Traveling wave formation in vertebrate segmentation.
In vertebrate somitogenesis, "segmentation clock" genes (such as her in zebrafish, hairy in chick, and hes in mouse) show oscillation, synchronized over nearby cells through cell-cell interaction. The locations of high gene expression appear with regular intervals and move like a wave from posterior to anterior with the speed slowing down toward the anterior end. We analyze traveling wave pattern of her gene expression when there is an anterior-posterior gradient of one of the reaction rates in the gene-protein kinetics. We adopt a model which includes the kinetics of mRNA and proteins of her gene in each cell and cell-cell interaction by Delta-Notch system explicitly. We show that the observed spatio-temporal pattern can be explained if mRNA degradation, protein translation, protein transportation to nucleus occurs faster, or mRNA transcription, Delta protein synthesis occurs slower in posterior than in anterior regions. All of these gradients are those that produce longer periodicity of oscillation of clock gene expression in the anterior than in the posterior. Based on this result, we derive a mathematical formula for how the peak of gene expression moves along the pre-somitic mesoderm.
Uriu
Koichiro
K
Department of Biology, Faculty of Sciences, Kyushu University, Fukuoka 812-8581, Japan. uriu@bio-math10.biology.kyushu-u.ac.jp
Morishita
Yoshihiro
Y
Iwasa
Yoh
Y
D000818:Animals; D051792:Basic Helix-Loop-Helix Proteins / Q000235:genetics / Q000378:metabolism; D001683:Biological Clocks / Q000235:genetics / Q000502:physiology; D002450:Cell Communication / Q000235:genetics; D047108:Embryonic Development / Q000235:genetics / Q000502:physiology; D018507:Gene Expression Regulation, Developmental / Q000502:physiology*; D008957:Models, Genetic; D012333:RNA, Messenger / Q000235:genetics; D019170:Somites / Q000196:embryology / Q000378:metabolism; D014714:Vertebrates / Q000196:embryology / Q000235:genetics* / Q000378:metabolism; D015027:Zebrafish / Q000196:embryology / Q000235:genetics / Q000378:metabolism; D029961:Zebrafish Proteins / Q000235:genetics / Q000378:metabolism
D051792:Basic Helix-Loop-Helix Proteins; D012333:RNA, Messenger; D029961:Zebrafish Proteins; C491619:her1 protein, zebrafish