EncoderMap: Dimensionality Reduction and Generation of Molecule Conformations

Abstract

Molecular simulation is one example where large amounts of high-dimensional (high-d) data are generated. To extract useful information, e.g., about relevant states and important conformational transitions, a form of dimensionality reduction is required. Dimensionality reduction algorithms diଏer in their ability to eଏciently project large amounts of data to an informative low-dimensional (low-d) representation and the way the low and high-d representations are linked. We propose a dimensionality reduction algorithm called EncoderMap that is based on a neural network autoencoder in combination with a nonlinear distance metric. A key advantage of this method is that it establishes a functional link from the high-d to the low-d representation and vice versa. This allows us not only to eଏciently project data points to the low-d representation but also to generate high-d representatives for any point in the low-d map. The potential of the algorithm is demonstrated for molecular simulation data of a small, highly ଏexible peptide as well as for folding simulations of the 20-residue Trp-cage protein. We demonstrate that the algorithm is able to eଏciently project the ensemble of high-d structures to a low-d map where major states can be identiଏed and important conformational transitions are revealed. We also show that molecular conformations can be generated for any point or any connecting line between points on the low-d map. This ability of inverse mapping from the low-d to the high-d representation is particularly relevant for the use in algorithms that enhance the exploration of conformational space or the sampling of transitions between conformational states.

Machine learning approaches for analyzing and enhancing molecular dynamics simulations

“…The EncoderMap approach of Lemke and Peter is another method that makes use of a NN encoderdecoder architecture [14]. In addition to a reconstruction loss analogous to Eq.…”

DiffNets: deep learning the structural determinants of proteins biochemical properties by comparing different structural ensembles

“…Standard autoencoders have been used in many applications to MD simulation data. 4,[30][31][32][33][34][35][36][37][38][39][40][41] They connect two separate neural networks, an encoder network and a decoder network, to perform an unsupervised dimensionality reduction on input data (e.g. a protein structure from a frame of an MD simulation).…”

Investigating the Conformational Ensembles of Intrinsically-Disordered Proteins with a Simple Physics-Based Model

“…S9). The nonlinear nature of this embedding results in structured free-energy landscapes, which are often not possible for disordered ensembles using linear techniques 64,65 . Row (c) of Fig.…”

“…Nonlinear manifold learning methods overcome the limited ability of linear methods to capture nonlinear relationships in the data and can determine the low-dimensional embedding based on a wide variety of criteria. These methods have been more successful in finding lowdimensional embeddings which provide a clear picture of distinct structures in disordered landscapes 64,65 . Here we employed UMAP (Uniform Manifold Approximation and Projection), a type of multidimensional-scaling algorithm that attempts to find a balance between resolving global and local properties of the conformational landscape 66 .…”