1. S. Wang, M.A. Al-Radhawi, D.A. Lauffenburger, and E.D. Sontag. How many time-points of single-cell omics data are necessary for recovering biomolecular network dynamics?. npj Systems Biology and Applications, 10, 2024. [PDF] Keyword(s): single-cell data, identifiability, network reconstruction, dynamical systems. Abstract:

   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.




2. S. Wang, E.D. Sontag, and D.A. Lauffenburger. What cannot be seen correctly in 2D visualizations of single-cell 'omics data?. Cell Systems, 14:723-731, 2023. [WWW] [PDF] Keyword(s): visualization, single-cell data, tSNE, UMAP. Abstract:

   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.

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