Statistical evidence for the presence of trajectory in single-cell data

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. RESULTS: 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, a p-value is calculated to quantify the statistical significance for the presence of trajectory in the data. CONCLUSIONS: Our work contributes new statistics to assess the level of uncertainty in trajectory inference to increase the understanding of biological system dynamics.