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

arXiv: https://arxiv.org/abs/2602.11189 · HTML: https://mlsanity.com/paper/2602.11189/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 41 references that are in the map.
- First posted on arXiv 30 Jan 2026.

## Builds on (most cited first, 11 of 11)

- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Flow Matching on General Geometries](https://mlsanity.com/paper/2302.03660/) (2023)
- [SE(3) diffusion model with application to protein backbone generation](https://mlsanity.com/paper/2302.02277/) (2023)
- [EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representations](https://mlsanity.com/paper/2306.12059/) (2023)
- [SE(3)-Stochastic Flow Matching for Protein Backbone Generation](https://mlsanity.com/paper/2310.02391/) (2023)
- [DiffPack: A Torsional Diffusion Model for Autoregressive Protein Side-Chain Packing](https://mlsanity.com/paper/2306.01794/) (2023)
- [SimpleFold: Folding Proteins is Simpler than You Think](https://mlsanity.com/paper/2509.18480/) (2025)
- [ReQFlow: Rectified Quaternion Flow for Efficient and High-Quality Protein Backbone Generation](https://mlsanity.com/paper/2502.14637/) (2025)
- [H-Packer: Holographic Rotationally Equivariant Convolutional Neural Network for Protein Side-Chain Packing](https://mlsanity.com/paper/2311.09312/) (2023)
- [WGFormer: An SE(3)-Transformer Driven by Wasserstein Gradient Flows for Molecular Ground-State Conformation Prediction](https://mlsanity.com/paper/2410.09795/) (2024)
- [Zero-Shot Cyclic Peptide Design via Composable Geometric Constraints](https://mlsanity.com/paper/2507.04225/) (2025)

## Abstract (arXiv)

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.