Variational embedding of protein folding simulations using gaussian mixture variational autoencoders

TL;DR

This paper introduces GMVAE, a machine learning approach that reduces dimensionality and clusters biomolecular conformations, effectively capturing the protein folding landscape and enabling kinetic analysis.

Contribution

The novel GMVAE method combines dimensionality reduction and clustering for protein folding data using a Gaussian mixture prior and Gumbel-softmax, providing interpretable free energy landscapes.

Findings

GMVAE captures the folding funnel structure.

Latent space enables accurate kinetic analysis.

Results agree with established dynamical models.

Abstract

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).