PUBLICATION
The kinetics in mathematical models on segmentation clock genes in zebrafish
- Authors
- Chen, K.W., Liao, K.L., Shih, C.W.
- ID
- ZDB-PUB-170527-5
- Date
- 2017
- Source
- Journal of mathematical biology 76(1-2): 97-150 (Journal)
- Registered Authors
- Keywords
- Delay equation, Gene regulation, Oscillation-arrested, Segmentation clock gene, Synchronous oscillation
- MeSH Terms
-
- Animals
- Body Patterning/genetics*
- Zebrafish Proteins/genetics
- Zebrafish Proteins/metabolism
- Mathematical Concepts
- Computer Simulation
- Kinetics
- Somites/embryology
- Somites/metabolism
- Gene Expression Regulation, Developmental
- Biological Clocks/genetics*
- Models, Biological*
- Zebrafish/embryology*
- Zebrafish/genetics*
- Zebrafish/metabolism
- Computational Biology
- Cell Communication/genetics
- PubMed
- 28547212 Full text @ J. Math. Biol.
Citation
Chen, K.W., Liao, K.L., Shih, C.W. (2017) The kinetics in mathematical models on segmentation clock genes in zebrafish. Journal of mathematical biology. 76(1-2):97-150.
Abstract
Somitogenesis is the process for the development of somites in vertebrate embryos. This process is timely regulated by synchronous oscillatory expression of the segmentation clock genes. Mathematical models expressed by delay equations or ODEs have been proposed to depict the kinetics of these genes in interacting cells. Through mathematical analysis, we investigate the parameter regimes for synchronous oscillations and oscillation-arrested in an ODE model and a model with transcriptional and translational delays, both with Michaelis-Menten type degradations. Comparisons between these regimes for the two models are made. The delay model has larger capacity to accommodate synchronous oscillations. Based on the analysis and numerical computations extended from the analysis, we explore how the periods and amplitudes of the oscillations vary with the degradation rates, synthesis rates, and coupling strength. For typical parameter values, the period and amplitude increase as some synthesis rate or the coupling strength increases in the ODE model. Such variational properties of oscillations depend also on the magnitudes of time delays in delay model. We also illustrate the difference between the dynamics in systems modeled with linear degradation and the ones in systems with Michaelis-Menten type reactions for the degradation. The chief concerns are the connections between the dynamics in these models and the mechanism for the segmentation clocks, and the pertinence of mathematical modeling on somitogenesis in zebrafish.
Genes / Markers
Expression
Phenotype
Mutations / Transgenics
Human Disease / Model
Sequence Targeting Reagents
Fish
Orthology
Engineered Foreign Genes
Mapping