Structure Module

The Structure Module begins with all residues placed at the origin. Each residue is represented as a rigid-body frame—a Euclidean transform consisting of a 3D translation (Cα position) and a 3x3 rotation matrix. This 'black hole' initialization ensures the network learns to generate the fold from scratch rather than memorizing starting configurations. The frames are iteratively updated to satisfy the geometric constraints encoded in the pair representation.

The core algorithmic innovation within the Structure Module. Standard attention is augmented with 3D spatial awareness by projecting learned 'invariant points' from each residue's local frame into global coordinates. Attention weights are then modulated by the squared Euclidean distance between these points, ensuring the mechanism is SE(3) equivariant—predictions transform consistently with rigid-body rotations and translations of the input. This allows the network to reason about spatial proximity without overfitting to absolute coordinates.

The Structure Module is applied 8 times recurrently, with shared weights across iterations. Each cycle takes the previous output frames as input, allowing the model to progressively refine the structure:

• Cycle 1-2: Rough secondary structure elements emerge
• Cycle 3-5: Tertiary packing and domain arrangement solidify
• Cycle 6-8: Fine side-chain positioning and loop closure This iterative refinement mimics the physical process of energy minimization but is learned end-to-end from data.

At each iteration, the IPA mechanism predicts a quaternion and translation update for every residue frame. The update is applied via a torsion-based parameterization that respects the fixed bond geometry of the protein backbone. The network predicts a rotation quaternion and a translation vector, which are composed with the current frame to produce the next frame. This parameterization guarantees that the output remains a valid set of rigid-body transforms without requiring post-hoc normalization.

In the final iteration, the Structure Module predicts up to 4 torsion angles (χ1–χ4) for each residue's side chain. These angles are output as discrete distributions over 36 bins (10° each), from which the most probable rotamer is selected. The network leverages the refined pair representation and local frame geometry to resolve steric clashes and optimize hydrogen bonding networks. The predicted torsions are then used to construct full-atom coordinates using ideal bond geometry from the AMBER99SB force field.

The Structure Module simultaneously outputs per-residue pLDDT (predicted Local Distance Difference Test) scores and the PAE (Predicted Aligned Error) matrix. These confidence metrics are generated by small auxiliary heads that consume the final single and pair representations. pLDDT values are used to color the predicted structure by confidence (blue=high, red=low), providing researchers with an immediate visual assessment of which regions—such as flexible loops or disordered termini—should be interpreted with caution.

The core algorithmic innovation within the Structure Module. IPA operates on a cloud of 3D points (residue gas) and updates both local frame orientations and spatial positions in a way that is SE(3) equivariant.

• Mechanism: Uses attention weights derived from 3D distances, not just sequence features.
• Key property: Predictions rotate and translate consistently with the input, ensuring physical plausibility.
• Output: Iteratively refined residue frames (rotation + translation) representing the backbone geometry.

The Structure Module initializes the protein as a residue gas—a set of unconnected, freely floating amino acid frames in 3D space. This abstract representation has no initial chain connectivity or steric constraints.

• Starting state: Each residue is a Euclidean transform (a frame) with a learned initial position.
• Evolution: The IPA mechanism iteratively moves and rotates these frames to satisfy the learned pairwise constraints from the Evoformer.
• Final step: The backbone is constructed by fitting N, Cα, and C atoms to the predicted residue frames.

A per-residue confidence metric output directly by the Structure Module. It estimates the local accuracy of the prediction on a scale from 0 to 100, corresponding to the predicted Local Distance Difference Test score.

• High confidence (pLDDT > 90): Residues are typically modeled with high accuracy, suitable for detailed functional analysis.
• Low confidence (pLDDT < 50): Indicates a strong prediction of intrinsic disorder or a highly flexible region.
• Usage: Essential for filtering reliable regions for downstream applications like drug docking or mutagenesis studies.

A 2D inter-residue confidence metric that estimates the expected positional error between any two residues (i and j) if the predicted and true structures were aligned on residue i.

• Domain packing: Low PAE values between two regions indicate a well-defined relative orientation, confirming domain packing.
• Flexible linkers: High PAE values between domains suggest conformational flexibility or uncertainty in relative positioning.
• Visualization: Typically rendered as a heatmap, where dark green blocks represent rigid, confidently predicted domains.

A fundamental mathematical constraint enforced by the Structure Module. An SE(3) equivariant network guarantees that if the input 3D coordinates are rotated and translated, the output coordinates undergo the exact same transformation.

• Invariance vs. Equivariance: The Evoformer is invariant (output doesn't change with input rotation), while the Structure Module is equivariant (output rotates with input).
• Implementation: Achieved through the IPA mechanism, which uses 3D point geometry in a carefully constrained manner.
• Physical necessity: Ensures the predicted structure is not dependent on an arbitrary coordinate frame.

While AlphaFold2 outputs all heavy atom positions, the final side-chain conformations are predicted by the Structure Module using a discrete rotamer library approach.

• Rotamer prediction: The network predicts chi angle distributions for each side chain based on the local backbone geometry and environment.
• Post-prediction refinement: Tools like AMBER molecular dynamics can be used to relax the raw AlphaFold2 output, resolving minor atomic clashes and strained bond geometries.
• Limitation: The predicted side chains represent a single static snapshot and may not capture alternative conformations or ligand-induced fit states.