Source-linked AI summary
EMBER: Predicting TCR--pMHC Binding Without a Docked Complex
Lin Ha, Chen Zhou, Haozheng Luo, Han Liu, Xiaoyu Zhang, Yan Chen
TL;DR
Predicted docked complexes make structure-based TCR–pMHC predictors depend on the accuracy of the predicted interface and relative pose. EMBER folds and encodes each molecule independently, then compares their representations without a shared coordinate frame. It leads six retrained baselines on every metric under all four folding tools, with improved MCC and cross-tool ranking stability over the strongest or structural baselines, respectively.
Problem
Structure-based TCR–pMHC predictors commonly infer binding from a predicted docked complex, making their features and input residues dependent on predicted relative pose, whose reliability in task-critical quantities had not been systematically tested.
Source: §1 · pp. 1–2Method
EMBER independently folds and encodes each molecule as an SE(3)-invariant residue graph, then scores binding through bidirectional attention without constructing a shared coordinate frame.
Source: §1 · p. 2Results
EMBER leads six published baselines on every metric under all four folding tools, improving MCC at the fixed threshold of 0.5 by 51 to 75% over the strongest baseline and ranking stability by 26 to 85% over structural baselines.
Source: §1 · p. 2, §6 · p. 10Takeaways & Limitations
By removing relative pose from the binding score, EMBER provides a scalable way to prioritize likely binders, including for unseen epitopes.
Source: §1 · pp. 1–2
Abstract
from arXiv · showhide
We propose EMBER, a structure-based framework for TCR--pMHC binding prediction that eliminates the need for a predicted docked complex, and with it the placement error that dominates such predictions. Traditional structure-based predictors utilize the co-folded complex structure of the receptor and the antigen and interpret binding from its contact surface. Consequently, every downstream feature inherits any deviation the structure-prediction tool introduced. Methodologically, EMBER folds the TCR and pMHC independently, encodes them as SE(3)-invariant residue graphs, and compares their learned representations without constructing a shared coordinate frame. A relative pose is therefore not an input of the model, so placement error cannot propagate into the prediction. Computationally, EMBER preprocesses $O(N{+}M)$ monomer folds where a complex-based predictor needs $O(NM)$ operations. Experimentally, under epitope-disjoint evaluation with six retrained baselines, EMBER is first on every metric under all four folding tools, by 0.9 to 14.4% in micro-AUROC, 18.5 to 25.3% in micro-AUPRC and 10.6 to 24.1% in MCC. Its ranking is also up to 85% more stable across folding tools.
1 Introduction
EMBER predicts TCR–pMHC binding without docking the molecules together, avoiding pose-dependent interface inputs. It independently encodes both monomers and compares them through attention; across four folding tools, it leads six retrained baselines on every metric.
1 Introduction
- Docked-complex predictors depend on predicted interfaces, so placement errors can alter both their geometric features and which residues and contacts enter the input graph.The reliability of predicted complexes for these task-critical quantities had not been systematically tested.Source: §1 · pp. 1–2
- Assembly-induced interface corruption (AIC) is the failure mode in which pose errors corrupt the residues and contacts presented to downstream predictors.EMBER is designed to remove complex assembly rather than correct its errors.Source: §1 · p. 2
- EMBER folds the TCR and pMHC independently, encodes each as an SE(3)-invariant residue graph, and scores the pair through bidirectional attention.The model never constructs a shared coordinate frame or uses the molecules’ relative pose.Source: §1 · p. 2
- EMBER preprocesses O(N+M) monomer folds, compared with O(NM) complex predictions for a complex-based predictor.The approach uses one unbound monomer fold for each molecule.Source: §1 · pp. 1–2
- EMBER leads six published baselines on every metric under all four folding tools and is significantly more stable to folding-tool choice.The baselines were retrained on identical data and splits.Source: §1 · p. 2
2 Related Work
Prior TCR–pMHC predictors use sequence or predicted structure, but structure-based methods commonly rely on a docked interface. EMBER instead retains both monomer structures while avoiding pose-dependent residue selection and contacts.
2 Related Work
- Sequence-based methods use larger datasets than solved TCR–pMHC complexes, but generalization to unseen epitopes remains limited.NetTCR and ERGO-II learn from amino-acid sequences; TEIM predicts residue contacts and HeteroTCR builds a graph over sequence embeddings.Source: §2 · p. 3
- Most structure-based predictors infer binding from a predicted complex interface, often using 8 to 14 Å cutoffs that make residue and contact selection pose-dependent.Other methods use only one partner’s structure or use structure during training without exploiting both molecules’ structural information.Source: §2 · p. 3
- EMBER processes each monomer in full and connects sequence-annotated residue sets, while TRAP drops receptor structure and caTCR omits MHC.Unlike caTCR’s pairwise-distance matrix and sequence-order neighborhoods, EMBER carries coordinates as an equivariant field and updates them at each layer.Source: §2 · p. 3
- Abeer et al.’s E(n)-equivariant joint-graph network remains exposed to relative pose, whereas EMBER removes it by Proposition 1.The whole-assembly motion invariance of the former does not remove relative pose from its input.Source: §2 · p. 3
3 Assembly-induced Interface Corruption
Across 49 class-I TCR–pMHC crystal structures, co-folding tools often fail to reproduce native interfaces, with errors concentrated in rigid-body assembly rather than monomer folding. Their placement errors are large and systematic, limiting what repeated sampling can correct.
