Unified Embedding and Clustering

In this paper, we introduce a novel algorithm that unifies manifold embedding and clustering (UEC) which efficiently predicts clustering assignments of the high dimensional data points in a new embedding space. The algorithm is based on a bi-objective optimisation problem combining embedding and clustering loss functions. Such original formulation will allow to simultaneously preserve the original structure of the data in the embedding space and produce better clustering assignments. The experimental results using a number of real-world datasets show that UEC is competitive with the state-of-art clustering methods.

Unified Embedding and Clustering

In this paper, we introduce a novel algorithm that unifies manifold embedding and clustering (UEC) which efficiently predicts clustering assignments of the high dimensional data points in a new embedding space. The algorithm is based on a bi-objective optimisation problem combining embedding and clustering loss functions. Such original formulation will allow to simultaneously preserve the original structure of the data in the embedding space and produce better clustering assignments. The experimental results using a number of real-world datasets show that UEC is competitive with the state-of-art clustering methods.

Visualizing conformational space of functional biomolecular complexes by deep manifold learning

The cellular functions are executed by biological macromolecular complexes in nonequilibrium dynamic processes, which exhibit a vast diversity of conformational states. Solving conformational continuum of important biomolecular complexes at atomic level is essential to understand their functional mechanisms and to guide structure-based drug discovery. Here we introduce a deep learning framework, named AlphaCryo4D, which enables atomic-level cryogenic electron microscopy reconstructions of conformational continuum. AlphaCryo4D integrates 3D deep residual learning with manifold embedding of energy landscapes, which directs 3D clustering of markedly improved accuracy via an energy-based particle-voting algorithm. By applications of this approach to analyze five experimental datasets, we examine its generality in breaking resolution limit of visualizing dynamic components of functional complexes, in discovering 'invisible' lowly populated intermediates and in exploring their hidden conformational space. Our approach expands the realm of structural ensemble determination to the nonequilibrium regime at atomic level, thus potentially transforming biomedical research and therapeutic development.

Recovery of conformational continuum from single-particle cryo-EM data: Optimization of ManifoldEM informed by ground-truth studies

This work is based on the manifold-embedding approach to the study of biological molecules exhibiting conformational changes in a continuum. Previous studies established a workflow capable of reconstructing atomic-level structures in the conformational continuum from cryo-EM images so as to reveal the latent space of macromolecules undergoing multiple degrees of freedom. Here, we introduce a new approach that is informed by detailed heuristic analysis of manifolds formed by simulated heterogeneous cryo-EM datasets. These simulated models were generated with increasing complexity to account for multiple motions, state occupancies and CTF in a wide range of signal-to-noise ratios. Using these datasets as ground-truth, we provide detailed exposition of our findings using several conformational motions while exploring the available parameter space. Guided by these insights, we build a framework to leverage the high-dimensional geometric information obtained towards reconstituting the quasi-continuum of conformational states in the form of an energy landscape and respective 3D maps for all states therein. This framework offers substantial enhancements relative to previous work, for which a direct comparison of outputs has been provided.