Predicted Aligned Error (PAE)

PAE provides a residue-by-residue error matrix rather than a single global score. For a protein with N residues, the output is an N×N matrix where position (i, j) represents the predicted error in Angstroms for residue i if the predicted and true structures were aligned on residue j. This pairwise granularity allows researchers to identify locally confident regions even within globally uncertain structures.

PAE excels at revealing the model's certainty about relative domain positioning. When two folded domains are predicted with high confidence internally but show high PAE values between them, it indicates the model is uncertain about their relative orientation. This is critical for assessing quaternary structure predictions and understanding whether a predicted complex reflects a biologically meaningful assembly or an arbitrary docking arrangement.

PAE values are measured in Angstroms (Å) and interpreted using established heuristics:

• < 5 Å: High confidence in relative position; domains are likely correctly packed
• 5-10 Å: Moderate confidence; general orientation may be correct but details are uncertain
• > 10 Å: Low confidence; relative positioning is unreliable
• > 15-20 Å: Essentially uninformative; the model cannot determine the spatial relationship

While pLDDT (predicted Local Distance Difference Test) measures per-residue local accuracy, PAE measures inter-residue spatial confidence. A structure can have high pLDDT scores—indicating well-predicted local geometry—yet exhibit high PAE values between domains, revealing that the model is uncertain about how those confidently folded domains are arranged relative to each other. These metrics are complementary and should be evaluated together.

PAE matrices are typically visualized as heatmaps where axes represent residue indices and color intensity indicates predicted error. Well-predicted domains appear as dark blocks along the diagonal, while inter-domain regions show lighter colors if uncertainty is high. Sharp boundaries between dark and light regions often correspond to domain boundaries or flexible linkers, making PAE plots powerful tools for domain parsing and assessing structural modularity.

In AlphaFold-Multimer, PAE is the primary metric for evaluating predicted protein-protein interfaces. Low inter-chain PAE values indicate high-confidence binding interfaces, while uniformly high inter-chain PAE suggests the model does not predict a stable interaction. Researchers routinely filter predicted complexes by requiring inter-chain PAE below 10 Å to identify biologically relevant assemblies from spurious co-folding artifacts.

A per-residue confidence metric output by AlphaFold2 that estimates the local accuracy of the predicted structure on a scale from 0 to 100.

• High pLDDT (>90): Indicates high confidence in the local backbone and side-chain conformation. These regions are typically suitable for detailed structural analysis.
• Low pLDDT (<50): Often corresponds to intrinsically disordered regions or flexible loops. These segments should be treated as unstructured and interpreted with extreme caution.
• Unlike PAE, which measures pairwise positional error, pLDDT is a self-assessment of local superposition quality, modeled on the lDDT-Cα metric used in CASP.

The primary scoring metric used in the CASP (Critical Assessment of Structure Prediction) competition to evaluate the global topology of a predicted model against an experimental structure.

• Mechanism: It calculates the largest set of residues that can be superimposed under a series of distance cutoffs (1, 2, 4, and 8 Ångströms).
• Interpretation: A GDT_TS score of 100 represents a perfect prediction. Scores above 80 generally indicate a correctly predicted global fold.
• While PAE estimates error without a ground truth, GDT_TS is a post-hoc evaluation metric requiring an experimentally solved reference structure.

A standard measure of the average distance between the atoms of superimposed protein structures, typically calculated over the Cα backbone atoms.

• Formula: RMSD quantifies the square root of the average squared distance between corresponding atoms after optimal rigid-body superposition.
• Limitations: RMSD is a global metric that can be disproportionately penalized by a single highly divergent loop, even if the core fold is correct. It does not provide the domain-pairing insight that PAE offers.
• Use PAE to assess relative domain orientation and RMSD to quantify overall backbone deviation when an experimental structure is available.

A core architectural mechanism in the AlphaFold2 Structure Module that operates directly on 3D point clouds to iteratively refine the protein backbone geometry.

• SE(3) Equivariance: IPA updates residue representations in a way that is invariant to global rotation and translation. If you rotate the input, the predicted structure rotates identically.
• Relationship to PAE: The IPA module produces the final 3D coordinates, and the PAE matrix is derived from the model's internal assessment of the error in these pairwise distances. The PAE head is trained to predict the error of the IPA's output.

The core neural network block in AlphaFold2 that processes the Multiple Sequence Alignment (MSA) and pairwise representations, acting as the information exchange engine.

• Function: It uses axial attention to flow information between rows (sequences) and columns (residues) of the MSA, while simultaneously updating a pairwise residue matrix that encodes proximity relationships.
• PAE Origin: The pairwise representation output by the Evoformer is the direct input to the PAE prediction head. The quality of the MSA and the Evoformer's processing fundamentally determine the sharpness and accuracy of the PAE plot.

Proteins or protein regions that lack a stable 3D structure under physiological conditions, existing as a dynamic ensemble of conformations.

• PAE Signature: IDPs and flexible linkers exhibit a characteristic pattern in PAE plots: high predicted error (red) for inter-residue distances within the disordered region, but low error (blue) for residues within adjacent structured domains.
• Interpretation: A high-PAE region with a corresponding low pLDDT score is a strong indicator of disorder, not a failure of the prediction algorithm. This pattern is biologically meaningful and should not be misinterpreted as a low-quality prediction.