Steady state and sensitivity analysis of a notch-delta signaling system of one single cell interacting with fixed environment

Matt Moore, Yican Zhang, Xiaoming Zheng

Research output: Contribution to journalArticlepeer-review

Abstract

The Notch-Delta signaling pathway is a highly conserved signaling system that partakes in a diverse process of growth, patterns and differentiation. Experiments have shown that Delta from different cells activates this pathway (trans-activation) while Delta from the same cell inhibits this pathway (cis-inhibition). The Notch-Delta interactions could switch a cell to one of the two opposite fates: either Sender (high Delta/low Notch) or Receiver (low Delta/high Notch). We studied a Notch-Delta signaling model from Sprinzak et al., (2010), to investigate the cell fate through steady state analysis. The focus was placed on a fundamental case of one single cell with fixed external Delta and Notch supplies. First, we proved there exists a unique steady state which is asymptotically stable. Second, we derived the increasing/decreasing and asymptotic properties of the steady state with respect to all the parameters. Third, we studied the sensitivity and discovered the cell fate is only sensitive to the production rates of Notch and Delta under strong cis-inhibition. Finally, we applied this model to multi-cellular cases and found that the lateral inhibition pattern could be created with the spatially varied Delta production rate. The Hopf bifurcation is not observed in the current model.

Original languageEnglish
Pages (from-to)337-363
Number of pages27
JournalJournal of Biological Systems
Volume27
Issue number3
DOIs
StatePublished - Sep 1 2019

Keywords

  • Cell Fate
  • Cis-Inhibition
  • Delta
  • Hopf Bifurcation
  • Lateral Inhibition
  • Notch
  • Pattern
  • Sensitivity
  • Steady State
  • Trans-Activation

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