Quantum annealing-based subgraph isomorphism algorithms can identify structural motifs in protein-ligand docking data that correlate with transcriptomic biomarkers of Multiple Sclerosis severity.

Quantum annealing-based subgraph isomorphism (QA-SI) algorithms, when applied to molecular graphs derived from protein-ligand docking poses of CTSS, ZNF740/BRD3, and DNMT1 inhibitors, will identify recurring structural motifs (subgraphs with ≥3 nodes, edge-weight similarity ≥0.75) whose presence in a compound's docking graph correlates (Spearman ρ ≥ 0.40, FDR < 0.05) with the transcriptomic severity biomarker signature defined by CA-RIM-upregulated DEGs (log2FC ≥ +0.5, FDR < 0.1) in smoldering MS lesion tissue — specifically the CTSS (log2FC +1.16), DNMT1 (log2FC +1.59), and ZNF740 (log2FC +1.15) expression axes — such that motif presence predicts compound efficacy rank better than standard docking score alone (ΔAUC ≥ 0.10 vs. Glide/Vina score baseline).

PHASE 0 — Benchmark Setup (Days 1–7): Establish classical baseline using VF2 subgraph isomorphism on 20-node molecular graphs; record wall-clock time and motif recovery rate as comparison standard.

PHASE 1 — Docking Library Generation (Days 1–14): Retrieve crystal structures for CTSS (3H27), BRD3 (4MEN), DNMT1 (4DA4). Prepare protein grids using Schrödinger Glide SP or AutoDock Vina 1.2. Dock ChEMBL inhibitor sets: CTSS (n=120 compounds, pChEMBL ≥ 5.0), BRD3/BET (n=80 compounds including JQ1, birabresib, mivebresib, pelabresib + analogs), DNMT1 (n=60 compounds including azacitidine, decitabine analogs). Output: docking pose coordinates + Glide/Vina scores for all compounds.

PHASE 2 — Molecular Graph Construction (Days 8–18): Convert docking poses to attributed molecular graphs: nodes = heavy atoms with feature vector [atom_type, partial_charge, H-bond_donor, H-bond_acceptor, aromaticity]; edges = bonds + proximity contacts (≤ 4.0 Å) with edge weights encoding bond order and distance. Protein-ligand interaction graphs include binding-pocket residue nodes (≤ 5 Å shell). Target graph size: 25–45 nodes per complex.

PHASE 3 — QUBO Formulation & Quantum Annealing (Days 15–28): Encode subgraph isomorphism as QUBO: binary variables x_{ij} = 1 if query node i maps to target node j; objective minimizes mismatch penalty with λ_constraint = 15. Submit to D-Wave Advantage via Leap API (or simulate via SimulatedAnnealingSampler for graphs ≤ 20 nodes). Run 1,000 annealing reads per graph pair; extract top-10 motif candidates per target. Validate motif recovery against VF2 ground truth on 50-graph benchmark subset.

PHASE 4 — Motif-Biomarker Correlation (Days 22–35): For each identified motif M_k, compute presence/absence binary vector across all docked compounds. Retrieve transcriptomic severity scores: (a) bulk: CTSS/DNMT1/ZNF740 log2FC from GSE193770+GSE108000 pipeline; (b) single-cell: CD8+ T-cell cluster expression from scVI atlas (gs://aegismind-tpu-results/ms_phase2/results/). Compute Spearman ρ between motif presence and composite severity score. Apply BH FDR correction across all motif-biomarker pairs.

PHASE 5 — Predictive Modeling & Validation (Days 30–42): Train gradient boosting classifier (XGBoost) using motif presence vectors as features to predict efficacy rank (top/bottom tertile by pChEMBL). 80/20 train/test split stratified by target. Compare AUC vs. docking-score-only baseline. Replicate top motif-biomarker correlations in GSE138614 (CTSS log2FC +1.024, FDR 0.111 available).

# ============================================================
# QA-SI MOTIF-BIOMARKER CORRELATION PIPELINE
# Quantum Annealing Subgraph Isomorphism for MS Drug Discovery
# ============================================================

# --- DEPENDENCIES ---
# rdkit, networkx, dimod, dwave-ocean-sdk, xgboost, scipy
# scvi-tools, anndata, pandas, numpy, matplotlib, seaborn

import numpy as np
import pandas as pd
import networkx as nx
from rdkit import Chem
from rdkit.Chem import AllChem, rdMolDescriptors
import dimod
from dwave.system import DWaveSampler, EmbeddingComposite
from dwave.samplers import SimulatedAnnealingSampler
from sklearn.metrics import roc_auc_score
import xgboost as xgb
from scipy.stats import spearmanr
from statsmodels.stats.multitest import multipletests

# ============================================================
# MODULE 1: MOLECULAR GRAPH CONSTRUCTION
# ============================================================

def mol_to_attributed_graph(mol, pose_coords=None):
    """
    Convert RDKit mol + docking pose to attributed NetworkX graph.
    Nodes: heavy atoms with 13-dim feature vector
    Edges: covalent bonds + proximity contacts <= 4.0 Å
    """
    G = nx.Graph()
    conf = mol.GetConformer() if pose_coords is None else pose_coords
    
    for atom in mol.GetAtoms():
        idx = atom.GetIdx()
        pos = conf.GetAtomPosition(idx)
        features = {
            'atom_type': atom.GetAtomicNum(),          # int
            'partial_charge': atom.GetFormalCharge(),   # float
            'hbd': int(atom.GetTotalNumHs() > 0),       # bool
            'hba': int(atom.GetAtomicNum() in [7,8]),   # bool
            'aromatic': int(atom.GetIsAromatic()),       # bool
            'ring': int(atom.IsInRing()),                # bool
            'degree': atom.GetDegree(),                  # int
            'position