VTPE: Virtual Trajectory Position Encoding for Biomolecular Complex Structure Prediction

AlphaFold-style co-folding methods have achieved near-experimental accuracy on protein monomers, yet structure prediction for biomolecular complexes remains challenging. A key difficulty is that biomolecular complexes contain many atoms that engage in long-range interactions: the position of one atom constrains the positions of numerous other atoms at varying distances, all at long range. Diffusion-based structure prediction resolves these constraints progressively over denoising steps, but supervision is defined only on the final denoised structure, leaving the relationships among intermediate states unmodeled. Consequently, the atomic adjustment process and the coordination among distant atoms remain difficult to capture. In this paper, we view these intermediate structures as a virtual trajectory and propose Virtual Trajectory Position Encoding (VTPE), which encodes atomic coordinates along this virtual trajectory as positional encoding. This enables the model to represent how distant atoms move relative to one another over the course of denoising. Since long-range interactions are precisely the couplings that produce such coordinated adjustments, exposing the model to these adjustments provides a direct signal for learning long-range interactions. We evaluate VTPE at multiple parameter scales of Protenix, the open-source reproduction of AlphaFold 3 (AF3), and observe consistent improvements over the corresponding baselines across benchmarks with limited additional overhead. Experiments confirm the contribution of virtual trajectory position encoding to complex structure prediction.