MuCO: Generative Peptide Cyclization Empowered by Multi-stage Conformation Optimization

Angxiao Yue; Fanmeng Wang; Hongteng Xu; Wentao Guo; Yaning Cui; Yitian Wang

REVIEW 4 major objections 5 minor 8 references

MuCO: Generative Peptide Cyclization Empowered by Multi-stage Conformation Optimization

T0 review · 4 major / 5 minor · reviewed 2026-08-03 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Peptide cyclization is reformulated as generative ensemble modeling, and the paper claims a three-stage flow-matching pipeline outperforms deterministic folding on diversity, energy, and speed.

desk verdict Useful generative pipeline for cyclic peptide conformations, but the benchmark ground truth and metrics are soft enough that 'consistently outperforms' is conditional. read the letter →

arxiv 2602.11189 v2 pith:OMGBLEHN submitted 2026-01-30 q-bio.BM cs.AI

Yitian Wang , Fanmeng Wang , Angxiao Yue , Wentao Guo , Yaning Cui , Hongteng Xu This is my paper

classification q-bio.BMcs.AI

keywords peptidecyclizationconformationalensemblesflowmatchingside-chainpackingcyclicdrugdesignringclosureforce-fieldoptimizationgenerativemodeling

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper argues that predicting the ring-shaped conformations a cyclic peptide adopts cannot be done by adapting linear-peptide folding models, because those models collapse to a single high-energy structure. Its proposal, MuCO, treats cyclization as a conditional generative modeling problem: given a linear peptide sequence, sample from the distribution of cyclic backbones and then from the distribution of side-chain rotamers for that backbone, before relaxing each all-atom sample with a molecular force field. The central claim is that this factorization—backbone flow matching, side-chain flow matching, force-field minimization—yields ensembles that are simultaneously diverse and physically stable. On a large database of cyclic peptide conformations, the paper reports lower mean potential energy, higher mode and secondary-structure diversity, and much lower amortized sampling cost than AlphaFold2-based cyclization methods. If correct, MuCO makes large-scale conformational screening of cyclic peptide drug candidates practical.

What carries the argument

The load-bearing mechanism is the factorized conditional model p(X|S)=p(B|S)p(C|B,S), implemented as three connected stages. Stage 1 uses sequence-conditioned flow matching on SE(3)^L × T^L to generate backbones; training on cyclic data makes ring closure an emergent property. Stage 2 uses torsional flow matching on T^{4L} conditioned on the generated backbone, with cyclic relative positional encoding that rewires residue 1 and L as neighbors to prevent steric clashes at the junction. Stage 3 runs rule-based topology detection and CHARMM36 energy minimization, monotonically lowering potential energy. The tree-structured K×M sampling strategy is what converts these stages into fast, diverse e

What would settle it

Take the 85 experimentally determined CPSea-PDB structures as a clean test set: if MuCO's generated ensemble (even at K×M=100) does not place at least one conformation within a few Ångströms RMSD of each experimental structure while an AlphaFold2-based baseline does, or if its lower-energy advantage disappears when training and evaluation exclude AF2-derived conformations, the central claim would be falsified.

Watch

Extended reading notes

Core claim

The paper's own claim is that p(X|S), the conditional distribution of cyclic peptide conformations given a linear sequence, can be factorized exactly as p(B|S)p(C|B,S) and learned in two independent generative stages: an SE(3) flow-matching model generates ring-closed backbones on the manifold (SE(3)×T)^L, and a torsional flow-matching model generates side-chain angles on T^{4L}, with a cyclic relative positional encoding so that the ring closure junction is treated as adjacent. A third stage minimizes each sample under the CHARMM36 force field with automatically inferred cyclization topology. Trained directly on cyclic peptide data, the backbone flow learns ring closure implicitly rather th

Load-bearing premise

The benchmark treats CPSea's largely AlphaFold2-derived conformations as valid ground truth and assumes the functional-annotation split prevents sequence-level leakage; if those predicted structures encode the biases of AF2-style models, the reported energy and diversity gains may not transfer to experimentally determined cyclic peptides.

