The kinetics in mathematical models on segmentation clock genes in zebrafish

doi:10.1007/s00285-017-1138-1

機構典藏 > College of Sciences > Graduate Institute & Department of Mathematics > Journal Article > Item 987654321/111824

Please use this identifier to cite or link to this item: https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/111824

Title:	The kinetics in mathematical models on segmentation clock genes in zebrafish
Authors:	Kuan-Wei Chen;Kang-Ling Liao;Chih-Wen Shih
Keywords:	Gene regulation;Segmentation clock gene;Synchronous oscillation;Oscillation-arrested;Delay equation
Date:	2017-05
Issue Date:	2017-10-25 02:10:50 (UTC+8)
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.
Relation:	Journal of Mathematical Biology v.76, p.97-150
DOI:	10.1007/s00285-017-1138-1
Appears in Collections:	[Graduate Institute & Department of Mathematics] Journal Article

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