self.coalitions = generate_all_coalitions(genes)
    def payoff(self, coalition):
        return self.fitness_matrix[coalition]

4. Model Fitting & Simulation:

• Fit model parameters to experimental data (e.g., least-squares for fitness penalties, MCMC for mutation rates).
• Simulate evolutionary dynamics using replicator equations or agent-based models.

def fit_parameters(fitness_data, mutation_data):
    # Fit fitness penalties using nonlinear regression
    params = optimize_least_squares(fitness_model, fitness_data)
    # Fit mutation rates to observed frequencies
    mutation_params = infer_mutation_rates(mutation_data)
    return params, mutation_params

def simulate_evolution(params, mutation_params, generations=100):
    pop = initialize_population()
    for gen in range(generations):
        pop = evolve_population(pop, params, mutation_params)
    return pop

5. Analysis & Output Visualization:

• Compare model predictions with observed population frequencies and fitness.
• Report key metrics: RMSE, AUC, fitness penalty reductions.

def evaluate_model(predictions, observations):
    rmse = calc_rmse(predictions, observations)
    auc = calc_auc(predictions, observations)
    return rmse, auc

def report_results(rmse, auc, penalty_reduction):
    print(f"RMSE: {rmse}, AUC: {auc}, Penalty Reduction: {penalty_reduction}")
    plot_fitness_landscape()
    plot_population_dynamics()

Controls:

• Parallel experiments with models omitting coalition terms.
• Control populations without selective pressure.

Outputs:

• Quantitative tables: fitness penalties, model fit statistics, parameter regimes.
• Visualizations: fitness landscapes, population dynamics, coalition stability diagrams.