Researchers at Kyushu University have introduced a new computational method, ddHodge, designed to reconstruct the complex processes by which cells determine their fate. The study was published in Nature Communications.
The process of cell differentiation—how a cell decides to become a nerve or muscle cell—is central to both biology and medicine. Scientists typically use single-cell RNA sequencing (scRNA-seq) to examine gene activity within individual cells. However, scRNA-seq only provides static snapshots, limiting the ability to track changes over time.
Existing computational tools such as RNA velocity attempt to predict future states of cells but often reduce the complexity of cellular data into fewer dimensions. This simplification can result in loss of important information about the stability and plasticity of cell states.
Associate Professor Kazumitsu Maehara from Kyushu University's Faculty of Medical Sciences and Professor Yasuyuki Ohkawa from the Medical Institute of Bioregulation developed ddHodge as a geometry-preserving approach that more accurately models how cell states change.
"My background is in statistical science, and during my graduate training, I was exposed to HodgeRank, a method used in ranking problems such as PageRank," said Maehara. "When I later moved into life-science research, I realized that the same mathematical idea could help interpret the complex, high-dimensional transitions in single-cell data."
The ddHodge technique uses Hodge decomposition—a mathematical theorem—to break down cell movements across possible states into three measurable components: gradient (overall direction), curl (cyclical flows), and harmonic components (repeating processes like the cell cycle).
"ddHodge can be viewed as an effort to adapt techniques and concepts developed in modern mathematical sciences, such as differential geometry and numerical computation, to the practical demands of life science data analysis," explained Maehara.
Testing ddHodge on scRNA-seq data from around 46,000 mouse embryonic cells showed that more than 88% of gene expression dynamics during early development could be attributed to directional flow toward stable states. This supports established theories in developmental biology regarding how cells commit to specific lineages. The researchers also identified key genes involved in maintaining or driving these stable or unstable points.
Simulations demonstrated that ddHodge reliably reconstructed cell state dynamics even with incomplete or noisy data and achieved approximately 100 times greater accuracy than conventional methods.
Maehara added: "ddHodge can quantitatively describe, within a high-dimensional space, in which direction, how fast, and how stably cells change. We expect it to contribute broadly to understanding diverse biological phenomena, including embryonic development, tissue regeneration, and cancer progression." The tool may also aid early detection of disease-relevant cell states and assist scientists analyzing large datasets for pharmaceutical research.
Beyond biology and medicine, ddHodge may offer insights into other evolving systems such as material degradation or climate patterns by applying modern mathematics concepts to analyze high-dimensional datasets.
