Calibrated Weighted Rank Aggregation for Virtual Screening Independently Rediscovers Privileged Vitamin D Receptor Ligand Scaffolds

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Abstract
Computational drug discovery relies on virtual screening to prioritize a small number of compounds for experimental testing, yet combining heterogeneous in silico scoring methods into a single robust ranking remains challenging. We present Calibrated Weighted Rank Aggregation (CWRA), a data-driven rank-optimized score-fusion framework that (a) direction-corrects modality outputs, (b) harmonizes them via per-modality normalization, and (c) learns nonnegative fusion weights from known actives by optimizing a rank-based early-recognition objective (Boltzmann-enhanced discrimination of receiver operating characteristic [BEDROC]) under simplex constraints. Applied to the vitamin D receptor (VDR), we fuse machine-learning affinity predictors (GraphDTA endpoints, MLT-LE, TankBind, DrugBAN, and MolTrans), structure-based scores (AutoDock Vina and Boltz-2 affinity and confidence), and ligand similarity (Uni-Mol; computed in a split-honest manner by recomputing the active-set centroid on the training splits). Across 5 repeated random splits over the P = 503 known VDR binders, evaluated on the drug-likeness prefiltered pool of N ′ = 14 , 902 compounds, CWRA achieves strong early enrichment on held-out actives ( EF @ 1 % = 21.32 ± 6.41 , corresponding to 16 ± 5 recovered binders within the top 1% of the ranked list), substantially outperforming equal-weight fusion ( EF @ 1 % = 10.79 ± 2.81 ) and the strongest single modality (GraphDTA IC 50 ; EF @ 1 % = 16.32 ± 3.96 ). Performance remains strong at broader cutoffs ( EF @ 2.5 % = 14.13 ± 2.34 , EF @ 5 % = 9.47 ± 0.60 , and EF @ 10 % = 7.13 ± 0.72 ), indicating that BEDROC-optimized fusion of normalized scores improves both early prioritization and moderate-depth screening. To assess generalization beyond VDR, we further applied CWRA to the mechanistically distinct γ-aminobutyric acid type A (GABA A ) receptor. Target-specific calibration again improved very early enrichment ( EF @ 1 % = 25.41 ± 3.96 ) over both equal-weight fusion ( EF @ 1 % = 17.47 ± 6.17 ) and the best individual modality at this cutoff (Boltz-2 confidence; EF @ 1 % = 11.64 ± 2.12 ). Strict cross-target source-model transfer between VDR and GABA A was weaker than target-specific recalibration, indicating that CWRA should be interpreted as a transferable target-adaptive framework rather than a universal fixed-weight model. A qualitative review of the top-ranked generated candidates suggests that CWRA preferentially selects chemically coherent VDR-like chemotypes, recapitulating established VDR pharmacophore patterns without imposing handcrafted structural rules.
Funding Information
  • Ministry of Education and Science of the Republic of Kazakhstan (AP23488419)
  • Nazarbayev University (040225FD4734)
  • Nazarbayev University (20122022FD4120)
  • Nazarbayev University (040225FD4745)

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