scEGOT: Single-cell trajectory inference framework based on entropic Gaussian mixture optimal transport

Abstract

Time-series single-cell RNA sequencing (scRNA-seq) data have opened a door to elucidate cell differentiation processes. In this context, the optimal transport (OT) theory has attracted attention to interpolate scRNA-seq data and infer the trajectories of cell differentiation. However, there remain critical issues in interpretability and computational cost. This paper presents scEGOT, a novel comprehensive trajectory inference framework for single-cell data based on entropic Gaussian mixture optimal transport (EGOT). By constructing a theory of EGOT via an explicit construction of the entropic transport plan and its connection to a continuous OT with its error estimates, EGOT is realized as a generative model with high interpretability and low computational cost, dramatically facilitating the inference of cell trajectories and dynamics from time-series data. The scEGOT framework provides comprehensive outputs from multiple perspectives, including cell state graphs, velocity fields of cell differentiation, time interpolations of single-cell data, space-time continuous videos of cell differentiation with gene expressions, gene regulatory networks, and reconstructions of Waddington's epigenetic landscape. To demonstrate that scEGOT is a powerful and versatile tool for single-cell biology, we applied it to time-series scRNA-seq data of the human primordial germ cell-like cell (human PGCLC) induction system. Using scEGOT, we precisely identified the PGCLC progenitor population and the bifurcation time of the segregation. Our analysis suggests that a known marker gene TFAP2A alone is not sufficient to identify the PGCLC progenitor cell population, but that NKX1-2 is also required. In addition, we found that MESP1 and GATA6 may also be crucial for PGCLC/somatic cell segregation.