An Expanded Notch-Delta Model Exhibiting Long-Range Patterning and Incorporating MicroRNA Regulation

Notch-Delta signaling is a fundamental cell-cell communication mechanism that governs the differentiation of many cell types. Most existing mathematical models of Notch-Delta signaling are based on a feedback loop between Notch and Delta leading to lateral inhibition of neighboring cells. These models result in a checkerboard spatial pattern whereby adjacent cells express opposing levels of Notch and Delta, leading to alternate cell fates. However, a growing body of biological evidence suggests that Notch-Delta signaling produces other patterns that are not checkerboard, and therefore a new model is needed. Here, we present an expanded Notch-Delta model that builds upon previous models, adding a local Notch activity gradient, which affects long-range patterning, and the activity of a regulatory microRNA. This model is motivated by our experiments in the ascidian Ciona intestinalis showing that the peripheral sensory neurons, whose specification is in part regulated by the coordinate activity of Notch-Delta signaling and the microRNA miR-124, exhibit a sparse spatial pattern whereby consecutive neurons may be spaced over a dozen cells apart. We perform rigorous stability and bifurcation analyses, and demonstrate that our model is able to accurately explain and reproduce the neuronal pattern in Ciona. Using Monte Carlo simulations of our model along with miR-124 transgene over-expression assays, we demonstrate that the activity of miR-124 can be incorporated into the Notch decay rate parameter of our model. Finally, we motivate the general applicability of our model to Notch-Delta signaling in other animals by providing evidence that microRNAs regulate Notch-Delta signaling in analogous cell types in other organisms, and by discussing evidence in other organisms of sparse spatial patterns in tissues where Notch-Delta signaling is active.Author Summary: The nervous system of many animals, including the marine invertebrate Ciona intestinalis in our study, develops through a cell-to-cell communication mechanism called Notch-Delta signaling. Mathematical models for Notch-Delta signaling have been developed that can explain the development of animal nervous systems with a dense arrangement of neurons. However, there are several cases where the spatial arrangement is much more sparse; we found that the peripheral nervous system of Ciona is one such example. Here, we develop an expanded mathematical model that is able to account for this sparser spacing, and furthermore demonstrate that the spacing can be widened or shortened through changing a single parameter that is influenced by the concentration of a regulatory microRNA called miR-124. The underlying differential equations contain only two variables representing the activity levels of Notch and Delta, and are thus general enough to be applicable to a wide variety of physical and biological systems that exhibit a similar sparse patterning.