scEGOT: Single-cell trajectory inference framework based on entropic Gaussian mixture optimal transport. We present scEGOT, a comprehensive single-cell trajectory inference framework based on entropic Gaussian mixture optimal transport. The main advantage of scEGOT allows us to go back and forth between continuous and discrete problems, and it provides versatile trajectory inference methods at a low computational cost. Applied to the human primordial germ cell-like cell (PGCLC) induction system, scEGOT identified the PGCLC progenitor population and bifurcation time of segregation. Our analysis shows TFAP2A is insufficient for identifying PGCLC progenitors, requiring NKX1-2. ------------------------------------------------------------------------------------------------------------ Spatiotemporal reconstruction of gene expression on the human axioloid using optimal transport theory Abstract: Human axioloid development is induced by genes with spatial and temporal gene expression patterns. For example, HES7 with oscillation pattern forms the segmentation of somite; TBX18 with stripe pattern determines the segment position of somite. We aim to find new genes with spatiotemporal expression patterns in the human axioloid via scRNA-seq data analysis. However, without spatiotemporal information in scRNA-seq data, we may overlook gene functions constructing space and time structures using only scRNA-seq data. In this study, we focused on optimal transport theory that solves the optimal transport plan between two distributions. We have developed a spatiotemporal reconstruction method of gene expression by combining optimal transport-based spatial and time reconstruction methods, NovaSpaRc and scEGOT. The proposed method outputs a time development of spatial gene expression from scRNA-seq and spatial image data. Furthermore, we developed a spatiotemporal clustering method from spatiotemporal reconstructed gene expressions using a functional clustering. We succeeded in capturing the time evolution of the gene expression pattern with dynamical growth of human axioloid shape. In addition, we identified genes with stripe patterns such as TBX18 using gene clustering. ------------------------------------------------------------------------------------------------------------ Cross-species analysis of omics data via Gromov-Wasserstein optimal transport theory Abstract: Although the genomes and genes of mammals are well conserved as nucleotide sequences, there are differences in gene expression, function, and the epigenome in the individual cells of each species due to species differences. Genomic and epigenomic information at the cellular level forms big data known as omics data, but the features and samples differ across species, and no comprehensive method for comparative analysis has been established. In this talk, we propose a method for cross-species analysis of omics data via Gromov-Wasserstein optimal transport theory, and report the validation results of our method through applying it to real data from the germ cell lineage of mammalian cells. This is joint work with K. Fujiwara, T. Nakamura, M. Saitou, Y. Imoto, and Y. Hiraoka.