TDTAC: a generalized time-dependent torsion angle correlation framework for resolving directional coordination in large biomolecular assemblies

Proteins function through coordinated, time-dependent conformational motions, yet conventional analyses often obscure how these dynamics propagate across complex assemblies. Here, we introduce a generalized Time-Dependent Torsion Angle Correlation (TDTAC) framework that incorporates explicit time lags between residues, enabling quantitative mapping of directional, sequential correlations. By analyzing dihedral rotations, TDTAC reveals conformational dynamics through a physically meaningful representation of residue-level fluctuations. We apply this framework to examine how a small-molecule degrader may induce time-lagged structural rearrangements that facilitate targeted protein degradation. We analyzed the PROteolysis TArgeting Chimera (PROTAC) dBET70, a bifunctional small molecule in complex with its target protein, bromodomain-containing protein 4 (BRD4 BD1 ), and assembled within the full degradation complex Cullin-RING Ligase 4A (CRL4A) E3 ligase scaffold. The full assembly comprises nine components: dBET70, BRD4 BD1 , and the seven-protein degradation complex CRBN, DDB1, CUL4A, NEDD8, RBX1, E2, and Ub. TDTAC analysis reveals that motions originating at the DDB1–CUL4A region propagate along two dominant pathways: one extending through DDB1 toward the CRBN–BRD4 interface, and the second extending through CUL4A toward the RBX1–Ub interface. These coordinated, time-delayed rearrangements are associated with configurations that bring BRD4, E2, Ub, and the PROTAC into a ubiquitination-competent state. Both pathways exhibit similar lag-dependent propagation behavior, consistent with a network of time-delayed residue-residue coordination linking local torsional dynamics to distal catalytic interfaces. More broadly, TDTAC provides a generalizable framework for resolving dynamic information flow in large biomolecular assemblies.