Covalent: Interpretable and Discriminative Collective Variables Reveal Ligand-Dependent Switching in Human Cellular Retinol-Binding Protein 2.

Identifying collective variables (CVs) that are both discriminative and interpretable remains a central challenge for enhanced sampling and mechanistic analysis of biomolecular systems. We present Covalent (Collective variables learnt by a computer), a supervised machine learning-based CV discovery pipeline that combines a filter-wrapper-substitution feature funnel with an improved, Riemannian-optimized variant of harmonic linear discriminant analysis (GDHLDA) and a post hoc subspace rotation to concentrate pairwise transition information. Applied to unbiased molecular dynamics (MD) trajectories of human cellular retinol-binding protein II (CRBP2) in apo, retinol-bound, and 2-lauroylglycerol (2-LaG)-bound states, Covalent yields linear CVs with clear mechanistic interpretations and better class separability than principal component analysis. The learned CVs highlight gating switches that involve portal loop motion with ligand-induced "locking" of Ser76 and coordinated rearrangements around the cavity (Lys40, Phe57) with reduced Tyr60 flexibility upon binding and indicate a 3-4% decrease in internal void volume consistent with tighter β-barrel packing. Covalent also resolves ligand-specific interaction-state switching: Asp113 toggles mutually exclusive salt bridges with Lys114/Lys132, with 2-LaG strongly biasing the Asp113-Lys114 contact; Glu72 exhibits ligand-dependent hydrogen bonding with Thr60/Gln97. Importantly, when used in well-tempered metadynamics simulations initiated from the apo state, the CVs generate a single dominant free energy basin, with no minima corresponding to the holo conformations, supporting that the holo states are not preorganized in the apo protein but require ligand-induced stabilization. Collectively, these results establish Covalent as a practical route to physically transparent CVs that bridge MD data and mechanism and are readily portable to other problems beyond CRBP2.