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ABSTRACT Inspired by Waddington's illustration of an epigenetic landscape, cell-fate transitions have been envisioned as bifurcating dynamical systems, wherein exogenous signaling dynamics couple to the enormously complex signaling and transcriptional machinery of a cell to elicit qualitative transitions in its collective state. 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 variations of a myriad of genes. Here, we present a mathematical formalism for rigorously evaluating, from a dynamical systems perspective, whether scRNA-seq trajectories display statistical signatures consistent with bifurcations and, as a case study, pinpoint regions of multistability along the neutrophil branch of hematopoeitic differentiation. Additionally, we leverage the geometric features of linear instability to identify the low-dimensional phase plane in gene expression space within which the multistability unfolds, highlighting novel genetic players that are crucial for neutrophil differentiation. Broadly, we show that a dynamical systems treatment of scRNA-seq data provides mechanistic insights into the high-dimensional processes of cellular differentiation, taking a step toward systematic construction of mathematical models for transcriptomic dynamics. 

Abstract Background During embryogenesis, the developmental potential of initially pluripotent cells becomes progressively restricted as they transit to lineage restricted states. The pluripotent cells of  Xenopus  blastula-stage embryos are an ideal system in which to study cell state transitions during developmental decision-making, as gene expression dynamics can be followed at high temporal resolution. Results Here we use transcriptomics to interrogate the process by which pluripotent cells transit to four different lineage-restricted states: neural progenitors, epidermis, endoderm and ventral mesoderm, providing quantitative insights into the dynamics of Waddington’s landscape. Our findings provide novel insights into why the neural progenitor state is the default lineage state for pluripotent cells and uncover novel components of lineage-specific gene regulation. These data reveal an unexpected overlap in the transcriptional responses to BMP4/7 and Activin signaling and provide mechanistic insight into how the timing of signaling inputs such as BMP are temporally controlled to ensure correct lineage decisions. Conclusions Together these analyses provide quantitative insights into the logic and dynamics of developmental decision making in early embryos. They also provide valuable lineage-specific time series data following the acquisition of specific lineage states during development. 

During embryogenesis, the developmental potential of initially pluripotent cells becomes progressively restricted as they transit to lineage restricted states. The pluripotent cells of Xenopus blastula-stage embryos are an ideal system in which to study cell state transitions during developmental decision-making, as gene expression dynamics can be followed at high temporal resolution. Here we use transcriptomics to interrogate the process by which pluripotent cells transit to four different lineage-restricted states: neural progenitors, epidermis, endoderm and ventral mesoderm, providing quantitative insights into the dynamics of Waddington’s landscape. Our findings shed light on why the neural progenitor state is the default lineage state for pluripotent cells, and uncover novel components of lineage-specific gene regulation. These data reveal an unexpected overlap in the transcriptional responses to BMP4/7 and activin signaling, and provide mechanistic insight into how the timing of signaling inputs such as BMP are temporally controlled to ensure correct lineage decisions. Together these analyses provide quantitative insights into the logic and dynamics of developmental decision making in early embryos.