3 Assembly-induced Interface Corruption
- On 10 targets released after Boltz-2’s training cutoff, its contact Jaccard at 5 Å falls from 0.833 to 0.155, while ESMFold2 changes from 0.459 to 0.393 and AlphaFold-Multimer from 0.308 to 0.303.The evaluation covers six co-folding tools and 49 class-I TCR–pMHC crystal structures; 39 targets were seen by Boltz-2 during training.Source: §3 · p. 3
- Excluding Boltz-2, median contact Jaccard at 5 Å ranges from 0.188 to 0.459 and median receptor Cα RMSD from 5.87 to 8.09 Å.The authors report that no tool reconstructs the native interface reliably.Source: §3 · p. 3
- Across tools, receptor placements differ by 5.10 to 7.80 Å, while independently folded TCR monomers agree within 0.96 to 1.23 Å over 250 monomers.The tools largely agree on individual molecular structures and disagree on how to assemble them.Source: §3 · pp. 3–4
- Repeated assembly errors are directionally coherent: five tools reach γ of 0.84 to 0.992 across 20 folds, and averaging shifts displacement by only −2.5% to +6.7%.Across five tools, cross-tool γ is 0.621, with above-random agreement on 40 of 48 targets (p = 3.3 × 10−6).Source: §3 · p. 4
- Rigid-body assembly is the dominant structural error, large enough to change downstream graph inputs and systematic enough that sampling and ensembling cannot remove it.AIC names the failure mode in which placement error changes the interface presented to the downstream model.Source: §3 · pp. 3–4
4 Method
EMBER independently encodes the TCR and pMHC as residue graphs, then compares their representations without using the molecules’ relative pose. Its pose-independent score is invariant to independent rigid motions of the two molecules.
4 Method
- EMBER encodes the independently folded TCR and pMHC as residue graphs, processes them with a shared encoder, and scores the pair using bidirectional attention.The two encoder towers exchange no messages; the contact head compares their residue representations and produces the binding score.Source: §4 · p. 4, Figure 3 · p. 5
- Each encoder layer applies chemistry-gated messages and rebuilds its nearest-neighbor graph from updated coordinates.The identity-only gate modulates geometry passed in messages; without rebuilding the graph, updated coordinates would not influence node features.Source: §4 · p. 5
- The contact head uses sequence-annotated CDR3β and peptide residues, with peptide pooling mapped to nine canonical slots across peptide lengths.Class-I peptide anchors map to fixed slots, while interior residues are spread over the remaining slots.Source: §4 · p. 6
4.1 Theoretical Analysis
- EMBER’s binding score is unchanged by independent rotations and translations of the TCR and pMHC, so their relative pose is not an input.The method therefore avoids errors from inaccurate complex assembly entering through pose-dependent features.Source: §4.1 · p. 7
5 Experiments
Across epitope-disjoint evaluation, EMBER leads six retrained baselines on every metric under all four folding tools, and its rankings are more stable across tools. Ablations and preprocessing measurements examine structural inputs and computational cost.
5 Experiments
- The evaluation spans four public datasets, 45,909 TCR–pMHC pairs, 343 epitopes, five epitope-disjoint folds, and three seeds.The dataset includes 7,371 measured binders augmented with sampled non-binders.Source: §5 · p. 7
5.1 Binding Prediction and Stability against Retrained Baselines
- EMBER leads every cell: 0.9–14.4% in micro-AUROC, 18.5–25.3% in micro-AUPRC, and 10.6–24.1% in MCC∗ over the second-best methods.The comparison uses epitope-disjoint five-fold evaluation, averaging five folds and three seeds; the table covers all four folding tools.Source: §5.1 · p. 7, Table 1 · p. 8
- EMBER’s cross-tool concordance is W = 0.840, 26% to 85% higher than the four structure-consuming baselines.Across tools, 81.4% of candidate pairs retain their relative order, versus 60.5% to 70.9% for baselines.Source: §5.1 · p. 9
5.2 Influence of Structure
- Complex confidence separates binders from decoys, but complex-based methods average a 16% gain, below the sequence baselines’ 17%.Removing EMBER’s structure costs 11.1% of its micro-AUPRC margin; replacing monomers with a predicted complex costs 12.3%.Source: §5.2 · p. 9
- Removing EMBER’s canonical peptide frame reduces MCC@0.5 by 23.4%, versus an 8.3% reduction with a test-fold-tuned threshold.The ablation arms use ESMFold2 structures, selected because they provide the most favourable input among the tested tools.Source: §5.2 · p. 9, Table 3 · p. 9
- Monomer preprocessing costs 4.2 GPU-h with tFold-TCR, versus 80.7 to 1,602.3 GPU-h for complex predictions, saving up to 19.4×.EMBER reuses each monomer structure across the candidate pairs in which it appears.Source: §5.2 · pp. 9–10
6 Conclusion
EMBER predicts TCR–pMHC binding without assembling a docked complex, and the conclusion reports gains in accuracy, cross-tool stability, and preprocessing cost. The notation section specifies that indices range over residues of a single monomer.