Editorial extensions

If this is right

Given one linear peptide, MuCO can generate many distinct ring-closed conformations, including different cyclization modes (head-to-tail, disulfide, isopeptide), instead of a single deterministic prediction.
In benchmark comparisons, MuCO's single-sample outputs achieve much lower average CHARMM36 energy and higher Shannon-entropy diversity than AlphaFold2-derived cyclization methods, which collapse to one mode.
Raising the sampling budget K×M pushes success rate to 100% and reaches energies comparable to or lower than the reference conformations, supporting ensemble-based virtual screening.
Parallel sampling gives an amortized cost of roughly 41 ms per conformation on one consumer GPU, more than 100× faster than folding-based baselines, making large-scale screening feasible.
Training on native cyclic peptides lets ring closure be learned rather than imposed, avoiding the unnatural strain caused by forced cyclization of linear-predicted structures.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Because most of the benchmark data is itself AlphaFold2 output, part of MuCO's apparent advantage may come from learning the same predictive biases it is compared against; the 85 experimental PDB structures are the only fully independent check.
The same factorized architecture could be conditioned on experimental restraints (NMR-derived distances, rotamer preferences) or extended to lasso and branched macrocycles, giving immediate testable variants.
MuCO's cheap ensemble generation could act as a seeding mechanism for molecular dynamics or as a coverage oracle for evaluating other generative peptide models.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: this is a real method paper, not a solved-problem paper. The staged architecture—SE(3) flow matching for backbones, torsional flow matching with a cyclic relative positional encoding for side chains, then CHARMM36 patching and refinement—is a sensible and genuinely new combination for cyclic peptides, and the paired linear-cyclic benchmark is a useful resource. The decoupled sampling strategy is well motivated and the measured efficiency gain is real: 41 ms amortized per conformation on a 4090, with ablations showing each stage contributes. The citations look fair: FoldFlow2, FlowPacker, HighFold2, and CPSea are all properly credited.

Where I push back is the abstract's "significantly and consistently outperforms" claim. The stress test's main concern holds. The non-PDB CPSea ground truth is largely AF2-derived, and the test sets are drawn from that same source. The train/test split is by functional annotation, not sequence clustering, and no redundancy analysis is reported. The AF2-based baselines were pretrained on data that includes CPSea, so the comparison could partly be between models that have memorized the same AF2 bias rather than a test of physical prediction. The CPSea-PDB subset is cleaner, but there are only 85 structures and no error bars or significance tests anywhere in the paper.

The metrics have issues too. The diversity metric is Shannon entropy over mode or secondary-structure clusters, which rewards a balanced mixture rather than agreement with the ground-truth distribution; on CPSea-PDB, MuCO's H=0.88 versus GT's 0.54 is not obviously a win. And the energy comparison is measured after the same CHARMM36 minimization that is MuCO's Stage-3, so it partly measures seed quality for that optimizer. The abrupt coil-to-helix transition after Stage-3 in Table 10 is dramatic and inadequately explained, though force-field minimization can legitimately do that.

None of this kills the method. The pipeline is coherent, the PDB subset results are not embarrassing, and the paper's own limitations paragraph is honest about missing pharma metrics and wet-lab validation. But the headline claim is conditional: I would want error bars, a sequence-redundancy analysis, and ideally validation on experimentally determined structures or independent MD before trusting the benchmark numbers.

For a computational peptide-design audience, this is worth reading and citing as a representative generative cyclization method. I would send it to peer review rather than desk reject, with a request to harden the benchmark and soften the claims.

