# Learning residue level protein dynamics with multiscale Gaussians

arXiv: https://arxiv.org/abs/2509.01038 · HTML: https://mlsanity.com/paper/2509.01038/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 38 references that are in the map.
- First posted on arXiv 1 Sep 2025.

## Builds on (most cited first, 4 of 4)

- [AlphaFold Meets Flow Matching for Generating Protein Ensembles](https://mlsanity.com/paper/2402.04845/) (2024)
- [Protein Conformation Generation via Force-Guided SE(3) Diffusion Models](https://mlsanity.com/paper/2403.14088/) (2024)
- [Structure Language Models for Protein Conformation Generation](https://mlsanity.com/paper/2410.18403/) (2024)
- [Riemannian Metric Learning for Symmetric Positive Definite Matrices](https://mlsanity.com/paper/1501.02393/) (2015)

## Built on by (most cited first, 4 of 4)

- [AI-based Methods for Simulating, Sampling, and Predicting Protein Ensembles](https://mlsanity.com/paper/2509.17224/) (2025)
- [Learning Structure, Energy, and Dynamics: A Survey of Artificial Intelligence for Protein Dynamics](https://mlsanity.com/paper/2604.25244/) (2026)
- [PhiFold: Towards Dynamic Protein Design with Physics-Structured Covariance Modeling](https://mlsanity.com/paper/2609.32309/) (2026)
- [RNADyn: A Benchmark for Generating and Understanding RNA Dynamics](https://mlsanity.com/paper/2610.03712/) (2026)

## Abstract (arXiv)

Many methods have been developed to predict static protein structures, however understanding the dynamics of protein structure is essential for elucidating biological function. While molecular dynamics (MD) simulations remain the in silico gold standard, its high computational cost limits scalability. We present DynaProt, a lightweight, SE(3)-invariant framework that predicts rich descriptors of protein dynamics directly from static structures. By casting the problem through the lens of multivariate Gaussians, DynaProt estimates dynamics at two complementary scales: (1) per-residue marginal anisotropy as 3 × 3 covariance matrices capturing local flexibility, and (2) joint scalar covariances encoding pairwise dynamic coupling across residues. From these dynamics outputs, DynaProt achieves high accuracy in predicting residue-level flexibility (RMSF) and, remarkably, enables reasonable reconstruction of the full covariance matrix for fast ensemble generation. Notably, it does so using orders of magnitude fewer parameters than prior methods. Our results highlight the potential of direct protein dynamics prediction as a scalable alternative to existing methods.