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 <i>Covalent</i> (<i>Collective variables learnt by a computer</i>), 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, <i>Covalent</i> 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. <i>Covalent</i> 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 <i>Covalent</i> as a practical route to physically transparent CVs that bridge MD data and mechanism and are readily portable to other problems beyond CRBP2.