Referee Report

4 major / 5 minor

Summary. The paper proposes MuCO, a three-stage generative pipeline for cyclic peptide conformation ensembles conditioned on the linear peptide sequence: (1) an SE(3) flow-matching backbone generator trained on cyclic peptide data to implicitly enforce ring closure; (2) a torsional flow-matching side-chain packer augmented with cyclic relative positional encodings; and (3) a CHARMM36-based physics-aware refinement with rule-based topology detection. The authors evaluate MuCO on the CPSea-derived benchmark they construct (CPTrans, CPBind, CPCore, CPSea-PDB) and report that MuCO achieves lower mean potential energy, higher Shannon-entropy diversity, better secondary-structure recovery, and lower amortized sampling latency than AF2-based (HighFold2, AfCycDesign) and geometric-deep-learning (EGNN, WGFormer) baselines. The core algorithmic decomposition is coherent and the efficiency analysis is concrete, but the empirical claims rest on benchmark and metric choices that require further validation before the headline claim of 'significantly and consistently outperforms' can be accepted.

Significance. If substantiated, MuCO would be a practically useful generative tool for cyclic peptide conformation exploration, combining a principled coarse-to-fine decomposition, a large-scale training set, and an efficient KxM hierarchical sampling scheme. The paper's strengths include a clear three-stage formulation (Eq. 1-2), use of cyclic-aware encoding in the packing module, a public demo/code release, detailed ablations of the generative stages and the optimization stage, and an explicit latency/parameter comparison. However, the manuscript's central empirical claim is currently conditional: the benchmark largely uses AF2-derived conformations as ground truth, the diversity metric rewards balance rather than fidelity to the ground-truth mode distribution, and the energy metric is computed after the same minimization routine that constitutes MuCO's Stage-3. These issues do not prove the method fails, but they make the 'significantly and consistently outperforms' claim exceed what the current evidence supports.

major comments (4)

[Section 4.1, Appendix A.2, Appendix C.2] The benchmark's external validity is undermined by the provenance of the ground truth. The paper states in Appendix A.2 that CPSea, excluding the PDB subset, is 'largely derived from AF2 predictions,' and MuCO is trained on CPSea-Train, while CPTrans, CPBind, and CPCore are drawn from the same source. The AF2-based baselines are described as having 'prior exposure to the underlying data distribution.' The train/test split is by functional annotation, with no reported sequence-identity clustering or redundancy analysis. Consequently, the reported improvements on the non-PDB test sets may largely reflect memorization of the AF2 conformational bias shared by training and test data. I request a sequence-level redundancy analysis, an evaluation on the 85 experimental CPSea-PDB structures with confidence intervals, and a clear statement of performance transferability to experimentally determin
[Appendix D.1, Table 5] The diversity metric H (Shannon entropy) does not measure agreement with the ground truth; it rewards a balanced distribution across the three cyclization-mode categories. On CPSea-PDB, MuCO reports H=0.88 with mode distribution 30.0/70.0/0.0, while the ground truth has H=0.54 with distribution 11.9/86.9/1.2. A model that assigned equal probabilities to all modes would score higher than the ground truth despite being less faithful. The claim of 'structural diversity recovery' therefore conflates dispersion with accuracy. In addition to H, report a distributional divergence (e.g., KL or Jensen-Shannon divergence) between the generated and ground-truth mode distributions and secondary-structure distributions, and report per-dataset bootstrap confidence intervals.
[Appendix D.2, Appendix B, Stage-3] The physical-stability metric is measured after the same CHARMM36 minimization pipeline that constitutes MuCO's Stage-3. Appendix D.2 states that 'all candidate structures, including MuCO generations, baseline predictions, and the original Ground Truth samples, are processed through the identical force-field optimization pipeline before any metrics are calculated.' This makes the energy comparison a measure of seed quality for that specific minimizer rather than an independent test of physical stability. The comparison is internally consistent, but it is partly circular for MuCO, whose Stage-3 is exactly that minimizer. Please report energies both before and after Stage-3 refinement, add RMSD to the ground-truth conformation, and, if possible, validate a subset with an independent relaxation protocol or short MD.
[Tables 1, 5-10] The headline claim that MuCO 'significantly and consistently outperforms' is not supported by any error bars, confidence intervals, or statistical tests. All tables report single point estimates. Given the stochasticity of training and sampling, I request at least three independent training seeds or, at minimum, multiple sampling runs with reported mean±std and a paired significance test for the main metrics (energy, diversity, secondary-structure composition) on each test set. This is particularly important for the CPSea-PDB subset, which contains only 85 structures.

