Towards a mathematical theory of development

New technologies like single-cell RNA sequencing can observe biological processes at unprecedented resolution. One of the most exciting prospects associated with this new trove of data is the possibility of studying temporal processes, such as differentiation and development. How are cell types stabilized? How do they destabilize in diseases like cancer and with age? However, it is not currently possible to record dynamic changes in gene expression, because current measurement technologies are destructive. A number of recent efforts have tackled this by collecting snap-shots of single cell expression profiles along a time-course and then computationally inferring trajectories from the static snap-shots. We argue that this inference problem is easier with more data, and the right way to measure the “size” of a data set is really the number of time-points, not the number of cells. We propose to collect the first single cell RNA-seq time-course with more than one thousand distinct temporal snapshots, and we develop a novel mathematical and conceptual framework to analyze the data. This tremendous temporal resolution will give us unprecedented statistical power to discover the genetic forces controlling development.