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Updated: Aug 5, 2026

Spatiotemporal Control of Protein Activity through Optogenetic Allosteric Regulation
Published on: October 4, 2024
Bistability analysis of a hybrid notch-delta signaling model in a single cell interacting with fixed external
Yuxin Liang1, Ling Xue1, Kun Zhao1
1College of Mathematical Sciences, Harbin Engineering University, Harbin, Heilongjiang, 150001, China.
Abstract:
Notch-Delta signaling is a juxtacrine cell-fate pathway that drives lateral inhibition, whereby neighboring cells adopt alternating Sender (high Delta/low Notch) and Receiver (high Notch/low Delta) states. This bistability is captured by the single-cell Notch-Delta circuit model with external Notch and Delta inputs introduced by Boareto et al. [1], which underlies many computational frameworks. The model incorporates negative feedback in Delta production and cis-inhibition of Notch by Delta. In this work, a rigorous mathematical analysis of the model is presented. It is shown that, generically in parameter space, the system admits at most three equilibria. For Hill coefficients equal to one and two, sufficient conditions for the existence of three equilibria are derived. When exactly three distinct nondegenerate equilibria exist and the Hill coefficient lies in 0
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