minor comments (5)

[Abstract] Typo/grammar: 'significantly outperforms state-of-the-art methods in consistently in physical stability.' The word 'consistently' appears misplaced.
[Appendix A.2] The sentence 'the CPSea dataset (excluding the PDB subset) is largely derived from AF2 predictions; thus, these models can be considered to have prior exposure to the underlying data distribution' is an explicit acknowledgment of benchmark contamination. This should be moved to the Limitations section or addressed by additional experiments, not used as a justification for not fine-tuning baselines.
[Remark 3 / Appendix B.2] Remark 3 states that the energy is reduced 'monotonically during optimization' and mentions Langevin thermostat, while Appendix B.2 says the protocol uses 500 steps of Steepest Descent. These are inconsistent; please clarify which optimizer is used.
[Table 7] Table 7 lists both Energy (kJ/mol) and Energy (eV) columns that appear to be the same quantity in different units but with inconsistent conversions (e.g., -3.9 kJ/mol is not -0.049 eV). Clarify whether these are two separate metrics or remove the duplicate.
[Figure 3] The legend abbreviations 'GT EGNN WG AfCyc HF2 MuCO' are not expanded in the caption. Define each method name to make the figure self-contained.

Circularity Check

1 steps flagged · score 4.0 of 10

No equation-level circularity; benchmark circularity from AF2-derived CPSea ground truth and training source.

other [Appendix A.2 (Hardware and Other Training Details); Section 4.1 (Dataset Construction)]
"This is justified by the fact that the CPSea dataset (excluding the PDB subset) is largely derived from AF2 predictions; thus, these models can be considered to have prior exposure to the underlying data distribution."

Section 4.1 defines the test subsets CPTrans/CPBind/CPCore as part of CPSea and states 'These conformations work as the Ground Truth (GT)'. MuCO is trained on CPSea-Train from the same repository. Since the non-PDB portion of CPSea is admittedly 'largely derived from AF2 predictions', the evaluation mainly measures agreement with AF2-derived conformations that the training distribution already encodes. The functional-annotation split does not prevent sequence-level redundancy; no clustering or identity filtering is reported. The 85-structure CPSea-PDB subset is the only external gold standard and is too small to support the abstract's broad claim. This is benchmark-source circularity, not a fitted-parameter prediction.

full rationale

The method's mathematical derivation is self-contained: Eq. (1) is the identity p(X|S)=p(B|S)p(C|B,S) under the backbone/side-chain reparametrization, and Stages 1-3 are trained with flow-matching and force-field objectives rather than fitted to the evaluation metrics. No fitted constant is relabeled as a prediction; no self-citation is load-bearing (WGFormer and ReQFlow are cited as baselines/related work only); no uniqueness theorem is invoked. The main circularity is in the benchmark: CPSea (except the 85 PDB structures) is largely AF2-derived, MuCO is trained on CPSea, and the 'Ground Truth' test conformations come from the same repository. This makes the headline CPSea gains partly a measure of agreement with AF2's conformational biases. The energy metric also shares the Charmm36 objective with Stage-3, though because all baselines are passed through the same minimization pipeline the comparison is fair as a seed-quality test. Overall, the central architecture is not circular, but the empirical claim is only as strong as the CPSea ground-truth provenance; hence a moderate score of 4.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

The central claims rest on a chain of modelling and dataset choices: the validity of the CPSea ground truth, the accuracy of SimpleFold-generated linear precursors, the suitability of CHARMM36 and the hand-set thresholds for defining success, and the interpretation of Shannon entropy as 'diversity.' None of these are machine-checked or independently reproduced.

free parameters (7)

