  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).
