A Protein Dances to the Music of Fourier express
A protein in a cell is not a frozen sculpture. It is constantly in motion: bending, breathing, jittering. This motion, its dynamics, determines how the protein works. But peering directly into the dance is hard, and computer simulations often demand enormous computing power.
A new approach, named DynaMode, views protein motion as a musical piece. The Fourier transform decomposes the complex trajectory of atoms into simple frequencies, like separating the bass line of slow bends from the high ring of fast vibrations. The model learns to predict not individual atomic positions but entire spectral patterns that depend on temperature. Low frequencies in such a pattern directly indicate how flexible each region of the protein is.
Training on the mdCATH dataset allowed the model to quickly generate plausible trajectories. On held-out tests, DynaMode achieved a Pearson correlation of 0.844 for root-mean-square fluctuations of atoms (RMSF — a measure of how much an atom deviates from its average position). This means that the predicted mobility matches the real one well. The model doesn't just guess: it captures the physics of the process: the separation into slow and fast motions is built into the architecture itself.
Such a spectral view opens the door to rapid screening: you can assess in minutes how a mutation or a change in temperature will affect the protein's dance. And that means faster drug discovery or understanding of disease causes.
Original abstract
as written by the authors arXiv:2607.04134
Generative models present a promising alternative to expensive molecular dynamics for computationally querying protein dynamics, yet many existing approaches treat ensembles as unordered snapshots rather than temporally coherent trajectories, or scale poorly with protein size. We present a new physics-informed representation using Fourier transforms as an inductive bias for the multiscale temporal nature of protein dynamics. Diffusion in the spectral domain allows for disentangling of dynamics into slow conformational modes and fast atomic jitter, enabling rapid and improved prediction of dynamics across a range of temperatures. This is facilitated by denoising of structure and temperature conditioned spectral volumes where the low frequencies directly encode per-residue flexibility. Trained on the mdCATH dataset, we evaluate our model, DynaMode, on a held-out test set achieving strong performance across a set of ensemble-based metrics including a Root Mean Squared Fluctuation (RMSF) pearson $$r$$ of $$0.844$$. Code is available at https://github.com/HPuntu/DynaMode.
The root-mean-square fluctuation of an atom in a protein at room temperature can reach 1–2 angstroms — about a tenth of a nanometer, but for a molecule that is a noticeable amplitude.