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Constrained Diffusion for Protein Design with Hard Structural Constraints

Jacob K. Christopher, Austin Seamann, Jingyi Cui, Sagar Khare, Ferdinando Fioretto

TL;DR

This work addresses enforcing strict geometric and functional constraints in diffusion-based protein design by introducing a stochastic proximal diffusion framework. It treats reverse diffusion as a proximal optimization with final-state corrections and employs a consensus ADMM decomposition to separate local stereochemistry from global topology, providing theoretical feasibility guarantees. Empirical validation on challenging tasks, including PDZ motif scaffolding and vacancy-constrained pockets, demonstrates state-of-the-art constraint satisfaction while preserving structural diversity, and introduces a novel PDZ benchmark. The approach offers practical impact for modular domain engineering and ligand-binding design by enabling reliable designs that strictly meet hard constraints. Overall, the method advances constrained generative modeling for proteins by combining principled optimization with diffusion-based sampling to achieve exact feasibility without sacrificing design variety.

Abstract

Diffusion models offer a powerful means of capturing the manifold of realistic protein structures, enabling rapid design for protein engineering tasks. However, existing approaches observe critical failure modes when precise constraints are necessary for functional design. To this end, we present a constrained diffusion framework for structure-guided protein design, ensuring strict adherence to functional requirements while maintaining precise stereochemical and geometric feasibility. The approach integrates proximal feasibility updates with ADMM decomposition into the generative process, scaling effectively to the complex constraint sets of this domain. We evaluate on challenging protein design tasks, including motif scaffolding and vacancy-constrained pocket design, while introducing a novel curated benchmark dataset for motif scaffolding in the PDZ domain. Our approach achieves state-of-the-art, providing perfect satisfaction of bonding and geometric constraints with no degradation in structural diversity.

Constrained Diffusion for Protein Design with Hard Structural Constraints

TL;DR

This work addresses enforcing strict geometric and functional constraints in diffusion-based protein design by introducing a stochastic proximal diffusion framework. It treats reverse diffusion as a proximal optimization with final-state corrections and employs a consensus ADMM decomposition to separate local stereochemistry from global topology, providing theoretical feasibility guarantees. Empirical validation on challenging tasks, including PDZ motif scaffolding and vacancy-constrained pockets, demonstrates state-of-the-art constraint satisfaction while preserving structural diversity, and introduces a novel PDZ benchmark. The approach offers practical impact for modular domain engineering and ligand-binding design by enabling reliable designs that strictly meet hard constraints. Overall, the method advances constrained generative modeling for proteins by combining principled optimization with diffusion-based sampling to achieve exact feasibility without sacrificing design variety.

Abstract

Diffusion models offer a powerful means of capturing the manifold of realistic protein structures, enabling rapid design for protein engineering tasks. However, existing approaches observe critical failure modes when precise constraints are necessary for functional design. To this end, we present a constrained diffusion framework for structure-guided protein design, ensuring strict adherence to functional requirements while maintaining precise stereochemical and geometric feasibility. The approach integrates proximal feasibility updates with ADMM decomposition into the generative process, scaling effectively to the complex constraint sets of this domain. We evaluate on challenging protein design tasks, including motif scaffolding and vacancy-constrained pocket design, while introducing a novel curated benchmark dataset for motif scaffolding in the PDZ domain. Our approach achieves state-of-the-art, providing perfect satisfaction of bonding and geometric constraints with no degradation in structural diversity.
Paper Structure (25 sections, 4 theorems, 35 equations, 4 figures, 4 tables)

This paper contains 25 sections, 4 theorems, 35 equations, 4 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Settings and Background
  3. Challenges with Constrained Diffusion
  4. Reverse Diffusion as Proximal Optimization
  5. Decoupling Global Topology from Local Geometry via ADMM
  6. Theoretical Analysis
  7. Experiments
  8. PDZ Domain: Covalent Bonds
  9. Molecule Encapsulation: Vacancy Constraints
  10. Related Work
  11. Conclusion
  12. Limitations and Future Work
  13. Experimental Details
  14. PDZ Domain: Covalent Bonds
  15. Recenter of Mass Guidance.
  16. ...and 10 more sections

Key Result

Theorem 6.1

Consider a feasibility potential $g(\bm{x}) = \tfrac{\lambda_t}{2} \mathrm{dist}_\mathcal{C}(\bm{x})^2$ defined as in Equation eq:prox. Then, the proximal minimizer $\tilde{\bm{x}}_0$ satisfies:

Figures (4)

  • Figure 1: Illustration of our stochastic proximal sampling for structured-constrained protein design.
  • Figure 2: Visualization of randomly selected samples generated by (a) our proximal method and by (b) Standard RFDiffusion on our introduced PDZ domain benchmark.
  • Figure 3: Visualization of randomly selected samples for the molecule encapsulation experiment; green parts of the structure fall within feasible regions, while the red parts violate the constraints.
  • Figure 4: Dataset filtering details expanded.

Theorems & Definitions (7)

  • Theorem 6.1
  • Theorem 6.2
  • Theorem 6.3
  • proof : Proof of Theorem \ref{['theorem:feasibility']}
  • Lemma F.1
  • proof : Proof of Theorem \ref{['cor:schedule']}
  • proof : Proof of Theorem \ref{['theorem:local-solution']}