# Accurate and Efficient Structural Ensemble Generation of Macrocyclic Peptides using Internal Coordinate Diffusion

arXiv: https://arxiv.org/abs/2305.19800 · HTML: https://mlsanity.com/paper/2305.19800/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 73 references that are in the map.
- First posted on arXiv 30 May 2023.

## Builds on (most cited first, 22 of 22)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Fast R-CNN](https://mlsanity.com/paper/1504.08083/) (2015)
- [Self-Attention with Relative Position Representations](https://mlsanity.com/paper/1803.02155/) (2018)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [Torsional Diffusion for Molecular Conformer Generation](https://mlsanity.com/paper/2206.01729/) (2022)
- [GEOM: Energy-annotated molecular conformations for property prediction and molecular generation](https://mlsanity.com/paper/2006.05531/) (2020)
- [SE(3) diffusion model with application to protein backbone generation](https://mlsanity.com/paper/2302.02277/) (2023)
- [EquiBind: Geometric Deep Learning for Drug Binding Structure Prediction](https://mlsanity.com/paper/2202.05146/) (2022)
- [Protein structure generation via folding diffusion](https://mlsanity.com/paper/2209.15611/) (2022)
- [GeoMol: Torsional Geometric Generation of Molecular 3D Conformer Ensembles](https://mlsanity.com/paper/2106.07802/) (2021)
- [Molecular geometry prediction using a deep generative graph neural network](https://mlsanity.com/paper/1904.00314/) (2019)
- [Learning Neural Generative Dynamics for Molecular Conformation Generation](https://mlsanity.com/paper/2102.10240/) (2021)
- [A Generative Model for Molecular Distance Geometry](https://mlsanity.com/paper/1909.11459/) (2019)
- [Diffusion Models for Constrained Domains](https://mlsanity.com/paper/2304.05364/) (2023)
- [Direct Molecular Conformation Generation](https://mlsanity.com/paper/2202.01356/) (2022)
- [CREMP: Conformer-rotamer ensembles of macrocyclic peptides for machine learning](https://mlsanity.com/paper/2305.08057/) (2023)

## Built on by (most cited first, 3 of 3)

- [Generating Cyclic Conformers with Flow Matching in Cremer-Pople Coordinates](https://mlsanity.com/paper/2601.12859/) (2026)
- [Vilya-1: An all-atom foundation model for macrocycle structure prediction and design](https://mlsanity.com/paper/2607.09998/) (2026)
- [MacroGuide: Topological Guidance for Macrocycle Generation](https://mlsanity.com/paper/2602.14977/) (2026)

## Abstract (arXiv)

Macrocyclic peptides are an emerging therapeutic modality, yet computational approaches for accurately sampling their diverse 3D ensembles remain challenging due to their conformational diversity and geometric constraints. Here, we introduce RINGER, a diffusion-based transformer model using a redundant internal coordinate representation that generates three-dimensional conformational ensembles of macrocyclic peptides from their 2D representations. RINGER provides fast backbone and side-chain sampling while respecting key structural invariances of cyclic peptides. Through extensive benchmarking and analysis against gold-standard conformer ensembles of cyclic peptides generated with metadynamics, we demonstrate how RINGER generates both high-quality and diverse geometries at a fraction of the computational cost. Our work lays the foundation for improved sampling of cyclic geometries and the development of geometric learning methods for peptides.