Recovering biomolecular network dynamics from single-cell omics data requires three time points

Single-cell omics technologies can measure millions of cells for up to thousands of biomolecular features, enabling data-driven studies of complex biological networks. However, these high-throughput experimental techniques often cannot track individual cells over time, thus complicating the understanding of dynamics such as time trajectories of cell states. These "dynamical phenotypes" are key to understanding biological phenomena such as differentiation fates. We show by mathematical analysis that, in spite of high dimensionality and lack of individual cell traces, three time-points of single-cell omics data are theoretically necessary and sufficient to uniquely determine the network interaction matrix and associated dynamics. Moreover, we show through numerical simulations that an interaction matrix can be accurately determined with three or more time-points even in the presence of sampling and measurement noise typical of single-cell omics. Our results can guide the design of single-cell omics time-course experiments, and provide a tool for data-driven phase-space analysis.