Computational equilibrium strategies can predict optimal drug combinations to overcome evolutionary trade-offs in antibiotic resistance.

Computational equilibrium strategies (specifically evolutionary game theory and Nash equilibrium modeling) can identify drug combinations that exploit collateral sensitivity trade-offs in antibiotic-resistant bacterial populations, such that the predicted combinations achieve ≥2-fold greater reduction in minimum inhibitory concentration (MIC) compared to empirically selected combinations in ≥70% of tested resistant strains, and suppress resistance evolution by ≥50% over 30-day serial passage experiments relative to standard-of-care combinations.

Phase 1 — Computational Model Construction (Days 1–30): Build evolutionary game theory models using empirical fitness landscapes from published collateral sensitivity datasets. Parameterize payoff matrices for pairwise drug interactions. Compute Nash equilibria and evolutionarily stable strategies (ESS) for drug cycling and combination schedules.

Phase 2 — In Vitro Validation (Days 31–90): Test top-5 computationally predicted combinations vs. top-5 empirically selected combinations vs. single-drug controls in E. coli K-12 MG1655 and clinical ESKAPE pathogen isolates (minimum n=3 species, n=6 strains each). Measure MIC, kill curves, and resistance emergence via serial passage (30 days, daily transfer at sub-MIC concentrations).

Phase 3 — Mechanistic Verification (Days 91–120): Whole-genome sequencing of evolved populations at days 0, 10, 20, 30. Quantify mutation frequency, identify resistance mutations, and verify that predicted trade-off loci are under selection as modeled.

Phase 4 — Predictive Generalization (Days 121–150): Apply trained model to 3 novel drug pairs not used in training. Assess prediction accuracy on held-out data. Compute ROC-AUC for binary classification of "effective vs. ineffective" combinations.

# Evolutionary Game Theory Drug Combination Optimizer
# Architecture Overview

## MODULE 1: Data Ingestion & Preprocessing
class CollateralSensitivityLoader:
    def load_mic_data(sources=["CARD", "PATRIC", "literature_csv"]):
        # Returns: DataFrame[strain_id, drug_A, drug_B, MIC_A, MIC_B, 
        #                     MIC_A_after_resistance_to_B, MIC_B_after_resistance_to_A]
        pass
    
    def compute_collateral_coefficient(mic_baseline, mic_after_resistance):
        # CS_coeff = log2(MIC_after / MIC_baseline)
        # Negative = collateral sensitivity, Positive = cross-resistance
        return np.log2(mic_after_resistance / mic_baseline)
    
    def build_payoff_matrix(drugs: List[str], strains: List[str]):
        # Shape: [n_drugs × n_drugs × n_strains]
        # payoff[i,j,k] = fitness of bacteria resistant to drug_i when exposed to drug_j in strain_k
        pass

## MODULE 2: Nash Equilibrium Solver
class EvolutionaryEquilibriumSolver:
    def __init__(self, payoff_matrix: np.ndarray):
        self.payoff = payoff_matrix  # [n_strategies × n_strategies]
        self.game = nashpy.Game(payoff_matrix, -payoff_matrix)  # zero-sum approximation
    
    def find_nash_equilibria(self):
        # Use support enumeration for exact solutions
        equilibria = list(self.game.support_enumeration())
        return equilibria  # List of (sigma_row, sigma_col) mixed strategy pairs
    
    def check_ess(self, strategy: np.ndarray, epsilon=0.01):
        # ESS condition: f(s,s) > f(s_mutant, s) for all mutants
        # Returns: bool, stability_score (float)
        for mutant in self.generate_mutant_strategies(strategy, epsilon):
            if self.fitness(mutant, strategy) >= self.fitness(strategy, strategy):
                return False, 0.0
        return True, self.compute_stability_margin(strategy)
    
    def rank_combinations(self, equilibria):
        # Score = ESS_stability × collateral_sensitivity_coefficient
        # Returns: ranked list of drug combinations
        pass

## MODULE 3: Experimental Design Generator
class ExperimentalDesigner:
    def select_top_combinations(ranked_combinations, n=5):
        # Returns top-N combinations for wet lab validation
        pass
    
    def generate_checkerboard_layout(drug_A, drug_B, conc_range):
        # 8×8 96-well plate layout for MIC checkerboard
        # Returns: plate_map DataFrame
        pass
    
    def design_serial_passage_schedule(combinations, days=30):
        # Daily transfer protocol with MIC measurement schedule
        pass

## MODULE 4: Statistical Analysis Pipeline
class ValidationAnalyzer:
    def compute_fici(mic_A_alone, mic_B_alone, mic_A_combo, mic_B_combo):
        return (mic_A_combo / mic_A_alone) + (mic_B_combo / mic_B_alone)
        # FICI < 0.5: synergy, 0.5-4.0: indifference, >4.0: antagonism
    
    def kaplan_meier_resistance_emergence(time_to_4fold_mic_increase):
        # Returns: survival curve, log-rank p-value vs. comparator
        from lifelines import KaplanMeierFitter
        pass
    
    def model_calibration(predicted_cs_coefficients, observed_cs_coefficients):
        pearson_r, p_value = scipy.stats.pearsonr(predicted, observed)
        brier_score = sklearn.metrics.brier_score_loss(binary_labels, predicted_probs)
        return pearson_r, brier_score
    
    def roc_analysis(predicted_scores, true_synergy_labels):
        auc = sklearn.metrics.roc_auc_score(true_synergy_labels, predicted_scores)
        return auc

## MODULE 5: WGS Analysis Pipeline (Snakemake workflow)
# Rule 1: FastQC quality control
# Rule 2: BWA-MEM2 alignment to reference genome
# Rule 3: GATK HaplotypeCaller variant calling
# Rule 4: CARD RGI resistance gene annotation
# Rule 5: Compute mutation frequency at predicted trade-off loci
# Rule 6: Compare observed vs. predicted resistance mutation spectrum

## MAIN EXECUTION FLOW:
if __name__ == "__main__":
    # 1. Load and preprocess data
    data = CollateralSensitivityLoader.load_mic_data()
    payoff_matrices = data.build_payoff_matrix(drugs=DRUG_LIST, strains=STRAIN_LIST)
    
    # 2. Solve for equilibria per strain
    all_predictions = {}
    for strain in STRAIN_LIST:
        solver = EvolutionaryEquilibriumSolver(payoff_matrices[:,:,strain])
        equilibria = solver.find_nash_equilibria()
        ess_combinations = [(e, solver.check_ess(e)) for e in equilibria]
        all_predictions[strain] = solver.rank_combinations(ess_combinations)
    
    # 3. Aggregate predictions across strains (consensus ranking)
    consensus = aggregate_cross_strain_predictions(all_predictions)
    top5 = ExperimentalDesigner.select_top_combinations(consensus, n=5)
    
    # 4. Generate experimental protocols
    protocols = ExperimentalDesigner.design_serial_passage_schedule(top5)
    
    # 5. [WET LAB PHASE - external]
    
    # 6. Analyze results
    results = ValidationAnalyzer.compute_fici(experimental_data)
    survival = ValidationAnalyzer.kaplan_meier_resistance_emergence(passage_data)
    calibration = ValidationAnalyzer.model_calibration(predicted, observed)
    auc = ValidationAnalyzer.roc_analysis(scores, labels)
    
    # 7. Report
    generate_validation_report(results, survival, calibration, auc)