Closure tolerance δ = 0.1 Å
Hand-set in Appendix B.1 to define success/failure of cyclization; directly controls the Success Rate metric.
Failure energy threshold = 103 kJ/mol
Manually chosen in Appendix D.2; structures above this are counted as cyclization failures, so it directly shapes the headline success-rate numbers.
Disulfide detection threshold = 2.5 Å
Hand-set in Algorithm 2 (Appendix B.2) for prioritizing Cys-Cys topology detection; affects which mode is refined and whether closure succeeds.
Sequence length filter = 8–16 residues
Hand-selected in Appendix C.1; restricts all train/test subsets, so results only cover this length regime.
Backbone mass ratio filter = ResSum > 0.20
Hand-set filter in Appendix C.1 to exclude conformations dominated by external chains; changes the data distribution.
Stage-1 coordinate scaling factor = 0.1
Chosen in Appendix A.1.1 to normalize translational variance; affects flow-matching training but not the evaluation claim directly.
Stage-3 regularization weight w = not reported
Defined in Remark 3 as w/2 ||X - fX||^2 but the numerical value is not stated; Stage-3 energy minimization depends on it.

assumptions (6)

standard math Riemannian flow matching on SE(3)^L × T^L and T^{4L} learns the target conditional distributions.
Invoked in Section 3.2, Eqs. (3)-(4); if the flow-matching objective is not well-calibrated, the generated samples are not from p(B|S) or p(C|B,S).
domain assumption CPSea's recorded cyclic conformations are valid ground truth for physical stability and diversity.
Section 4.1 / Appendix C; the paper itself notes CPSea (except PDB) is largely AF2-derived, making this assumption fragile.
domain assumption SimpleFold 3M produces accurate linear precursor conformations for baseline conditioning.
Section 4.1 dataset construction; baselines are trained on these generated linear conformations, so errors propagate into the comparison.
domain assumption CHARMM36 with custom patches is an appropriate arbiter of physical stability and success.
Appendices B and D; success rate and physical stability are defined exclusively via this force field and its bond-length tolerances.
ad hoc to paper Training on cyclic peptides makes ring-closure an implicit constraint learned by the backbone flow field.
Remark 1, Section 3.2; no proof or analysis demonstrates that the backbone flow model reliably closes the ring; the paper only asserts it.
domain assumption Shannon entropy over cyclization modes and secondary structure classes measures useful structural diversity.
Appendix D.1; entropy does not measure agreement with the GT distribution, so high H can be achieved by a uniform mode mix that does not match real cyclic peptides.

how reviews work

0 comments

Cite this review

Pith. "Pith review of MuCO: Generative Peptide Cyclization Empowered by Multi-stage Conformation Optimization." pith.science (2026). https://pith.science/paper/OMGBLEHN

@misc{pith2026260211189,
  author       = {Pith},
  title        = {Pith review of: MuCO: Generative Peptide Cyclization Empowered by Multi-stage Conformation Optimization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OMGBLEHN}},
  note         = {Machine review of arXiv:2602.11189}
}

read the original abstract

Modeling peptide cyclization is critical for the virtual screening of candidate peptides with desirable physical and pharmaceutical properties. This task is challenging because a cyclic peptide often exhibits diverse, ring-shaped conformations, which cannot be well captured by deterministic prediction models derived from linear peptide folding. In this study, we propose MuCO (Multi-stage Conformation Optimization), a generative peptide cyclization method that models the distribution of cyclic peptide conformations conditioned on the corresponding linear peptide. In principle, MuCO decouples the peptide cyclization task into three stages: topology-aware backbone design, generative side-chain packing, and physics-aware all-atom optimization, thereby generating and optimizing conformations of cyclic peptides in a coarse-to-fine manner. This multi-stage framework enables an efficient parallel sampling strategy for conformation generation and allows for rapid exploration of diverse, low-energy conformations. Experiments on the large-scale CPSea dataset demonstrate that MuCO significantly and consistently outperforms state-of-the-art methods in physical stability, structural diversity, secondary structure recovery, and computational efficiency, making it a promising computational tool for exploring and designing cyclic peptides. The demo of the proposed method can be found at https://github.com/mianqiu00/MuCO.

