The Graph Fourier Transform Recasts Rouse Modes to Encode Polymer Sequence

Abstract

Rouse modes diagonalize the polymer connectivity matrix to describe how conformational motion is distributed over structural modes, yet the chemistry distributed along that same chain is traditionally encoded through hand-crafted, system-specific descriptors. Here, we generalize Rouse modes from bead coordinates to bead identity through a Graph Fourier Transform (GFT), which projects a chemically specific sequence signal onto the eigenbasis of the polymer graph Laplacian. The correspondence is exact for the combinatorial Laplacian, and holds by close analogy for its degree-weighted normalized counterpart. GFT descriptors predict the radius of gyration of architecturally diverse coarse-grained copolymers with accuracy comparable to a bespoke graph neural network and, with only the signal redefined, resolve liquid-liquid phase separation propensity in intrinsically disordered proteins. Predictive performance degrades with the degeneracy introduced by symmetric architectures. Generalized Rouse modes thus offer an architecture-adaptive and interpretable alternative to bespoke descriptors for sequence-controlled macromolecules.