# Protein Sequence and Structure Co-Design with Equivariant Translation

arXiv: https://arxiv.org/abs/2210.08761 · HTML: https://mlsanity.com/paper/2210.08761/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 56 references that are in the map.
- First posted on arXiv 17 Oct 2022.

## Builds on (most cited first, 18 of 18)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [Learning from Protein Structure with Geometric Vector Perceptrons](https://mlsanity.com/paper/2009.01411/) (2020)
- [Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities](https://mlsanity.com/paper/2006.02425/) (2020)
- [Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problem](https://mlsanity.com/paper/2206.04119/) (2022)
- [Learning Gradient Fields for Molecular Conformation Generation](https://mlsanity.com/paper/2105.03902/) (2021)
- [Protein Structure and Sequence Generation with Equivariant Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2205.15019/) (2022)
- [Iterative Refinement Graph Neural Network for Antibody Sequence-Structure Co-design](https://mlsanity.com/paper/2110.04624/) (2021)
- [Conditional Antibody Design as 3D Equivariant Graph Translation](https://mlsanity.com/paper/2208.06073/) (2022)
- [Direct Molecular Conformation Generation](https://mlsanity.com/paper/2202.01356/) (2022)
- [Deep Learning in Protein Structural Modeling and Design](https://mlsanity.com/paper/2007.08383/) (2020)
- [Roto-translated Local Coordinate Frames For Interacting Dynamical Systems](https://mlsanity.com/paper/2110.14961/) (2021)

## Built on by (most cited first, 30 of 31)

- [Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Design](https://mlsanity.com/paper/2402.04997/) (2024)
- [MiDi: Mixed Graph and 3D Denoising Diffusion for Molecule Generation](https://mlsanity.com/paper/2302.09048/) (2023)
- [DPLM-2: A Multimodal Diffusion Protein Language Model](https://mlsanity.com/paper/2410.13782/) (2024)
- [Equivariant Flow Matching with Hybrid Probability Transport](https://mlsanity.com/paper/2312.07168/) (2023)
- [AbDiffuser: Full-Atom Generation of in vitro Functioning Antibodies](https://mlsanity.com/paper/2308.05027/) (2023)
- [Str2Str: A Score-based Framework for Zero-shot Protein Conformation Sampling](https://mlsanity.com/paper/2306.03117/) (2023)
- [A Survey of Generative AI for de novo Drug Design: New Frontiers in Molecule and Protein Generation](https://mlsanity.com/paper/2402.08703/) (2024)
- [A Latent Diffusion Model for Protein Structure Generation](https://mlsanity.com/paper/2305.04120/) (2023)
- [A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applications](https://mlsanity.com/paper/2403.00485/) (2024)
- [FoldToken: Learning Protein Language via Vector Quantization and Beyond](https://mlsanity.com/paper/2403.09673/) (2024)
- [Generalist Equivariant Transformer Towards 3D Molecular Interaction Learning](https://mlsanity.com/paper/2306.01474/) (2023)
- [A Periodic Bayesian Flow for Material Generation](https://mlsanity.com/paper/2502.02016/) (2025)
- [AbODE: Ab Initio Antibody Design using Conjoined ODEs](https://mlsanity.com/paper/2306.01005/) (2023)
- [A Hierarchical Training Paradigm for Antibody Structure-sequence Co-design](https://mlsanity.com/paper/2311.16126/) (2023)
- [A Multi-Modal Contrastive Diffusion Model for Therapeutic Peptide Generation](https://mlsanity.com/paper/2312.15665/) (2023)
- [dyAb: Flow Matching for Flexible Antibody Design with AlphaFold-driven Pre-binding Antigen](https://mlsanity.com/paper/2503.01910/) (2025)
- [An All-Atom Generative Model for Designing Protein Complexes](https://mlsanity.com/paper/2504.13075/) (2025)
- [Annotation-guided Protein Design with Multi-Level Domain Alignment](https://mlsanity.com/paper/2404.16866/) (2024)
- [Cross-Gate MLP with Protein Complex Invariant Embedding is A One-Shot Antibody Designer](https://mlsanity.com/paper/2305.09480/) (2023)
- [Equivariant Map and Agent Geometry for Autonomous Driving Motion Prediction](https://mlsanity.com/paper/2310.13922/) (2023)
- [PDB-Struct: A Comprehensive Benchmark for Structure-based Protein Design](https://mlsanity.com/paper/2312.00080/) (2023)
- [Generative Enzyme Design Guided by Functionally Important Sites and Small-Molecule Substrates](https://mlsanity.com/paper/2405.08205/) (2024)
- [Joint Design of Protein Sequence and Structure based on Motifs](https://mlsanity.com/paper/2310.02546/) (2023)
- [Functional Geometry Guided Protein Sequence and Backbone Structure Co-Design](https://mlsanity.com/paper/2310.04343/) (2023)
- [Diffusion-based Graph Generative Methods](https://mlsanity.com/paper/2401.15617/) (2024)
- [Fusing Neural and Physical: Augment Protein Conformation Sampling with Tractable Simulations](https://mlsanity.com/paper/2402.10433/) (2024)
- [A Model-Centric Review of Deep Learning for Protein Design](https://mlsanity.com/paper/2502.19173/) (2025)
- [EnzyControl: Adding Functional and Substrate-Specific Control for Enzyme Backbone Generation](https://mlsanity.com/paper/2510.25132/) (2025)
- [SimpleDesign: A Joint Model for Protein Sequence and Structure Codesign](https://mlsanity.com/paper/2609.03377/) (2026)
- [What Ails Generative Structure-based Drug Design: Expressivity is Too Little or Too Much?](https://mlsanity.com/paper/2408.06050/) (2024)

## Abstract (arXiv)

Proteins are macromolecules that perform essential functions in all living organisms. Designing novel proteins with specific structures and desired functions has been a long-standing challenge in the field of bioengineering. Existing approaches generate both protein sequence and structure using either autoregressive models or diffusion models, both of which suffer from high inference costs. In this paper, we propose a new approach capable of protein sequence and structure co-design, which iteratively translates both protein sequence and structure into the desired state from random initialization, based on context features given a priori. Our model consists of a trigonometry-aware encoder that reasons geometrical constraints and interactions from context features, and a roto-translation equivariant decoder that translates protein sequence and structure interdependently. Notably, all protein amino acids are updated in one shot in each translation step, which significantly accelerates the inference process. Experimental results across multiple tasks show that our model outperforms previous state-of-the-art baselines by a large margin, and is able to design proteins of high fidelity as regards both sequence and structure, with running time orders of magnitude less than sampling-based methods.