# Variational embedding of protein folding simulations using gaussian mixture variational autoencoders

arXiv: https://arxiv.org/abs/2108.12493 · HTML: https://mlsanity.com/paper/2108.12493/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 57 references that are in the map.
- First posted on arXiv 27 Aug 2021.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Deep Unsupervised Clustering with Gaussian Mixture Variational Autoencoders](https://mlsanity.com/paper/1611.02648/) (2016)
- [Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics](https://mlsanity.com/paper/1710.11239/) (2017)
- [Molecular enhanced sampling with autoencoders: On-the-fly collective variable discovery and accelerated free energy landscape exploration](https://mlsanity.com/paper/1801.00203/) (2017)
- [Interpretable Embeddings From Molecular Simulations Using Gaussian Mixture Variational Autoencoders](https://mlsanity.com/paper/1912.12175/) (2019)
- [High-resolution Markov state models for the dynamics of Trp-cage miniprotein constructed over slow folding modes identified by state-free reversible VAMPnets](https://mlsanity.com/paper/1906.04890/) (2019)
- [Predictive Collective Variable Discovery with Deep Bayesian Models](https://mlsanity.com/paper/1809.06913/) (2018)
- [Capabilities and Limitations of Time-lagged Autoencoders for Slow Mode Discovery in Dynamical Systems](https://mlsanity.com/paper/1906.00325/) (2019)

## Built on by (most cited first, 3 of 3)

- [GraphVAMPNet, using graph neural networks and variational approach to markov processes for dynamical modeling of biomolecules](https://mlsanity.com/paper/2201.04609/) (2022)
- [Fast conformational clustering of extensive molecular dynamics simulation data](https://mlsanity.com/paper/2301.04492/) (2023)
- [Physically Interpretable Representation Learning with Gaussian Mixture Variational AutoEncoder (GM-VAE)](https://mlsanity.com/paper/2511.21883/) (2025)

## Abstract (arXiv)

Conformational sampling of biomolecules using molecular dynamics simulations often produces large amount of high dimensional data that makes it difficult to interpret using conventional analysis techniques. Dimensionality reduction methods are thus required to extract useful and relevant information. Here we devise a machine learning method, Gaussian mixture variational autoencoder (GMVAE) that can simultaneously perform dimensionality reduction and clustering of biomolecular conformations in an unsupervised way. We show that GMVAE can learn a reduced representation of the free energy landscape of protein folding with highly separated clusters that correspond to the metastable states during folding. Since GMVAE uses a mixture of Gaussians as the prior, it can directly acknowledge the multi-basin nature of protein folding free-energy landscape. To make the model end-to-end differentialble, we use a Gumbel-softmax distribution. We test the model on three long-timescale protein folding trajectories and show that GMVAE embedding resembles the folding funnel with folded states down the funnel and unfolded states outer in the funnel path. Additionally, we show that the latent space of GMVAE can be used for kinetic analysis and Markov state models built on this embedding produce folding and unfolding timescales that are in close agreement with other rigorous dynamical embeddings such as time independent component analysis (TICA).