Symmetric protein complexes without retraining: ZeUS generates them zero-shot, reaching 10,000 residues on one GPU

Symmetric protein complex generation can now be carried out on a single canonical subunit, with the full assembly recovered by applying the symmetry group, instead of running the network over every residue. Earlier symmetric backbone generation treated design as full-complex generation, running a forward pass over all residues of the assembly at each denoising step and then propagating the designated subunit's update to the others according to the target symmetry group. Across FrameDiff, FoldFlow and RFdiffusion, ZeUS shows a mean signed scRMSD difference of only about 0.01 angstrom relative to the chain-permutation-equivariant RFdiffusion full-complex ablation, matching the design quality of that ablated model.

The approach treats a symmetric assembly as a point in a quotient space: a k-fold symmetric assembly is uniquely determined by one representative subunit plus the group elements, so the model only handles that representative. Operations in the quotient space are hard to parameterize directly, so phantom copies translate each quotient-space operation back into the ambient space, letting the canonical subunit consult copies transformed by group elements during computation. The implementation covers the IPA-based FrameDiff and FoldFlow and the axial-attention RFdiffusion, producing designs distributionally similar to full-complex inference across five cyclic symmetries plus dihedral and polyhedral symmetries.

The memory and runtime savings come from removing redundancy: an equivariant model's internal representations on a symmetric assembly are duplicated k times by the group action, so keeping only the canonical subunit suffices. Node and edge features in a full-complex forward pass grow with assembly size, and the pairwise tensor of axial attention is the largest memory consumer. At a fixed memory budget, the total residues ZeUS can fit grow with the order of the symmetry group, generating complexes of about 12,000 residues at 12-fold symmetry versus about 1,000 residues for the full-complex baseline.

The demonstrated scope is backbone generation: on a single NVIDIA A100-40GB, FrameDiff generates 10,000-residue cyclic and dihedral complexes, a 6,000-residue icosahedral complex and a 4,500-residue helical complex, and the buried-surface-area distributions of these designs overlap those of natural PDB proteins. Cyclic design quality is measured by self-consistency of ProteinMPNN sequences refolded with ESMFold; polyhedral symmetries are compared only at the distribution level because folding models are unreliable on large symmetric complexes.

The equivalence relies on SE(3) equivariance and chain-permutation equivariance; RFdiffusion's inter-chain relative position encoding breaks the latter, making cross-chain block equivalence approximate, and infinite groups such as helical and lattice symmetries require distance-based truncation of phantom copies. Self-consistency evaluation is unreliable for polyhedral symmetries, so a refolding failure cannot distinguish an undesignable design from a folding-model failure; designs above 10,000 residues are backbone-only, and assessing designability at that scale is intractable.