PhiFold: Towards Dynamic Protein Design with Physics-Structured Covariance Modeling

2026-09-26

AI Summary

Existing generative models treat dynamics as a downstream property, hindering function-aware dynamic protein design. This work proposes a unified framework that jointly generates protein backbones and second-order dynamics. By leveraging low-rank matrix factorization and physics-constrained covariance assembly, the method structurally models local flexibility, collective motions, and participation ratios to construct compact, positive-definite covariance representations. This enables the integration of structure generation with explicit equilibrium dynamics and bidirectional flexibility control. The proposed approach significantly improves the recovery of local fluctuations and long-range couplings while preserving backbone designability, thereby laying the foundation for designing proteins by their modes of motion.

Abstract

Protein design is moving beyond structural correctness toward function-aware design, yet existing generative models typically treat dynamics as a downstream property estimated through simulation or prediction after structure generation. Using MD trajectories as a generative target is also undesirable because stochastic, path-dependent trajectories over-specify the underlying equilibrium ensemble. We introduce PhiFold, a framework for jointly generating protein backbones and their second-order dynamics, represented by residue-displacement covariance. Rather than predicting the quadratically sized full covariance, PhiFold decomposes dynamics into three interpretable components: local flexibility, a low-rank collective-motion representation, and residue-wise collective participation. These components are assembled into a positive-definite covariance matrix with exact marginal consistency, yielding a compact and physically constrained representation of equilibrium dynamics. Across generated proteins, PhiFold improves recovery of local fluctuations and long-range residue coupling while remaining competitive on dominant collective-motion subspaces. It further enables bidirectional control of residue flexibility while preserving backbone designability. By unifying structure generation with an explicit representation of equilibrium dynamics, PhiFold lays a foundation for designing proteins not only by how they look, but also by how they move.

Problem

• Protein design
• Equilibrium dynamics
• Covariance modeling
• Generative models
• Residue flexibility

Innovation

• Protein Design
• Covariance Modeling
• Equilibrium Dynamics
• Generative Model
• Low-rank Decomposition