Tensorizing Pairwise Structural Analysis: GPU-Accelerated RMSD and FCC Clustering in HADDOCK3 Without Structural Regression.

Integrative macromolecular docking pipelines generate thousands of candidate structural decoys, relying on downstream pairwise ensemble analysis, including Root-Mean-Square Deviation (RMSD) matrices and Fraction of Common Contacts (FCC) clustering, to identify biologically relevant binding poses. However, pairwise structural comparisons scale quadratically (O(N^2)), and canonical workflows in HADDOCK3 historically rely on disk-bound trajectory serialization and iterative CPU set operations, creating a quadratic computational and storage bottleneck for large ensembles. Here, we demonstrate that these operations can be reformulated as continuous linear algebra on GPU-resident tensors: structural superposition via batched Singular Value Decomposition (SVD) and residue contact overlap via binary matrix multiplication (M = A A^T). Across empirical benchmarks spanning N = 200 to 10,000 models (evaluating up to 49,995,000 decoy pairs), our GPU implementation achieves a 6.41-fold compute speedup on Apple Silicon (MPS) and up to 12.2-fold end-to-end acceleration in an N = 5,000 ablation on NVIDIA CUDA by eliminating trajectory disk I/O. Crucially, the implementation achieves zero downstream structural regression relative to canonical baselines, preserving identical cluster assignments (Adjusted Rand Index ARI = 1.0000, zero differing assignments) with sub-microangstrom RMSD concordance (Delta_max <= 4.07 x 10^-7 Angstrom on single-precision MPS; machine-precision Delta_max <= 8.88 x 10^-16 Angstrom on double-precision CUDA). The accelerated code, test suites, and benchmarking workflows are openly accessible on GitHub under the Apache-2.0 license.