Recent advances in Single-Cell RNA sequencing allow to infer both the gene expression of a cell and the so-called "velocity vector" initializing the changes in that expression. In this project, we investigate how to leverage the resulting discrete vector field from a set of observations in order to recover the dynamics of the cells, that is their trajectory in the space of gene expressions. One of the challenges of this question lies in the non-linearity of the data. Indeed, the gene expression of a given type of cell has been modeled in the literature as a point of some lower-dimensional submanifold -- referred as the "phenotypic manifold" -- of the space of all (theoretically) possible gene expressions. Given the discrete and noisy nature of such data, it is particularly crucial to take full account of their underlying geometry to obtain correct estimates of their dynamics.

Single-cell RNA velocity