6 Conclusion
- EMBER independently encodes the TCR and pMHC to remove relative pose from its binding score and avoid assembly-induced interface corruption.The conclusion frames the approach as using the trustworthy part of predicted structures for this task.Source: §6 · p. 10
- 51 to 75% higher MCC at threshold 0.5, 26 to 85% greater ranking stability across folding tools, and up to 19.4× less preprocessing are reported for EMBER.The comparisons are against the strongest baseline for MCC, structural baselines for stability, and complex-based predictors for preprocessing.Source: §6 · p. 10
A Notation
- Indices i and j range over residues of one monomer, not both molecules together.The notation makes explicit that no symbol ranges across the two molecules at once.Source: A Notation · p. 14
B Proof of Main Text
The proof establishes that EMBER's score is invariant to independent rigid motions of the two molecule graphs. Its feature construction and released receptor scope support that pose-independent design.
B.1 Lemma 4.1
- The encoder’s coordinate update preserves rigid-motion equivariance because its learned coordinate weights are unchanged and translations cancel within pairwise differences.The rebuilt edge set also remains unchanged after the update.Source: §B.1 · p. 16
B Proof of Main Text
- Independent rotations and translations of the receptor and antigen leave their respective graph representations unchanged, so the score does not depend on either molecule’s frame.The proof applies the input invariance lemma through the encoder layers and uses a head with no position argument.Source: §B.2 · p. 16, B Proof of Main Text · p. 16
B.2 Proposition 1
- Unlike a docked-complex equivariant model such as Siriarchawatana et al., EMBER’s guarantee removes relative pose itself, not just the joint laboratory frame.The head’s signature gives this guarantee regardless of its weights or training.Source: §B.2 · p. 16
C Graph Construction and Features
- Node and edge features depend on residue identity or relative geometry, while the inverse-distance edge term supplies the charge product’s Coulomb form.A monotone radial term multiplied by the charge column represents 1/d without changing the invariance argument.Source: C Graph Construction and Features · pp. 16–17
D Scope of the Released Model
- The released encoder uses the TCR β chain alone; paired α/β records confirm 6,759 of 21,477 receptors, a lower-bound count.The source records cover only part of the set, and the available provenance makes the matched count a lower bound.Source: D Scope of the Released Model · p. 18
E AIC Observation Details
The AIC observations assess predicted interface contacts and placement across crystal structures, with controls for template leakage and tool-specific caveats. The reported matched comparison shows Boltz-2’s contact ranking changes on targets beyond its training cutoff.
E AIC Observation Details
- The evaluation covers 49 class-I complexes with 35 peptides and 31 MHC heavy chains, using the same five crystal-entry chains for each folding tool.This preserves residue correspondence with the native structure without an alignment step.Source: E AIC Observation Details · p. 18
- Template dates were capped before each target’s deposition, and the possibly-seen half performed worse on docking than the other half (p = 0.010).This date-split check is reported as evidence that the template cap is sufficient.Source: E AIC Observation Details · p. 18
- On the 10 targets beyond Boltz-2’s training cutoff, it shifts from first on every contact metric to last on Jaccard and precision in the matched comparison.The other five tools move far less on this subset.Source: Table 9 · p. 19
- Boltz-2’s 0.754 Å median cannot be read as accuracy: 39 of 49 targets predate its training cutoff, and the within- versus outside-window medians are 0.68 Å and 1.72 Å.The split is significant at Mann–Whitney p = 7.6 × 10^-5; AF-Multimer’s confidence value is also not comparable across tools because it substitutes a global score.Source: E AIC Observation Details · p. 19
- Table 10 summarizes 20 co-folds per stochastic tool across 49 targets; γ measures directional coherence against 0.21 for random directions, while the oracle is unavailable to deployed systems.AIC is the median over targets of per-target medians; the change is the median of 1 − equal/single.Source: Table 10 · p. 19
F.1 Evaluation Protocol
The evaluation uses epitope-disjoint folds and reports fold-level averages rather than pooled scores. It also retains all folds, including baseline failures, while describing the sampled non-binder pool and metric aggregation rationale.
