[Paper Review] Efficient Protein Optimization via Structure-aware Hamiltonian Dynamics

Jiahao Wang, Shuangjia Zheng|arXiv (Cornell University)|Jan 16, 2026

Protein Structure and Dynamics0 citations

TL;DR

HADES combines structure-informed Bayesian optimization with Hamiltonian dynamics to efficiently explore protein sequence space and design high-fitness, structurally compatible variants, outperforming baselines in in-silico tests on GB1 and PhoQ.

ABSTRACT

The ability to engineer optimized protein variants has transformative potential for biotechnology and medicine. Prior sequence-based optimization methods struggle with the high-dimensional complexities due to the epistasis effect and the disregard for structural constraints. To address this, we propose HADES, a Bayesian optimization method utilizing Hamiltonian dynamics to efficiently sample from a structure-aware approximated posterior. Leveraging momentum and uncertainty in the simulated physical movements, HADES enables rapid transition of proposals toward promising areas. A position discretization procedure is introduced to propose discrete protein sequences from such a continuous state system. The posterior surrogate is powered by a two-stage encoder-decoder framework to determine the structure and function relationships between mutant neighbors, consequently learning a smoothed landscape to sample from. Extensive experiments demonstrate that our method outperforms state-of-the-art baselines in in-silico evaluations across most metrics. Remarkably, our approach offers a unique advantage by leveraging the mutual constraints between protein structure and sequence, facilitating the design of protein sequences with similar structures and optimized properties. The code and data are publicly available at https://github.com/GENTEL-lab/HADES.

Motivation & Objective

• Motivate protein engineering as a high-dimensional, epistasis-rich optimization problem.
• Leverage protein structure as a prior to smooth the fitness landscape.
• Develop a structure-aware, Bayesian optimization framework to sample promising variants.
• Enable discrete sequence proposals from a continuous representation via a position discretization routine.

Proposed method

• Use Hamiltonian dynamics to propose distant samples in a continuous protein-state space.
• Define potential energy U(q) as negative log-probability under the surrogate predictor, with momentum-based kinetic energy K(p).
• Discretize the continuous state to discrete amino acid sequences using a virtual-barrier/bounce mechanism during leapfrog updates.
• Employ an ensemble of surrogate models and uncertainty-aware acquisition via upper confidence bound (UCB).
• Implement a two-stage encoder-decoder surrogate: a shared sequence encoder plus separate structure and fitness decoders, trained with RMSD priors from ESMFold.

Experimental results

Research questions

• RQ1 Can structure-aware priors stabilize and accelerate Bayesian optimization for protein design?
• RQ2 Does Hamiltonian dynamics-based sampling improve exploration in high-dimensional, discrete sequence spaces?
• RQ3 How does incorporating structure perturbations as priors affect the quality and diversity of designed proteins?
• RQ4 What is the impact of uncertainty estimation and discretization constraints on design performance?

Key findings

• HADES outperforms state-of-the-art baselines on GB1 and PhoQ in cumulative max fitness, mean fitness, and diversity metrics.
• On GB1, HADES identifiably found the optimal sequence in all 10 runs with zero variance.
• On PhoQ, HADES achieves higher maximum fitness and maintains functional diversity (fDiv) across runs.
• Ablation shows removing Hamiltonian sampling or structure priors reduces performance, and uncertainty and virtual barriers improve robustness against discretization errors.
• Results scale favorably with larger query budgets (K) and rounds, widening the gap to baselines at higher K.