Figures

Figures reproduced from arXiv: 2602.11189 by the authors.

**Figure 1.** An illustration of the 3-stage scheme of MuCO. The generation process is decoupled into three stages, including i) Topology-Aware Backbone Generation for backbone scaffold B by SE(3) flow matching on condition of sequence embedding, ii) Generative Side-chain Packing for side chain sampling via conditional flow matching with cyclic RPE, iii) Physics-Aware Optimization by Charmm36 forcefield to yield final energy mini… view at source ↗

**Figure 2.** MuCO framework overview. The process decouples into three stages: (1) cyclic backbone generation on MB, (2) side-chain packing on MC with Cyclic RPE, and (3) physics-aware refinement to reach the local energy minimum X. Unlike the above end-to-end folding methods, some methods generate peptide conformations by two steps: backbone design and side-chain packing. For backbone design, FrameDiff (Yim et al., 2023b) and F… view at source ↗

**Figure 3.** (a) Success Rate (%): Percentage of successful cyclization. (b) Mean Potential Energy (E): Physical stability calculated via Charmm36. (c) Structural Diversity (HC): Shannon entropy of conformational clusters. (d) Mode distribution coverage on the CPTrans dataset. 8 [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

Figures from the paper (11 more)

**Figure 4.** Figure 4: (a) Secondary Structural Diversity (HSS) across different test sets; MuCO maintains superior ensemble diversity compared to all baselines. (b) Secondary structure composition (Helix, Sheet, and Coil) on the CPSea-PDB dataset. MuCO significantly improves the recovery of…

**Figure 5.** Figure 5: Case study on structural fidelity. Visual comparison of predicted conformations for a representative sample from the CPSea PDB dataset. Under single sampling, MuCO reconstructs the native-like α-helical motif and achieves significantly lower potential energy (E) compar…

**Figure 6.** Figure 6: , we analyze the impact of increasing the sampling budget (K Backbone states × M Side-chain states). We observe a significant improvement in effectiveness: increasing the sampling budget drastically improves the cyclization mode coverage and achieves a success rate of …

**Figure 7.** Figure 7: The heatmaps display the mean potential energy for (a) CPCore and (b) CPSea PDB as a function of Stage-1 (backbone generation) and Stage-2 (side-chain packing) sample sizes. MuCO is capable of identifying metastable states with energies comparable to or lower than the …

**Figure 8.** Figure 8: Comparison between the full MuCO model and the variants with EGNN-based deterministic Stage-1 or Stage-2. (a-b) Success rate and mean energy; (c-d) Secondary structure diversity and distribution. Necessity of Physics-Aware Optimization [PITH_FULL_IMAGE:figures/full_fi…

**Figure 9.** Figure 9: (a) Recovery of structural diversity (HSS) before and after optimization. (b) Comparison of α-helix content recovery against Ground Truth and baselines. Stage-3 refines stochastically sampled coordinates around potential wells into physically realizable local minima an…

**Figure 10.** Figure 10: Venn diagram illustrating the relationships between different CPSea subsets. CPSea PDB serves as an external high-confidence validation set. C.3 Data Statistics and Distributions We provide a comprehensive statistical summary of the sequence and structural features ac…

**Figure 11.** Figure 11: Distributions of sequence length, backbone mass ratio (Residue Summary), and cyclization modes across the five subsets. Top row shows absolute counts; bottom row shows normalized frequencies. 20 [PITH_FULL_IMAGE:figures/full_fig_p020_11.png]

**Figure 12.** Figure 12: Visual Comparison of predicted cyclic peptide conformations across diverse sub-datasets. Even in single sample mode, MuCO consistently achieves significantly lower potential energy (E) compared to HighFold2 and EGNN baselines. Notably, MuCO demonstrates superior fidel…

