Prior drift for torsional degrees on SO(2)^M integrated with autoregressive sidechain updates

Develop an explicit, computationally tractable formulation for the prior drift term on the torsion manifold SO(2)^M within the geometric diffusion prior bridge for flexible protein–ligand docking by adapting the torsion force—defined as the difference between the torques applied on each side of a rotatable bond—to the SO(2)^M manifold and integrating it with the autoregressive sidechain torsion update scheme used for pocket sidechains.

Background

The Re-Dock framework extends diffusion bridges to non-Euclidean geometric manifolds to jointly generate ligand poses and pocket sidechain conformations. Energy-to-geometry mapping based on the Newton–Euler equations provides prior drift terms for translation and rotation, enabling interaction-aware guidance.

However, the authors explicitly omit the calculation of prior drift on the torsion manifold SO(2)^M due to its computational complexity. They note that torsion forces can be defined as differences in torques across rotatable bonds, but adapting this formulation to the SO(2)^M manifold and to their autoregressive sidechain torsion update scheme is non-trivial and left for future work. Addressing this gap would enable explicit prior-guided torsional updates within their geometric diffusion bridge.