CODesign: Consistency from Data to Trajectory in All-Atom Protein Binder Co-Design

• The framework targets scarce self-consistent complex data and sampling-time incompatibility between residue identities and evolving geometry.Existing approaches may use auxiliary sequence revision or external structure-prediction guidance, with substantial computational overhead.Source: §1 · p. 2
• CODesign constructs 104.5k distilled sequence–structure pairs and extends Proteína-Atomística to target-conditioned all-atom binder co-design.Source: §1 · p. 2
• CAR selectively resamples incompatible residue identities with local atomic states, then uses self-conditioning to adapt Cα trajectories without coordinate resets.It does not rely on an external inverse-folding model or folding-based reward oracle.Source: §1 · p. 2
• CODesign achieves state-of-the-art performance and the highest in silico unique success rates among evaluated baselines on protein- and ligand-target benchmarks.Source: §1 · p. 2

• Target-conditioned binder methods extend co-design with objectives or guidance tailored to intermolecular interfaces [5] [10].Discrete all-atom design models residue identities and masked atom slots, while another family jointly models structures and continuous sequence embeddings [24] [10] [13] [14].Source: §2 · p. 2

3 Methods

• Target-conditioned co-design models the joint distribution of binder sequence, Cα coordinates, and non-Cα coordinates given a protein or small-molecule target.The modalities evolve together in a shared sampling trajectory, allowing sequence and structure predictions to influence one another.Source: §3 · p. 3
• Consistency requires sequence compatibility with target-conditioned backbone geometry and recovery of the complete all-atom structure from sequence in the target's presence.The framework approximates these complementary relationships with sequence compatibility and structural recoverability terms.Source: §3 · p. 3
• CODesign addresses inconsistency through Codimer data, independently sampled modality times for learning conditional regimes, and joint resampling of incompatible residues with their local atomic states.Source: §3 · p. 3

3.1 Codimer: Consistency-Distilled Protein Dimers

• The high-confidence AFDB heterodimers cited as a data limitation are recovered by folding oracles within 2 Å complex-level Cα scRMSD in only 8.49% of cases.Source: §3.1 · p. 3
• Codimer uses ProteinMPNN to jointly redesign both chains into K = 4 candidate sequence pairs, then co-folds them with ESMFold2-Fast.The method approximates the two conditional terms in the consistency formulation through inverse folding and co-folding.Source: Consistency distillation · p. 3

Consistency distillation.

• 104,528 distilled sequence–structure pairs are produced from 191,836 reference complexes by redesigning, co-folding, confidence filtering, and selecting the lowest-reference-RMSD candidate.Candidate sequences are sampled with ProteinMPNN and co-folded; qualifying candidates are ranked by complex-level Cα RMSD to the reference.Source: Consistency distillation · pp. 3–4

3.2 Multi-Modal Flow Matching

• CODesign jointly evolves residue identities, Cα backbones, and local atom coordinates under target conditioning, with independently sampled modality times exposing structure-to-sequence and sequence-to-structure regimes.Atom37 represents 37 heavy-atom slots per residue and masks nonexistent atoms; masked-residue atoms are hidden to prevent revealing identity.Source: §3.2 · pp. 4–5

3.3 Consistency-Aware Joint Resampling

• CAR reassesses revealed residues against the predicted clean backbone, selects the largest sequence-prediction mismatches, and jointly remasks identities and local atoms while revised self-conditioning lets backbone updates respond.The selected residues are chosen by gaps between current identities and the model’s preferred residue types; Cα coordinates are not reset directly.Source: §3.3 · pp. 6–7

3.4 Stagewise Training

• Protein models train first on Teddymer and experimental PDB data for 60k iterations, then add Codimer for 10k; ligand adaptation uses LoRA on PLINDER complexes and CDDB monomers.The target-specific variants share the explicit generation and CAR formulations.Source: §3.4 · p. 7

4.1 Protein-conditioned Protein Binder Design; 4.2 Ligand-conditioned Protein Binder Design

• CODesign has the highest unique-success counts across protein-target sequence settings and the highest mean unique successes on ligand targets, outperforming DISCO in successes with less inference time.The ligand benchmark ranks CODesign first on OQO and IAI and second on FAD.Source: Table 2 · p. 8, §4.1 · p. 8, §4.2 · p. 8
• PXDesign achieves the highest fraction of protein designs with scRMSD ≤2 Å after ProteinMPNN redesign, but with substantially lower diversity and novelty; Complexa is faster and more diverse but yields fewer ligand successes.CODesign maintains a stronger balance across consistency, diversity, and novelty on protein targets, and the second-highest diversity among ligand co-design methods.Source: §4.1 · p. 8, §4.2 · p. 8