**Figure 13.** Figure 13: Sample of 1JD6_A_16_31 generated by MuCO. Column (A) shows the Stage-1 backbone scaffolds (cyan), while columns (B) show the corresponding all-atom samples (green) after Stage 2 and 3. The diversity of k-to-de and head-to-tail cycles highlights the model’s capacity to…

**Figure 14.** Figure 14: Sample of AF-X1M060-F1_0_15_29 generated by MuCO. Column (A) shows the Stage-1 backbone scaffolds (cyan), while columns (B) show the corresponding all-atom samples (green) after Stage 2 and 3. The peptide structures demonstrate that MuCO effectively identifies and inc…

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

8 extracted references · 2 linked inside Pith

[2]

Zero-shot cyclic peptide design via composable geometric constraints.arXiv preprint arXiv:2507.04225,

Dapeng Jiang, Xiangzhe Kong, Jiaqi Han, Mingyu Li, Rui Jiao, Wenbing Huang, Stefano Ermon, Jianzhu Ma, and Yang Liu. Zero-shot cyclic peptide design via composable geometric constraints.arXiv preprint arXiv:2507.04225,

arXiv
[3]

Language models of protein sequences at the scale of evolution enable accurate structure prediction.bioRxiv, 2022:500902,

Zeming Lin, Halil Akin, Roshan Rao, Brian Hie, Zhongkai Zhu, Wenting Lu, Allan dos Santos Costa, et al. Language models of protein sequences at the scale of evolution enable accurate structure prediction.bioRxiv, 2022:500902,

2022
[4]

WGFormer: An SE(3)-transformer driven by Wasserstein gradient flows for molecular ground-state conformation prediction

Fanmeng Wang, Minjie Cheng, and Hongteng Xu. WGFormer: An SE(3)-transformer driven by Wasserstein gradient flows for molecular ground-state conformation prediction. In42nd International Conference on Machine Learning (ICML), 2025a. Yuyang Wang, Jiarui Lu, Navdeep Jaitly, Josh Susskind, and Miguel Angel Bautista. Simplefold: Folding proteins is simpler tha...

arXiv 2024
[64]

The training objective Lbackbone is a multi-task composite loss that penalizes errors in flow prediction and structural geometry

The model operates on the SE(3) manifold with a coordinate scaling factor of0.1to normalize the translational variance. The training objective Lbackbone is a multi-task composite loss that penalizes errors in flow prediction and structural geometry. We define total loss as a weighted sum of five components: Lbackbone =L trans + 0.5Lrot +L bb_atom +L dist_...

2024
[2013]

Standard residue templates are insufficient for cyclic bonds because of atom loss

for local geometry refinement. Standard residue templates are insufficient for cyclic bonds because of atom loss. We implemented custom patches to handle these transitions: the Cys template removes sulfur hydrogen (HG); the Lys template removes two hydrogens from the Nζ amine; the Asp/Glu templates remove the hydroxyl group (OH) from the side-chain carbox...

2025
[2017]

Each component is stacked with 2 blocks of Invariant Point Attention (IPA) or transformer layers

14 A Training Details A.1 Training Protocols and Hyperparameters A.1.1 Stage-1: Backbone Flow Matching The backbone generation module is built on the FoldFlow-2 architecture (Huguet et al., 2024), employing a tripartite structure of an encoder, a multi-modal fusion trunk, and a geometric decoder. Each component is stacked with 2 blocks of Invariant Point ...

2024
[2024]

Chai-1: Decoding the molecular interactions of life.bioRxiv, pages 2024–10,

12 Chai Discovery team, Jacques Boitreaud, Jack Dent, Matthew McPartlon, Joshua Meier, Vinicius Reis, Alex Ro- gozhonikov, and Kevin Wu. Chai-1: Decoding the molecular interactions of life.bioRxiv, pages 2024–10,

2024
[2025]

Jason Yim, Andrew Campbell, Andrew Y . K. Foong, Michael Gastegger, José Jiménez-Luna, Sarah Lewis, Victor Garcia Satorras, et al. Fast protein backbone generation with SE(3) flow matching.arXiv preprint arXiv:2310.05297, 2023a. Jason Yim, Brian L. Trippe, Valentin De Bortoli, Emile Mathieu, Arnaud Doucet, Regina Barzilay, and Tommi S. Jaakkola. SE(3) dif...

arXiv

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.

