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  1. Abstract Background

    Cells progressing from an early state to a developed state give rise to lineages in cell differentiation. Knowledge of these lineages is central to developmental biology. Each biological lineage corresponds to a trajectory in a dynamical system. Emerging single-cell technologies such as single-cell RNA sequencing can capture molecular abundance in diverse cell types in a developing tissue. Many computational methods have been developed to infer trajectories from single-cell data. However, to our knowledge, none of the existing methods address the problem of determining the existence of a trajectory in observed data before attempting trajectory inference.


    We introduce a method to identify the existence of a trajectory using three graph-based statistics. A permutation test is utilized to calculate the empirical distribution of the test statistic under the null hypothesis that a trajectory does not exist. Finally, ap-value is calculated to quantify the statistical significance for the presence of trajectory in the data.


    Our work contributes new statistics to assess the level of uncertainty in trajectory inference to increase the understanding of biological system dynamics.

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  2. Iakoucheva, Lilia M. (Ed.)
    The complexity of biological processes such as cell differentiation is reflected in dynamic transitions between cellular states. Trajectory inference arranges the states into a progression using methodologies propelled by single-cell biology. However, current methods, all returning a best trajectory, do not adequately assess statistical significance of noisy patterns, leading to uncertainty in inferred trajectories. We introduce a tree dimension test for trajectory presence in multivariate data by a dimension measure of Euclidean minimum spanning tree, a test statistic, and a null distribution. Computable in linear time to tree size, the tree dimension measure summarizes the extent of branching more effectively than globally insensitive number of leaves or tree diameter indifferent to secondary branches. The test statistic quantifies trajectory presence and its null distribution is estimated under the null hypothesis of no trajectory in data. On simulated and real single-cell datasets, the test outperformed the intuitive number of leaves and tree diameter statistics. Next, we developed a measure for the tissue specificity of the dynamics of a subset, based on the minimum subtree cover of the subset in a minimum spanning tree. We found that tissue specificity of pathway gene expression dynamics is conserved in human and mouse development: several signal transduction pathways including calcium and Wnt signaling are most tissue specific, while genetic information processing pathways such as ribosome and mismatch repair are least so. Neither the tree dimension test nor the subset specificity measure has any user parameter to tune. Our work opens a window to prioritize cellular dynamics and pathways in development and other multivariate dynamical systems. 
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