Cell trajectory inference based on schrödinger problem and a mechanistic model of stochastic gene expression

Cellular differentiation is the biological process that leads a cell to opt for a particular cellular identity. Recently, single-cell RNA sequencing has enabled the simultaneous measurement of gene expression levels at specific times for a large number of individual cells and a large number of genes. Repeating such measurements at different time points gives them access to the temporal variation, or transport, of a distribution on a gene expression space. The whole temporal trajectory of distributions thus characterizes the differentiation process at the population level, but trajectories of individual cells are still out of reach since most measurement techniques are destructive. The optimal transport theory that has been used so far to infer cellular differentiation trajectories from time-stamped single-cell RNA-seq data involves solving the so-called Schrödinger problem in its most common version. This implies assuming that cells move, in the gene expression space, by diffusion. Yet, real gene dynamics are much more complex. In the present work, we assume that mRNA dynamics are characterized by brief and important production of RNA, with long periods of inactivity in between, and consider the so-called Bursty model of gene dynamics. We use this model to define a reference process for the Schrödinger problem. By comparing the solutions of the Schrödinger problems with a Diffusive and a Bursty reference process, under different conditions, we show that the Bursty model provides a better approximation of the underlying gene dynamics than the standard Diffusive process when inferring cell trajectories.