4.3 Ablation Studies

• 70.9% (9.46 vs. 5.54) improvement in mean unique successes across 19 protein targets is associated with including Codimer during training.Codimer improves performance across 12/19 targets and primarily improves interface and local-structure plausibility and complex-level consistency.Source: §4.3 · p. 9
• 4% more average unique successes across 19 protein targets with negligible additional computational cost when CAR is enabled.The comparison uses the same Codimer-trained model with CAR enabled or disabled.Source: §4.3 · p. 9

5 Conclusions

• CODesign improves sequence–structure consistency through distilled training pairs and consistency-aware joint resampling to generate compatible sequences, backbones, and local atomic structures.The framework targets protein and small-molecule binders.Source: §5 · p. 9
• CODesign achieves state-of-the-art in-silico success rates on protein- and small-molecule-target benchmarks, with ablations validating both framework components.Figure 4 compares CAR's average unique successes across 19 protein targets with per-sample generation time.Source: §5 · p. 9, Figure 4 · p. 9
• Wet-lab validation is still needed to establish whether the in-silico gains translate into higher binding affinity and experimental success.Evaluation is limited to in-silico metrics, and reliance on AlphaFold-based structure prediction and ProteinMPNN-based inverse folding may amplify the apparent importance of consistency.Source: §5 · p. 9

A.1 Data Sources and Preprocessing

• 191,836 reference dimers are collected from AFDB high-confidence heterodimers, HumanPPI, and filtered native holo dimers from PINDER.The collections contribute 25,837, 9,757, and 156,242 dimers, respectively.Source: §A.1 · p. 12

A.2 Consistency Distillation

• For each input dimer, both chains are redesigned jointly, four sequence pairs are co-folded, and confidence-qualified candidates are ranked by complex-level Cα RMSD to the reference.Inputs without a confidence-qualified candidate are discarded; the selected pair and its co-folded all-atom structure form one Codimer sample.Source: §A.2 · p. 12
• 104,528 synthetic sequence–structure pairs are produced by consistency distillation.Source: §A.2 · p. 12

B.1 Training Datasets

• Teddymer and PDB examples provide domain interactions, binder–target pairs, and monomers; Codimer is added during the second protein-training stage.Source: §B.1 · pp. 12–13
• CDDB supplies consistency-distilled monomers, while PLINDER supplies protein–small-molecule examples with the ligand retained as fixed conditioning information.Mixing the sources preserves protein sequence–structure supervision while adapting the model to ligand-specific interactions.Source: §B.1 · p. 13

B.2 Cropping and Geometric Preprocessing

• Protein-target crops select a binder segment around an interface seed and nearby target residues, with a 500-residue combined budget and at least 50 target residues for valid conditioning.Source: §B.2 · p. 13
• Small-molecule crops use a 300-token budget within 15 Å; ligand coordinates and chemical features are fixed, and only the protein is generated.Coordinates are converted to nanometers, randomly rotated, and centered on the target for conditioned examples or the protein for monomers.Source: §B.2 · p. 13

C.1 Residue and Atom Representations

• Masked residues contribute a Cα token and zero-coordinate pseudo-atom token; the pseudo-atom output supplies coordinates for valid slots after identity sampling.This keeps the state dimension fixed while allowing sampled amino acids to instantiate different atom sets.Source: §C.1 · pp. 13–14

C.2 Target Conditioning and Information Exchange

• Protein targets use residue-level features, while small-molecule targets use heavy-atom features; both are combined with binder embeddings and pair features.Pair features encode sequence separation, chain membership, hotspots, and available distances; ligand pairs also encode bond connectivity and order.Source: §C.2 · p. 14
• The atom encoder, residue Transformer, and atom decoder exchange context through cross-attention, while pair-biased attention processes the joint binder–target representation.Pair features remain fixed during each forward evaluation, with no triangular pair updates.Source: §C.2 · p. 14

