Variational encoding of complex dynamics

Abstract

Often the analysis of time-dependent chemical and biophysical systems produces high-dimensional time-series data for which it can be difficult to interpret which individual features are most salient. While recent work from our group and others has demonstrated the utility of time-lagged covariate models to study such systems, linearity assumptions can limit the compression of inherently nonlinear dynamics into just a few characteristic components. Recent work in the field of deep learning has led to the development of the variational autoencoder (VAE), which is able to compress complex datasets into simpler manifolds. We present the use of a time-lagged VAE, or variational dynamics encoder (VDE), to reduce complex, nonlinear processes to a single embedding with high fidelity to the underlying dynamics. We demonstrate how the VDE is able to capture nontrivial dynamics in a variety of examples, including Brownian dynamics and atomistic protein folding. Additionally, we demonstrate a method for analyzing the VDE model, inspired by saliency mapping, to determine what features are selected by the VDE model to describe dynamics. The VDE presents an important step in applying techniques from deep learning to more accurately model and interpret complex biophysics.

Characterizing chromatin folding coordinate and landscape with deep learning

“…In this study, we apply similar ideas to determine the chromatin folding coordinate by analyzing an ensemble of structures obtained from single-cell super-resolution imaging (30). Specifically, we used the deep learning framework VAE to derive a deep generative model (49)(50)(51). Compared to existing approaches, the generative model not only compresses the data into a lowdimensional space for reaction coordinate analysis, but also provides an estimation of the probability for each configuration.…”

Visual Analytics for Deep Embeddings of Large Scale Molecular Dynamics Simulations

“…The dimensionality reduction process can be conducted using an autoencoder, a self-supervised deep learning model, which can be trained to reconstruct a dateset after encoding it into a reduced latent space [20]. Various autoencoders have been developed and successfully constructed lowdimensional underlying representations of the 3D protein conformations [7]- [9]. In this study, an application of a convolutional variational autoencoder (CVAE) was adapted to automatically reduce the high dimensional conformations from MD simulations into scattering points in 3D latent space where those points are also grouped according to shared structural and energetic characteristics [7], [8], [21]- [24].…”

“…One of the popular approaches to evaluate the embedding models and analyze the underlying features is to visualize them. The interactive visualization of these embeddings allows one to not only verify dimensional reduction methods (i.e., how models accurately capture certain similarity across groups of simulation frames), but also potentially interpret biomolecular mechanisms that lead to specific observations across MD simulations [7]- [9]. However, most existing visualizations for embeddings have some limitations in evaluating the embedding models and understanding the complex MD simulations.…”

Modelling Intrinsically Disordered Protein Dynamics as Networks of Transient Secondary Structure

“…This principle implies that a model with longer characteristic timescales is closer to representing the true processes in the data than a model with shorter characteristic timescales. This principle has been used to develop several methods for maximizing eigenvalue-based scores (12,20,21), one of these being the Generalized Matrix Rayleigh Quotient (GMRQ) (12).…”