[1] [2]

Zero-shot cyclic peptide design via composable geometric constraints.arXiv preprint arXiv:2507.04225,

Dapeng Jiang, Xiangzhe Kong, Jiaqi Han, Mingyu Li, Rui Jiao, Wenbing Huang, Stefano Ermon, Jianzhu Ma, and Yang Liu. Zero-shot cyclic peptide design via composable geometric constraints.arXiv preprint arXiv:2507.04225,

arXiv

[2] [3]

Language models of protein sequences at the scale of evolution enable accurate structure prediction.bioRxiv, 2022:500902,

Zeming Lin, Halil Akin, Roshan Rao, Brian Hie, Zhongkai Zhu, Wenting Lu, Allan dos Santos Costa, et al. Language models of protein sequences at the scale of evolution enable accurate structure prediction.bioRxiv, 2022:500902,

2022

[3] [4]

WGFormer: An SE(3)-transformer driven by Wasserstein gradient flows for molecular ground-state conformation prediction

Fanmeng Wang, Minjie Cheng, and Hongteng Xu. WGFormer: An SE(3)-transformer driven by Wasserstein gradient flows for molecular ground-state conformation prediction. In42nd International Conference on Machine Learning (ICML), 2025a. Yuyang Wang, Jiarui Lu, Navdeep Jaitly, Josh Susskind, and Miguel Angel Bautista. Simplefold: Folding proteins is simpler tha...

arXiv 2024

[4] [64]

The training objective Lbackbone is a multi-task composite loss that penalizes errors in flow prediction and structural geometry

The model operates on the SE(3) manifold with a coordinate scaling factor of0.1to normalize the translational variance. The training objective Lbackbone is a multi-task composite loss that penalizes errors in flow prediction and structural geometry. We define total loss as a weighted sum of five components: Lbackbone =L trans + 0.5Lrot +L bb_atom +L dist_...

2024

[5] [2013]

Standard residue templates are insufficient for cyclic bonds because of atom loss

for local geometry refinement. Standard residue templates are insufficient for cyclic bonds because of atom loss. We implemented custom patches to handle these transitions: the Cys template removes sulfur hydrogen (HG); the Lys template removes two hydrogens from the Nζ amine; the Asp/Glu templates remove the hydroxyl group (OH) from the side-chain carbox...

2025

[6] [2017]

Each component is stacked with 2 blocks of Invariant Point Attention (IPA) or transformer layers

14 A Training Details A.1 Training Protocols and Hyperparameters A.1.1 Stage-1: Backbone Flow Matching The backbone generation module is built on the FoldFlow-2 architecture (Huguet et al., 2024), employing a tripartite structure of an encoder, a multi-modal fusion trunk, and a geometric decoder. Each component is stacked with 2 blocks of Invariant Point ...

2024

[7] [2024]

Chai-1: Decoding the molecular interactions of life.bioRxiv, pages 2024–10,

12 Chai Discovery team, Jacques Boitreaud, Jack Dent, Matthew McPartlon, Joshua Meier, Vinicius Reis, Alex Ro- gozhonikov, and Kevin Wu. Chai-1: Decoding the molecular interactions of life.bioRxiv, pages 2024–10,

2024

[8] [2025]

Jason Yim, Andrew Campbell, Andrew Y . K. Foong, Michael Gastegger, José Jiménez-Luna, Sarah Lewis, Victor Garcia Satorras, et al. Fast protein backbone generation with SE(3) flow matching.arXiv preprint arXiv:2310.05297, 2023a. Jason Yim, Brian L. Trippe, Valentin De Bortoli, Emile Mathieu, Arnaud Doucet, Regina Barzilay, and Tommi S. Jaakkola. SE(3) dif...

arXiv