Revealing lineage-related signals in single-cell gene expression using random matrix theory

Principled and interpretable alignability testing and integration of single-cell data

Single-cell data integration can provide a comprehensive molecular view of cells, and many algorithms have been developed to remove unwanted technical or biological variations and integrate heterogeneous single-cell datasets. Despite their wide usage, existing methods suffer from several fundamental limitations. In particular, we lack a rigorous statistical test for whether two high-dimensional single-cell datasets are alignable (and therefore should even be aligned). Moreover, popular methods can substantially distort the data during alignment, making the aligned data and downstream analysis difficult to interpret. To overcome these limitations, we present a spectral manifold alignment and inference (SMAI) framework, which enables principled and interpretable alignability testing and structure-preserving integration of single-cell data with the same type of features. SMAI provides a statistical test to robustly assess the alignability between datasets to avoid misleading inference and is justified by high-dimensional statistical theory. On a diverse range of real and simulated benchmark datasets, it outperforms commonly used alignment methods. Moreover, we show that SMAI improves various downstream analyses such as identification of differentially expressed genes and imputation of single-cell spatial transcriptomics, providing further biological insights. SMAI's interpretability also enables quantification and a deeper understanding of the sources of technical confounders in single-cell data.

An evolution-based framework for describing human gut bacteria

The human gut microbiome contains many bacterial strains of the same species ('strain-level variants'). Describing strains in a biologically meaningful way rather than purely taxonomically is an important goal but challenging due to the genetic complexity of strain-level variation. Here, we measured patterns of co-evolution across >7,000 strains spanning the bacterial tree-of-life. Using these patterns as a prior for studying hundreds of gut commensal strains that we isolated, sequenced, and metabolically profiled revealed widespread structure beneath the phylogenetic level of species. Defining strains by their co-evolutionary signatures enabled predicting their metabolic phenotypes and engineering consortia from strain genome content alone. Our findings demonstrate a biologically relevant organization to strain-level variation and motivate a new schema for describing bacterial strains based on their evolutionary history.

scPrisma infers, filters and enhances topological signals in single-cell data using spectral template matching

Single-cell RNA sequencing has been instrumental in uncovering cellular spatiotemporal context. This task is challenging as cells simultaneously encode multiple, potentially cross-interfering, biological signals. Here we propose scPrisma, a spectral computational method that uses topological priors to decouple, enhance and filter different classes of biological processes in single-cell data, such as periodic and linear signals. We apply scPrisma to the analysis of the cell cycle in HeLa cells, circadian rhythm and spatial zonation in liver lobules, diurnal cycle in Chlamydomonas and circadian rhythm in the suprachiasmatic nucleus in the brain. scPrisma can be used to distinguish mixed cellular populations by specific characteristics such as cell type and uncover regulatory networks and cell-cell interactions specific to predefined biological signals, such as the circadian rhythm. We show scPrisma's flexibility in incorporating prior knowledge, inference of topologically informative genes and generalization to additional diverse templates and systems. scPrisma can be used as a stand-alone workflow for signal analysis and as a prior step for downstream single-cell analysis.

Phase separation in fluids with many interacting components

Fluids in natural systems, like the cytoplasm of a cell, often contain thousands of molecular species that are organized into multiple coexisting phases that enable diverse and specific functions. How interactions between numerous molecular species encode for various emergent phases is not well understood. Here, we leverage approaches from random-matrix theory and statistical physics to describe the emergent phase behavior of fluid mixtures with many species whose interactions are drawn randomly from an underlying distribution. Through numerical simulation and stability analyses, we show that these mixtures exhibit staged phase-separation kinetics and are characterized by multiple coexisting phases at steady state with distinct compositions. Random-matrix theory predicts the number of coexisting phases, validated by simulations with diverse component numbers and interaction parameters. Surprisingly, this model predicts an upper bound on the number of phases, derived from dynamical considerations, that is much lower than the limit from the Gibbs phase rule, which is obtained from equilibrium thermodynamic constraints. We design ensembles that encode either linear or nonmonotonic scaling relationships between the number of components and coexisting phases, which we validate through simulation and theory. Finally, inspired by parallels in biological systems, we show that including nonequilibrium turnover of components through chemical reactions can tunably modulate the number of coexisting phases at steady state without changing overall fluid composition. Together, our study provides a model framework that describes the emergent dynamical and steady-state phase behavior of liquid-like mixtures with many interacting constituents.