| Publications about 'single-cell data' |
| Articles in journal or book chapters |
| Single-cell omics technologies can measure millions of cells for up to thousands of biomolecular features, which enables the data-driven study of highly complex biological networks. However, these high-throughput experimental techniques often cannot track individual cells over time, thus complicating the understanding of dynamics such as the time trajectories of cell states. These ``dynamical phenotypes'' are key to understanding biological phenomena such as differentiation fates. We show by mathematical analysis that, in spite of high-dimensionality and lack of individual cell traces, three timepoints of single-cell omics data are theoretically necessary and sufficient in order to uniquely determine the network interaction matrix and associated dynamics. Moreover, we show through numerical simulations that an interaction matrix can be accurately determined with three or more timepoints even in the presence of sampling and measurement noise typical of single-cell omics. Our results can guide the design of single-cell omics time-course experiments, and provide a tool for data-driven phase-space analysis. |
| Single-cell -omics datasets are high-dimensional and difficult to visualize. A common strategy for exploring such data is to create and analyze 2D projections. Such projections may be highly nonlinear, and implementation algorithms are designed with the goal of preserving aspects of the original high-dimensional shape of data such as neighborhood relationships or metrics. However, important aspects of high-dimensional geometry are known from mathematical theory to have no equivalent representation in 2D, or are subject to large distortions, and will therefore be misrepresented or even invisible in any possible 2D representation. We show that features such as quantitative distances, relative positioning, and qualitative neighborhoods of high-dimensional data points will always be misrepresented in 2D projections. Our results rely upon concepts from differential geometry, combinatorial geometry, and algebraic topology. As an illustrative example, we show that even a simple single-cell RNA sequencing dataset will always be distorted, no matter what 2D projection is employed. We also discuss how certain recently developed computational tools can help describe the high-dimensional geometric features that will be necessarily missing from any possible 2D projections. |
| The goal of many single-cell studies on eukaryotic cells is to gain insight into the biochemical reactions that control cell fate and state. This paper introduces the concept of effective stoichiometric space (ESS) to guide the reconstruction of biochemical networks from multiplexed, fixed time-point, single-cell data. In contrast to methods based solely on statistical models of data, the ESS method leverages the power of the geometric theory of toric varieties to begin unraveling the structure of chemical reaction networks (CRN). This application of toric theory enables a data-driven mapping of covariance relationships in single cell measurements into stoichiometric information, one in which each cell subpopulation has its associated ESS interpreted in terms of CRN theory. In the development of ESS we reframe certain aspects of the theory of CRN to better match data analysis. As an application of our approach we process cytomery- and image-based single-cell datasets and identify differences in cells treated with kinase inhibitors. Our approach is directly applicable to data acquired using readily accessible experimental methods such as Fluorescence Activated Cell Sorting (FACS) and multiplex immunofluorescence. |
| Reverse engineering of biological pathways involves an iterative process between experiments, data processing, and theoretical analysis. In this work, we engineer synthetic circuits, subject them to perturbations, and then infer network connections using a combination of nonparametric single-cell data resampling and modular response analysis. Intriguingly, we discover that recovered weights of specific network edges undergo divergent shifts under differential perturbations, and that the particular behavior is markedly different between different topologies. Investigating topological changes under differential perturbations may address the longstanding problem of discriminating direct and indirect connectivities in biological networks. |
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