# Learning Topological Representations of Protein Structure and Dynamics

arXiv: https://arxiv.org/abs/2606.14737 · HTML: https://mlsanity.com/paper/2606.14737/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 75 references that are in the map.
- First posted on arXiv 2 Jun 2026.

## Builds on (most cited first, 17 of 17)

- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Learning from Protein Structure with Geometric Vector Perceptrons](https://mlsanity.com/paper/2009.01411/) (2020)
- [Machine Learning Force Fields](https://mlsanity.com/paper/2010.07067/) (2020)
- [VAMPnets: Deep learning of molecular kinetics](https://mlsanity.com/paper/1710.06012/) (2017)
- [Generative Modeling of Molecular Dynamics Trajectories](https://mlsanity.com/paper/2409.17808/) (2024)
- [Deeptime: a Python library for machine learning dynamical models from time series data](https://mlsanity.com/paper/2110.15013/) (2021)
- [Machine Learning Coarse-Grained Potentials of Protein Thermodynamics](https://mlsanity.com/paper/2212.07492/) (2022)
- [Consistent Sampling and Simulation: Molecular Dynamics with Energy-Based Diffusion Models](https://mlsanity.com/paper/2506.17139/) (2025)
- [FlashMD: long-stride, universal prediction of molecular dynamics](https://mlsanity.com/paper/2505.19350/) (2025)
- [Variational Selection of Features for Molecular Kinetics](https://mlsanity.com/paper/1811.11714/) (2018)
- [Accelerating Protein Molecular Dynamics Simulation with DeepJump](https://mlsanity.com/paper/2509.13294/) (2025)
- [The Flood Complex: Large-Scale Persistent Homology on Millions of Points](https://mlsanity.com/paper/2509.22432/) (2025)
- [MarS-FM: Generative Modeling of Molecular Dynamics via Markov State Models](https://mlsanity.com/paper/2509.24779/) (2025)
- [Advances in Protein Representation Learning: Methods, Applications, and Future Directions](https://mlsanity.com/paper/2503.16659/) (2025)
- [OneProt: Towards Multi-Modal Protein Foundation Models](https://mlsanity.com/paper/2411.04863/) (2024)

## Abstract (arXiv)

Modern protein representation models support tasks such as enzyme design and drug discovery, but their reliance on static data such as sequence and native structure limits their ability to capture the conformational dynamics that drive protein function. We investigate whether persistent homology (PH) can provide descriptors shared across diverse proteins that retain global structure, fine-grained conformational variability, and kinetically relevant information without large-scale pretraining. We introduce the masked Flood complex, i.e., an adaptation of a recently proposed simplicial complex construction, that incorporates domain knowledge to emphasize inter-residue structure at low computational cost. We then use it to compute PH on molecular dynamics (MD) sampled structures, vectorize the persistence diagrams into a shared coordinate system, and probe the capacity of these representations in terms of the aforementioned aspects. To assess the amount of kinetic information, we learn low-dimensional embeddings from time-lagged observations and evaluate Markov state models (MSMs) estimated from them. Using these MSMs to guide training of the recent marsfm generative framework improves several ensemble statistics relative to the original model. After finetuning on lower-temperature MD data and adapting the sampling procedure, the resulting model also shows promising transfer to fast folding proteins.