[SS11] Interdisciplinary approaches to diverse biological rhythms

[SS11-01] Statistical description of vertebrate segmentation clock

*Koichiro Uriu¹, Luis G. Morelli² (1. Institute of Science Tokyo (Japan), 2. Instituto de Investigacion en Biomedicina de Buenos Aires (Argentine))

Keywords:

coupled oscillators,cell movement,pattern formation,synchronization,stochastic process

Synchronization of biological rhythms is ubiquitously found in nature. One such example is the synchronized ultradian rhythms, referred to as the segmentation clock, that regulate the formation of vertebrate body segment. The segmented vertebrate body plan is derived from somites that are formed in early development. These somites are bud off from the unsegmented tissue, called presomitic mesoderm (PSM), one by one with a species-specific temporal period. The period of segment formation is determined by the rhythmic gene expression patterns across the PSM. Cells in the PSM communicate with contacting cells via Delta-Notch signaling to send and receive the information of oscillation phase of the segmentation clock. In addition, these cells move around in the PSM exchanging neighboring cells over time. Thus, the PSM is a dynamic tissue, including cell movement, axis elongation and gene expression pattern. The question is how the synchronization of the segmentation clock occurs in such a dynamic tissue. To address this question, we develop a statistical description of the segmentation clock based on a coupled phase oscillator model that includes oscillators’ random movement in a lattice space. We obtain the time evolution of the probability density of oscillation phases as the Chapman-Kolmogorov equation. Using the probability density, we derive the equations for the average phase and variance that reveal how cell mobility promotes synchronization of the segmentation clock in the PSM. We also discuss the effect of cell mobility and axis elongation on the gene expression pattern across the PSM by using the statistical description.