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

Accepted by ICML 2026

MuCO is a generative framework for cyclic peptide conformation modeling via multi-stage conformation optimization. Given a linear peptide, MuCO decomposes peptide cyclization into three coordinated stages: topology-aware backbone generation, generative side-chain packing, and physics-aware all-atom refinement.

This repository contains the official implementation of MuCO, accompanying our ICML 2026 paper on generative peptide cyclization.

Overview

Cyclic peptides are important molecular scaffolds for therapeutic discovery because they often exhibit improved stability, proteolytic resistance, membrane permeability, and target-binding specificity relative to linear peptides. Their conformational landscape is, however, highly constrained and multi-modal, which makes direct deterministic prediction inadequate for capturing diverse low-energy ring-closed structures.

MuCO addresses this challenge by factorizing cyclic peptide generation into a coarse-to-fine pipeline:

1. Topology-Aware Backbone Generation with sequence-conditioned SE(3) flow matching.
2. Generative Side-chain Packing with equivariant conditional flow modeling.
3. Physics-Aware Optimization with force-field-based refinement and cyclization validation.

This decomposition enables efficient parallel exploration of candidate conformations while preserving physical plausibility and structural diversity.

News

• [2026-05] MuCO has been accepted to ICML 2026.
• [2026-01] arXiv preprint prepared. Replace the placeholder arXiv identifier below once the public preprint is available.

Paper

MuCO: Generative Peptide Cyclization Empowered by Multi-stage Conformation Optimization
Yitian Wang, Fanmeng Wang, Angxiao Yue, Wentao Guo, Yaning Cui, Hongteng Xu

• Conference: International Conference on Machine Learning (ICML), 2026
• Preprint: https://arxiv.org/abs/2602.11189

Abstract

Modeling peptide cyclization is critical for the virtual screening of candidate peptides with desirable physical and pharmaceutical properties. This task is challenging because cyclic peptides often exhibit diverse ring-shaped conformations that are not well captured by deterministic prediction models derived from linear peptide folding. MuCO models the distribution of cyclic peptide conformations conditioned on the corresponding linear peptide through a three-stage pipeline: topology-aware backbone design, generative side-chain packing, and physics-aware all-atom optimization. This coarse-to-fine formulation supports efficient parallel sampling, rapid exploration of diverse low-energy conformations, and improved physical realism. Experiments on the large-scale CPSea dataset show that MuCO outperforms strong baselines in physical stability, structural diversity, secondary-structure recovery, and computational efficiency.

Framework Figure

Figure 1. Illustration of the 3-stage MuCO scheme: topology-aware backbone generation, generative side-chain packing, and physics-aware optimization.

Figure 2. Framework overview of MuCO with decoupled backbone generation, side-chain packing, and energy-guided refinement.

Key Highlights

• Multi-stage generation: decouples cyclic peptide modeling into backbone generation, side-chain packing, and physics-guided refinement.
• Improved physical stability: achieves substantially lower potential energy than deterministic folding baselines.
• Higher conformational diversity: alleviates mode collapse and better recovers cyclization-mode and secondary-structure distributions.
• Efficient hierarchical sampling: supports parallel K x M exploration over backbone and side-chain states.
• Practical cyclization support: includes head-to-tail, disulfide, and Lys-Asp/Glu isopeptide cyclization modes.

Main Results

On the curated CPSea benchmarks, MuCO demonstrates strong empirical performance in:

• Physical stability measured by CHARMM36 potential energy.
• Structural diversity measured by entropy over conformational clusters and cyclization modes.
• Secondary-structure recovery relative to reference cyclic conformations.
• Inference efficiency through parallel hierarchical sampling.

Representative observations reported in the paper include:

• MuCO achieves the lowest mean potential energy among compared methods in the main benchmark.
• MuCO improves diversity relative to AF2-based cyclic peptide baselines that exhibit severe mode collapse.
• MuCO reaches 41 ms amortized latency per sample under parallel sampling, compared with multi-second latency for folding-based baselines.

## Installation

### Prerequisites

- Linux server or workstation with an NVIDIA GPU.
- NVIDIA driver compatible with CUDA 11.8.
- Docker and Docker Compose v2.
- NVIDIA Container Toolkit for GPU access inside Docker.
- Conda is only required if you run MuCO directly from source instead of Docker.

