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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.
Mathematical Biosciences
|August 3, 2026
Summary
This study analyzes the Notch-Delta cell-fate model, revealing that while bistability is possible, monostable Sender and Receiver phenotypes are dominant. The quasi-steady-state model accurately reflects this behavior, simplifying analysis.
Area of Science:
- Cell biology
- Mathematical modeling
- Systems biology
Background:
- Notch-Delta signaling governs cell-fate decisions through lateral inhibition, creating Sender and Receiver cell states.
- The Boareto et al. model captures this bistability with negative feedback and cis-inhibition.
- Understanding model dynamics is crucial for computational frameworks in developmental biology.
Purpose of the Study:
- To rigorously analyze the mathematical model of Notch-Delta signaling.
- To determine conditions for bistability and identify robust phenotypes.
- To introduce a simplified stability analysis framework.
Main Methods:
- Mathematical analysis of model equilibria and stability.
- Bifurcation analysis and randomized parameter sweeps.
- Quasi-steady-state (QSS) reduction and convergence analysis.
Main Results:
- The system generically admits at most three equilibria.
- Bistability occurs under specific conditions on the Hill coefficient (0
- QSS reduction mirrors full model bistability; monostable phenotypes are robust, while bistable ones are rare.
Conclusions:
- The Notch-Delta model's dynamics are mathematically characterized.
- Monostable phenotypes dominate, with bistable states being sensitive to parameter variations.
- A novel stability analysis framework simplifies analysis for various Hill coefficients.
Keywords:
BistabilityCis-inhibitionDeterminant reduction theoremsLateral inhibitionNotch–Delta signalingSingular perturbationMore Related Videos
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