Alternative approaches to single-cell trajectory inference using a commute time matrix

Single-cell technology has enhanced the high-resolution analysis of dynamic developmental cell fate decisions. A number of elegant mathematical and computational approaches have been developed for using single-cell genomics data to identify gene regulatory events and cell state changes during embryonic development and related processes. These approaches are typically used in combination to model dynamic cell differentiation trajectories but have different underlying mathematical foundations. The extent to which commonly used algorithms for trajectory modeling, such as data imputation, pseudotemporal ordering, and cell fate probability modeling, might be derived from the same underlying approach has not been widely explored. This work describes the use of a matrix based on the commute time of a graph as a single consistent kernel for cell fate trajectory modeling. The commute time kernel is derived from significant eigenvectors of the pseudo-inverse of the graph Laplacian in a manner that preserves commute time. This kernel matrix is used directly in trajectory inference methods and recapitulates the results obtained using different algorithms using three benchmark datasets. Additionally, a comparison of commute time kernels between spliced and unspliced counts was effective for identifying populations of circadian-cycling progenitor cells in differentiating pancreatic endocrine cells. Overall, this work identifies the commute time kernel as a potential parsimonious measure for multiple aspects of trajectory inference.