  Single-cell RNA sequencing (scRNA-seq) has emerged as a transformative
technology, offering unparalleled insights into the intricate landscape of
cellular diversity and gene expression dynamics. The analysis of scRNA-seq data
poses challenges attributed to both sparsity and the extensive number of genes
implicated. An increasing number of computational tools are devised for
analyzing and interpreting scRNA-seq data. We present a multiscale differential
geometry (MDG) strategy to exploit the geometric and biological properties
inherent in scRNA-seq data. We assume that those intrinsic properties of cells
lies on a family of low-dimensional manifolds embedded in the high-dimensional
space of scRNA-seq data. Subsequently, we explore these properties via
multiscale cell-cell interactive manifolds. Our multiscale curvature-based
representation serves as a powerful approach to effectively encapsulate the
complex relationships in the cell-cell network. We showcase the utility of our
novel approach by demonstrating its effectiveness in classifying cell types.
This innovative application of differential geometry in scRNA-seq analysis
opens new avenues for understanding the intricacies of biological networks and
holds great potential for network analysis in other fields.
