Evaluation of heuristic reductions of a model for the segmentation clock in zebrafish

Time‐delayed interactions between DNA, mRNA, and proteins play an important role in the periodic somite segmentation of vertebrates. A mathematical model of the segmentation clock in zebrafish that illustrates the dynamics between proteins and mRNA has recently been proposed; however, the complexity...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:IEEJ transactions on electrical and electronic engineering 2018-02, Vol.13 (2), p.271-279
Hauptverfasser: Shimono, Yuki, Yamaguchi, Ikuhiro, Ishimatsu, Kana, Akao, Akihiko, Ogawa, Yutaro, Jimbo, Yasuhiko, Kotani, Kiyoshi
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:Time‐delayed interactions between DNA, mRNA, and proteins play an important role in the periodic somite segmentation of vertebrates. A mathematical model of the segmentation clock in zebrafish that illustrates the dynamics between proteins and mRNA has recently been proposed; however, the complexity of the model makes solving it analytically unrealistic. In this study, we derived a first‐order delay‐differential equation (DDE) model by following two heuristic reduction approaches: simplifying protein–mRNA interactions and protein dimerization. Then, we calculated the eigenvalues of the model and found that the maximum eigenvalue and the oscillatory dynamics are qualitatively equivalent when some parameters are varied. This result enabled us to illustrate the effectiveness of using eigenvalues to assess the dynamics of the reduced model. Further, we extended the reduction methods to a complete model of somite segmentation considering the interaction of four genes, and derived a reduced model with four variables and four delay terms. Although the oscillation period of our reduced model decreased by ∼10% compared to the original model, the amplitude differed by less than 10%. The dynamic features for genetic conditions are also qualitatively reproduced by the reduced model. Our model demonstrates that it is possible to identify key parameters and to reveal the interactions among the parameters. © 2017 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.
ISSN:1931-4973
1931-4981
DOI:10.1002/tee.22523