Check that Docker can see the GPU:

```bash
docker run --rm --gpus all nvidia/cuda:11.8.0-base-ubuntu22.04 nvidia-smi

Model Weights

Pretrained MuCO checkpoints are not stored in this repository. Download the weights from the Google Drive link in params/link.md and place them under params/ before running inference, the API server, or the web demo:

params/foldflow.pth
params/flowpacker.pth

The params/ directory is ignored by Git except for params/link.md, so local checkpoint files will not be committed accidentally.

Docker Web Demo

The recommended way to run MuCO is the Docker Compose web stack. It starts both services:

• muco-api: FastAPI backend on port 8000, using GPU through Dockerfile.api.
• web: Next.js frontend on port 3000, using app/Dockerfile.web.

From the repository root:

docker compose build
docker compose up -d

Open the web interface:

http://localhost:3000

If running on a remote server, replace localhost with the server IP:

http://SERVER_IP:3000

The frontend talks to the backend through the Compose service URL:

MUCO_API_URL=http://muco-api:8000

This is already configured in docker-compose.yml. You normally do not need to change it unless the frontend and API are deployed separately.

Useful commands:

docker compose ps
docker compose logs -f
docker compose logs -f muco-api
docker compose logs -f web
docker compose down

Generated jobs and logs are stored on the host under:

runs/jobs/
runs/logs/

These runtime outputs are ignored by Git.

Backend-Only Docker API

If you only need the inference API without the web interface:

docker compose -f docker-compose.api.yml build
docker compose -f docker-compose.api.yml up -d

Health checks:

curl http://127.0.0.1:8000/health
curl http://127.0.0.1:8000/ready
curl http://127.0.0.1:8000/resources

Submit a small smoke-test job:

curl -X POST http://127.0.0.1:8000/jobs \
  -H 'content-type: application/json' \
  -d '{
    "sequence": "ACDEFGHIK",
    "K": 1,
    "M": 1,
    "backbone_steps": 10,
    "sidechain_steps": 3,
    "make_zip": false
  }'

See API_DEPLOYMENT.md for the full backend deployment handoff.

Local Source Environment

For development or non-Docker execution, create the Conda environment:

conda env create -f environment.yml
conda activate muco

environment.yml contains the backend runtime dependencies used by both local execution and Dockerfile.api, including PyTorch CUDA 11.8, FastAPI, OpenMM, PyMOL, and MuCO model dependencies.

Method Pipeline

Stage 1: Backbone Generation

The backbone generator builds cyclic peptide backbones with sequence-conditioned SE(3) flow matching, using ESM2 representations and geometry-aware transformers.

python backbone_train.py

Sampling example:

python backbone_sample.py \
    --config_timestamp {timestamp} \
    --ckpt_epoch 100 \
    --output ./data/inference/pdb/coarse \
    --device 0 \
    --batch_size 1024 \
    --split CPBind

Stage 2: Side-chain Packing

The side-chain module predicts torsional configurations conditioned on the generated backbone using EquiformerV2 within a conditional normalizing-flow framework.

python sidechain_train.py config/sidechain_train.yaml \
    --devices 4 \
    --strategy auto \
    --precision 32-true

Resume training:

python sidechain_train.py config/sidechain_train.yaml --resume

Sampling example:

python sidechain_sample.py config/sidechain_sample.yaml output_name \
    --seed 42 \
    --save_traj False

Stage 3: Physics-Aware Optimization

The final stage applies OpenMM-based refinement to improve local geometry, reduce steric clashes, and validate chemically valid ring closure.

Supported cyclization modes:

• Head-to-tail cyclization
• Cys-to-Cys disulfide cyclization
• Lys-Asp/Glu isopeptide cyclization

Single-structure relaxation:

python relaxer/auto.py input.pdb output.pdb

Batch relaxation:

python relaxer/relax.py

Quick Start

For a standard generation workflow, run the three stages sequentially:

1. Generate cyclic peptide backbones.
2. Pack side chains on sampled backbones.
3. Refine generated conformations with the relaxation module.

If you maintain a project-specific inference wrapper, start from muco_infer.py and the scripts under runner/.

Docker And API Deployment

Backend API deployment is documented in API_DEPLOYMENT.md. API job and log directories are server-managed through JOB_ROOT and LOG_ROOT; clients do not submit filesystem paths. The command-line wrapper still supports explicit local output and log directories for operator workflows:

python muco_infer.py input.json \
    --output ./runs/cli/job-001 \
    --log_dir ./runs/cli_logs/job-001 \
    --K 1 \
    --M 1

Evaluation

The paper evaluates MuCO using the following criteria:

• Success Rate: percentage of conformations satisfying cyclization geometry constraints.
• Physical Stability: mean potential energy computed with CHARMM36.
• Diversity: entropy over cyclization modes and secondary-structure clusters.
• Secondary-Structure Recovery: agreement with reference conformational distributions.

Benchmarks are constructed on filtered subsets derived from CPSea, including CP-Bind, CP-Trans, CP-Core, and CPSea-PDB.

Citation

If you find this repository useful, please cite our paper:

@inproceedings{wang2026muco,
  title     = {MuCO: Generative Peptide Cyclization Empowered by Multi-stage Conformation Optimization},
  author    = {Wang, Yitian and Wang, Fanmeng and Yue, Angxiao and Guo, Wentao and Cui, Yaning and Xu, Hongteng},
  booktitle = {Proceedings of the International Conference on Machine Learning},
  year      = {2026},
  note      = {Accepted by ICML 2026},
  url       = {https://arxiv.org/abs/2602.11189}
}

After the arXiv page is public, replace the placeholder URL with the official identifier.

Contact

For questions about the paper or repository, please contact:

• Hongteng Xu: hongtengxu@ruc.edu.cn

If you would like, you can also add maintainer contacts for code-level issues in this section.

Acknowledgments

MuCO builds upon several influential open-source and scientific software projects, including:

• FoldFlow
• EquiformerV2
• OpenFold
• ESM
• OpenMM

License

This repository is intended for academic research use. See LICENSE for the current licensing terms.