Integrating subgraph isomorphism methods from quantum annealer-based molecular docking with evolutionary modeling will enable prediction of compensatory mutation networks that mitigate fitness costs in antibiotic-resistant bacteria.

Integrating subgraph isomorphism algorithms derived from quantum annealer-based molecular docking with evolutionary modeling enables statistically significant, accurate prediction (AUC > 0.80, p < 0.05) of compensatory mutation networks that mitigate fitness costs in antibiotic-resistant bacteria, as validated on experimentally characterized datasets.

• Compare three approaches on standardized datasets:
  1. Evolutionary modeling only (baseline).
  2. Evolutionary + classical subgraph isomorphism.
  3. Evolutionary + quantum annealer-inspired subgraph isomorphism.
• For each, predict compensatory mutation networks from sequence and structure data.
• Measure predictive accuracy (AUC, precision, recall) against experimentally validated mutation-fitness data.
• Perform statistical comparisons (e.g., paired t-tests, DeLong's test) to assess significance.

System Architecture Overview:

• Modules:
  1. Data Ingest & Preprocessing
  2. Protein Structure Graph Builder
  3. Subgraph Isomorphism Solver (Classical & Quantum-Inspired)
  4. Evolutionary Simulation Engine
  5. Network Prediction & Evaluation
  6. Results Aggregator & Reporter

Detailed Pseudocode/Workflow:

# 1. Data Ingest
structures = fetch_structures(["E_coli", "S_aureus"], targets=["PBP2", "gyrA"])
mutation_data = fetch_mutations(["PATRIC", "CARD"], targets=["PBP2", "gyrA"])
fitness_data = fetch_fitness_landscapes(["literature", "experiments"])

# 2. Structure Graph Building
for protein in structures:
    graph = build_residue_graph(protein.pdb, distance_cutoff=5.0)
    map_mutations(graph, mutation_data[protein])

# 3. Subgraph Isomorphism
for graph in all_graphs:
    # Classical VF2
    vf2_matches = vf2_subgraph_search(graph, motif_library)
    # Quantum Annealer-Inspired (QUBO)
    qubo_problem = encode_subgraph_qubo(graph, motif_library)
    qubo_solution = qbsolv_solve(qubo_problem)
    quantum_matches = extract_matches(qubo_solution)
    # Baseline (Random)
    random_matches = random_subgraph_search(graph, motif_library)

# 4. Evolutionary Modeling
for approach in ["evo_only", "evo+VF2", "evo+Quantum"]:
    for dataset in datasets:
        if approach == "evo_only":
            constraints = None
        elif approach == "evo+VF2":
            constraints = vf2_matches
        elif approach == "evo+Quantum":
            constraints = quantum_matches
        sim_results = run_evolutionary_simulation(
            dataset.sequence_data,
            fitness_data[dataset],
            constraints=constraints, # influences mutation fixation probabilities
            n_generations=10000,
            pop_size=1000,
            mutation_rate=1e-7,
            random_seed=42
        )
        predicted_networks[approach][dataset] = extract_compensatory_networks(sim_results)

# 5. Validation & Evaluation
for approach in predicted_networks:
    for dataset in predicted_networks[approach]:
        y_true = get_experimental_compensatory_networks(dataset)
        y_pred = predicted_networks[approach][dataset]
        metrics = evaluate_prediction(y_true, y_pred, metrics=["AUC", "precision", "recall"])
        results[approach][dataset] = metrics

# 6. Statistical Comparison
stat_test = compare_methods(
    results["evo_only"], results["evo+VF2"], results["evo+Quantum"],
    test="DeLong", alpha=0.05
)
report_results(results, stat_test)
archive_all_data_code()

# Controls:
# - Run random-motif subgraph as negative control
# - Permute fitness data to test for overfitting

# Outputs:
# - Quantitative metrics per method, per dataset
# - Statistical significance tables
# - Detailed logs and reproducible code/data archive

Data Flow:
Data → Graphs → Subgraph Matching (Classical/Quantum/Random) → Evolutionary Simulation (with/without subgraph constraints) → Compensatory Network Prediction → Experimental Validation → Statistical Analysis → Report.

Core Algorithm:

• Key innovation: Quantum-inspired QUBO subgraph isomorphism module influences evolutionary simulation by restricting or re-weighting mutation fixation likelihoods based on structural motif matches.

Controls:

• Random subgraph motifs as negative controls.
• Permuted fitness landscapes to test for spurious correlations.

Outputs:

• AUC, precision, recall for compensatory network prediction per method and dataset.
• Statistical comparison tables.
• Full reproducibility package (code, parameters, seeds, logs).