# Plug & Play Directed Evolution of Proteins with Gradient-based Discrete MCMC

arXiv: https://arxiv.org/abs/2212.09925 · HTML: https://mlsanity.com/paper/2212.09925/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 62 references that are in the map.
- First posted on arXiv 20 Dec 2022.

## Builds on (most cited first, 30 of 30)

- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Plug and Play Language Models: A Simple Approach to Controlled Text Generation](https://mlsanity.com/paper/1912.02164/) (2019)
- [Automatic chemical design using a data-driven continuous representation of molecules](https://mlsanity.com/paper/1610.02415/) (2016)
- [Biological Sequence Design with GFlowNets](https://mlsanity.com/paper/2203.04115/) (2022)
- [COLD Decoding: Energy-based Constrained Text Generation with Langevin Dynamics](https://mlsanity.com/paper/2202.11705/) (2022)
- [ProGen2: Exploring the Boundaries of Protein Language Models](https://mlsanity.com/paper/2206.13517/) (2022)
- [ProGen: Language Modeling for Protein Generation](https://mlsanity.com/paper/2004.03497/) (2020)
- [Learning to Write with Cooperative Discriminators](https://mlsanity.com/paper/1805.06087/) (2018)
- [Conditioning by adaptive sampling for robust design](https://mlsanity.com/paper/1901.10060/) (2019)
- [Design-Bench: Benchmarks for Data-Driven Offline Model-Based Optimization](https://mlsanity.com/paper/2202.08450/) (2022)
- [Oops I Took A Gradient: Scalable Sampling for Discrete Distributions](https://mlsanity.com/paper/2102.04509/) (2021)
- [Conservative Objective Models for Effective Offline Model-Based Optimization](https://mlsanity.com/paper/2107.06882/) (2021)
- [Model Inversion Networks for Model-Based Optimization](https://mlsanity.com/paper/1912.13464/) (2019)
- [Tranception: protein fitness prediction with autoregressive transformers and inference-time retrieval](https://mlsanity.com/paper/2205.13760/) (2022)
- [AdaLead: A simple and robust adaptive greedy search algorithm for sequence design](https://mlsanity.com/paper/2010.02141/) (2020)
- [Autofocused oracles for model-based design](https://mlsanity.com/paper/2006.08052/) (2020)
- [A Langevin-like Sampler for Discrete Distributions](https://mlsanity.com/paper/2206.09914/) (2022)
- [RITA: a Study on Scaling Up Generative Protein Sequence Models](https://mlsanity.com/paper/2205.05789/) (2022)
- [Protein sequence design with deep generative models](https://mlsanity.com/paper/2104.04457/) (2021)
- [Design by adaptive sampling](https://mlsanity.com/paper/1810.03714/) (2018)
- [Generating and designing DNA with deep generative models](https://mlsanity.com/paper/1712.06148/) (2017)
- [Population-Based Black-Box Optimization for Biological Sequence Design](https://mlsanity.com/paper/2006.03227/) (2020)
- [Discrete Langevin Sampler via Wasserstein Gradient Flow](https://mlsanity.com/paper/2206.14897/) (2022)
- [Deep Extrapolation for Attribute-Enhanced Generation](https://mlsanity.com/paper/2107.02968/) (2021)
- [Unifying Likelihood-free Inference with Black-box Optimization and Beyond](https://mlsanity.com/paper/2110.03372/) (2021)
- [Feedback GAN (FBGAN) for DNA: a Novel Feedback-Loop Architecture for Optimizing Protein Functions](https://mlsanity.com/paper/1804.01694/) (2018)
- [ReLSO: A Transformer-based Model for Latent Space Optimization and Generation of Proteins](https://mlsanity.com/paper/2201.09948/) (2022)

## Built on by (most cited first, 17 of 17)

- [Protein Design with Guided Discrete Diffusion](https://mlsanity.com/paper/2305.20009/) (2023)
- [Unlocking Guidance for Discrete State-Space Diffusion and Flow Models](https://mlsanity.com/paper/2406.01572/) (2024)
- [How Discrete and Continuous Diffusion Meet: Comprehensive Analysis of Discrete Diffusion Models via a Stochastic Integral Framework](https://mlsanity.com/paper/2410.03601/) (2024)
- [Fast Solvers for Discrete Diffusion Models: Theory and Applications of High-Order Algorithms](https://mlsanity.com/paper/2502.00234/) (2025)
- [Improving Protein Optimization with Smoothed Fitness Landscapes](https://mlsanity.com/paper/2307.00494/) (2023)
- [Discrete Feynman-Kac Correctors](https://mlsanity.com/paper/2601.10403/) (2026)
- [Generative AI for Controllable Protein Sequence Design: A Survey](https://mlsanity.com/paper/2402.10516/) (2024)
- [Energy-Based Modelling for Discrete and Mixed Data via Heat Equations on Structured Spaces](https://mlsanity.com/paper/2412.01019/) (2024)
- [A Variational Perspective on Generative Protein Fitness Optimization](https://mlsanity.com/paper/2501.19200/) (2025)
- [Advances in Protein Representation Learning: Methods, Applications, and Future Directions](https://mlsanity.com/paper/2503.16659/) (2025)
- [Three Pathways to Neurosymbolic Reinforcement Learning with Interpretable Model and Policy Networks](https://mlsanity.com/paper/2402.05307/) (2024)
- [MutaPLM: Protein Language Modeling for Mutation Explanation and Engineering](https://mlsanity.com/paper/2410.22949/) (2024)
- [AgentPLM: Agentic Protein Language Models with Reasoning-Augmented Decoding for Protein Sequence Design](https://mlsanity.com/paper/2606.02386/) (2026)
- [Training Discrete Energy-Based Models with Energy Discrepancy](https://mlsanity.com/paper/2307.07595/) (2023)
- [Repurposing Protein Language Models for Latent Flow-Based Fitness Optimization](https://mlsanity.com/paper/2602.02425/) (2026)
- [BOAT: Navigating the Sea of In Silico Predictors for Antibody Design via Multi-Objective Bayesian Optimization](https://mlsanity.com/paper/2604.13980/) (2026)
- [Conditional generation of antibody sequences with classifier-guided germline-absorbing discrete diffusion](https://mlsanity.com/paper/2605.06720/) (2026)

## Abstract (arXiv)

A long-standing goal of machine-learning-based protein engineering is to accelerate the discovery of novel mutations that improve the function of a known protein. We introduce a sampling framework for evolving proteins in silico that supports mixing and matching a variety of unsupervised models, such as protein language models, and supervised models that predict protein function from sequence. By composing these models, we aim to improve our ability to evaluate unseen mutations and constrain search to regions of sequence space likely to contain functional proteins. Our framework achieves this without any model fine-tuning or re-training by constructing a product of experts distribution directly in discrete protein space. Instead of resorting to brute force search or random sampling, which is typical of classic directed evolution, we introduce a fast MCMC sampler that uses gradients to propose promising mutations. We conduct in silico directed evolution experiments on wide fitness landscapes and across a range of different pre-trained unsupervised models, including a 650M parameter protein language model. Our results demonstrate an ability to efficiently discover variants with high evolutionary likelihood as well as estimated activity multiple mutations away from a wild type protein, suggesting our sampler provides a practical and effective new paradigm for machine-learning-based protein engineering.