WorkshopsMathematical models and analysis in somitogenesis
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Somitogenesis describes the formation of vertebral precursors, known as somites. This developmental process has been identified with oscillatory gene activities. A widely agreed hypothesis for the process is that a somite prepattern arises via a clock and wavefront mechanism. Since the discovery of oscillatory gene products, much research has been directed toward elucidating the molecular basis of the so-called segmentation clock. Segmentation clock comprises a multicellular genetic network of oscillators acting in the presomitic mesoderm to drive periodic expression of the cyclic genes. Key cycling genes for the segmentation clock are Hes1 and Hes7 in mouse, hairy1 and hairy2 in chick, and her1 and her7 in zebrafish. Cell-cell communication, controlled by components of the Notch-Delta pathway, synchronizes the gene oscillations between neighboring cells. Modeling cell-level oscillations during somitogenesis started from Lewis in 2003, based on the idea of negative regulation of mRNA transcription by protein products, with delays in transcription and translation. For the cell-cell kinetic model, we employ delay Hopf bifurcation theory to generate the synchronous oscillations with period about 30 minutes which match the time taken to generate a somite. Replacing the time delay by taking into account certain intermediate process in the cell, namely, the translocation of Her protein from cytoplasm to nucleus, Iwasa et al studied an ODE model. It appears that mathematical tool such as Hopf bifurcation theory is infeasible in analyzing the existence of synchronous oscillations in such an ODE model. In this talk, we shall introduce Lewis’s model, for both homodimer and heterodimer cases, the model taking into account signaling molecule FGF (fibroblast growth factor), the model with consideration of number of protein transcription binding sites and differential decay rates, and lattice models with traveling waves. We will also mention the studies on phase dynamics of coupled oscillators, which forgets the internal machinery of each cell’s segmentation clock. Those phase-coupled oscillators, developed by Kuramoto, were adopted due to a reason, as remarked in a recent article “the kinetic models are incredibly difficult to analyze mathematically, and computer is the only way forward. The snag here is….”
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Chih-Wen Shih
2012-01-06
11:20:00 - 12:10:00
101 , Mathematics Research Center Building (ori. New Math. Bldg.)
Somitogenesis describes the formation of vertebral precursors, known as somites. This developmental process has been identified with oscillatory gene activities. A widely agreed hypothesis for the process is that a somite prepattern arises via a clock and wavefront mechanism. Since the discovery of oscillatory gene products, much research has been directed toward elucidating the molecular basis of the so-called segmentation clock. Segmentation clock comprises a multicellular genetic network of oscillators acting in the presomitic mesoderm to drive periodic expression of the cyclic genes. Key cycling genes for the segmentation clock are Hes1 and Hes7 in mouse, hairy1 and hairy2 in chick, and her1 and her7 in zebrafish. Cell-cell communication, controlled by components of the Notch-Delta pathway, synchronizes the gene oscillations between neighboring cells. Modeling cell-level oscillations during somitogenesis started from Lewis in 2003, based on the idea of negative regulation of mRNA transcription by protein products, with delays in transcription and translation. For the cell-cell kinetic model, we employ delay Hopf bifurcation theory to generate the synchronous oscillations with period about 30 minutes which match the time taken to generate a somite. Replacing the time delay by taking into account certain intermediate process in the cell, namely, the translocation of Her protein from cytoplasm to nucleus, Iwasa et al studied an ODE model. It appears that mathematical tool such as Hopf bifurcation theory is infeasible in analyzing the existence of synchronous oscillations in such an ODE model. In this talk, we shall introduce Lewis’s model, for both homodimer and heterodimer cases, the model taking into account signaling molecule FGF (fibroblast growth factor), the model with consideration of number of protein transcription binding sites and differential decay rates, and lattice models with traveling waves. We will also mention the studies on phase dynamics of coupled oscillators, which forgets the internal machinery of each cell’s segmentation clock. Those phase-coupled oscillators, developed by Kuramoto, were adopted due to a reason, as remarked in a recent article “the kinetic models are incredibly difficult to analyze mathematically, and computer is the only way forward. The snag here is….”
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