A lattice model on somitogenesis of zebrafish

Kang Ling Liao, Chih-Wen Shih*

*Corresponding author for this work

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

Somitogenesis is the process of the development of somites which are segmental structure in vertebrate embryos. This process depends on the expression of segmentation clock genes. In this investigation, we consider lattice systems which describe the kinetics of the chief segmentation clock genes in zebrafish under negative feedback regulation with delay through interaction with the Delta-Notch signaling among neighboring cells. We first derive the analytical theories for the oscillation-arrested and synchronous oscillation in an autonomous lattice model. Based on the parameter regimes in the theories, we design suitable gradients of degradation rates and delays in a non-autonomous lattice model. Such a lattice system can generate synchronous oscillations, oscillatory traveling waves, oscillation slowing down, oscillation-arrested, and high-low expression levels. We further distinguish between different gradient structures which lead to normal and abnormal segmentations respectively and connect these structures to the dynamical regimes in the cell-cell model.

Original languageEnglish
Pages (from-to)2789-2814
Number of pages26
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume17
Issue number8
DOIs
StatePublished - 1 Nov 2012

Keywords

  • Lattice model
  • Oscillation-arrested
  • Somitogenesis
  • Synchronous oscillation
  • Traveling wave

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