In adult zebrafish telencephalon, the Notch signalling pathway helps regulate quiescence and neurogenesis in the neural stem cell population.
A key component of this pathway is the interaction between the Notch3 receptor and the DeltaA ligand.
As a result of this ligand-receptor binding, the Notch3 Intracellular Domain (N3ICD) of the receiving cell is cleaved and translocates to the cell nucleus, regulating the transcription of the deltaA gene.
In this talk, we quantify this phenomenon across different populations by leveraging the theory of marked spatial point processes, where the marks correspond to measurements of N3ICD activity.
By estimating a marked version of Ripley’s L function, we show that cells with low N3ICD activity are surrounded by higher levels of N3ICD than those expected under a uniform random model for the marks. Envelopes of significance are obtained via a permutation approach, demonstrating statistical significance at close distances.
Finally, we present some open questions concerning the spatial analysis of this tissue.