Transition state characteristics during cell differentiation

Abstract

Models describing the process of stem-cell differentiation are plentiful, and may offer insights into the underlying mechanisms and experimentally observed behaviour. Waddington’s epigenetic landscape has been providing a conceptual framework for differentiation processes since its inception. It also allows, however, for detailed mathematical and quantitative analyses, as the landscape can, at least in principle, be related to mathematical models of dynamical systems. Here we focus on a set of dynamical systems features that are intimately linked to cell differentiation, by considering exemplar dynamical models that capture important aspects of stem cell differentiation dynamics. These models allow us to map the paths that cells take through gene expression space as they move from one fate to another, e.g. from a stem-cell to a more specialized cell type. Our analysis highlights the role of the transition state (TS) that separates distinct cell fates, and how the nature of the TS changes as the underlying landscape changes—change that can be induced by e.g. cellular signaling. We demonstrate that models for stem cell differentiation may be interpreted in terms of either a static or transitory landscape. For the static case the TS represents a particular transcriptional profile that all cells approach during differentiation. Alternatively, the TS may refer to the commonly observed period of heterogeneity as cells undergo stochastic transitions.

Author summary

Current emphasis on single cell analysis, especially in the context of the human and mouse cell atlas projects, is on characterizing the transcriptomic signatures of different cell states. This is clearly of great importance, as even the number of different cell types, e.g. in humans, is not known with any satisfying degree of certainty. There are enormous challenges in mapping these states, but this will still only provide a partial answer. Importantly, the way in which cells differentiate, and the way in which gene expression changes over the course of differentiation will still be unknown. Here we use a dynamical systems perspective to consider the nature of, and dynamics during, the transition between different cell types (or cell states). We show how the developmental landscape (in Waddington’s sense) and the nature of the transition states change in response to external stimuli and discuss this in the context of stem cell differentiation (as well as its potential reversal). In particular, we discuss how the nature of the landscape at the transition state, as well as the presence of non-gradient dynamics, has strong implications for the identifiability of differentiation dynamics from experimental data.