A dynamical systems treatment of transcriptomic trajectories in hematopoiesis

Abstract

Inspired by Waddington’s illustration of an epigenetic landscape, cell-fate transitions have been envisioned as bifurcating dynamical systems, wherein the dynamics of an exogenous signal couples to a cell’s enormously complex signaling and transcriptional machinery, eliciting a qualitative transition in the collective state of a cell – its fate. It remains unclear, however, whether the dynamical systems framework can go beyond a word-based caricature of the system and provide sharp quantitative insights that further our understanding of differentiation. Single-cell RNA sequencing (scRNA-seq), which measures the distributions of possible transcriptional states in large populations of differentiating cells, provides an alternate view, in which development is marked by the individual concentration variations of a myriad of genes. Here, starting from formal mathematical derivations, we challenge these transcriptomic trajectories to a rigorous statistical evaluation of whether they display signatures consistent with bifurcations. After pinpointing bifurcations along transcriptomic trajectories of the neutrophil branch of hematopoeitic differentiation we are able to further leverage the primitive features of a linear instability to identify the single-direction in gene expression space along which the bifurcation unfolds and identify possible gene contributors. This scheme identifies transcription factors long viewed to play a crucial role in the process of neutrophil differentiation in addition to identifying a host of other novel genetic players. Most broadly speaking, we provide evidence that, though very high-dimensional, a bifurcating dynamical systems formalism might be appropriate for the process of cellular differentiation and that it can be leveraged to provide insights. Ambitiously, our work attempts to take a step beyond data-analysis and towards the construction of falsifiable mathematical models that describe the dynamics of the entire transcriptome.