SummaryDuring development, cells undergo dramatic changes in their morphology. By affecting contact geometry, these morphological changes could influence cellular communication. However, it has remained unclear whether and how signaling depends on contact geometry. This question is particularly relevant for Notch signaling, which coordinates neighboring cell fates through direct cell-cell signaling. Using micropatterning with a receptor trans-endocytosis assay, we show that signaling between pairs of cells correlates with their contact area. This relationship extends across contact diameters ranging from microns to tens of microns. Mathematical modeling predicts that dependence of signaling on contact area can bias cellular differentiation in Notch-mediated lateral inhibition processes, such that smaller cells are more likely to differentiate into signal-producing cells. Consistent with this prediction, analysis of developing chick inner ear revealed that ligand-producing hair cell precursors have smaller apical footprints than non-hair cells. Together, these results highlight the influence of cell morphology on fate determination processes.

Summary Neural stem cell (NSC) populations persist in the adult vertebrate brain over a lifetime, and their homeostasis is controlled at the population level through unknown mechanisms. Here, we combine dynamic imaging of entire NSC populations in their in vivo niche over several weeks with pharmacological manipulations, mathematical modeling, and spatial statistics and demonstrate that NSCs use spatiotemporally resolved local feedback signals to coordinate their decision to divide in adult zebrafish brains. These involve Notch-mediated short-range inhibition from transient neural progenitors and a dispersion effect from the dividing NSCs themselves exerted with a delay of 9–12 days. Simulations from a stochastic NSC lattice model capturing these interactions demonstrate that these signals are linked by lineage progression and control the spatiotemporal distribution of output neurons. These results highlight how local and temporally delayed interactions occurring between brain germinal cells generate self-propagating dynamics that maintain NSC population homeostasis and coordinate specific spatiotemporal correlations.

Notch signaling is ubiquitously used to coordinate differentiation between adjacent cells across metazoans. Whereas Notch pathway components have been studied extensively, the effect of membrane distribution and dynamics of Notch receptors and ligands remains poorly understood. It is also unclear how cellular morphology affects these distributions and, ultimately, the signaling between cells. Here, we combine live-cell imaging and mathematical modeling to address these questions. We use a FRAP-TIRF assay to measure the diffusion and endocytosis rates of Delta-like 1 (Dll1) in mammalian cells. We find large cell-to-cell variability in the diffusion coefficients of Dll1 measured in single cells within the same population. Using a simple reaction-diffusion model, we show how membrane dynamics and cell morphology affect cell-cell signaling. We find that differences in the diffusion coefficients, as observed experimentally, can dramatically affect signaling between cells. Together, these results elucidate how membrane dynamics and cellular geometry can affect cell-cell signaling.

NOTCH signaling regulates developmental processes in all tissues and all organisms across the animal kingdom. It is often involved in coordinating the differentiation of neighboring cells into different cell types. As our knowledge on the structural, molecular and cellular properties of the NOTCH pathway expands, there is a greater need for quantitative methodologies to get a better understanding of the processes controlled by NOTCH signaling. In recent years, theoretical and computational approaches to NOTCH signaling and NOTCH mediated patterning are gaining popularity. Mathematical models of NOTCH mediated patterning provide insight into complex and counterintuitive behaviors and can help generate predictions that can guide experiments. In this chapter, we review the recent advances in modeling NOTCH mediated patterning processes. We discuss new modeling approaches to lateral inhibition patterning that take into account cis-interactions between NOTCH receptors and ligands, signaling through long cellular protrusions, cell division processes, and coupling to external signals. We also describe models of somitogenesis, where NOTCH signaling is used for synchronizing cellular oscillations. We then discuss modeling approaches that consider the effect of cell morphology on NOTCH signaling and NOTCH mediated patterning. Finally, we consider models of boundary formation and how they are influenced by the combinatorial action of multiple ligands. Together, these topics cover the main advances in the field of modeling the NOTCH response.

SUMMARYNeural stem cell (NSC) populations persist in the adult vertebrate brain over a life time, and their homeostasis is controlled at the population level. The nature and properties of these coordination mechanisms remain unknown. Here we combine dynamic imaging of entire NSC populations in their in vivo niche over weeks, pharmacological manipulations, mathematical modeling and spatial statistics, and demonstrate that NSCs use spatiotemporally resolved local feedbacks to coordinate their decision to divide. These involve a Notch-mediated inhibition from transient neural progenitors, and a dispersion effect from dividing NSCs themselves, exerted with a delay of 9-12 days. Simulations from a stochastic NSC lattice model capturing these interactions demonstrate that they are linked by lineage progression and control the spatiotemporal distribution of output neurons. These results highlight how local and temporally delayed interactions occurring between brain germinal cells generate self-propagating dynamics that maintain NSC population homeostasis with specific spatiotemporal correlations.

The emergence of the sensory organ precursor (SOP) from an equivalence group in Drosophila is a paradigm for studying single-cell fate specification through Notch-mediated lateral inhibition. Yet, it remains unclear how only a single SOP is selected from a relatively large group of cells. We show here that a critical aspect of SOP selection is controlled by cis-inhibition (CI), whereby the Notch ligands, Delta (Dl), cis-inhibit Notch receptors in the same cell. Based on the observation that the mammalian ligand Dl-like 1 cannot cis-inhibit Notch in Drosophila , we probe the role of CI in vivo. We develop a mathematical model for SOP selection where Dl activity is independently regulated by the ubiquitin ligases Neuralized and Mindbomb1. We show theoretically and experimentally that Mindbomb1 induces basal Notch activity, which is suppressed by CI. Our results highlight the trade-off between basal Notch activity and CI as a mechanism for singling out a SOP from a large equivalence group.

A gradient of EGFR-ERK signaling has been classically implicated in various developmental processes. In this issue of Developmental Cell, Ogura et al. (2018) show that in the Drosophila tracheal placode, EGFR-ERK signaling propagates via a cell-by-cell relay mechanism rather than a gradient, and this sequential ERK activation controls proper placode invagination.

The emergence of the sensory organ precursor (SOP) from the proneural equivalence group in Drosophila melanogaster is a paradigm for studying single cell fate specification through the process of lateral inhibition. Classical lateral inhibition models describing this selection process are based on a transcriptional feedback mechanism where inhibitory signals between neighbouring cells, mediated by Notch pathway, are coupled to an intracellular circuit regulating the expression of the Notch ligand Delta (Dl). It was previously shown that in addition to its ability to trans-activate Notch in neighbouring cells, Dl can also cis-inhibit Notch in the same cell. However, it remains unclear what role does cis-inhibition play during SOP selection, and how it contributes to the selection of only one SOP. Here we address these questions using the unexpected observation that the mammalian ligand Delta-like 1 (Dll1) can trans-activate but not cis-inhibit Notch in Drosophila. We develop a mathematical model for SOP selection, termed the two-channel SOP (TCS) model, where Dl activity, but not its expression, is regulated by two channels associated with the two E3 ubiquitin ligases Neuralized (Neur) and Mindbomb1 (Mib1). While the Neur-dependent channel is regulated by Notch signalling, the Mib1-dependent channel is not, leading to tissue-wide basal inhibitory activity. We show theoretically and experimentally that cis-inhibition is required for suppressing Mib1-dependent basal Notch activity. Thus, our results highlight the trade-off between basal Notch activity and cis-inhibition as a mechanism for singling out an SOP from the proneural equivalence group.