PI-Mamba: Linear-Time Protein Backbone Generation via Spectrally Initialized Flow Matching

TL;DR

PI-Mamba is a novel protein backbone generative model that guarantees geometric validity, operates in linear time, and scales efficiently to long sequences using spectral initialization and a flow-matching framework.

Contribution

It introduces a physics-informed, spectrally initialized flow model that enforces local geometry and scales linearly for large protein sequences.

Findings

Achieves 0.0% local geometry violations.

High designability with scTM = 0.91 ± 0.03.

Scales to proteins over 2,000 residues on a single GPU.

Abstract

Motivation: Generative models for protein backbone design have to simultaneously ensure geometric validity, sampling efficiency, and scalability to long sequences. However, most existing approaches rely on iterative refinement, quadratic attention mechanisms, or post-hoc geometry correction, leading to a persistent trade-off between computational efficiency and structural fidelity. Results: We present Physics-Informed Mamba (PI-Mamba), a generative model that enforces exact local covalent geometry by construction while enabling linear-time inference. PI-Mamba integrates a differentiable constraint-enforcement operator into a flow-matching framework and couples it with a Mamba-based state-space architecture. To improve optimisation stability and backbone realism, we introduce a spectral initialization derived from the Rouse polymer model and an auxiliary cis-proline awareness head. Across benchmark tasks, PI-Mamba achieves 0.0\% local geometry violations and high designability (scTM = $0.91\pm 0.03$, n = 100), while scaling to proteins exceeding 2,000 residues on a single A5000 GPU (24 GB).