D.1 Stagewise Optimization

• Protein training progresses from Teddymer and PDB data to a mixture that adds Codimer; ligand adaptation starts from the protein model and trains LoRA adapters.The first stage initializes from a pretrained Complexa checkpoint, the second from the first-stage EMA weights, and ligand adaptation freezes base weights and biases.Source: §D.1 · p. 14
• Protein- and ligand-conditioned variants use the same architecture dimensions and layer counts, with different target feature encoders.Training settings and checkpoint steps are reported by stage.Source: Table 5 · p. 15, Table 6 · p. 15

D.2 Backbone Noise and Modality-Time Sampling

• The initial backbone noise is centered across binder residues and given a random three-dimensional center, encouraging the denoiser to infer placement relative to the target.The randomized center prevents the clean binder center from being determined directly from centered-noise interpolation.Source: §D.2 · pp. 15–16
• Sequence and coordinate modality times are sampled independently, exposing the network to varying combinations of sequence and structure uncertainty.The coordinate-time distribution combines a uniform component for noise-level coverage with a beta component emphasizing more resolved structures.Source: §D.2 · p. 16

D.3 Self-Conditioning and Conditional Training

• Self-conditioning uses detached preliminary clean-coordinate and residue-identity predictions in half of training evaluations, while clean-backbone or clean-sequence conditioning is enabled in selected iterations.The two clean-conditioning modes are mutually exclusive and equally likely, with combined probability 0.1 during protein training and 0.15 during ligand adaptation.Source: §D.3 · p. 16

D.4 Loss Normalization and Auxiliary Supervision

• The training objective combines backbone, sequence, and local-atom losses with a binder–target distance term enabled only when tx > 0.3.The auxiliary distance term is zero for monomer examples and directly supervises distances to target reference points.Source: §D.4 · p. 16

E.1 Modality Schedules

• A trajectory has 1,000 global updates; backbone and sequence schedules end after 500, while local-atom refinement continues throughout.The schedule allows CAR to revise residue decisions while sequence generation remains active.Source: §E.1 · p. 17

E.2 Coordinate and Sequence Updates

• Sequence updates sample residue identities from denoiser probabilities, reveal the most confident masked positions, and may remask positions during the trajectory.At completion, existing non-Cα offsets are added to final Cα coordinates to reconstruct the all-atom binder.Source: §E.2 · p. 18

E.3 Consistency-Aware Joint Resampling

• CAR assesses sequence–structure compatibility every 20 updates when tx ≥ 0.95 and sequence updates remain active, then jointly resets selected residue identities and local atomic states.It leaves backbone coordinates unchanged; with default schedules, nine assessments add at most 18 denoiser forwards beyond the 1,000 ordinary forwards.Source: §E.3 · pp. 18–19

F.1 Reporting Conventions

• Benchmark runs generate 200 binders per target, summarize quality metrics across five seeds, and report per-target and aggregate statistics using specified averaging procedures.Generation times use batch size one on a single GPU.Source: §F.1 · p. 19

F.2 Protein-Conditioned Binder Design

• Protein-conditioned supplements report aggregate and per-target unique successes and structural-consistency metrics, including mean scRMSD and the fraction at or below 2 Å.The tables distinguish self-generated sequences from MPNN@1 and MPNN@8 sequences.Source: §F.2 · pp. 19, 22, Table 8 · p. 20, Table 9 · p. 20

F.3 Ligand-Conditioned Binder Design

• Ligand-conditioned supplements report per-target unique successes and a four-target mean, using generated sequences for co-design methods and one LigandMPNN sequence per backbone for two-stage methods.The aggregate is computed within each seed before summarization.Source: §F.3 · p. 22, Table 18 · p. 22

Effect of Codimer

• The Codimer ablation compares models trained with and without Codimer while disabling CAR in both variants and holding architecture and training hyperparameters constant.Both variants are evaluated with self-generated sequences on 19 protein targets.Source: §F.4 · p. 22

Effect of CAR

• The CAR ablation compares enabled and disabled inference-time correction using the same Codimer-trained checkpoint and unchanged generation and evaluation settings.The comparison isolates inference-time correction from changes in training; quality metrics are summarized across five seeds.Source: §F.4 · p. 22

Ablation reporting

• The ablation tables report aggregate quality entries and per-target unique successes for Self sequences, with quality means and standard deviations across five seeds.Complex scRMSD and the percentage at or below 2 Å are reported separately in the supplementary benchmark tables.Source: Table 15 · p. 24, Table 19 · p. 25, Table 20 · p. 26