F.1 Evaluation Protocol
- 7,371 measured binders and 38,538 sampled non-binders form 45,909 rows across 343 epitopes, with binder prevalence 0.161 and a long-tailed epitope distribution.The ten most frequent epitopes account for most entries, motivating side-by-side macro and micro aggregation.Source: §F.1 · p. 20
- Non-binders are used from the STAG release without resampling; training redraws three per binder each epoch, while evaluation scores every row.The release combines dextramer-panel non-binders and TCR-swapped pairs, but has no provenance column to separate them.Source: §F.1 · p. 20
- Each epitope cluster is assigned to exactly one fold, so no epitope appears in more than one of the five folds.For each test fold, the next fold is validation and the other three are training; test data do not guide checkpoint selection.Source: §F.1 · p. 20, Table 12 · p. 20
- Metrics are computed within each fold and then averaged, because pooling separately trained models lets between-model score offsets drive AUROC and weights folds by size.An earlier pooled analysis reported micro-AUROC 0.676 for a configuration whose fold-averaged value was 0.642.Source: §F.1 · pp. 20–21
- All five folds are retained even when baselines collapse or cannot cross the fixed 0.5 threshold, and results are averaged across them.SageTCR becomes constant on fold 0 under all four structure sources; TRAP has threshold-crossing failures on folds 0 and 4.Source: §F.1 · p. 21
F.2 Metric Definitions
The appendix defines ranking, stability, and threshold-based metrics, describes training and checkpoint selection, and reports fold-level results and paired comparisons.
F.2 Metric Definitions
- MCC@0.5 uses a fixed 0.5 threshold, MCC* uses a test-fold oracle threshold, and MCC@t is fitted on the other four folds.Micro metrics are dominated by frequent epitopes, while macro metrics count each epitope once; stability also uses pairwise ranking agreement, concordance W, and Overlap@k.Source: §F.2 · p. 21
F.3 Hyperparameter
- The objective combines cross-entropy and Bradley–Terry ranking losses; negatives are redrawn each epoch and checkpoints use a rolling three-epoch validation micro-AUROC mean.The rolling mean is used because selecting the single best epoch selects on the validation fold.Source: §F.3 · p. 22
F.4 Binding Prediction, Fold by Fold
- Fold 0 is easiest on micro metrics for methods that separate classes, but no method peaks there on macro metrics.The macro metrics discount the one large epitope; means in Table 1 average five per-fold values.Source: §F.4 · p. 23
- EMBER wins all five folds in 16 of 24 cells; the exceptions include small micro-metric leads and oracle MCC* comparisons.Table 15 pairs methods by fold, averaging seeds within each fold; no cell can yield a stronger one-sided Wilcoxon test than five wins in five paired observations.Source: §F.4 · p. 23, Table 15 · p. 24
F.5 Architecture Ablations
The ablations test the role of graph neighborhoods and the TCR α chain, and describe a docked-complex arm that restores shared-frame interactions while holding model capacity fixed.
F.5 Architecture Ablations
- Removing the graph costs 13.1% of the control’s micro-AUPRC margin above chance, while restoring the TCR α chain costs 8.6% of that margin and 10.0% of MCC@0.5.The authors interpret the graph result as showing that most structural contribution arrives through neighborhood information rather than per-residue descriptors; the α-chain result informs the scope decision.Source: §F.5 · p. 28, Table 21 · p. 28
- The docked-complex arm replaces monomer structures with an ESMFold2 co-folded complex and rebuilds cross-molecular edges, using the same encoder and 3,027,721 parameters as the control.Unlike the control, this arm is not invariant to independent motions of the two molecules.Source: §F.5 · p. 28
F.6 Preprocessing Benchmark
The preprocessing benchmark times inference separately from model loading and excludes first-run autotuning; its reported speed advantage has scope and measurement caveats.
F.6 Preprocessing Benchmark
- Timing uses a shared sample across four folding tools, with inference-only GPU time and the first structure of each run excluded.Median lengths are 228 residues for a receptor, 382 for a target, and 610 for a complex; model load is timed separately.Source: §F.6 · p. 28
- TCRmodel2 spends 45–48% of wall-clock time outside inference, while Boltz-2’s reported timing excludes its required multiple-sequence alignment.The alignment is not included in its row, and the benchmark uses an explicit alignment path for each chain but none for the 9-mer peptide.Source: §F.6 · p. 28
- On a fixed candidate set, folding a complex yields only a constant-factor advantage, and each timing cell is a single measurement without an error bar.Within-cell spread is reported as tight, with p90 over median ranging from 1.03 to 1.08.Source: §F.6 · p. 28