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

Links

• Paper: arXiv:2609.32309
• Code: TBD — add GitHub repository URL

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.

Contribution

Co-first author (equal contribution).

^#These authors contributed equally. ^†Corresponding author.

Recommended citation: Yutian Liu#, Mujie Lin#, Lanqian Zhang#, Meng Fan, Chang Liu†, Zhiwei Nie†, Siwei Ma†. "PhiFold: Towards Dynamic Protein Design with Physics-Structured Covariance Modeling." arXiv preprint arXiv:2609.32309, 2026.
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