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

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, a p-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.