Abstract
During vertebrate development, the body axis segments sequentially from the head to the tail of the embryo. This process is driven by genetic oscillators together with a moving determination front that slows down and arrests the oscillators. As a result, waves of gene expression propagate along the body axis. We propose a theoretical description based on coupled phase oscillators that describes the patterns of gene expression observed in experiments, both in wild type and mutants. Based on experimental evidence our description introduces a frequency profile, together with a moving boundary that describes axis elongation. To account for the time it takes for signaling molecules to be produced and exported to the cell membrane we include a time delay in the coupling. We derive analytical expressions for the wavelength of the patterns and the period of oscillations.
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